crypto: use go-ethereum secp256k1 package to avoid symbol conflict (#374)

95 files changed, 22644 insertions, 0 deletions

diff --git a/vendor/github.com/ethereum/go-ethereum/COPYING b/vendor/github.com/ethereum/go-ethereum/COPYING
new file mode 100644
index 000000000..8d66e8772
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/COPYING
@@ -0,0 +1,619 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2014 The go-ethereum Authors.
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+the GNU General Public License is intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.  We, the Free Software Foundation, use the
+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors.  You can apply it to
+your programs, too.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights.  Therefore, you have
+certain responsibilities if you distribute copies of the software, or if
+you modify it: responsibilities to respect the freedom of others.
+
+  For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must pass on to the recipients the same
+freedoms that you received.  You must make sure that they, too, receive
+or can get the source code.  And you must show them these terms so they
+know their rights.
+
+  Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+  For the developers' and authors' protection, the GPL clearly explains
+that there is no warranty for this free software.  For both users' and
+authors' sake, the GPL requires that modified versions be marked as
+changed, so that their problems will not be attributed erroneously to
+authors of previous versions.
+
+  Some devices are designed to deny users access to install or run
+modified versions of the software inside them, although the manufacturer
+can do so.  This is fundamentally incompatible with the aim of
+protecting users' freedom to change the software.  The systematic
+pattern of such abuse occurs in the area of products for individuals to
+use, which is precisely where it is most unacceptable.  Therefore, we
+have designed this version of the GPL to prohibit the practice for those
+products.  If such problems arise substantially in other domains, we
+stand ready to extend this provision to those domains in future versions
+of the GPL, as needed to protect the freedom of users.
+
+  Finally, every program is threatened constantly by software patents.
+States should not allow patents to restrict development and use of
+software on general-purpose computers, but in those that do, we wish to
+avoid the special danger that patents applied to a free program could
+make it effectively proprietary.  To prevent this, the GPL assures that
+patents cannot be used to render the program non-free.
+
+  The precise terms and conditions for copying, distribution and
+modification follow.
+
+                       TERMS AND CONDITIONS
+
+  0. Definitions.
+
+  "This License" refers to version 3 of the GNU General Public License.
+
+  "Copyright" also means copyright-like laws that apply to other kinds of
+works, such as semiconductor masks.
+
+  "The Program" refers to any copyrightable work licensed under this
+License.  Each licensee is addressed as "you".  "Licensees" and
+"recipients" may be individuals or organizations.
+
+  To "modify" a work means to copy from or adapt all or part of the work
+in a fashion requiring copyright permission, other than the making of an
+exact copy.  The resulting work is called a "modified version" of the
+earlier work or a work "based on" the earlier work.
+
+  A "covered work" means either the unmodified Program or a work based
+on the Program.
+
+  To "propagate" a work means to do anything with it that, without
+permission, would make you directly or secondarily liable for
+infringement under applicable copyright law, except executing it on a
+computer or modifying a private copy.  Propagation includes copying,
+distribution (with or without modification), making available to the
+public, and in some countries other activities as well.
+
+  To "convey" a work means any kind of propagation that enables other
+parties to make or receive copies.  Mere interaction with a user through
+a computer network, with no transfer of a copy, is not conveying.
+
+  An interactive user interface displays "Appropriate Legal Notices"
+to the extent that it includes a convenient and prominently visible
+feature that (1) displays an appropriate copyright notice, and (2)
+tells the user that there is no warranty for the work (except to the
+extent that warranties are provided), that licensees may convey the
+work under this License, and how to view a copy of this License.  If
+the interface presents a list of user commands or options, such as a
+menu, a prominent item in the list meets this criterion.
+
+  1. Source Code.
+
+  The "source code" for a work means the preferred form of the work
+for making modifications to it.  "Object code" means any non-source
+form of a work.
+
+  A "Standard Interface" means an interface that either is an official
+standard defined by a recognized standards body, or, in the case of
+interfaces specified for a particular programming language, one that
+is widely used among developers working in that language.
+
+  The "System Libraries" of an executable work include anything, other
+than the work as a whole, that (a) is included in the normal form of
+packaging a Major Component, but which is not part of that Major
+Component, and (b) serves only to enable use of the work with that
+Major Component, or to implement a Standard Interface for which an
+implementation is available to the public in source code form.  A
+"Major Component", in this context, means a major essential component
+(kernel, window system, and so on) of the specific operating system
+(if any) on which the executable work runs, or a compiler used to
+produce the work, or an object code interpreter used to run it.
+
+  The "Corresponding Source" for a work in object code form means all
+the source code needed to generate, install, and (for an executable
+work) run the object code and to modify the work, including scripts to
+control those activities.  However, it does not include the work's
+System Libraries, or general-purpose tools or generally available free
+programs which are used unmodified in performing those activities but
+which are not part of the work.  For example, Corresponding Source
+includes interface definition files associated with source files for
+the work, and the source code for shared libraries and dynamically
+linked subprograms that the work is specifically designed to require,
+such as by intimate data communication or control flow between those
+subprograms and other parts of the work.
+
+  The Corresponding Source need not include anything that users
+can regenerate automatically from other parts of the Corresponding
+Source.
+
+  The Corresponding Source for a work in source code form is that
+same work.
+
+  2. Basic Permissions.
+
+  All rights granted under this License are granted for the term of
+copyright on the Program, and are irrevocable provided the stated
+conditions are met.  This License explicitly affirms your unlimited
+permission to run the unmodified Program.  The output from running a
+covered work is covered by this License only if the output, given its
+content, constitutes a covered work.  This License acknowledges your
+rights of fair use or other equivalent, as provided by copyright law.
+
+  You may make, run and propagate covered works that you do not
+convey, without conditions so long as your license otherwise remains
+in force.  You may convey covered works to others for the sole purpose
+of having them make modifications exclusively for you, or provide you
+with facilities for running those works, provided that you comply with
+the terms of this License in conveying all material for which you do
+not control copyright.  Those thus making or running the covered works
+for you must do so exclusively on your behalf, under your direction
+and control, on terms that prohibit them from making any copies of
+your copyrighted material outside their relationship with you.
+
+  Conveying under any other circumstances is permitted solely under
+the conditions stated below.  Sublicensing is not allowed; section 10
+makes it unnecessary.
+
+  3. Protecting Users' Legal Rights From Anti-Circumvention Law.
+
+  No covered work shall be deemed part of an effective technological
+measure under any applicable law fulfilling obligations under article
+11 of the WIPO copyright treaty adopted on 20 December 1996, or
+similar laws prohibiting or restricting circumvention of such
+measures.
+
+  When you convey a covered work, you waive any legal power to forbid
+circumvention of technological measures to the extent such circumvention
+is effected by exercising rights under this License with respect to
+the covered work, and you disclaim any intention to limit operation or
+modification of the work as a means of enforcing, against the work's
+users, your or third parties' legal rights to forbid circumvention of
+technological measures.
+
+  4. Conveying Verbatim Copies.
+
+  You may convey verbatim copies of the Program's source code as you
+receive it, in any medium, provided that you conspicuously and
+appropriately publish on each copy an appropriate copyright notice;
+keep intact all notices stating that this License and any
+non-permissive terms added in accord with section 7 apply to the code;
+keep intact all notices of the absence of any warranty; and give all
+recipients a copy of this License along with the Program.
+
+  You may charge any price or no price for each copy that you convey,
+and you may offer support or warranty protection for a fee.
+
+  5. Conveying Modified Source Versions.
+
+  You may convey a work based on the Program, or the modifications to
+produce it from the Program, in the form of source code under the
+terms of section 4, provided that you also meet all of these conditions:
+
+    a) The work must carry prominent notices stating that you modified
+    it, and giving a relevant date.
+
+    b) The work must carry prominent notices stating that it is
+    released under this License and any conditions added under section
+    7.  This requirement modifies the requirement in section 4 to
+    "keep intact all notices".
+
+    c) You must license the entire work, as a whole, under this
+    License to anyone who comes into possession of a copy.  This
+    License will therefore apply, along with any applicable section 7
+    additional terms, to the whole of the work, and all its parts,
+    regardless of how they are packaged.  This License gives no
+    permission to license the work in any other way, but it does not
+    invalidate such permission if you have separately received it.
+
+    d) If the work has interactive user interfaces, each must display
+    Appropriate Legal Notices; however, if the Program has interactive
+    interfaces that do not display Appropriate Legal Notices, your
+    work need not make them do so.
+
+  A compilation of a covered work with other separate and independent
+works, which are not by their nature extensions of the covered work,
+and which are not combined with it such as to form a larger program,
+in or on a volume of a storage or distribution medium, is called an
+"aggregate" if the compilation and its resulting copyright are not
+used to limit the access or legal rights of the compilation's users
+beyond what the individual works permit.  Inclusion of a covered work
+in an aggregate does not cause this License to apply to the other
+parts of the aggregate.
+
+  6. Conveying Non-Source Forms.
+
+  You may convey a covered work in object code form under the terms
+of sections 4 and 5, provided that you also convey the
+machine-readable Corresponding Source under the terms of this License,
+in one of these ways:
+
+    a) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by the
+    Corresponding Source fixed on a durable physical medium
+    customarily used for software interchange.
+
+    b) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by a
+    written offer, valid for at least three years and valid for as
+    long as you offer spare parts or customer support for that product
+    model, to give anyone who possesses the object code either (1) a
+    copy of the Corresponding Source for all the software in the
+    product that is covered by this License, on a durable physical
+    medium customarily used for software interchange, for a price no
+    more than your reasonable cost of physically performing this
+    conveying of source, or (2) access to copy the
+    Corresponding Source from a network server at no charge.
+
+    c) Convey individual copies of the object code with a copy of the
+    written offer to provide the Corresponding Source.  This
+    alternative is allowed only occasionally and noncommercially, and
+    only if you received the object code with such an offer, in accord
+    with subsection 6b.
+
+    d) Convey the object code by offering access from a designated
+    place (gratis or for a charge), and offer equivalent access to the
+    Corresponding Source in the same way through the same place at no
+    further charge.  You need not require recipients to copy the
+    Corresponding Source along with the object code.  If the place to
+    copy the object code is a network server, the Corresponding Source
+    may be on a different server (operated by you or a third party)
+    that supports equivalent copying facilities, provided you maintain
+    clear directions next to the object code saying where to find the
+    Corresponding Source.  Regardless of what server hosts the
+    Corresponding Source, you remain obligated to ensure that it is
+    available for as long as needed to satisfy these requirements.
+
+    e) Convey the object code using peer-to-peer transmission, provided
+    you inform other peers where the object code and Corresponding
+    Source of the work are being offered to the general public at no
+    charge under subsection 6d.
+
+  A separable portion of the object code, whose source code is excluded
+from the Corresponding Source as a System Library, need not be
+included in conveying the object code work.
+
+  A "User Product" is either (1) a "consumer product", which means any
+tangible personal property which is normally used for personal, family,
+or household purposes, or (2) anything designed or sold for incorporation
+into a dwelling.  In determining whether a product is a consumer product,
+doubtful cases shall be resolved in favor of coverage.  For a particular
+product received by a particular user, "normally used" refers to a
+typical or common use of that class of product, regardless of the status
+of the particular user or of the way in which the particular user
+actually uses, or expects or is expected to use, the product.  A product
+is a consumer product regardless of whether the product has substantial
+commercial, industrial or non-consumer uses, unless such uses represent
+the only significant mode of use of the product.
+
+  "Installation Information" for a User Product means any methods,
+procedures, authorization keys, or other information required to install
+and execute modified versions of a covered work in that User Product from
+a modified version of its Corresponding Source.  The information must
+suffice to ensure that the continued functioning of the modified object
+code is in no case prevented or interfered with solely because
+modification has been made.
+
+  If you convey an object code work under this section in, or with, or
+specifically for use in, a User Product, and the conveying occurs as
+part of a transaction in which the right of possession and use of the
+User Product is transferred to the recipient in perpetuity or for a
+fixed term (regardless of how the transaction is characterized), the
+Corresponding Source conveyed under this section must be accompanied
+by the Installation Information.  But this requirement does not apply
+if neither you nor any third party retains the ability to install
+modified object code on the User Product (for example, the work has
+been installed in ROM).
+
+  The requirement to provide Installation Information does not include a
+requirement to continue to provide support service, warranty, or updates
+for a work that has been modified or installed by the recipient, or for
+the User Product in which it has been modified or installed.  Access to a
+network may be denied when the modification itself materially and
+adversely affects the operation of the network or violates the rules and
+protocols for communication across the network.
+
+  Corresponding Source conveyed, and Installation Information provided,
+in accord with this section must be in a format that is publicly
+documented (and with an implementation available to the public in
+source code form), and must require no special password or key for
+unpacking, reading or copying.
+
+  7. Additional Terms.
+
+  "Additional permissions" are terms that supplement the terms of this
+License by making exceptions from one or more of its conditions.
+Additional permissions that are applicable to the entire Program shall
+be treated as though they were included in this License, to the extent
+that they are valid under applicable law.  If additional permissions
+apply only to part of the Program, that part may be used separately
+under those permissions, but the entire Program remains governed by
+this License without regard to the additional permissions.
+
+  When you convey a copy of a covered work, you may at your option
+remove any additional permissions from that copy, or from any part of
+it.  (Additional permissions may be written to require their own
+removal in certain cases when you modify the work.)  You may place
+additional permissions on material, added by you to a covered work,
+for which you have or can give appropriate copyright permission.
+
+  Notwithstanding any other provision of this License, for material you
+add to a covered work, you may (if authorized by the copyright holders of
+that material) supplement the terms of this License with terms:
+
+    a) Disclaiming warranty or limiting liability differently from the
+    terms of sections 15 and 16 of this License; or
+
+    b) Requiring preservation of specified reasonable legal notices or
+    author attributions in that material or in the Appropriate Legal
+    Notices displayed by works containing it; or
+
+    c) Prohibiting misrepresentation of the origin of that material, or
+    requiring that modified versions of such material be marked in
+    reasonable ways as different from the original version; or
+
+    d) Limiting the use for publicity purposes of names of licensors or
+    authors of the material; or
+
+    e) Declining to grant rights under trademark law for use of some
+    trade names, trademarks, or service marks; or
+
+    f) Requiring indemnification of licensors and authors of that
+    material by anyone who conveys the material (or modified versions of
+    it) with contractual assumptions of liability to the recipient, for
+    any liability that these contractual assumptions directly impose on
+    those licensors and authors.
+
+  All other non-permissive additional terms are considered "further
+restrictions" within the meaning of section 10.  If the Program as you
+received it, or any part of it, contains a notice stating that it is
+governed by this License along with a term that is a further
+restriction, you may remove that term.  If a license document contains
+a further restriction but permits relicensing or conveying under this
+License, you may add to a covered work material governed by the terms
+of that license document, provided that the further restriction does
+not survive such relicensing or conveying.
+
+  If you add terms to a covered work in accord with this section, you
+must place, in the relevant source files, a statement of the
+additional terms that apply to those files, or a notice indicating
+where to find the applicable terms.
+
+  Additional terms, permissive or non-permissive, may be stated in the
+form of a separately written license, or stated as exceptions;
+the above requirements apply either way.
+
+  8. Termination.
+
+  You may not propagate or modify a covered work except as expressly
+provided under this License.  Any attempt otherwise to propagate or
+modify it is void, and will automatically terminate your rights under
+this License (including any patent licenses granted under the third
+paragraph of section 11).
+
+  However, if you cease all violation of this License, then your
+license from a particular copyright holder is reinstated (a)
+provisionally, unless and until the copyright holder explicitly and
+finally terminates your license, and (b) permanently, if the copyright
+holder fails to notify you of the violation by some reasonable means
+prior to 60 days after the cessation.
+
+  Moreover, your license from a particular copyright holder is
+reinstated permanently if the copyright holder notifies you of the
+violation by some reasonable means, this is the first time you have
+received notice of violation of this License (for any work) from that
+copyright holder, and you cure the violation prior to 30 days after
+your receipt of the notice.
+
+  Termination of your rights under this section does not terminate the
+licenses of parties who have received copies or rights from you under
+this License.  If your rights have been terminated and not permanently
+reinstated, you do not qualify to receive new licenses for the same
+material under section 10.
+
+  9. Acceptance Not Required for Having Copies.
+
+  You are not required to accept this License in order to receive or
+run a copy of the Program.  Ancillary propagation of a covered work
+occurring solely as a consequence of using peer-to-peer transmission
+to receive a copy likewise does not require acceptance.  However,
+nothing other than this License grants you permission to propagate or
+modify any covered work.  These actions infringe copyright if you do
+not accept this License.  Therefore, by modifying or propagating a
+covered work, you indicate your acceptance of this License to do so.
+
+  10. Automatic Licensing of Downstream Recipients.
+
+  Each time you convey a covered work, the recipient automatically
+receives a license from the original licensors, to run, modify and
+propagate that work, subject to this License.  You are not responsible
+for enforcing compliance by third parties with this License.
+
+  An "entity transaction" is a transaction transferring control of an
+organization, or substantially all assets of one, or subdividing an
+organization, or merging organizations.  If propagation of a covered
+work results from an entity transaction, each party to that
+transaction who receives a copy of the work also receives whatever
+licenses to the work the party's predecessor in interest had or could
+give under the previous paragraph, plus a right to possession of the
+Corresponding Source of the work from the predecessor in interest, if
+the predecessor has it or can get it with reasonable efforts.
+
+  You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License.  For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+  11. Patents.
+
+  A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based.  The
+work thus licensed is called the contributor's "contributor version".
+
+  A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version.  For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+  Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+  In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement).  To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+  If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients.  "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+  If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+  A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License.  You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
+to the third party based on the extent of your activity of conveying
+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
+patent license (a) in connection with copies of the covered work
+conveyed by you (or copies made from those copies), or (b) primarily
+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+  Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+  12. No Surrender of Others' Freedom.
+
+  If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License.  If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all.  For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+  13. Use with the GNU Affero General Public License.
+
+  Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
+combined work, and to convey the resulting work.  The terms of this
+License will continue to apply to the part which is the covered work,
+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+  14. Revised Versions of this License.
+
+  The Free Software Foundation may publish revised and/or new versions of
+the GNU General Public License from time to time.  Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+  Each version is given a distinguishing version number.  If the
+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation.  If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
\ No newline at end of file
diff --git a/vendor/github.com/ethereum/go-ethereum/COPYING.LESSER b/vendor/github.com/ethereum/go-ethereum/COPYING.LESSER
new file mode 100644
index 000000000..65c5ca88a
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/COPYING.LESSER
@@ -0,0 +1,165 @@
+                   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
+engineering for debugging such modifications, if you also do each of
+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
+   execution, include the copyright notice for the Library among
+   these notices, as well as a reference directing the user to the
+   copies of the GNU GPL and this license document.
+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
+       License, and the Corresponding Application Code in a form
+       suitable for, and under terms that permit, the user to
+       recombine or relink the Application with a modified version of
+       the Linked Version to produce a modified Combined Work, in the
+       manner specified by section 6 of the GNU GPL for conveying
+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
+       Version.
+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/LICENSE b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/LICENSE
new file mode 100644
index 000000000..f9090e142
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/LICENSE
@@ -0,0 +1,31 @@
+Copyright (c) 2010 The Go Authors. All rights reserved.
+Copyright (c) 2011 ThePiachu. All rights reserved.
+Copyright (c) 2015 Jeffrey Wilcke. All rights reserved.
+Copyright (c) 2015 Felix Lange. All rights reserved.
+Copyright (c) 2015 Gustav Simonsson. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+   * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+   * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+   * Neither the name of the copyright holder. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/curve.go b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/curve.go
new file mode 100644
index 000000000..5409ee1d2
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/curve.go
@@ -0,0 +1,325 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Copyright 2011 ThePiachu. All rights reserved.
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+// * Redistributions of source code must retain the above copyright
+//   notice, this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above
+//   copyright notice, this list of conditions and the following disclaimer
+//   in the documentation and/or other materials provided with the
+//   distribution.
+// * Neither the name of Google Inc. nor the names of its
+//   contributors may be used to endorse or promote products derived from
+//   this software without specific prior written permission.
+// * The name of ThePiachu may not be used to endorse or promote products
+//   derived from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+package secp256k1
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"unsafe"
+)
+
+/*
+#include "libsecp256k1/include/secp256k1.h"
+extern int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, const unsigned char *point, const unsigned char *scalar);
+*/
+import "C"
+
+const (
+	// number of bits in a big.Word
+	wordBits = 32 << (uint64(^big.Word(0)) >> 63)
+	// number of bytes in a big.Word
+	wordBytes = wordBits / 8
+)
+
+// readBits encodes the absolute value of bigint as big-endian bytes. Callers
+// must ensure that buf has enough space. If buf is too short the result will
+// be incomplete.
+func readBits(bigint *big.Int, buf []byte) {
+	i := len(buf)
+	for _, d := range bigint.Bits() {
+		for j := 0; j < wordBytes && i > 0; j++ {
+			i--
+			buf[i] = byte(d)
+			d >>= 8
+		}
+	}
+}
+
+// This code is from https://github.com/ThePiachu/GoBit and implements
+// several Koblitz elliptic curves over prime fields.
+//
+// The curve methods, internally, on Jacobian coordinates. For a given
+// (x, y) position on the curve, the Jacobian coordinates are (x1, y1,
+// z1) where x = x1/z1² and y = y1/z1³. The greatest speedups come
+// when the whole calculation can be performed within the transform
+// (as in ScalarMult and ScalarBaseMult). But even for Add and Double,
+// it's faster to apply and reverse the transform than to operate in
+// affine coordinates.
+
+// A BitCurve represents a Koblitz Curve with a=0.
+// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
+type BitCurve struct {
+	P       *big.Int // the order of the underlying field
+	N       *big.Int // the order of the base point
+	B       *big.Int // the constant of the BitCurve equation
+	Gx, Gy  *big.Int // (x,y) of the base point
+	BitSize int      // the size of the underlying field
+}
+
+func (BitCurve *BitCurve) Params() *elliptic.CurveParams {
+	return &elliptic.CurveParams{
+		P:       BitCurve.P,
+		N:       BitCurve.N,
+		B:       BitCurve.B,
+		Gx:      BitCurve.Gx,
+		Gy:      BitCurve.Gy,
+		BitSize: BitCurve.BitSize,
+	}
+}
+
+// IsOnCurve returns true if the given (x,y) lies on the BitCurve.
+func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool {
+	// y² = x³ + b
+	y2 := new(big.Int).Mul(y, y) //y²
+	y2.Mod(y2, BitCurve.P)       //y²%P
+
+	x3 := new(big.Int).Mul(x, x) //x²
+	x3.Mul(x3, x)                //x³
+
+	x3.Add(x3, BitCurve.B) //x³+B
+	x3.Mod(x3, BitCurve.P) //(x³+B)%P
+
+	return x3.Cmp(y2) == 0
+}
+
+//TODO: double check if the function is okay
+// affineFromJacobian reverses the Jacobian transform. See the comment at the
+// top of the file.
+func (BitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
+	zinv := new(big.Int).ModInverse(z, BitCurve.P)
+	zinvsq := new(big.Int).Mul(zinv, zinv)
+
+	xOut = new(big.Int).Mul(x, zinvsq)
+	xOut.Mod(xOut, BitCurve.P)
+	zinvsq.Mul(zinvsq, zinv)
+	yOut = new(big.Int).Mul(y, zinvsq)
+	yOut.Mod(yOut, BitCurve.P)
+	return
+}
+
+// Add returns the sum of (x1,y1) and (x2,y2)
+func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	z := new(big.Int).SetInt64(1)
+	return BitCurve.affineFromJacobian(BitCurve.addJacobian(x1, y1, z, x2, y2, z))
+}
+
+// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
+// (x2, y2, z2) and returns their sum, also in Jacobian form.
+func (BitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
+	z1z1 := new(big.Int).Mul(z1, z1)
+	z1z1.Mod(z1z1, BitCurve.P)
+	z2z2 := new(big.Int).Mul(z2, z2)
+	z2z2.Mod(z2z2, BitCurve.P)
+
+	u1 := new(big.Int).Mul(x1, z2z2)
+	u1.Mod(u1, BitCurve.P)
+	u2 := new(big.Int).Mul(x2, z1z1)
+	u2.Mod(u2, BitCurve.P)
+	h := new(big.Int).Sub(u2, u1)
+	if h.Sign() == -1 {
+		h.Add(h, BitCurve.P)
+	}
+	i := new(big.Int).Lsh(h, 1)
+	i.Mul(i, i)
+	j := new(big.Int).Mul(h, i)
+
+	s1 := new(big.Int).Mul(y1, z2)
+	s1.Mul(s1, z2z2)
+	s1.Mod(s1, BitCurve.P)
+	s2 := new(big.Int).Mul(y2, z1)
+	s2.Mul(s2, z1z1)
+	s2.Mod(s2, BitCurve.P)
+	r := new(big.Int).Sub(s2, s1)
+	if r.Sign() == -1 {
+		r.Add(r, BitCurve.P)
+	}
+	r.Lsh(r, 1)
+	v := new(big.Int).Mul(u1, i)
+
+	x3 := new(big.Int).Set(r)
+	x3.Mul(x3, x3)
+	x3.Sub(x3, j)
+	x3.Sub(x3, v)
+	x3.Sub(x3, v)
+	x3.Mod(x3, BitCurve.P)
+
+	y3 := new(big.Int).Set(r)
+	v.Sub(v, x3)
+	y3.Mul(y3, v)
+	s1.Mul(s1, j)
+	s1.Lsh(s1, 1)
+	y3.Sub(y3, s1)
+	y3.Mod(y3, BitCurve.P)
+
+	z3 := new(big.Int).Add(z1, z2)
+	z3.Mul(z3, z3)
+	z3.Sub(z3, z1z1)
+	if z3.Sign() == -1 {
+		z3.Add(z3, BitCurve.P)
+	}
+	z3.Sub(z3, z2z2)
+	if z3.Sign() == -1 {
+		z3.Add(z3, BitCurve.P)
+	}
+	z3.Mul(z3, h)
+	z3.Mod(z3, BitCurve.P)
+
+	return x3, y3, z3
+}
+
+// Double returns 2*(x,y)
+func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	z1 := new(big.Int).SetInt64(1)
+	return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z1))
+}
+
+// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
+// returns its double, also in Jacobian form.
+func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+
+	a := new(big.Int).Mul(x, x) //X1²
+	b := new(big.Int).Mul(y, y) //Y1²
+	c := new(big.Int).Mul(b, b) //B²
+
+	d := new(big.Int).Add(x, b) //X1+B
+	d.Mul(d, d)                 //(X1+B)²
+	d.Sub(d, a)                 //(X1+B)²-A
+	d.Sub(d, c)                 //(X1+B)²-A-C
+	d.Mul(d, big.NewInt(2))     //2*((X1+B)²-A-C)
+
+	e := new(big.Int).Mul(big.NewInt(3), a) //3*A
+	f := new(big.Int).Mul(e, e)             //E²
+
+	x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
+	x3.Sub(f, x3)                            //F-2*D
+	x3.Mod(x3, BitCurve.P)
+
+	y3 := new(big.Int).Sub(d, x3)                  //D-X3
+	y3.Mul(e, y3)                                  //E*(D-X3)
+	y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
+	y3.Mod(y3, BitCurve.P)
+
+	z3 := new(big.Int).Mul(y, z) //Y1*Z1
+	z3.Mul(big.NewInt(2), z3)    //3*Y1*Z1
+	z3.Mod(z3, BitCurve.P)
+
+	return x3, y3, z3
+}
+
+func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
+	// Ensure scalar is exactly 32 bytes. We pad always, even if
+	// scalar is 32 bytes long, to avoid a timing side channel.
+	if len(scalar) > 32 {
+		panic("can't handle scalars > 256 bits")
+	}
+	// NOTE: potential timing issue
+	padded := make([]byte, 32)
+	copy(padded[32-len(scalar):], scalar)
+	scalar = padded
+
+	// Do the multiplication in C, updating point.
+	point := make([]byte, 64)
+	readBits(Bx, point[:32])
+	readBits(By, point[32:])
+
+	pointPtr := (*C.uchar)(unsafe.Pointer(&point[0]))
+	scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0]))
+	res := C.secp256k1_ext_scalar_mul(context, pointPtr, scalarPtr)
+
+	// Unpack the result and clear temporaries.
+	x := new(big.Int).SetBytes(point[:32])
+	y := new(big.Int).SetBytes(point[32:])
+	for i := range point {
+		point[i] = 0
+	}
+	for i := range padded {
+		scalar[i] = 0
+	}
+	if res != 1 {
+		return nil, nil
+	}
+	return x, y
+}
+
+// ScalarBaseMult returns k*G, where G is the base point of the group and k is
+// an integer in big-endian form.
+func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	return BitCurve.ScalarMult(BitCurve.Gx, BitCurve.Gy, k)
+}
+
+// Marshal converts a point into the form specified in section 4.3.6 of ANSI
+// X9.62.
+func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte {
+	byteLen := (BitCurve.BitSize + 7) >> 3
+	ret := make([]byte, 1+2*byteLen)
+	ret[0] = 4 // uncompressed point flag
+	readBits(x, ret[1:1+byteLen])
+	readBits(y, ret[1+byteLen:])
+	return ret
+}
+
+// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On
+// error, x = nil.
+func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) {
+	byteLen := (BitCurve.BitSize + 7) >> 3
+	if len(data) != 1+2*byteLen {
+		return
+	}
+	if data[0] != 4 { // uncompressed form
+		return
+	}
+	x = new(big.Int).SetBytes(data[1 : 1+byteLen])
+	y = new(big.Int).SetBytes(data[1+byteLen:])
+	return
+}
+
+var theCurve = new(BitCurve)
+
+func init() {
+	// See SEC 2 section 2.7.1
+	// curve parameters taken from:
+	// http://www.secg.org/sec2-v2.pdf
+	theCurve.P, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 0)
+	theCurve.N, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 0)
+	theCurve.B, _ = new(big.Int).SetString("0x0000000000000000000000000000000000000000000000000000000000000007", 0)
+	theCurve.Gx, _ = new(big.Int).SetString("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 0)
+	theCurve.Gy, _ = new(big.Int).SetString("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 0)
+	theCurve.BitSize = 256
+}
+
+// S256 returns a BitCurve which implements secp256k1.
+func S256() *BitCurve {
+	return theCurve
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/ext.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/ext.h
new file mode 100644
index 000000000..e422fe4b4
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/ext.h
@@ -0,0 +1,130 @@
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be found in
+// the LICENSE file.
+
+// secp256k1_context_create_sign_verify creates a context for signing and signature verification.
+static secp256k1_context* secp256k1_context_create_sign_verify() {
+	return secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+}
+
+// secp256k1_ext_ecdsa_recover recovers the public key of an encoded compact signature.
+//
+// Returns: 1: recovery was successful
+//          0: recovery was not successful
+// Args:    ctx:        pointer to a context object (cannot be NULL)
+//  Out:    pubkey_out: the serialized 65-byte public key of the signer (cannot be NULL)
+//  In:     sigdata:    pointer to a 65-byte signature with the recovery id at the end (cannot be NULL)
+//          msgdata:    pointer to a 32-byte message (cannot be NULL)
+static int secp256k1_ext_ecdsa_recover(
+	const secp256k1_context* ctx,
+	unsigned char *pubkey_out,
+	const unsigned char *sigdata,
+	const unsigned char *msgdata
+) {
+	secp256k1_ecdsa_recoverable_signature sig;
+	secp256k1_pubkey pubkey;
+
+	if (!secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &sig, sigdata, (int)sigdata[64])) {
+		return 0;
+	}
+	if (!secp256k1_ecdsa_recover(ctx, &pubkey, &sig, msgdata)) {
+		return 0;
+	}
+	size_t outputlen = 65;
+	return secp256k1_ec_pubkey_serialize(ctx, pubkey_out, &outputlen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
+}
+
+// secp256k1_ext_ecdsa_verify verifies an encoded compact signature.
+//
+// Returns: 1: signature is valid
+//          0: signature is invalid
+// Args:    ctx:        pointer to a context object (cannot be NULL)
+//  In:     sigdata:    pointer to a 64-byte signature (cannot be NULL)
+//          msgdata:    pointer to a 32-byte message (cannot be NULL)
+//          pubkeydata: pointer to public key data (cannot be NULL)
+//          pubkeylen:  length of pubkeydata
+static int secp256k1_ext_ecdsa_verify(
+	const secp256k1_context* ctx,
+	const unsigned char *sigdata,
+	const unsigned char *msgdata,
+	const unsigned char *pubkeydata,
+	size_t pubkeylen
+) {
+	secp256k1_ecdsa_signature sig;
+	secp256k1_pubkey pubkey;
+
+	if (!secp256k1_ecdsa_signature_parse_compact(ctx, &sig, sigdata)) {
+		return 0;
+	}
+	if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeydata, pubkeylen)) {
+		return 0;
+	}
+	return secp256k1_ecdsa_verify(ctx, &sig, msgdata, &pubkey);
+}
+
+// secp256k1_ext_reencode_pubkey decodes then encodes a public key. It can be used to
+// convert between public key formats. The input/output formats are chosen depending on the
+// length of the input/output buffers.
+//
+// Returns: 1: conversion successful
+//          0: conversion unsuccessful
+// Args:    ctx:        pointer to a context object (cannot be NULL)
+//  Out:    out:        output buffer that will contain the reencoded key (cannot be NULL)
+//  In:     outlen:     length of out (33 for compressed keys, 65 for uncompressed keys)
+//          pubkeydata: the input public key (cannot be NULL)
+//          pubkeylen:  length of pubkeydata
+static int secp256k1_ext_reencode_pubkey(
+	const secp256k1_context* ctx,
+	unsigned char *out,
+	size_t outlen,
+	const unsigned char *pubkeydata,
+	size_t pubkeylen
+) {
+	secp256k1_pubkey pubkey;
+
+	if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeydata, pubkeylen)) {
+		return 0;
+	}
+	unsigned int flag = (outlen == 33) ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED;
+	return secp256k1_ec_pubkey_serialize(ctx, out, &outlen, &pubkey, flag);
+}
+
+// secp256k1_ext_scalar_mul multiplies a point by a scalar in constant time.
+//
+// Returns: 1: multiplication was successful
+//          0: scalar was invalid (zero or overflow)
+// Args:    ctx:      pointer to a context object (cannot be NULL)
+//  Out:    point:    the multiplied point (usually secret)
+//  In:     point:    pointer to a 64-byte public point,
+//                    encoded as two 256bit big-endian numbers.
+//          scalar:   a 32-byte scalar with which to multiply the point
+int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, unsigned char *point, const unsigned char *scalar) {
+	int ret = 0;
+	int overflow = 0;
+	secp256k1_fe feX, feY;
+	secp256k1_gej res;
+	secp256k1_ge ge;
+	secp256k1_scalar s;
+	ARG_CHECK(point != NULL);
+	ARG_CHECK(scalar != NULL);
+	(void)ctx;
+
+	secp256k1_fe_set_b32(&feX, point);
+	secp256k1_fe_set_b32(&feY, point+32);
+	secp256k1_ge_set_xy(&ge, &feX, &feY);
+	secp256k1_scalar_set_b32(&s, scalar, &overflow);
+	if (overflow || secp256k1_scalar_is_zero(&s)) {
+		ret = 0;
+	} else {
+		secp256k1_ecmult_const(&res, &ge, &s);
+		secp256k1_ge_set_gej(&ge, &res);
+		/* Note: can't use secp256k1_pubkey_save here because it is not constant time. */
+		secp256k1_fe_normalize(&ge.x);
+		secp256k1_fe_normalize(&ge.y);
+		secp256k1_fe_get_b32(point, &ge.x);
+		secp256k1_fe_get_b32(point+32, &ge.y);
+		ret = 1;
+	}
+	secp256k1_scalar_clear(&s);
+	return ret;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.gitignore b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.gitignore
new file mode 100644
index 000000000..87fea161b
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.gitignore
@@ -0,0 +1,49 @@
+bench_inv
+bench_ecdh
+bench_sign
+bench_verify
+bench_schnorr_verify
+bench_recover
+bench_internal
+tests
+exhaustive_tests
+gen_context
+*.exe
+*.so
+*.a
+!.gitignore
+
+Makefile
+configure
+.libs/
+Makefile.in
+aclocal.m4
+autom4te.cache/
+config.log
+config.status
+*.tar.gz
+*.la
+libtool
+.deps/
+.dirstamp
+*.lo
+*.o
+*~
+src/libsecp256k1-config.h
+src/libsecp256k1-config.h.in
+src/ecmult_static_context.h
+build-aux/config.guess
+build-aux/config.sub
+build-aux/depcomp
+build-aux/install-sh
+build-aux/ltmain.sh
+build-aux/m4/libtool.m4
+build-aux/m4/lt~obsolete.m4
+build-aux/m4/ltoptions.m4
+build-aux/m4/ltsugar.m4
+build-aux/m4/ltversion.m4
+build-aux/missing
+build-aux/compile
+build-aux/test-driver
+src/stamp-h1
+libsecp256k1.pc
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.travis.yml b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.travis.yml
new file mode 100644
index 000000000..243952924
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/.travis.yml
@@ -0,0 +1,69 @@
+language: c
+sudo: false
+addons:
+  apt:
+    packages: libgmp-dev
+compiler:
+  - clang
+  - gcc
+cache:
+  directories:
+  - src/java/guava/
+env:
+  global:
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no  EXPERIMENTAL=no
+    - GUAVA_URL=https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar GUAVA_JAR=src/java/guava/guava-18.0.jar
+  matrix:
+    - SCALAR=32bit    RECOVERY=yes
+    - SCALAR=32bit    FIELD=32bit       ECDH=yes  EXPERIMENTAL=yes
+    - SCALAR=64bit
+    - FIELD=64bit     RECOVERY=yes
+    - FIELD=64bit     ENDOMORPHISM=yes
+    - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes EXPERIMENTAL=yes
+    - FIELD=64bit                       ASM=x86_64
+    - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
+    - FIELD=32bit     ENDOMORPHISM=yes
+    - BIGNUM=no
+    - BIGNUM=no       ENDOMORPHISM=yes RECOVERY=yes EXPERIMENTAL=yes
+    - BIGNUM=no       STATICPRECOMPUTATION=no
+    - BUILD=distcheck
+    - EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
+    - EXTRAFLAGS=CFLAGS=-O0
+    - BUILD=check-java ECDH=yes EXPERIMENTAL=yes
+matrix:
+  fast_finish: true
+  include:
+    - compiler: clang
+      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+            - libgmp-dev:i386
+    - compiler: clang
+      env: HOST=i686-linux-gnu
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+    - compiler: gcc
+      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+    - compiler: gcc
+      env: HOST=i686-linux-gnu
+      addons:
+        apt:
+          packages:
+            - gcc-multilib
+            - libgmp-dev:i386
+before_install: mkdir -p `dirname $GUAVA_JAR`
+install: if [ ! -f $GUAVA_JAR ]; then wget $GUAVA_URL -O $GUAVA_JAR; fi
+before_script: ./autogen.sh
+script:
+ - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
+ - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
+ - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+os: linux
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/COPYING b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/COPYING
new file mode 100644
index 000000000..4522a5990
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/COPYING
@@ -0,0 +1,19 @@
+Copyright (c) 2013 Pieter Wuille
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/Makefile.am b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/Makefile.am
new file mode 100644
index 000000000..c071fbe27
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/Makefile.am
@@ -0,0 +1,177 @@
+ACLOCAL_AMFLAGS = -I build-aux/m4
+
+lib_LTLIBRARIES = libsecp256k1.la
+if USE_JNI
+JNI_LIB = libsecp256k1_jni.la
+noinst_LTLIBRARIES = $(JNI_LIB)
+else
+JNI_LIB =
+endif
+include_HEADERS = include/secp256k1.h
+noinst_HEADERS =
+noinst_HEADERS += src/scalar.h
+noinst_HEADERS += src/scalar_4x64.h
+noinst_HEADERS += src/scalar_8x32.h
+noinst_HEADERS += src/scalar_low.h
+noinst_HEADERS += src/scalar_impl.h
+noinst_HEADERS += src/scalar_4x64_impl.h
+noinst_HEADERS += src/scalar_8x32_impl.h
+noinst_HEADERS += src/scalar_low_impl.h
+noinst_HEADERS += src/group.h
+noinst_HEADERS += src/group_impl.h
+noinst_HEADERS += src/num_gmp.h
+noinst_HEADERS += src/num_gmp_impl.h
+noinst_HEADERS += src/ecdsa.h
+noinst_HEADERS += src/ecdsa_impl.h
+noinst_HEADERS += src/eckey.h
+noinst_HEADERS += src/eckey_impl.h
+noinst_HEADERS += src/ecmult.h
+noinst_HEADERS += src/ecmult_impl.h
+noinst_HEADERS += src/ecmult_const.h
+noinst_HEADERS += src/ecmult_const_impl.h
+noinst_HEADERS += src/ecmult_gen.h
+noinst_HEADERS += src/ecmult_gen_impl.h
+noinst_HEADERS += src/num.h
+noinst_HEADERS += src/num_impl.h
+noinst_HEADERS += src/field_10x26.h
+noinst_HEADERS += src/field_10x26_impl.h
+noinst_HEADERS += src/field_5x52.h
+noinst_HEADERS += src/field_5x52_impl.h
+noinst_HEADERS += src/field_5x52_int128_impl.h
+noinst_HEADERS += src/field_5x52_asm_impl.h
+noinst_HEADERS += src/java/org_bitcoin_NativeSecp256k1.h
+noinst_HEADERS += src/java/org_bitcoin_Secp256k1Context.h
+noinst_HEADERS += src/util.h
+noinst_HEADERS += src/testrand.h
+noinst_HEADERS += src/testrand_impl.h
+noinst_HEADERS += src/hash.h
+noinst_HEADERS += src/hash_impl.h
+noinst_HEADERS += src/field.h
+noinst_HEADERS += src/field_impl.h
+noinst_HEADERS += src/bench.h
+noinst_HEADERS += contrib/lax_der_parsing.h
+noinst_HEADERS += contrib/lax_der_parsing.c
+noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
+noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
+
+if USE_EXTERNAL_ASM
+COMMON_LIB = libsecp256k1_common.la
+noinst_LTLIBRARIES = $(COMMON_LIB)
+else
+COMMON_LIB =
+endif
+
+pkgconfigdir = $(libdir)/pkgconfig
+pkgconfig_DATA = libsecp256k1.pc
+
+if USE_EXTERNAL_ASM
+if USE_ASM_ARM
+libsecp256k1_common_la_SOURCES = src/asm/field_10x26_arm.s
+endif
+endif
+
+libsecp256k1_la_SOURCES = src/secp256k1.c
+libsecp256k1_la_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
+libsecp256k1_la_LIBADD = $(JNI_LIB) $(SECP_LIBS) $(COMMON_LIB)
+
+libsecp256k1_jni_la_SOURCES  = src/java/org_bitcoin_NativeSecp256k1.c src/java/org_bitcoin_Secp256k1Context.c
+libsecp256k1_jni_la_CPPFLAGS = -DSECP256K1_BUILD $(JNI_INCLUDES)
+
+noinst_PROGRAMS =
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_verify bench_sign bench_internal
+bench_verify_SOURCES = src/bench_verify.c
+bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+bench_sign_SOURCES = src/bench_sign.c
+bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+bench_internal_SOURCES = src/bench_internal.c
+bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
+endif
+
+TESTS =
+if USE_TESTS
+noinst_PROGRAMS += tests
+tests_SOURCES = src/tests.c
+tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+if !ENABLE_COVERAGE
+tests_CPPFLAGS += -DVERIFY
+endif
+tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
+tests_LDFLAGS = -static
+TESTS += tests
+endif
+
+if USE_EXHAUSTIVE_TESTS
+noinst_PROGRAMS += exhaustive_tests
+exhaustive_tests_SOURCES = src/tests_exhaustive.c
+exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src $(SECP_INCLUDES)
+if !ENABLE_COVERAGE
+exhaustive_tests_CPPFLAGS += -DVERIFY
+endif
+exhaustive_tests_LDADD = $(SECP_LIBS)
+exhaustive_tests_LDFLAGS = -static
+TESTS += exhaustive_tests
+endif
+
+JAVAROOT=src/java
+JAVAORG=org/bitcoin
+JAVA_GUAVA=$(srcdir)/$(JAVAROOT)/guava/guava-18.0.jar
+CLASSPATH_ENV=CLASSPATH=$(JAVA_GUAVA)
+JAVA_FILES= \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1.java \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Test.java \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Util.java \
+  $(JAVAROOT)/$(JAVAORG)/Secp256k1Context.java
+
+if USE_JNI
+
+$(JAVA_GUAVA):
+	@echo Guava is missing. Fetch it via: \
+	wget https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar -O $(@)
+	@false
+
+.stamp-java: $(JAVA_FILES)
+	@echo   Compiling $^
+	$(AM_V_at)$(CLASSPATH_ENV) javac $^
+	@touch $@
+
+if USE_TESTS
+
+check-java: libsecp256k1.la $(JAVA_GUAVA) .stamp-java
+	$(AM_V_at)java -Djava.library.path="./:./src:./src/.libs:.libs/" -cp "$(JAVA_GUAVA):$(JAVAROOT)" $(JAVAORG)/NativeSecp256k1Test
+
+endif
+endif
+
+if USE_ECMULT_STATIC_PRECOMPUTATION
+CPPFLAGS_FOR_BUILD +=-I$(top_srcdir)
+CFLAGS_FOR_BUILD += -Wall -Wextra -Wno-unused-function
+
+gen_context_OBJECTS = gen_context.o
+gen_context_BIN = gen_context$(BUILD_EXEEXT)
+gen_%.o: src/gen_%.c
+	$(CC_FOR_BUILD) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@
+
+$(gen_context_BIN): $(gen_context_OBJECTS)
+	$(CC_FOR_BUILD) $^ -o $@
+
+$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h
+$(tests_OBJECTS): src/ecmult_static_context.h
+$(bench_internal_OBJECTS): src/ecmult_static_context.h
+
+src/ecmult_static_context.h: $(gen_context_BIN)
+	./$(gen_context_BIN)
+
+CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h $(JAVAROOT)/$(JAVAORG)/*.class .stamp-java
+endif
+
+EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h $(JAVA_FILES)
+
+if ENABLE_MODULE_ECDH
+include src/modules/ecdh/Makefile.am.include
+endif
+
+if ENABLE_MODULE_RECOVERY
+include src/modules/recovery/Makefile.am.include
+endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/README.md b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/README.md
new file mode 100644
index 000000000..8cd344ea8
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/README.md
@@ -0,0 +1,61 @@
+libsecp256k1
+============
+
+[![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1)
+
+Optimized C library for EC operations on curve secp256k1.
+
+This library is a work in progress and is being used to research best practices. Use at your own risk.
+
+Features:
+* secp256k1 ECDSA signing/verification and key generation.
+* Adding/multiplying private/public keys.
+* Serialization/parsing of private keys, public keys, signatures.
+* Constant time, constant memory access signing and pubkey generation.
+* Derandomized DSA (via RFC6979 or with a caller provided function.)
+* Very efficient implementation.
+
+Implementation details
+----------------------
+
+* General
+  * No runtime heap allocation.
+  * Extensive testing infrastructure.
+  * Structured to facilitate review and analysis.
+  * Intended to be portable to any system with a C89 compiler and uint64_t support.
+  * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
+* Field operations
+  * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
+    * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
+    * Using 10 26-bit limbs.
+  * Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
+* Scalar operations
+  * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
+    * Using 4 64-bit limbs (relying on __int128 support in the compiler).
+    * Using 8 32-bit limbs.
+* Group operations
+  * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
+  * Use addition between points in Jacobian and affine coordinates where possible.
+  * Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
+  * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
+* Point multiplication for verification (a*P + b*G).
+  * Use wNAF notation for point multiplicands.
+  * Use a much larger window for multiples of G, using precomputed multiples.
+  * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
+  * Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
+* Point multiplication for signing
+  * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
+  * Access the table with branch-free conditional moves so memory access is uniform.
+  * No data-dependent branches
+  * The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally.
+
+Build steps
+-----------
+
+libsecp256k1 is built using autotools:
+
+    $ ./autogen.sh
+    $ ./configure
+    $ make
+    $ ./tests
+    $ sudo make install  # optional
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/TODO b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/TODO
new file mode 100644
index 000000000..a300e1c5e
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/TODO
@@ -0,0 +1,3 @@
+* Unit tests for fieldelem/groupelem, including ones intended to
+  trigger fieldelem's boundary cases.
+* Complete constant-time operations for signing/keygen
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/autogen.sh b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/autogen.sh
new file mode 100755
index 000000000..65286b935
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/autogen.sh
@@ -0,0 +1,3 @@
+#!/bin/sh
+set -e
+autoreconf -if --warnings=all
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_jni_include_dir.m4 b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_jni_include_dir.m4
new file mode 100644
index 000000000..1fc362761
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_jni_include_dir.m4
@@ -0,0 +1,140 @@
+# ===========================================================================
+#    http://www.gnu.org/software/autoconf-archive/ax_jni_include_dir.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_JNI_INCLUDE_DIR
+#
+# DESCRIPTION
+#
+#   AX_JNI_INCLUDE_DIR finds include directories needed for compiling
+#   programs using the JNI interface.
+#
+#   JNI include directories are usually in the Java distribution. This is
+#   deduced from the value of $JAVA_HOME, $JAVAC, or the path to "javac", in
+#   that order. When this macro completes, a list of directories is left in
+#   the variable JNI_INCLUDE_DIRS.
+#
+#   Example usage follows:
+#
+#     AX_JNI_INCLUDE_DIR
+#
+#     for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS
+#     do
+#             CPPFLAGS="$CPPFLAGS -I$JNI_INCLUDE_DIR"
+#     done
+#
+#   If you want to force a specific compiler:
+#
+#   - at the configure.in level, set JAVAC=yourcompiler before calling
+#   AX_JNI_INCLUDE_DIR
+#
+#   - at the configure level, setenv JAVAC
+#
+#   Note: This macro can work with the autoconf M4 macros for Java programs.
+#   This particular macro is not part of the original set of macros.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Don Anderson <dda@sleepycat.com>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 10
+
+AU_ALIAS([AC_JNI_INCLUDE_DIR], [AX_JNI_INCLUDE_DIR])
+AC_DEFUN([AX_JNI_INCLUDE_DIR],[
+
+JNI_INCLUDE_DIRS=""
+
+if test "x$JAVA_HOME" != x; then
+	_JTOPDIR="$JAVA_HOME"
+else
+	if test "x$JAVAC" = x; then
+		JAVAC=javac
+	fi
+	AC_PATH_PROG([_ACJNI_JAVAC], [$JAVAC], [no])
+	if test "x$_ACJNI_JAVAC" = xno; then
+		AC_MSG_WARN([cannot find JDK; try setting \$JAVAC or \$JAVA_HOME])
+	fi
+	_ACJNI_FOLLOW_SYMLINKS("$_ACJNI_JAVAC")
+	_JTOPDIR=`echo "$_ACJNI_FOLLOWED" | sed -e 's://*:/:g' -e 's:/[[^/]]*$::'`
+fi
+
+case "$host_os" in
+        darwin*)        _JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
+                        _JINC="$_JTOPDIR/Headers";;
+        *)              _JINC="$_JTOPDIR/include";;
+esac
+_AS_ECHO_LOG([_JTOPDIR=$_JTOPDIR])
+_AS_ECHO_LOG([_JINC=$_JINC])
+
+# On Mac OS X 10.6.4, jni.h is a symlink:
+# /System/Library/Frameworks/JavaVM.framework/Versions/Current/Headers/jni.h
+# -> ../../CurrentJDK/Headers/jni.h.
+
+AC_CACHE_CHECK(jni headers, ac_cv_jni_header_path,
+[
+if test -f "$_JINC/jni.h"; then
+  ac_cv_jni_header_path="$_JINC"
+  JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
+else
+  _JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
+  if test -f "$_JTOPDIR/include/jni.h"; then
+    ac_cv_jni_header_path="$_JTOPDIR/include"
+    JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
+  else
+    ac_cv_jni_header_path=none
+  fi
+fi
+])
+
+
+
+# get the likely subdirectories for system specific java includes
+case "$host_os" in
+bsdi*)          _JNI_INC_SUBDIRS="bsdos";;
+darwin*)        _JNI_INC_SUBDIRS="darwin";;
+freebsd*)       _JNI_INC_SUBDIRS="freebsd";;
+linux*)         _JNI_INC_SUBDIRS="linux genunix";;
+osf*)           _JNI_INC_SUBDIRS="alpha";;
+solaris*)       _JNI_INC_SUBDIRS="solaris";;
+mingw*)		_JNI_INC_SUBDIRS="win32";;
+cygwin*)	_JNI_INC_SUBDIRS="win32";;
+*)              _JNI_INC_SUBDIRS="genunix";;
+esac
+
+if test "x$ac_cv_jni_header_path" != "xnone"; then
+  # add any subdirectories that are present
+  for JINCSUBDIR in $_JNI_INC_SUBDIRS
+  do
+      if test -d "$_JTOPDIR/include/$JINCSUBDIR"; then
+           JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $_JTOPDIR/include/$JINCSUBDIR"
+      fi
+  done
+fi
+])
+
+# _ACJNI_FOLLOW_SYMLINKS <path>
+# Follows symbolic links on <path>,
+# finally setting variable _ACJNI_FOLLOWED
+# ----------------------------------------
+AC_DEFUN([_ACJNI_FOLLOW_SYMLINKS],[
+# find the include directory relative to the javac executable
+_cur="$1"
+while ls -ld "$_cur" 2>/dev/null | grep " -> " >/dev/null; do
+        AC_MSG_CHECKING([symlink for $_cur])
+        _slink=`ls -ld "$_cur" | sed 's/.* -> //'`
+        case "$_slink" in
+        /*) _cur="$_slink";;
+        # 'X' avoids triggering unwanted echo options.
+        *) _cur=`echo "X$_cur" | sed -e 's/^X//' -e 's:[[^/]]*$::'`"$_slink";;
+        esac
+        AC_MSG_RESULT([$_cur])
+done
+_ACJNI_FOLLOWED="$_cur"
+])# _ACJNI
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4 b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4
new file mode 100644
index 000000000..77fd346a7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4
@@ -0,0 +1,125 @@
+# ===========================================================================
+#   http://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_PROG_CC_FOR_BUILD
+#
+# DESCRIPTION
+#
+#   This macro searches for a C compiler that generates native executables,
+#   that is a C compiler that surely is not a cross-compiler. This can be
+#   useful if you have to generate source code at compile-time like for
+#   example GCC does.
+#
+#   The macro sets the CC_FOR_BUILD and CPP_FOR_BUILD macros to anything
+#   needed to compile or link (CC_FOR_BUILD) and preprocess (CPP_FOR_BUILD).
+#   The value of these variables can be overridden by the user by specifying
+#   a compiler with an environment variable (like you do for standard CC).
+#
+#   It also sets BUILD_EXEEXT and BUILD_OBJEXT to the executable and object
+#   file extensions for the build platform, and GCC_FOR_BUILD to `yes' if
+#   the compiler we found is GCC. All these variables but GCC_FOR_BUILD are
+#   substituted in the Makefile.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Paolo Bonzini <bonzini@gnu.org>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 8
+
+AU_ALIAS([AC_PROG_CC_FOR_BUILD], [AX_PROG_CC_FOR_BUILD])
+AC_DEFUN([AX_PROG_CC_FOR_BUILD], [dnl
+AC_REQUIRE([AC_PROG_CC])dnl
+AC_REQUIRE([AC_PROG_CPP])dnl
+AC_REQUIRE([AC_EXEEXT])dnl
+AC_REQUIRE([AC_CANONICAL_HOST])dnl
+
+dnl Use the standard macros, but make them use other variable names
+dnl
+pushdef([ac_cv_prog_CPP], ac_cv_build_prog_CPP)dnl
+pushdef([ac_cv_prog_gcc], ac_cv_build_prog_gcc)dnl
+pushdef([ac_cv_prog_cc_works], ac_cv_build_prog_cc_works)dnl
+pushdef([ac_cv_prog_cc_cross], ac_cv_build_prog_cc_cross)dnl
+pushdef([ac_cv_prog_cc_g], ac_cv_build_prog_cc_g)dnl
+pushdef([ac_cv_exeext], ac_cv_build_exeext)dnl
+pushdef([ac_cv_objext], ac_cv_build_objext)dnl
+pushdef([ac_exeext], ac_build_exeext)dnl
+pushdef([ac_objext], ac_build_objext)dnl
+pushdef([CC], CC_FOR_BUILD)dnl
+pushdef([CPP], CPP_FOR_BUILD)dnl
+pushdef([CFLAGS], CFLAGS_FOR_BUILD)dnl
+pushdef([CPPFLAGS], CPPFLAGS_FOR_BUILD)dnl
+pushdef([LDFLAGS], LDFLAGS_FOR_BUILD)dnl
+pushdef([host], build)dnl
+pushdef([host_alias], build_alias)dnl
+pushdef([host_cpu], build_cpu)dnl
+pushdef([host_vendor], build_vendor)dnl
+pushdef([host_os], build_os)dnl
+pushdef([ac_cv_host], ac_cv_build)dnl
+pushdef([ac_cv_host_alias], ac_cv_build_alias)dnl
+pushdef([ac_cv_host_cpu], ac_cv_build_cpu)dnl
+pushdef([ac_cv_host_vendor], ac_cv_build_vendor)dnl
+pushdef([ac_cv_host_os], ac_cv_build_os)dnl
+pushdef([ac_cpp], ac_build_cpp)dnl
+pushdef([ac_compile], ac_build_compile)dnl
+pushdef([ac_link], ac_build_link)dnl
+
+save_cross_compiling=$cross_compiling
+save_ac_tool_prefix=$ac_tool_prefix
+cross_compiling=no
+ac_tool_prefix=
+
+AC_PROG_CC
+AC_PROG_CPP
+AC_EXEEXT
+
+ac_tool_prefix=$save_ac_tool_prefix
+cross_compiling=$save_cross_compiling
+
+dnl Restore the old definitions
+dnl
+popdef([ac_link])dnl
+popdef([ac_compile])dnl
+popdef([ac_cpp])dnl
+popdef([ac_cv_host_os])dnl
+popdef([ac_cv_host_vendor])dnl
+popdef([ac_cv_host_cpu])dnl
+popdef([ac_cv_host_alias])dnl
+popdef([ac_cv_host])dnl
+popdef([host_os])dnl
+popdef([host_vendor])dnl
+popdef([host_cpu])dnl
+popdef([host_alias])dnl
+popdef([host])dnl
+popdef([LDFLAGS])dnl
+popdef([CPPFLAGS])dnl
+popdef([CFLAGS])dnl
+popdef([CPP])dnl
+popdef([CC])dnl
+popdef([ac_objext])dnl
+popdef([ac_exeext])dnl
+popdef([ac_cv_objext])dnl
+popdef([ac_cv_exeext])dnl
+popdef([ac_cv_prog_cc_g])dnl
+popdef([ac_cv_prog_cc_cross])dnl
+popdef([ac_cv_prog_cc_works])dnl
+popdef([ac_cv_prog_gcc])dnl
+popdef([ac_cv_prog_CPP])dnl
+
+dnl Finally, set Makefile variables
+dnl
+BUILD_EXEEXT=$ac_build_exeext
+BUILD_OBJEXT=$ac_build_objext
+AC_SUBST(BUILD_EXEEXT)dnl
+AC_SUBST(BUILD_OBJEXT)dnl
+AC_SUBST([CFLAGS_FOR_BUILD])dnl
+AC_SUBST([CPPFLAGS_FOR_BUILD])dnl
+AC_SUBST([LDFLAGS_FOR_BUILD])dnl
+])
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/bitcoin_secp.m4 b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/bitcoin_secp.m4
new file mode 100644
index 000000000..b74acb8c1
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/build-aux/m4/bitcoin_secp.m4
@@ -0,0 +1,69 @@
+dnl libsecp25k1 helper checks
+AC_DEFUN([SECP_INT128_CHECK],[
+has_int128=$ac_cv_type___int128
+])
+
+dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
+AC_DEFUN([SECP_64BIT_ASM_CHECK],[
+AC_MSG_CHECKING(for x86_64 assembly availability)
+AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+  #include <stdint.h>]],[[
+  uint64_t a = 11, tmp;
+  __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
+  ]])],[has_64bit_asm=yes],[has_64bit_asm=no])
+AC_MSG_RESULT([$has_64bit_asm])
+])
+
+dnl
+AC_DEFUN([SECP_OPENSSL_CHECK],[
+  has_libcrypto=no
+  m4_ifdef([PKG_CHECK_MODULES],[
+    PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no])
+    if test x"$has_libcrypto" = x"yes"; then
+      TEMP_LIBS="$LIBS"
+      LIBS="$LIBS $CRYPTO_LIBS"
+      AC_CHECK_LIB(crypto, main,[AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])],[has_libcrypto=no])
+      LIBS="$TEMP_LIBS"
+    fi
+  ])
+  if test x$has_libcrypto = xno; then
+    AC_CHECK_HEADER(openssl/crypto.h,[
+      AC_CHECK_LIB(crypto, main,[
+        has_libcrypto=yes
+        CRYPTO_LIBS=-lcrypto
+        AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])
+      ])
+    ])
+    LIBS=
+  fi
+if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
+  AC_MSG_CHECKING(for EC functions in libcrypto)
+  AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+    #include <openssl/ec.h>
+    #include <openssl/ecdsa.h>
+    #include <openssl/obj_mac.h>]],[[
+    EC_KEY *eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
+    ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
+    ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
+    EC_KEY_free(eckey);
+    ECDSA_SIG *sig_openssl;
+    sig_openssl = ECDSA_SIG_new();
+    (void)sig_openssl->r;
+    ECDSA_SIG_free(sig_openssl);
+  ]])],[has_openssl_ec=yes],[has_openssl_ec=no])
+  AC_MSG_RESULT([$has_openssl_ec])
+fi
+])
+
+dnl
+AC_DEFUN([SECP_GMP_CHECK],[
+if test x"$has_gmp" != x"yes"; then
+  CPPFLAGS_TEMP="$CPPFLAGS"
+  CPPFLAGS="$GMP_CPPFLAGS $CPPFLAGS"
+  LIBS_TEMP="$LIBS"
+  LIBS="$GMP_LIBS $LIBS"
+  AC_CHECK_HEADER(gmp.h,[AC_CHECK_LIB(gmp, __gmpz_init,[has_gmp=yes; GMP_LIBS="$GMP_LIBS -lgmp"; AC_DEFINE(HAVE_LIBGMP,1,[Define this symbol if libgmp is installed])])])
+  CPPFLAGS="$CPPFLAGS_TEMP"
+  LIBS="$LIBS_TEMP"
+fi
+])
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/configure.ac b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/configure.ac
new file mode 100644
index 000000000..e5fcbcb4e
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/configure.ac
@@ -0,0 +1,493 @@
+AC_PREREQ([2.60])
+AC_INIT([libsecp256k1],[0.1])
+AC_CONFIG_AUX_DIR([build-aux])
+AC_CONFIG_MACRO_DIR([build-aux/m4])
+AC_CANONICAL_HOST
+AH_TOP([#ifndef LIBSECP256K1_CONFIG_H])
+AH_TOP([#define LIBSECP256K1_CONFIG_H])
+AH_BOTTOM([#endif /*LIBSECP256K1_CONFIG_H*/])
+AM_INIT_AUTOMAKE([foreign subdir-objects])
+LT_INIT
+
+dnl make the compilation flags quiet unless V=1 is used
+m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])])
+
+PKG_PROG_PKG_CONFIG
+
+AC_PATH_TOOL(AR, ar)
+AC_PATH_TOOL(RANLIB, ranlib)
+AC_PATH_TOOL(STRIP, strip)
+AX_PROG_CC_FOR_BUILD
+
+if test "x$CFLAGS" = "x"; then
+  CFLAGS="-g"
+fi
+
+AM_PROG_CC_C_O
+
+AC_PROG_CC_C89
+if test x"$ac_cv_prog_cc_c89" = x"no"; then
+  AC_MSG_ERROR([c89 compiler support required])
+fi
+AM_PROG_AS
+
+case $host_os in
+  *darwin*)
+     if  test x$cross_compiling != xyes; then
+       AC_PATH_PROG([BREW],brew,)
+       if test x$BREW != x; then
+         dnl These Homebrew packages may be keg-only, meaning that they won't be found
+         dnl in expected paths because they may conflict with system files. Ask
+         dnl Homebrew where each one is located, then adjust paths accordingly.
+
+         openssl_prefix=`$BREW --prefix openssl 2>/dev/null`
+         gmp_prefix=`$BREW --prefix gmp 2>/dev/null`
+         if test x$openssl_prefix != x; then
+           PKG_CONFIG_PATH="$openssl_prefix/lib/pkgconfig:$PKG_CONFIG_PATH"
+           export PKG_CONFIG_PATH
+         fi
+         if test x$gmp_prefix != x; then
+           GMP_CPPFLAGS="-I$gmp_prefix/include"
+           GMP_LIBS="-L$gmp_prefix/lib"
+         fi
+       else
+         AC_PATH_PROG([PORT],port,)
+         dnl if homebrew isn't installed and macports is, add the macports default paths
+         dnl as a last resort.
+         if test x$PORT != x; then
+           CPPFLAGS="$CPPFLAGS -isystem /opt/local/include"
+           LDFLAGS="$LDFLAGS -L/opt/local/lib"
+         fi
+       fi
+     fi
+   ;;
+esac
+
+CFLAGS="$CFLAGS -W"
+
+warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS $warn_CFLAGS"
+AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
+
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS -fvisibility=hidden"
+AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
+
+AC_ARG_ENABLE(benchmark,
+    AS_HELP_STRING([--enable-benchmark],[compile benchmark (default is no)]),
+    [use_benchmark=$enableval],
+    [use_benchmark=no])
+
+AC_ARG_ENABLE(coverage,
+    AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis]),
+    [enable_coverage=$enableval],
+    [enable_coverage=no])
+
+AC_ARG_ENABLE(tests,
+    AS_HELP_STRING([--enable-tests],[compile tests (default is yes)]),
+    [use_tests=$enableval],
+    [use_tests=yes])
+
+AC_ARG_ENABLE(openssl_tests,
+    AS_HELP_STRING([--enable-openssl-tests],[enable OpenSSL tests, if OpenSSL is available (default is auto)]),
+    [enable_openssl_tests=$enableval],
+    [enable_openssl_tests=auto])
+
+AC_ARG_ENABLE(experimental,
+    AS_HELP_STRING([--enable-experimental],[allow experimental configure options (default is no)]),
+    [use_experimental=$enableval],
+    [use_experimental=no])
+
+AC_ARG_ENABLE(exhaustive_tests,
+    AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests (default is yes)]),
+    [use_exhaustive_tests=$enableval],
+    [use_exhaustive_tests=yes])
+
+AC_ARG_ENABLE(endomorphism,
+    AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
+    [use_endomorphism=$enableval],
+    [use_endomorphism=no])
+
+AC_ARG_ENABLE(ecmult_static_precomputation,
+    AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing (default is yes)]),
+    [use_ecmult_static_precomputation=$enableval],
+    [use_ecmult_static_precomputation=auto])
+
+AC_ARG_ENABLE(module_ecdh,
+    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (experimental)]),
+    [enable_module_ecdh=$enableval],
+    [enable_module_ecdh=no])
+
+AC_ARG_ENABLE(module_recovery,
+    AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module (default is no)]),
+    [enable_module_recovery=$enableval],
+    [enable_module_recovery=no])
+
+AC_ARG_ENABLE(jni,
+    AS_HELP_STRING([--enable-jni],[enable libsecp256k1_jni (default is auto)]),
+    [use_jni=$enableval],
+    [use_jni=auto])
+
+AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
+[Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
+
+AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto],
+[Specify Bignum Implementation. Default is auto])],[req_bignum=$withval], [req_bignum=auto])
+
+AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
+[Specify scalar implementation. Default is auto])],[req_scalar=$withval], [req_scalar=auto])
+
+AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto]
+[Specify assembly optimizations to use. Default is auto (experimental: arm)])],[req_asm=$withval], [req_asm=auto])
+
+AC_CHECK_TYPES([__int128])
+
+AC_MSG_CHECKING([for __builtin_expect])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])],
+    [ AC_MSG_RESULT([yes]);AC_DEFINE(HAVE_BUILTIN_EXPECT,1,[Define this symbol if __builtin_expect is available]) ],
+    [ AC_MSG_RESULT([no])
+    ])
+
+if test x"$enable_coverage" = x"yes"; then
+    AC_DEFINE(COVERAGE, 1, [Define this symbol to compile out all VERIFY code])
+    CFLAGS="$CFLAGS -O0 --coverage"
+    LDFLAGS="--coverage"
+else
+    CFLAGS="$CFLAGS -O3"
+fi
+
+if test x"$use_ecmult_static_precomputation" != x"no"; then
+  save_cross_compiling=$cross_compiling
+  cross_compiling=no
+  TEMP_CC="$CC"
+  CC="$CC_FOR_BUILD"
+  AC_MSG_CHECKING([native compiler: ${CC_FOR_BUILD}])
+  AC_RUN_IFELSE(
+    [AC_LANG_PROGRAM([], [return 0])],
+    [working_native_cc=yes],
+    [working_native_cc=no],[dnl])
+  CC="$TEMP_CC"
+  cross_compiling=$save_cross_compiling
+
+  if test x"$working_native_cc" = x"no"; then
+    set_precomp=no
+    if test x"$use_ecmult_static_precomputation" = x"yes";  then
+      AC_MSG_ERROR([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
+    else
+      AC_MSG_RESULT([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
+    fi
+  else
+    AC_MSG_RESULT([ok])
+    set_precomp=yes
+  fi
+else
+  set_precomp=no
+fi
+
+if test x"$req_asm" = x"auto"; then
+  SECP_64BIT_ASM_CHECK
+  if test x"$has_64bit_asm" = x"yes"; then
+    set_asm=x86_64
+  fi
+  if test x"$set_asm" = x; then
+    set_asm=no
+  fi
+else
+  set_asm=$req_asm
+  case $set_asm in
+  x86_64)
+    SECP_64BIT_ASM_CHECK
+    if test x"$has_64bit_asm" != x"yes"; then
+      AC_MSG_ERROR([x86_64 assembly optimization requested but not available])
+    fi
+    ;;
+  arm)
+    ;;
+  no)
+    ;;
+  *)
+    AC_MSG_ERROR([invalid assembly optimization selection])
+    ;;
+  esac
+fi
+
+if test x"$req_field" = x"auto"; then
+  if test x"set_asm" = x"x86_64"; then
+    set_field=64bit
+  fi
+  if test x"$set_field" = x; then
+    SECP_INT128_CHECK
+    if test x"$has_int128" = x"yes"; then
+      set_field=64bit
+    fi
+  fi
+  if test x"$set_field" = x; then
+    set_field=32bit
+  fi
+else
+  set_field=$req_field
+  case $set_field in
+  64bit)
+    if test x"$set_asm" != x"x86_64"; then
+      SECP_INT128_CHECK
+      if test x"$has_int128" != x"yes"; then
+        AC_MSG_ERROR([64bit field explicitly requested but neither __int128 support or x86_64 assembly available])
+      fi
+    fi
+    ;;
+  32bit)
+    ;;
+  *)
+    AC_MSG_ERROR([invalid field implementation selection])
+    ;;
+  esac
+fi
+
+if test x"$req_scalar" = x"auto"; then
+  SECP_INT128_CHECK
+  if test x"$has_int128" = x"yes"; then
+    set_scalar=64bit
+  fi
+  if test x"$set_scalar" = x; then
+    set_scalar=32bit
+  fi
+else
+  set_scalar=$req_scalar
+  case $set_scalar in
+  64bit)
+    SECP_INT128_CHECK
+    if test x"$has_int128" != x"yes"; then
+      AC_MSG_ERROR([64bit scalar explicitly requested but __int128 support not available])
+    fi
+    ;;
+  32bit)
+    ;;
+  *)
+    AC_MSG_ERROR([invalid scalar implementation selected])
+    ;;
+  esac
+fi
+
+if test x"$req_bignum" = x"auto"; then
+  SECP_GMP_CHECK
+  if test x"$has_gmp" = x"yes"; then
+    set_bignum=gmp
+  fi
+
+  if test x"$set_bignum" = x; then
+    set_bignum=no
+  fi
+else
+  set_bignum=$req_bignum
+  case $set_bignum in
+  gmp)
+    SECP_GMP_CHECK
+    if test x"$has_gmp" != x"yes"; then
+      AC_MSG_ERROR([gmp bignum explicitly requested but libgmp not available])
+    fi
+    ;;
+  no)
+    ;;
+  *)
+    AC_MSG_ERROR([invalid bignum implementation selection])
+    ;;
+  esac
+fi
+
+# select assembly optimization
+use_external_asm=no
+
+case $set_asm in
+x86_64)
+  AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations])
+  ;;
+arm)
+  use_external_asm=yes
+  ;;
+no)
+  ;;
+*)
+  AC_MSG_ERROR([invalid assembly optimizations])
+  ;;
+esac
+
+# select field implementation
+case $set_field in
+64bit)
+  AC_DEFINE(USE_FIELD_5X52, 1, [Define this symbol to use the FIELD_5X52 implementation])
+  ;;
+32bit)
+  AC_DEFINE(USE_FIELD_10X26, 1, [Define this symbol to use the FIELD_10X26 implementation])
+  ;;
+*)
+  AC_MSG_ERROR([invalid field implementation])
+  ;;
+esac
+
+# select bignum implementation
+case $set_bignum in
+gmp)
+  AC_DEFINE(HAVE_LIBGMP, 1, [Define this symbol if libgmp is installed])
+  AC_DEFINE(USE_NUM_GMP, 1, [Define this symbol to use the gmp implementation for num])
+  AC_DEFINE(USE_FIELD_INV_NUM, 1, [Define this symbol to use the num-based field inverse implementation])
+  AC_DEFINE(USE_SCALAR_INV_NUM, 1, [Define this symbol to use the num-based scalar inverse implementation])
+  ;;
+no)
+  AC_DEFINE(USE_NUM_NONE, 1, [Define this symbol to use no num implementation])
+  AC_DEFINE(USE_FIELD_INV_BUILTIN, 1, [Define this symbol to use the native field inverse implementation])
+  AC_DEFINE(USE_SCALAR_INV_BUILTIN, 1, [Define this symbol to use the native scalar inverse implementation])
+  ;;
+*)
+  AC_MSG_ERROR([invalid bignum implementation])
+  ;;
+esac
+
+#select scalar implementation
+case $set_scalar in
+64bit)
+  AC_DEFINE(USE_SCALAR_4X64, 1, [Define this symbol to use the 4x64 scalar implementation])
+  ;;
+32bit)
+  AC_DEFINE(USE_SCALAR_8X32, 1, [Define this symbol to use the 8x32 scalar implementation])
+  ;;
+*)
+  AC_MSG_ERROR([invalid scalar implementation])
+  ;;
+esac
+
+if test x"$use_tests" = x"yes"; then
+  SECP_OPENSSL_CHECK
+  if test x"$has_openssl_ec" = x"yes"; then
+    if test x"$enable_openssl_tests" != x"no"; then
+      AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
+      SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS"
+      SECP_TEST_LIBS="$CRYPTO_LIBS"
+
+      case $host in
+      *mingw*)
+        SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
+        ;;
+      esac
+    fi
+  else
+    if test x"$enable_openssl_tests" = x"yes"; then
+      AC_MSG_ERROR([OpenSSL tests requested but OpenSSL with EC support is not available])
+    fi
+  fi
+else
+  if test x"$enable_openssl_tests" = x"yes"; then
+    AC_MSG_ERROR([OpenSSL tests requested but tests are not enabled])
+  fi
+fi
+
+if test x"$use_jni" != x"no"; then
+  AX_JNI_INCLUDE_DIR
+  have_jni_dependencies=yes
+  if test x"$enable_module_ecdh" = x"no"; then
+    have_jni_dependencies=no
+  fi
+  if test "x$JNI_INCLUDE_DIRS" = "x"; then
+    have_jni_dependencies=no
+  fi
+  if test "x$have_jni_dependencies" = "xno"; then
+    if test x"$use_jni" = x"yes"; then
+      AC_MSG_ERROR([jni support explicitly requested but headers/dependencies were not found. Enable ECDH and try again.])
+    fi
+    AC_MSG_WARN([jni headers/dependencies not found. jni support disabled])
+    use_jni=no
+  else
+    use_jni=yes
+    for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS; do
+      JNI_INCLUDES="$JNI_INCLUDES -I$JNI_INCLUDE_DIR"
+    done
+  fi
+fi
+
+if test x"$set_bignum" = x"gmp"; then
+  SECP_LIBS="$SECP_LIBS $GMP_LIBS"
+  SECP_INCLUDES="$SECP_INCLUDES $GMP_CPPFLAGS"
+fi
+
+if test x"$use_endomorphism" = x"yes"; then
+  AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
+fi
+
+if test x"$set_precomp" = x"yes"; then
+  AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
+fi
+
+if test x"$enable_module_ecdh" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module])
+fi
+
+if test x"$enable_module_recovery" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_RECOVERY, 1, [Define this symbol to enable the ECDSA pubkey recovery module])
+fi
+
+AC_C_BIGENDIAN()
+
+if test x"$use_external_asm" = x"yes"; then
+  AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used])
+fi
+
+AC_MSG_NOTICE([Using static precomputation: $set_precomp])
+AC_MSG_NOTICE([Using assembly optimizations: $set_asm])
+AC_MSG_NOTICE([Using field implementation: $set_field])
+AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
+AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
+AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
+AC_MSG_NOTICE([Building for coverage analysis: $enable_coverage])
+AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
+AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
+AC_MSG_NOTICE([Using jni: $use_jni])
+
+if test x"$enable_experimental" = x"yes"; then
+  AC_MSG_NOTICE([******])
+  AC_MSG_NOTICE([WARNING: experimental build])
+  AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
+  AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
+  AC_MSG_NOTICE([******])
+else
+  if test x"$enable_module_ecdh" = x"yes"; then
+    AC_MSG_ERROR([ECDH module is experimental. Use --enable-experimental to allow.])
+  fi
+  if test x"$set_asm" = x"arm"; then
+    AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
+  fi
+fi
+
+AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
+AC_CONFIG_FILES([Makefile libsecp256k1.pc])
+AC_SUBST(JNI_INCLUDES)
+AC_SUBST(SECP_INCLUDES)
+AC_SUBST(SECP_LIBS)
+AC_SUBST(SECP_TEST_LIBS)
+AC_SUBST(SECP_TEST_INCLUDES)
+AM_CONDITIONAL([ENABLE_COVERAGE], [test x"$enable_coverage" = x"yes"])
+AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
+AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
+AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
+AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
+AM_CONDITIONAL([USE_JNI], [test x"$use_jni" == x"yes"])
+AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"])
+AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"])
+
+dnl make sure nothing new is exported so that we don't break the cache
+PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"
+unset PKG_CONFIG_PATH
+PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP"
+
+AC_OUTPUT
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c
new file mode 100644
index 000000000..5b141a994
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c
@@ -0,0 +1,150 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <secp256k1.h>
+
+#include "lax_der_parsing.h"
+
+int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    size_t rpos, rlen, spos, slen;
+    size_t pos = 0;
+    size_t lenbyte;
+    unsigned char tmpsig[64] = {0};
+    int overflow = 0;
+
+    /* Hack to initialize sig with a correctly-parsed but invalid signature. */
+    secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+
+    /* Sequence tag byte */
+    if (pos == inputlen || input[pos] != 0x30) {
+        return 0;
+    }
+    pos++;
+
+    /* Sequence length bytes */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        pos += lenbyte;
+    }
+
+    /* Integer tag byte for R */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for R */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        rlen = 0;
+        while (lenbyte > 0) {
+            rlen = (rlen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        rlen = lenbyte;
+    }
+    if (rlen > inputlen - pos) {
+        return 0;
+    }
+    rpos = pos;
+    pos += rlen;
+
+    /* Integer tag byte for S */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for S */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        slen = 0;
+        while (lenbyte > 0) {
+            slen = (slen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        slen = lenbyte;
+    }
+    if (slen > inputlen - pos) {
+        return 0;
+    }
+    spos = pos;
+    pos += slen;
+
+    /* Ignore leading zeroes in R */
+    while (rlen > 0 && input[rpos] == 0) {
+        rlen--;
+        rpos++;
+    }
+    /* Copy R value */
+    if (rlen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 32 - rlen, input + rpos, rlen);
+    }
+
+    /* Ignore leading zeroes in S */
+    while (slen > 0 && input[spos] == 0) {
+        slen--;
+        spos++;
+    }
+    /* Copy S value */
+    if (slen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 64 - slen, input + spos, slen);
+    }
+
+    if (!overflow) {
+        overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    if (overflow) {
+        memset(tmpsig, 0, 64);
+        secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    return 1;
+}
+
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h
new file mode 100644
index 000000000..6d27871a7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h
@@ -0,0 +1,91 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file defines a function that parses DER with various errors and
+ * violations. This is not a part of the library itself, because the allowed
+ * violations are chosen arbitrarily and do not follow or establish any
+ * standard.
+ *
+ * In many places it matters that different implementations do not only accept
+ * the same set of valid signatures, but also reject the same set of signatures.
+ * The only means to accomplish that is by strictly obeying a standard, and not
+ * accepting anything else.
+ *
+ * Nonetheless, sometimes there is a need for compatibility with systems that
+ * use signatures which do not strictly obey DER. The snippet below shows how
+ * certain violations are easily supported. You may need to adapt it.
+ *
+ * Do not use this for new systems. Use well-defined DER or compact signatures
+ * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and
+ * secp256k1_ecdsa_signature_parse_compact).
+ *
+ * The supported violations are:
+ * - All numbers are parsed as nonnegative integers, even though X.609-0207
+ *   section 8.3.3 specifies that integers are always encoded as two's
+ *   complement.
+ * - Integers can have length 0, even though section 8.3.1 says they can't.
+ * - Integers with overly long padding are accepted, violation section
+ *   8.3.2.
+ * - 127-byte long length descriptors are accepted, even though section
+ *   8.1.3.5.c says that they are not.
+ * - Trailing garbage data inside or after the signature is ignored.
+ * - The length descriptor of the sequence is ignored.
+ *
+ * Compared to for example OpenSSL, many violations are NOT supported:
+ * - Using overly long tag descriptors for the sequence or integers inside,
+ *   violating section 8.1.2.2.
+ * - Encoding primitive integers as constructed values, violating section
+ *   8.3.1.
+ */
+
+#ifndef _SECP256K1_CONTRIB_LAX_DER_PARSING_H_
+#define _SECP256K1_CONTRIB_LAX_DER_PARSING_H_
+
+#include <secp256k1.h>
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Parse a signature in "lax DER" format
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range. In addition, it will accept signatures
+ *  which violate the DER spec in various ways. Its purpose is to allow
+ *  validation of the Bitcoin blockchain, which includes non-DER signatures
+ *  from before the network rules were updated to enforce DER. Note that
+ *  the set of supported violations is a strict subset of what OpenSSL will
+ *  accept.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+int ecdsa_signature_parse_der_lax(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c
new file mode 100644
index 000000000..c2e63b4b8
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c
@@ -0,0 +1,113 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <secp256k1.h>
+
+#include "lax_der_privatekey_parsing.h"
+
+int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) {
+    const unsigned char *end = privkey + privkeylen;
+    int lenb = 0;
+    int len = 0;
+    memset(out32, 0, 32);
+    /* sequence header */
+    if (end < privkey+1 || *privkey != 0x30) {
+        return 0;
+    }
+    privkey++;
+    /* sequence length constructor */
+    if (end < privkey+1 || !(*privkey & 0x80)) {
+        return 0;
+    }
+    lenb = *privkey & ~0x80; privkey++;
+    if (lenb < 1 || lenb > 2) {
+        return 0;
+    }
+    if (end < privkey+lenb) {
+        return 0;
+    }
+    /* sequence length */
+    len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
+    privkey += lenb;
+    if (end < privkey+len) {
+        return 0;
+    }
+    /* sequence element 0: version number (=1) */
+    if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
+        return 0;
+    }
+    privkey += 3;
+    /* sequence element 1: octet string, up to 32 bytes */
+    if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
+        return 0;
+    }
+    memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]);
+    if (!secp256k1_ec_seckey_verify(ctx, out32)) {
+        memset(out32, 0, 32);
+        return 0;
+    }
+    return 1;
+}
+
+int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) {
+    secp256k1_pubkey pubkey;
+    size_t pubkeylen = 0;
+    if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) {
+        *privkeylen = 0;
+        return 0;
+    }
+    if (compressed) {
+        static const unsigned char begin[] = {
+            0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 33;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    } else {
+        static const unsigned char begin[] = {
+            0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
+            0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
+            0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 65;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    }
+    return 1;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h
new file mode 100644
index 000000000..2fd088f8a
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h
@@ -0,0 +1,90 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file contains code snippets that parse DER private keys with
+ * various errors and violations.  This is not a part of the library
+ * itself, because the allowed violations are chosen arbitrarily and
+ * do not follow or establish any standard.
+ *
+ * It also contains code to serialize private keys in a compatible
+ * manner.
+ *
+ * These functions are meant for compatibility with applications
+ * that require BER encoded keys. When working with secp256k1-specific
+ * code, the simple 32-byte private keys normally used by the
+ * library are sufficient.
+ */
+
+#ifndef _SECP256K1_CONTRIB_BER_PRIVATEKEY_H_
+#define _SECP256K1_CONTRIB_BER_PRIVATEKEY_H_
+
+#include <secp256k1.h>
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Export a private key in DER format.
+ *
+ *  Returns: 1 if the private key was valid.
+ *  Args: ctx:        pointer to a context object, initialized for signing (cannot
+ *                    be NULL)
+ *  Out: privkey:     pointer to an array for storing the private key in BER.
+ *                    Should have space for 279 bytes, and cannot be NULL.
+ *       privkeylen:  Pointer to an int where the length of the private key in
+ *                    privkey will be stored.
+ *  In:  seckey:      pointer to a 32-byte secret key to export.
+ *       compressed:  1 if the key should be exported in
+ *                    compressed format, 0 otherwise
+ *
+ *  This function is purely meant for compatibility with applications that
+ *  require BER encoded keys. When working with secp256k1-specific code, the
+ *  simple 32-byte private keys are sufficient.
+ *
+ *  Note that this function does not guarantee correct DER output. It is
+ *  guaranteed to be parsable by secp256k1_ec_privkey_import_der
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der(
+    const secp256k1_context* ctx,
+    unsigned char *privkey,
+    size_t *privkeylen,
+    const unsigned char *seckey,
+    int compressed
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Import a private key in DER format.
+ * Returns: 1 if a private key was extracted.
+ * Args: ctx:        pointer to a context object (cannot be NULL).
+ * Out:  seckey:     pointer to a 32-byte array for storing the private key.
+ *                   (cannot be NULL).
+ * In:   privkey:    pointer to a private key in DER format (cannot be NULL).
+ *       privkeylen: length of the DER private key pointed to be privkey.
+ *
+ * This function will accept more than just strict DER, and even allow some BER
+ * violations. The public key stored inside the DER-encoded private key is not
+ * verified for correctness, nor are the curve parameters. Use this function
+ * only if you know in advance it is supposed to contain a secp256k1 private
+ * key.
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *privkey,
+    size_t privkeylen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1.h
new file mode 100644
index 000000000..f268e309d
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1.h
@@ -0,0 +1,577 @@
+#ifndef _SECP256K1_
+# define _SECP256K1_
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+#include <stddef.h>
+
+/* These rules specify the order of arguments in API calls:
+ *
+ * 1. Context pointers go first, followed by output arguments, combined
+ *    output/input arguments, and finally input-only arguments.
+ * 2. Array lengths always immediately the follow the argument whose length
+ *    they describe, even if this violates rule 1.
+ * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated
+ *    later go first. This means: signatures, public nonces, private nonces,
+ *    messages, public keys, secret keys, tweaks.
+ * 4. Arguments that are not data pointers go last, from more complex to less
+ *    complex: function pointers, algorithm names, messages, void pointers,
+ *    counts, flags, booleans.
+ * 5. Opaque data pointers follow the function pointer they are to be passed to.
+ */
+
+/** Opaque data structure that holds context information (precomputed tables etc.).
+ *
+ *  The purpose of context structures is to cache large precomputed data tables
+ *  that are expensive to construct, and also to maintain the randomization data
+ *  for blinding.
+ *
+ *  Do not create a new context object for each operation, as construction is
+ *  far slower than all other API calls (~100 times slower than an ECDSA
+ *  verification).
+ *
+ *  A constructed context can safely be used from multiple threads
+ *  simultaneously, but API call that take a non-const pointer to a context
+ *  need exclusive access to it. In particular this is the case for
+ *  secp256k1_context_destroy and secp256k1_context_randomize.
+ *
+ *  Regarding randomization, either do it once at creation time (in which case
+ *  you do not need any locking for the other calls), or use a read-write lock.
+ */
+typedef struct secp256k1_context_struct secp256k1_context;
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_pubkey;
+
+/** Opaque data structured that holds a parsed ECDSA signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_serialize_* functions.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_ecdsa_signature;
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
+ * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
+ * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
+ *          key32:     pointer to a 32-byte secret key (will not be NULL)
+ *          algo16:    pointer to a 16-byte array describing the signature
+ *                     algorithm (will be NULL for ECDSA for compatibility).
+ *          data:      Arbitrary data pointer that is passed through.
+ *          attempt:   how many iterations we have tried to find a nonce.
+ *                     This will almost always be 0, but different attempt values
+ *                     are required to result in a different nonce.
+ *
+ * Except for test cases, this function should compute some cryptographic hash of
+ * the message, the algorithm, the key and the attempt.
+ */
+typedef int (*secp256k1_nonce_function)(
+    unsigned char *nonce32,
+    const unsigned char *msg32,
+    const unsigned char *key32,
+    const unsigned char *algo16,
+    void *data,
+    unsigned int attempt
+);
+
+# if !defined(SECP256K1_GNUC_PREREQ)
+#  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) \
+ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
+#  else
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) 0
+#  endif
+# endif
+
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(2,7)
+#   define SECP256K1_INLINE __inline__
+#  elif (defined(_MSC_VER))
+#   define SECP256K1_INLINE __inline
+#  else
+#   define SECP256K1_INLINE
+#  endif
+# else
+#  define SECP256K1_INLINE inline
+# endif
+
+#ifndef SECP256K1_API
+# if defined(_WIN32)
+#  ifdef SECP256K1_BUILD
+#   define SECP256K1_API __declspec(dllexport)
+#  else
+#   define SECP256K1_API
+#  endif
+# elif defined(__GNUC__) && defined(SECP256K1_BUILD)
+#  define SECP256K1_API __attribute__ ((visibility ("default")))
+# else
+#  define SECP256K1_API
+# endif
+#endif
+
+/**Warning attributes
+  * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
+  * some paranoid null checks. */
+# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
+# else
+#  define SECP256K1_WARN_UNUSED_RESULT
+# endif
+# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_ARG_NONNULL(_x)  __attribute__ ((__nonnull__(_x)))
+# else
+#  define SECP256K1_ARG_NONNULL(_x)
+# endif
+
+/** All flags' lower 8 bits indicate what they're for. Do not use directly. */
+#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1)
+#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0)
+#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1)
+/** The higher bits contain the actual data. Do not use directly. */
+#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8)
+#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9)
+#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8)
+
+/** Flags to pass to secp256k1_context_create. */
+#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY)
+#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN)
+#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
+
+/** Flag to pass to secp256k1_ec_pubkey_serialize and secp256k1_ec_privkey_export. */
+#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION)
+#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION)
+
+/** Create a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  In:      flags: which parts of the context to initialize.
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_create(
+    unsigned int flags
+) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Copies a secp256k1 context object.
+ *
+ *  Returns: a newly created context object.
+ *  Args:    ctx: an existing context to copy (cannot be NULL)
+ */
+SECP256K1_API secp256k1_context* secp256k1_context_clone(
+    const secp256k1_context* ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Destroy a secp256k1 context object.
+ *
+ *  The context pointer may not be used afterwards.
+ *  Args:   ctx: an existing context to destroy (cannot be NULL)
+ */
+SECP256K1_API void secp256k1_context_destroy(
+    secp256k1_context* ctx
+);
+
+/** Set a callback function to be called when an illegal argument is passed to
+ *  an API call. It will only trigger for violations that are mentioned
+ *  explicitly in the header.
+ *
+ *  The philosophy is that these shouldn't be dealt with through a
+ *  specific return value, as calling code should not have branches to deal with
+ *  the case that this code itself is broken.
+ *
+ *  On the other hand, during debug stage, one would want to be informed about
+ *  such mistakes, and the default (crashing) may be inadvisable.
+ *  When this callback is triggered, the API function called is guaranteed not
+ *  to cause a crash, though its return value and output arguments are
+ *  undefined.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an illegal argument is
+ *              passed to the API, taking a message and an opaque pointer
+ *              (NULL restores a default handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_illegal_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Set a callback function to be called when an internal consistency check
+ *  fails. The default is crashing.
+ *
+ *  This can only trigger in case of a hardware failure, miscompilation,
+ *  memory corruption, serious bug in the library, or other error would can
+ *  otherwise result in undefined behaviour. It will not trigger due to mere
+ *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
+ *  for that). After this callback returns, anything may happen, including
+ *  crashing.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an internal error occurs,
+ *              taking a message and an opaque pointer (NULL restores a default
+ *              handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_error_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Parse a variable-length public key into the pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *  Args: ctx:      a secp256k1 context object.
+ *  Out:  pubkey:   pointer to a pubkey object. If 1 is returned, it is set to a
+ *                  parsed version of input. If not, its value is undefined.
+ *  In:   input:    pointer to a serialized public key
+ *        inputlen: length of the array pointed to by input
+ *
+ *  This function supports parsing compressed (33 bytes, header byte 0x02 or
+ *  0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header
+ *  byte 0x06 or 0x07) format public keys.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey* pubkey,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a pubkey object into a serialized byte sequence.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx:        a secp256k1 context object.
+ *  Out:    output:     a pointer to a 65-byte (if compressed==0) or 33-byte (if
+ *                      compressed==1) byte array to place the serialized key
+ *                      in.
+ *  In/Out: outputlen:  a pointer to an integer which is initially set to the
+ *                      size of output, and is overwritten with the written
+ *                      size.
+ *  In:     pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                      initialized public key.
+ *          flags:      SECP256K1_EC_COMPRESSED if serialization should be in
+ *                      compressed format, otherwise SECP256K1_EC_UNCOMPRESSED.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_pubkey* pubkey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Parse an ECDSA signature in compact (64 bytes) format.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input64:  a pointer to the 64-byte array to parse
+ *
+ *  The signature must consist of a 32-byte big endian R value, followed by a
+ *  32-byte big endian S value. If R or S fall outside of [0..order-1], the
+ *  encoding is invalid. R and S with value 0 are allowed in the encoding.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or R or
+ *  S are zero, the resulting sig value is guaranteed to fail validation for any
+ *  message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a DER ECDSA signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in DER format.
+ *
+ *  Returns: 1 if enough space was available to serialize, 0 otherwise
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output:    a pointer to an array to store the DER serialization
+ *  In/Out: outputlen: a pointer to a length integer. Initially, this integer
+ *                     should be set to the length of output. After the call
+ *                     it will be set to the length of the serialization (even
+ *                     if 0 was returned).
+ *  In:     sig:       a pointer to an initialized signature object
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_der(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Serialize an ECDSA signature in compact (64 byte) format.
+ *
+ *  Returns: 1
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output64:  a pointer to a 64-byte array to store the compact serialization
+ *  In:     sig:       a pointer to an initialized signature object
+ *
+ *  See secp256k1_ecdsa_signature_parse_compact for details about the encoding.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Verify an ECDSA signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig:       the signature being verified (cannot be NULL)
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           pubkey:    pointer to an initialized public key to verify with (cannot be NULL)
+ *
+ * To avoid accepting malleable signatures, only ECDSA signatures in lower-S
+ * form are accepted.
+ *
+ * If you need to accept ECDSA signatures from sources that do not obey this
+ * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to
+ * validation, but be aware that doing so results in malleable signatures.
+ *
+ * For details, see the comments for that function.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Convert a signature to a normalized lower-S form.
+ *
+ *  Returns: 1 if sigin was not normalized, 0 if it already was.
+ *  Args: ctx:    a secp256k1 context object
+ *  Out:  sigout: a pointer to a signature to fill with the normalized form,
+ *                or copy if the input was already normalized. (can be NULL if
+ *                you're only interested in whether the input was already
+ *                normalized).
+ *  In:   sigin:  a pointer to a signature to check/normalize (cannot be NULL,
+ *                can be identical to sigout)
+ *
+ *  With ECDSA a third-party can forge a second distinct signature of the same
+ *  message, given a single initial signature, but without knowing the key. This
+ *  is done by negating the S value modulo the order of the curve, 'flipping'
+ *  the sign of the random point R which is not included in the signature.
+ *
+ *  Forgery of the same message isn't universally problematic, but in systems
+ *  where message malleability or uniqueness of signatures is important this can
+ *  cause issues. This forgery can be blocked by all verifiers forcing signers
+ *  to use a normalized form.
+ *
+ *  The lower-S form reduces the size of signatures slightly on average when
+ *  variable length encodings (such as DER) are used and is cheap to verify,
+ *  making it a good choice. Security of always using lower-S is assured because
+ *  anyone can trivially modify a signature after the fact to enforce this
+ *  property anyway.
+ *
+ *  The lower S value is always between 0x1 and
+ *  0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
+ *  inclusive.
+ *
+ *  No other forms of ECDSA malleability are known and none seem likely, but
+ *  there is no formal proof that ECDSA, even with this additional restriction,
+ *  is free of other malleability. Commonly used serialization schemes will also
+ *  accept various non-unique encodings, so care should be taken when this
+ *  property is required for an application.
+ *
+ *  The secp256k1_ecdsa_sign function will by default create signatures in the
+ *  lower-S form, and secp256k1_ecdsa_verify will not accept others. In case
+ *  signatures come from a system that cannot enforce this property,
+ *  secp256k1_ecdsa_signature_normalize must be called before verification.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_normalize(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sigout,
+    const secp256k1_ecdsa_signature *sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
+
+/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
+ * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
+ * extra entropy.
+ */
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979;
+
+/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_default;
+
+/** Create an ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *
+ * The created signature is always in lower-S form. See
+ * secp256k1_ecdsa_signature_normalize for more details.
+ */
+SECP256K1_API int secp256k1_ecdsa_sign(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify an ECDSA secret key.
+ *
+ *  Returns: 1: secret key is valid
+ *           0: secret key is invalid
+ *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
+    const secp256k1_context* ctx,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Compute the public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key stores
+ *           0: secret was invalid, try again
+ *  Args:   ctx:        pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:    pubkey:     pointer to the created public key (cannot be NULL)
+ *  In:     seckey:     pointer to a 32-byte private key (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a private key by adding tweak to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting private key
+ *          would be invalid (only when the tweak is the complement of the
+ *          private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object (cannot be NULL).
+ * In/Out:  seckey: pointer to a 32-byte private key.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by adding tweak times the generator to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting public key
+ *          would be invalid (only when the tweak is the complement of the
+ *          corresponding private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                  (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key object.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a private key by multiplying it by a tweak.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:   ctx:    pointer to a context object (cannot be NULL).
+ * In/Out: seckey: pointer to a 32-byte private key.
+ * In:     tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by multiplying it by a tweak value.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                 (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key obkect.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Updates the context randomization.
+ *  Returns: 1: randomization successfully updated
+ *           0: error
+ *  Args:    ctx:       pointer to a context object (cannot be NULL)
+ *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
+    secp256k1_context* ctx,
+    const unsigned char *seed32
+) SECP256K1_ARG_NONNULL(1);
+
+/** Add a number of public keys together.
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *  Args:   ctx:        pointer to a context object
+ *  Out:    out:        pointer to a public key object for placing the resulting public key
+ *                      (cannot be NULL)
+ *  In:     ins:        pointer to array of pointers to public keys (cannot be NULL)
+ *          n:          the number of public keys to add together (must be at least 1)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *out,
+    const secp256k1_pubkey * const * ins,
+    size_t n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_ecdh.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_ecdh.h
new file mode 100644
index 000000000..4b84d7a96
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_ecdh.h
@@ -0,0 +1,31 @@
+#ifndef _SECP256K1_ECDH_
+# define _SECP256K1_ECDH_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Compute an EC Diffie-Hellman secret in constant time
+ *  Returns: 1: exponentiation was successful
+ *           0: scalar was invalid (zero or overflow)
+ *  Args:    ctx:        pointer to a context object (cannot be NULL)
+ *  Out:     result:     a 32-byte array which will be populated by an ECDH
+ *                       secret computed from the point and scalar
+ *  In:      pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                       initialized public key
+ *           privkey:    a 32-byte scalar with which to multiply the point
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh(
+  const secp256k1_context* ctx,
+  unsigned char *result,
+  const secp256k1_pubkey *pubkey,
+  const unsigned char *privkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_recovery.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_recovery.h
new file mode 100644
index 000000000..055379725
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/include/secp256k1_recovery.h
@@ -0,0 +1,110 @@
+#ifndef _SECP256K1_RECOVERY_
+# define _SECP256K1_RECOVERY_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Opaque data structured that holds a parsed ECDSA signature,
+ *  supporting pubkey recovery.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 65 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ *
+ *  Furthermore, it is guaranteed that identical signatures (including their
+ *  recoverability) will have identical representation, so they can be
+ *  memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[65];
+} secp256k1_ecdsa_recoverable_signature;
+
+/** Parse a compact ECDSA signature (64 bytes + recovery id).
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise
+ *  Args: ctx:     a secp256k1 context object
+ *  Out:  sig:     a pointer to a signature object
+ *  In:   input64: a pointer to a 64-byte compact signature
+ *        recid:   the recovery id (0, 1, 2 or 3)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature* sig,
+    const unsigned char *input64,
+    int recid
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Convert a recoverable signature into a normal signature.
+ *
+ *  Returns: 1
+ *  Out: sig:    a pointer to a normal signature (cannot be NULL).
+ *  In:  sigin:  a pointer to a recoverable signature (cannot be NULL).
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const secp256k1_ecdsa_recoverable_signature* sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
+ *
+ *  Returns: 1
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  output64: a pointer to a 64-byte array of the compact signature (cannot be NULL)
+ *        recid:    a pointer to an integer to hold the recovery id (can be NULL).
+ *  In:   sig:      a pointer to an initialized signature object (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    int *recid,
+    const secp256k1_ecdsa_recoverable_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Create a recoverable ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an ECDSA public key from a signature.
+ *
+ *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to the recovered public key (cannot be NULL)
+ *  In:      sig:        pointer to initialized signature that supports pubkey recovery (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/libsecp256k1.pc.in b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/libsecp256k1.pc.in
new file mode 100644
index 000000000..a0d006f11
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/libsecp256k1.pc.in
@@ -0,0 +1,13 @@
+prefix=@prefix@
+exec_prefix=@exec_prefix@
+libdir=@libdir@
+includedir=@includedir@
+
+Name: libsecp256k1
+Description: Optimized C library for EC operations on curve secp256k1
+URL: https://github.com/bitcoin-core/secp256k1
+Version: @PACKAGE_VERSION@
+Cflags: -I${includedir}
+Libs.private: @SECP_LIBS@
+Libs: -L${libdir} -lsecp256k1
+
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/obj/.gitignore b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/obj/.gitignore
new file mode 100644
index 000000000..e69de29bb
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/obj/.gitignore
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/group_prover.sage b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/group_prover.sage
new file mode 100644
index 000000000..ab580c5b2
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/group_prover.sage
@@ -0,0 +1,322 @@
+# This code supports verifying group implementations which have branches
+# or conditional statements (like cmovs), by allowing each execution path
+# to independently set assumptions on input or intermediary variables.
+#
+# The general approach is:
+# * A constraint is a tuple of two sets of of symbolic expressions:
+#   the first of which are required to evaluate to zero, the second of which
+#   are required to evaluate to nonzero.
+#   - A constraint is said to be conflicting if any of its nonzero expressions
+#     is in the ideal with basis the zero expressions (in other words: when the
+#     zero expressions imply that one of the nonzero expressions are zero).
+# * There is a list of laws that describe the intended behaviour, including
+#   laws for addition and doubling. Each law is called with the symbolic point
+#   coordinates as arguments, and returns:
+#   - A constraint describing the assumptions under which it is applicable,
+#     called "assumeLaw"
+#   - A constraint describing the requirements of the law, called "require"
+# * Implementations are transliterated into functions that operate as well on
+#   algebraic input points, and are called once per combination of branches
+#   exectured. Each execution returns:
+#   - A constraint describing the assumptions this implementation requires
+#     (such as Z1=1), called "assumeFormula"
+#   - A constraint describing the assumptions this specific branch requires,
+#     but which is by construction guaranteed to cover the entire space by
+#     merging the results from all branches, called "assumeBranch"
+#   - The result of the computation
+# * All combinations of laws with implementation branches are tried, and:
+#   - If the combination of assumeLaw, assumeFormula, and assumeBranch results
+#     in a conflict, it means this law does not apply to this branch, and it is
+#     skipped.
+#   - For others, we try to prove the require constraints hold, assuming the
+#     information in assumeLaw + assumeFormula + assumeBranch, and if this does
+#     not succeed, we fail.
+#     + To prove an expression is zero, we check whether it belongs to the
+#       ideal with the assumed zero expressions as basis. This test is exact.
+#     + To prove an expression is nonzero, we check whether each of its
+#       factors is contained in the set of nonzero assumptions' factors.
+#       This test is not exact, so various combinations of original and
+#       reduced expressions' factors are tried.
+#   - If we succeed, we print out the assumptions from assumeFormula that
+#     weren't implied by assumeLaw already. Those from assumeBranch are skipped,
+#     as we assume that all constraints in it are complementary with each other.
+#
+# Based on the sage verification scripts used in the Explicit-Formulas Database
+# by Tanja Lange and others, see http://hyperelliptic.org/EFD
+
+class fastfrac:
+  """Fractions over rings."""
+
+  def __init__(self,R,top,bot=1):
+    """Construct a fractional, given a ring, a numerator, and denominator."""
+    self.R = R
+    if parent(top) == ZZ or parent(top) == R:
+      self.top = R(top)
+      self.bot = R(bot)
+    elif top.__class__ == fastfrac:
+      self.top = top.top
+      self.bot = top.bot * bot
+    else:
+      self.top = R(numerator(top))
+      self.bot = R(denominator(top)) * bot
+
+  def iszero(self,I):
+    """Return whether this fraction is zero given an ideal."""
+    return self.top in I and self.bot not in I
+
+  def reduce(self,assumeZero):
+    zero = self.R.ideal(map(numerator, assumeZero))
+    return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot))
+
+  def __add__(self,other):
+    """Add two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top + self.bot * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot + self.bot * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __sub__(self,other):
+    """Subtract two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top - self.bot * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot - self.bot * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __neg__(self):
+    """Return the negation of a fraction."""
+    return fastfrac(self.R,-self.top,self.bot)
+
+  def __mul__(self,other):
+    """Multiply two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __rmul__(self,other):
+    """Multiply something else with a fraction."""
+    return self.__mul__(other)
+
+  def __div__(self,other):
+    """Divide two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top,self.bot * other)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot,self.bot * other.top)
+    return NotImplemented
+
+  def __pow__(self,other):
+    """Compute a power of a fraction."""
+    if parent(other) == ZZ:
+      if other < 0:
+        # Negative powers require flipping top and bottom
+        return fastfrac(self.R,self.bot ^ (-other),self.top ^ (-other))
+      else:
+        return fastfrac(self.R,self.top ^ other,self.bot ^ other)
+    return NotImplemented
+
+  def __str__(self):
+    return "fastfrac((" + str(self.top) + ") / (" + str(self.bot) + "))"
+  def __repr__(self):
+    return "%s" % self
+
+  def numerator(self):
+    return self.top
+
+class constraints:
+  """A set of constraints, consisting of zero and nonzero expressions.
+
+  Constraints can either be used to express knowledge or a requirement.
+
+  Both the fields zero and nonzero are maps from expressions to description
+  strings. The expressions that are the keys in zero are required to be zero,
+  and the expressions that are the keys in nonzero are required to be nonzero.
+
+  Note that (a != 0) and (b != 0) is the same as (a*b != 0), so all keys in
+  nonzero could be multiplied into a single key. This is often much less
+  efficient to work with though, so we keep them separate inside the
+  constraints. This allows higher-level code to do fast checks on the individual
+  nonzero elements, or combine them if needed for stronger checks.
+
+  We can't multiply the different zero elements, as it would suffice for one of
+  the factors to be zero, instead of all of them. Instead, the zero elements are
+  typically combined into an ideal first.
+  """
+
+  def __init__(self, **kwargs):
+    if 'zero' in kwargs:
+      self.zero = dict(kwargs['zero'])
+    else:
+      self.zero = dict()
+    if 'nonzero' in kwargs:
+      self.nonzero = dict(kwargs['nonzero'])
+    else:
+      self.nonzero = dict()
+
+  def negate(self):
+    return constraints(zero=self.nonzero, nonzero=self.zero)
+
+  def __add__(self, other):
+    zero = self.zero.copy()
+    zero.update(other.zero)
+    nonzero = self.nonzero.copy()
+    nonzero.update(other.nonzero)
+    return constraints(zero=zero, nonzero=nonzero)
+
+  def __str__(self):
+    return "constraints(zero=%s,nonzero=%s)" % (self.zero, self.nonzero)
+
+  def __repr__(self):
+    return "%s" % self
+
+
+def conflicts(R, con):
+  """Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
+  zero = R.ideal(map(numerator, con.zero))
+  if 1 in zero:
+    return True
+  # First a cheap check whether any of the individual nonzero terms conflict on
+  # their own.
+  for nonzero in con.nonzero:
+    if nonzero.iszero(zero):
+      return True
+  # It can be the case that entries in the nonzero set do not individually
+  # conflict with the zero set, but their combination does. For example, knowing
+  # that either x or y is zero is equivalent to having x*y in the zero set.
+  # Having x or y individually in the nonzero set is not a conflict, but both
+  # simultaneously is, so that is the right thing to check for.
+  if reduce(lambda a,b: a * b, con.nonzero, fastfrac(R, 1)).iszero(zero):
+    return True
+  return False
+
+
+def get_nonzero_set(R, assume):
+  """Calculate a simple set of nonzero expressions"""
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = set()
+  for nz in map(numerator, assume.nonzero):
+    for (f,n) in nz.factor():
+      nonzero.add(f)
+    rnz = zero.reduce(nz)
+    for (f,n) in rnz.factor():
+      nonzero.add(f)
+  return nonzero
+
+
+def prove_nonzero(R, exprs, assume):
+  """Check whether an expression is provably nonzero, given assumptions"""
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = get_nonzero_set(R, assume)
+  expl = set()
+  ok = True
+  for expr in exprs:
+    if numerator(expr) in zero:
+      return (False, [exprs[expr]])
+  allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
+  for (f, n) in allexprs.factor():
+    if f not in nonzero:
+      ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for (f, n) in zero.reduce(numerator(allexprs)).factor():
+    if f not in nonzero:
+      ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for expr in exprs:
+    for (f,n) in numerator(expr).factor():
+      if f not in nonzero:
+        ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for expr in exprs:
+    for (f,n) in zero.reduce(numerator(expr)).factor():
+      if f not in nonzero:
+        expl.add(exprs[expr])
+  if expl:
+    return (False, list(expl))
+  else:
+    return (True, None)
+
+
+def prove_zero(R, exprs, assume):
+  """Check whether all of the passed expressions are provably zero, given assumptions"""
+  r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
+  if not r:
+    return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = prod(x for x in assume.nonzero)
+  expl = []
+  for expr in exprs:
+    if not expr.iszero(zero):
+      expl.append(exprs[expr])
+  if not expl:
+    return (True, None)
+  return (False, expl)
+
+
+def describe_extra(R, assume, assumeExtra):
+  """Describe what assumptions are added, given existing assumptions"""
+  zerox = assume.zero.copy()
+  zerox.update(assumeExtra.zero)
+  zero = R.ideal(map(numerator, assume.zero))
+  zeroextra = R.ideal(map(numerator, zerox))
+  nonzero = get_nonzero_set(R, assume)
+  ret = set()
+  # Iterate over the extra zero expressions
+  for base in assumeExtra.zero:
+    if base not in zero:
+      add = []
+      for (f, n) in numerator(base).factor():
+        if f not in nonzero:
+          add += ["%s" % f]
+      if add:
+        ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
+  # Iterate over the extra nonzero expressions
+  for nz in assumeExtra.nonzero:
+    nzr = zeroextra.reduce(numerator(nz))
+    if nzr not in zeroextra:
+      for (f,n) in nzr.factor():
+        if zeroextra.reduce(f) not in nonzero:
+          ret.add("%s != 0" % zeroextra.reduce(f))
+  return ", ".join(x for x in ret)
+
+
+def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require):
+  """Check a set of zero and nonzero requirements, given a set of zero and nonzero assumptions"""
+  assume = assumeLaw + assumeAssert + assumeBranch
+
+  if conflicts(R, assume):
+    # This formula does not apply
+    return None
+
+  describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert)
+
+  ok, msg = prove_zero(R, require.zero, assume)
+  if not ok:
+    return "FAIL, %s fails (assuming %s)" % (str(msg), describe)
+
+  res, expl = prove_nonzero(R, require.nonzero, assume)
+  if not res:
+    return "FAIL, %s fails (assuming %s)" % (str(expl), describe)
+
+  if describe != "":
+    return "OK (assuming %s)" % describe
+  else:
+    return "OK"
+
+
+def concrete_verify(c):
+  for k in c.zero:
+    if k != 0:
+      return (False, c.zero[k])
+  for k in c.nonzero:
+    if k == 0:
+      return (False, c.nonzero[k])
+  return (True, None)
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage
new file mode 100644
index 000000000..a97e732f7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage
@@ -0,0 +1,306 @@
+# Test libsecp256k1' group operation implementations using prover.sage
+
+import sys
+
+load("group_prover.sage")
+load("weierstrass_prover.sage")
+
+def formula_secp256k1_gej_double_var(a):
+  """libsecp256k1's secp256k1_gej_double_var, used by various addition functions"""
+  rz = a.Z * a.Y
+  rz = rz * 2
+  t1 = a.X^2
+  t1 = t1 * 3
+  t2 = t1^2
+  t3 = a.Y^2
+  t3 = t3 * 2
+  t4 = t3^2
+  t4 = t4 * 2
+  t3 = t3 * a.X
+  rx = t3
+  rx = rx * 4
+  rx = -rx
+  rx = rx + t2
+  t2 = -t2
+  t3 = t3 * 6
+  t3 = t3 + t2
+  ry = t1 * t3
+  t2 = -t4
+  ry = ry + t2
+  return jacobianpoint(rx, ry, rz)
+
+def formula_secp256k1_gej_add_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_var"""
+  if branch == 0:
+    return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
+  if branch == 1:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
+  z22 = b.Z^2
+  z12 = a.Z^2
+  u1 = a.X * z22
+  u2 = b.X * z12
+  s1 = a.Y * z22
+  s1 = s1 * b.Z
+  s2 = b.Y * z12
+  s2 = s2 * a.Z
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if branch == 2:
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
+  if branch == 3:
+    return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h2 * h
+  h = h * b.Z
+  rz = a.Z * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1"""
+  if branch == 0:
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
+  if branch == 1:
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
+  z12 = a.Z^2
+  u1 = a.X
+  u2 = b.X * z12
+  s1 = a.Y
+  s2 = b.Y * z12
+  s2 = s2 * a.Z
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if (branch == 2):
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
+  if (branch == 3):
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h * h2
+  rz = a.Z * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_zinv_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_zinv_var"""
+  bzinv = b.Z^(-1)
+  if branch == 0:
+    return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
+  if branch == 1:
+    bzinv2 = bzinv^2
+    bzinv3 = bzinv2 * bzinv
+    rx = b.X * bzinv2
+    ry = b.Y * bzinv3
+    rz = 1
+    return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
+  azz = a.Z * bzinv
+  z12 = azz^2
+  u1 = a.X
+  u2 = b.X * z12
+  s1 = a.Y
+  s2 = b.Y * z12
+  s2 = s2 * azz
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if branch == 2:
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
+  if branch == 3:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h * h2
+  rz = a.Z
+  rz = rz * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_ge"""
+  zeroes = {}
+  nonzeroes = {}
+  a_infinity = False
+  if (branch & 4) != 0:
+    nonzeroes.update({a.Infinity : 'a_infinite'})
+    a_infinity = True
+  else:
+    zeroes.update({a.Infinity : 'a_finite'})
+  zz = a.Z^2
+  u1 = a.X
+  u2 = b.X * zz
+  s1 = a.Y
+  s2 = b.Y * zz
+  s2 = s2 * a.Z
+  t = u1
+  t = t + u2
+  m = s1
+  m = m + s2
+  rr = t^2
+  m_alt = -u2
+  tt = u1 * m_alt
+  rr = rr + tt
+  degenerate = (branch & 3) == 3
+  if (branch & 1) != 0:
+    zeroes.update({m : 'm_zero'})
+  else:
+    nonzeroes.update({m : 'm_nonzero'})
+  if (branch & 2) != 0:
+    zeroes.update({rr : 'rr_zero'})
+  else:
+    nonzeroes.update({rr : 'rr_nonzero'})
+  rr_alt = s1
+  rr_alt = rr_alt * 2
+  m_alt = m_alt + u1
+  if not degenerate:
+    rr_alt = rr
+    m_alt = m
+  n = m_alt^2
+  q = n * t
+  n = n^2
+  if degenerate:
+    n = m
+  t = rr_alt^2
+  rz = a.Z * m_alt
+  infinity = False
+  if (branch & 8) != 0:
+    if not a_infinity:
+      infinity = True
+    zeroes.update({rz : 'r.z=0'})
+  else:
+    nonzeroes.update({rz : 'r.z!=0'})
+  rz = rz * 2
+  q = -q
+  t = t + q
+  rx = t
+  t = t * 2
+  t = t + q
+  t = t * rr_alt
+  t = t + n
+  ry = -t
+  rx = rx * 4
+  ry = ry * 4
+  if a_infinity:
+    rx = b.X
+    ry = b.Y
+    rz = 1
+  if infinity:
+    return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity())
+  return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge_old(branch, a, b):
+  """libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx"""
+  a_infinity = (branch & 1) != 0
+  zero = {}
+  nonzero = {}
+  if a_infinity:
+    nonzero.update({a.Infinity : 'a_infinite'})
+  else:
+    zero.update({a.Infinity : 'a_finite'})
+  zz = a.Z^2
+  u1 = a.X
+  u2 = b.X * zz
+  s1 = a.Y
+  s2 = b.Y * zz
+  s2 = s2 * a.Z
+  z = a.Z
+  t = u1
+  t = t + u2
+  m = s1
+  m = m + s2
+  n = m^2
+  q = n * t
+  n = n^2
+  rr = t^2
+  t = u1 * u2
+  t = -t
+  rr = rr + t
+  t = rr^2
+  rz = m * z
+  infinity = False
+  if (branch & 2) != 0:
+    if not a_infinity:
+      infinity = True
+    else:
+      return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity())
+    zero.update({rz : 'r.z=0'})
+  else:
+    nonzero.update({rz : 'r.z!=0'})
+  rz = rz * (0 if a_infinity else 2)
+  rx = t
+  q = -q
+  rx = rx + q
+  q = q * 3
+  t = t * 2
+  t = t + q
+  t = t * rr
+  t = t + n
+  ry = -t
+  rx = rx * (0 if a_infinity else 4)
+  ry = ry * (0 if a_infinity else 4)
+  t = b.X
+  t = t * (1 if a_infinity else 0)
+  rx = rx + t
+  t = b.Y
+  t = t * (1 if a_infinity else 0)
+  ry = ry + t
+  t = (1 if a_infinity else 0)
+  rz = rz + t
+  if infinity:
+    return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity())
+  return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
+
+if __name__ == "__main__":
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
+
+  if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/weierstrass_prover.sage b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/weierstrass_prover.sage
new file mode 100644
index 000000000..03ef2ec90
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/sage/weierstrass_prover.sage
@@ -0,0 +1,264 @@
+# Prover implementation for Weierstrass curves of the form
+# y^2 = x^3 + A * x + B, specifically with a = 0 and b = 7, with group laws
+# operating on affine and Jacobian coordinates, including the point at infinity
+# represented by a 4th variable in coordinates.
+
+load("group_prover.sage")
+
+
+class affinepoint:
+  def __init__(self, x, y, infinity=0):
+    self.x = x
+    self.y = y
+    self.infinity = infinity
+  def __str__(self):
+    return "affinepoint(x=%s,y=%s,inf=%s)" % (self.x, self.y, self.infinity)
+
+
+class jacobianpoint:
+  def __init__(self, x, y, z, infinity=0):
+    self.X = x
+    self.Y = y
+    self.Z = z
+    self.Infinity = infinity
+  def __str__(self):
+    return "jacobianpoint(X=%s,Y=%s,Z=%s,inf=%s)" % (self.X, self.Y, self.Z, self.Infinity)
+
+
+def point_at_infinity():
+  return jacobianpoint(1, 1, 1, 1)
+
+
+def negate(p):
+  if p.__class__ == affinepoint:
+    return affinepoint(p.x, -p.y)
+  if p.__class__ == jacobianpoint:
+    return jacobianpoint(p.X, -p.Y, p.Z)
+  assert(False)
+
+
+def on_weierstrass_curve(A, B, p):
+  """Return a set of zero-expressions for an affine point to be on the curve"""
+  return constraints(zero={p.x^3 + A*p.x + B - p.y^2: 'on_curve'})
+
+
+def tangential_to_weierstrass_curve(A, B, p12, p3):
+  """Return a set of zero-expressions for ((x12,y12),(x3,y3)) to be a line that is tangential to the curve at (x12,y12)"""
+  return constraints(zero={
+    (p12.y - p3.y) * (p12.y * 2) - (p12.x^2 * 3 + A) * (p12.x - p3.x): 'tangential_to_curve'
+  })
+
+
+def colinear(p1, p2, p3):
+  """Return a set of zero-expressions for ((x1,y1),(x2,y2),(x3,y3)) to be collinear"""
+  return constraints(zero={
+    (p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x): 'colinear_1',
+    (p2.y - p3.y) * (p2.x - p1.x) - (p2.y - p1.y) * (p2.x - p3.x): 'colinear_2',
+    (p3.y - p1.y) * (p3.x - p2.x) - (p3.y - p2.y) * (p3.x - p1.x): 'colinear_3'
+  })
+
+
+def good_affine_point(p):
+  return constraints(nonzero={p.x : 'nonzero_x', p.y : 'nonzero_y'})
+
+
+def good_jacobian_point(p):
+  return constraints(nonzero={p.X : 'nonzero_X', p.Y : 'nonzero_Y', p.Z^6 : 'nonzero_Z'})
+
+
+def good_point(p):
+  return constraints(nonzero={p.Z^6 : 'nonzero_X'})
+
+
+def finite(p, *affine_fns):
+  con = good_point(p) + constraints(zero={p.Infinity : 'finite_point'})
+  if p.Z != 0:
+    return con + reduce(lambda a, b: a + b, (f(affinepoint(p.X / p.Z^2, p.Y / p.Z^3)) for f in affine_fns), con)
+  else:
+    return con
+
+def infinite(p):
+  return constraints(nonzero={p.Infinity : 'infinite_point'})
+
+
+def law_jacobian_weierstrass_add(A, B, pa, pb, pA, pB, pC):
+  """Check whether the passed set of coordinates is a valid Jacobian add, given assumptions"""
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(nonzero={pa.x - pb.x : 'different_x'}))
+  require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
+             colinear(pa, pb, negate(pc))))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_double(A, B, pa, pb, pA, pB, pC):
+  """Check whether the passed set of coordinates is a valid Jacobian doubling, given assumptions"""
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(zero={pa.x - pb.x : 'equal_x', pa.y - pb.y : 'equal_y'}))
+  require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
+             tangential_to_weierstrass_curve(A, B, pa, negate(pc))))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_opposites(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(zero={pa.x - pb.x : 'equal_x', pa.y + pb.y : 'opposite_y'}))
+  require = infinite(pC)
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_a(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pb) +
+               infinite(pA) +
+               finite(pB))
+  require = finite(pC, lambda pc: constraints(zero={pc.x - pb.x : 'c.x=b.x', pc.y - pb.y : 'c.y=b.y'}))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_b(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               infinite(pB) +
+               finite(pA))
+  require = finite(pC, lambda pc: constraints(zero={pc.x - pa.x : 'c.x=a.x', pc.y - pa.y : 'c.y=a.y'}))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_ab(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               infinite(pA) +
+               infinite(pB))
+  require = infinite(pC)
+  return (assumeLaw, require)
+
+
+laws_jacobian_weierstrass = {
+  'add': law_jacobian_weierstrass_add,
+  'double': law_jacobian_weierstrass_double,
+  'add_opposite': law_jacobian_weierstrass_add_opposites,
+  'add_infinite_a': law_jacobian_weierstrass_add_infinite_a,
+  'add_infinite_b': law_jacobian_weierstrass_add_infinite_b,
+  'add_infinite_ab': law_jacobian_weierstrass_add_infinite_ab
+}
+
+
+def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
+  """Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field"""
+  F = Integers(p)
+  print "Formula %s on Z%i:" % (name, p)
+  points = []
+  for x in xrange(0, p):
+    for y in xrange(0, p):
+      point = affinepoint(F(x), F(y))
+      r, e = concrete_verify(on_weierstrass_curve(A, B, point))
+      if r:
+        points.append(point)
+
+  for za in xrange(1, p):
+    for zb in xrange(1, p):
+      for pa in points:
+        for pb in points:
+          for ia in xrange(2):
+            for ib in xrange(2):
+              pA = jacobianpoint(pa.x * F(za)^2, pa.y * F(za)^3, F(za), ia)
+              pB = jacobianpoint(pb.x * F(zb)^2, pb.y * F(zb)^3, F(zb), ib)
+              for branch in xrange(0, branches):
+                assumeAssert, assumeBranch, pC = formula(branch, pA, pB)
+                pC.X = F(pC.X)
+                pC.Y = F(pC.Y)
+                pC.Z = F(pC.Z)
+                pC.Infinity = F(pC.Infinity)
+                r, e = concrete_verify(assumeAssert + assumeBranch)
+                if r:
+                  match = False
+                  for key in laws_jacobian_weierstrass:
+                    assumeLaw, require = laws_jacobian_weierstrass[key](A, B, pa, pb, pA, pB, pC)
+                    r, e = concrete_verify(assumeLaw)
+                    if r:
+                      if match:
+                        print "  multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity)
+                      else:
+                        match = True
+                      r, e = concrete_verify(require)
+                      if not r:
+                        print "  failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e)
+  print
+
+
+def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC):
+  assumeLaw, require = f(A, B, pa, pb, pA, pB, pC)
+  return check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require)
+
+def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
+  """Verify an implementation of addition of Jacobian points on a Weierstrass curve symbolically"""
+  R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex')
+  lift = lambda x: fastfrac(R,x)
+  ax = lift(ax)
+  ay = lift(ay)
+  Az = lift(Az)
+  bx = lift(bx)
+  by = lift(by)
+  Bz = lift(Bz)
+  Ai = lift(Ai)
+  Bi = lift(Bi)
+
+  pa = affinepoint(ax, ay, Ai)
+  pb = affinepoint(bx, by, Bi)
+  pA = jacobianpoint(ax * Az^2, ay * Az^3, Az, Ai)
+  pB = jacobianpoint(bx * Bz^2, by * Bz^3, Bz, Bi)
+
+  res = {}
+
+  for key in laws_jacobian_weierstrass:
+    res[key] = []
+
+  print ("Formula " + name + ":")
+  count = 0
+  for branch in xrange(branches):
+    assumeFormula, assumeBranch, pC = formula(branch, pA, pB)
+    pC.X = lift(pC.X)
+    pC.Y = lift(pC.Y)
+    pC.Z = lift(pC.Z)
+    pC.Infinity = lift(pC.Infinity)
+
+    for key in laws_jacobian_weierstrass:
+      res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch))
+
+  for key in res:
+    print "  %s:" % key
+    val = res[key]
+    for x in val:
+      if x[0] is not None:
+        print "    branch %i: %s" % (x[1], x[0])
+
+  print
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/asm/field_10x26_arm.s b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/asm/field_10x26_arm.s
new file mode 100644
index 000000000..5df561f2f
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/asm/field_10x26_arm.s
@@ -0,0 +1,919 @@
+@ vim: set tabstop=8 softtabstop=8 shiftwidth=8 noexpandtab syntax=armasm:
+/**********************************************************************
+ * Copyright (c) 2014 Wladimir J. van der Laan                        *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+/*
+ARM implementation of field_10x26 inner loops.
+
+Note:
+
+- To avoid unnecessary loads and make use of available registers, two
+  'passes' have every time been interleaved, with the odd passes accumulating c' and d' 
+  which will be added to c and d respectively in the the even passes
+
+*/
+
+	.syntax unified
+	.arch armv7-a
+	@ eabi attributes - see readelf -A
+	.eabi_attribute 8, 1  @ Tag_ARM_ISA_use = yes
+	.eabi_attribute 9, 0  @ Tag_Thumb_ISA_use = no
+	.eabi_attribute 10, 0 @ Tag_FP_arch = none
+	.eabi_attribute 24, 1 @ Tag_ABI_align_needed = 8-byte
+	.eabi_attribute 25, 1 @ Tag_ABI_align_preserved = 8-byte, except leaf SP
+	.eabi_attribute 30, 2 @ Tag_ABI_optimization_goals = Agressive Speed
+	.eabi_attribute 34, 1 @ Tag_CPU_unaligned_access = v6
+	.text
+
+	@ Field constants
+	.set field_R0, 0x3d10
+	.set field_R1, 0x400
+	.set field_not_M, 0xfc000000	@ ~M = ~0x3ffffff
+
+	.align	2
+	.global secp256k1_fe_mul_inner
+	.type	secp256k1_fe_mul_inner, %function
+	@ Arguments:
+	@  r0  r      Restrict: can overlap with a, not with b
+	@  r1  a
+	@  r2  b
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_mul_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r7,r8   scratch
+	    r1       a (pointer)
+	    r2       b (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+
+	/* A - interleaved with B */
+	ldr	r7, [r1, #0*4]			@ a[0]
+	ldr	r8, [r2, #9*4]			@ b[9]
+	ldr	r0, [r1, #1*4]			@ a[1]
+	umull	r5, r6, r7, r8			@ d = a[0] * b[9]
+	ldr	r14, [r2, #8*4]			@ b[8]
+	umull	r9, r10, r0, r8			@ d' = a[1] * b[9]
+	ldr	r7, [r1, #2*4]			@ a[2]
+	umlal	r5, r6, r0, r14			@ d += a[1] * b[8]
+	ldr	r8, [r2, #7*4] 			@ b[7]
+	umlal	r9, r10, r7, r14		@ d' += a[2] * b[8]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r8   		@ d += a[2] * b[7]
+	ldr	r14, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r8  		@ d' += a[3] * b[7]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r14   		@ d += a[3] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r14  		@ d' += a[4] * b[6]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[5]
+	ldr	r14, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r8  		@ d' += a[5] * b[5]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r14   		@ d += a[5] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r14  		@ d' += a[6] * b[4]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[3]
+	ldr	r14, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r8  		@ d' += a[7] * b[3]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r14   		@ d += a[7] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal	r9, r10, r7, r14  		@ d' += a[8] * b[2]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[1]
+	ldr	r14, [r2, #0*4]   		@ b[0]
+	umlal	r9, r10, r0, r8  		@ d' += a[9] * b[1]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	umlal	r5, r6, r0, r14   		@ d += a[9] * b[0]
+	@ r7,r14 used in B
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 4*9]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	umull	r3, r4, r7, r14   		@ c = a[0] * b[0]
+	adds	r5, r5, r9       		@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C - interleaved with D */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[2]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[1]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[0]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r14   		@ d += a[2] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[3] * b[9]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r8   		@ d += a[3] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[4] * b[8]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r14   		@ d += a[4] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[5] * b[7]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r8   		@ d += a[5] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[6]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r14   		@ d' += a[7] * b[5]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[4]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[3]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[2]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E - interleaved with F */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal   r3, r4, r7, r8   		@ c += a[0] * b[3]
+	ldr	r7, [r1, #1*4]   		@ a[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[1] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r3, r4, r7, r8   		@ c += a[1] * b[2]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal   r3, r4, r7, r8   		@ c += a[2] * b[1]
+	ldr	r7, [r1, #3*4]   		@ a[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[3] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r3, r4, r7, r8   		@ c += a[3] * b[0]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[0]
+	ldr	r8, [r2, #9*4]   		@ b[9]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[9]
+	ldr	r7, [r1, #5*4]   		@ a[5]
+	umull	r9, r10, r7, r8   		@ d' = a[5] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umlal	r5, r6, r7, r8   		@ d += a[5] * b[8]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[8]
+	ldr	r8, [r2, #7*4]   		@ b[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[7]
+	ldr	r7, [r1, #7*4]   		@ a[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[7] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r5, r6, r7, r8   		@ d += a[7] * b[6]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[5]
+	ldr	r7, [r1, #9*4]   		@ a[9]
+	umlal	r9, r10, r7, r8   		@ d' += a[9] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r5, r6, r7, r8   		@ d += a[9] * b[4]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G - interleaved with H */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[6]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[5]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[4]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[3]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[2]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[1]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[0]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[7] * b[9]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[8]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[7]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[6]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I - interleaved with J */
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umull   r11, r12, r7, r8   		@ c' = a[0] * b[8]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[7]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[6]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[5]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[4]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[3]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[2]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal   r3, r4, r7, r14   		@ c += a[6] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[7] * b[1]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal   r3, r4, r0, r8   		@ c += a[7] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[8] * b[0]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14  		@ d' = a[9] * b[9]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[8]
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_mul_inner, .-secp256k1_fe_mul_inner
+
+	.align	2
+	.global secp256k1_fe_sqr_inner
+	.type	secp256k1_fe_sqr_inner, %function
+	@ Arguments:
+	@  r0  r	 Can overlap with a
+	@  r1  a
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_sqr_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r2,r7,r8   scratch
+	    r1       a (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+	/* A interleaved with B */
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r7, [r1, #0*4]			@ a[0]
+	mov	r0, r0, asl #1
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umull	r3, r4, r7, r7			@ c = a[0] * a[0]
+	ldr	r8, [r1, #8*4]			@ a[8]
+	mov	r7, r7, asl #1
+	umull	r5, r6, r7, r14			@ d = a[0]*2 * a[9]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umull	r9, r10, r0, r14		@ d' = a[1]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[1]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	umlal	r9, r10, r7, r8			@ d' += a[2]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[7]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umlal	r9, r10, r0, r14		@ d' += a[3]*2 * a[7]
+	ldr	r14, [r1, #5*4]			@ a[5]
+	mov	r7, r7, asl #1
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[6]
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[6]
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[5]
+	umlal	r9, r10, r14, r14		@ d' += a[5] * a[5]
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 9*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C interleaved with D */
+	ldr	r0, [r1, #0*4]			@ a[0]*2
+	ldr	r14, [r1, #1*4]			@ a[1]
+	mov	r0, r0, asl #1
+	ldr	r8, [r1, #2*4]			@ a[2]
+	umlal	r3, r4, r0, r14			@ c += a[0]*2 * a[1]
+	mov	r7, r8, asl #1                  @ a[2]*2
+	umull	r11, r12, r14, r14		@ c' = a[1] * a[1]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r11, r12, r0, r8		@ c' += a[0]*2 * a[2]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[9]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umull	r9, r10, r0, r14		@ d' = a[3]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[7]
+	umlal	r9, r10, r0, r14		@ d' += a[5]*2 * a[7]
+	umlal	r5, r6, r0, r8			@ d += a[5]*2 * a[6]
+	umlal	r9, r10, r8, r8			@ d' += a[6] * a[6]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E interleaved with F */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r14, [r1, #2*4]			@ a[2]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	ldr	r2, [r1, #4*4]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[3]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[4]
+	mov	r2, r2, asl #1			@ a[4]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[3]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[2]
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r11, r12, r14, r14		@ c' += a[2] * a[2]
+	ldr	r14, [r1, #8*4]			@ a[8]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r2, r8			@ d += a[4]*2 * a[9]
+	ldr	r7, [r1, #6*4]			@ a[6]*2
+	umull	r9, r10, r0, r8			@ d' = a[5]*2 * a[9]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r14			@ d += a[5]*2 * a[8]
+	umlal	r9, r10, r7, r14		@ d' += a[6]*2 * a[8]
+	umlal	r5, r6, r7, r8			@ d += a[6]*2 * a[7]
+	umlal	r9, r10, r8, r8			@ d' += a[7] * a[7]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G interleaved with H */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #5*4]			@ a[5]
+	ldr	r2, [r1, #6*4]			@ a[6]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[5]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[6]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[5]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[4]
+	mov	r0, r2, asl #1			@ a[6]*2
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[4]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[3]
+	ldr	r7, [r1, #7*4]			@ a[7]*2
+	umlal	r11, r12, r8, r8		@ c' += a[3] * a[3]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r0, r14			@ d += a[6]*2 * a[9]
+	umull	r9, r10, r7, r14		@ d' = a[7]*2 * a[9]
+	umlal	r5, r6, r7, r8			@ d += a[7]*2 * a[8]
+	umlal	r9, r10, r8, r8			@ d' += a[8] * a[8]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I interleaved with J */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	ldr	r2, [r1, #8*4]			@ a[8]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[7]
+	ldr	r14, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[8]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[7]
+	ldr	r8, [r1, #5*4]			@ a[5]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[6]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	mov	r7, r7, asl #1
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[6]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[5]
+	mov	r2, r2, asl #1			@ a[8]*2
+	umlal	r11, r12, r0, r8		@ c' += a[3]*2 * a[5]
+	umlal	r3, r4, r0, r14			@ c += a[3]*2 * a[4]
+	umlal	r11, r12, r14, r14		@ c' += a[4] * a[4]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r5, r6, r2, r8			@ d += a[8]*2 * a[9]
+	@ r8 will be used in J
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	umlal	r5, r6, r8, r8			@ d += a[9] * a[9]
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_sqr_inner, .-secp256k1_fe_sqr_inner
+
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/basic-config.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/basic-config.h
new file mode 100644
index 000000000..c4c16eb7c
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/basic-config.h
@@ -0,0 +1,32 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_BASIC_CONFIG_
+#define _SECP256K1_BASIC_CONFIG_
+
+#ifdef USE_BASIC_CONFIG
+
+#undef USE_ASM_X86_64
+#undef USE_ENDOMORPHISM
+#undef USE_FIELD_10X26
+#undef USE_FIELD_5X52
+#undef USE_FIELD_INV_BUILTIN
+#undef USE_FIELD_INV_NUM
+#undef USE_NUM_GMP
+#undef USE_NUM_NONE
+#undef USE_SCALAR_4X64
+#undef USE_SCALAR_8X32
+#undef USE_SCALAR_INV_BUILTIN
+#undef USE_SCALAR_INV_NUM
+
+#define USE_NUM_NONE 1
+#define USE_FIELD_INV_BUILTIN 1
+#define USE_SCALAR_INV_BUILTIN 1
+#define USE_FIELD_10X26 1
+#define USE_SCALAR_8X32 1
+
+#endif // USE_BASIC_CONFIG
+#endif // _SECP256K1_BASIC_CONFIG_
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench.h
new file mode 100644
index 000000000..3a71b4aaf
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench.h
@@ -0,0 +1,66 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_BENCH_H_
+#define _SECP256K1_BENCH_H_
+
+#include <stdio.h>
+#include <math.h>
+#include "sys/time.h"
+
+static double gettimedouble(void) {
+    struct timeval tv;
+    gettimeofday(&tv, NULL);
+    return tv.tv_usec * 0.000001 + tv.tv_sec;
+}
+
+void print_number(double x) {
+    double y = x;
+    int c = 0;
+    if (y < 0.0) {
+        y = -y;
+    }
+    while (y < 100.0) {
+        y *= 10.0;
+        c++;
+    }
+    printf("%.*f", c, x);
+}
+
+void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) {
+    int i;
+    double min = HUGE_VAL;
+    double sum = 0.0;
+    double max = 0.0;
+    for (i = 0; i < count; i++) {
+        double begin, total;
+        if (setup != NULL) {
+            setup(data);
+        }
+        begin = gettimedouble();
+        benchmark(data);
+        total = gettimedouble() - begin;
+        if (teardown != NULL) {
+            teardown(data);
+        }
+        if (total < min) {
+            min = total;
+        }
+        if (total > max) {
+            max = total;
+        }
+        sum += total;
+    }
+    printf("%s: min ", name);
+    print_number(min * 1000000.0 / iter);
+    printf("us / avg ");
+    print_number((sum / count) * 1000000.0 / iter);
+    printf("us / max ");
+    print_number(max * 1000000.0 / iter);
+    printf("us\n");
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_ecdh.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_ecdh.c
new file mode 100644
index 000000000..cde5e2dbb
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_ecdh.c
@@ -0,0 +1,54 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_ecdh.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char scalar[32];
+} bench_ecdh_t;
+
+static void bench_ecdh_setup(void* arg) {
+    int i;
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+
+    /* create a context with no capabilities */
+    data->ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT);
+    for (i = 0; i < 32; i++) {
+        data->scalar[i] = i + 1;
+    }
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+static void bench_ecdh(void* arg) {
+    int i;
+    unsigned char res[32];
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar) == 1);
+    }
+}
+
+int main(void) {
+    bench_ecdh_t data;
+
+    run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, 20000);
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_internal.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_internal.c
new file mode 100644
index 000000000..0809f77bd
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_internal.c
@@ -0,0 +1,382 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+#include <stdio.h>
+
+#include "include/secp256k1.h"
+
+#include "util.h"
+#include "hash_impl.h"
+#include "num_impl.h"
+#include "field_impl.h"
+#include "group_impl.h"
+#include "scalar_impl.h"
+#include "ecmult_const_impl.h"
+#include "ecmult_impl.h"
+#include "bench.h"
+#include "secp256k1.c"
+
+typedef struct {
+    secp256k1_scalar scalar_x, scalar_y;
+    secp256k1_fe fe_x, fe_y;
+    secp256k1_ge ge_x, ge_y;
+    secp256k1_gej gej_x, gej_y;
+    unsigned char data[64];
+    int wnaf[256];
+} bench_inv_t;
+
+void bench_setup(void* arg) {
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    static const unsigned char init_x[32] = {
+        0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13,
+        0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35,
+        0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59,
+        0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83
+    };
+
+    static const unsigned char init_y[32] = {
+        0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83,
+        0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5,
+        0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9,
+        0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3
+    };
+
+    secp256k1_scalar_set_b32(&data->scalar_x, init_x, NULL);
+    secp256k1_scalar_set_b32(&data->scalar_y, init_y, NULL);
+    secp256k1_fe_set_b32(&data->fe_x, init_x);
+    secp256k1_fe_set_b32(&data->fe_y, init_y);
+    CHECK(secp256k1_ge_set_xo_var(&data->ge_x, &data->fe_x, 0));
+    CHECK(secp256k1_ge_set_xo_var(&data->ge_y, &data->fe_y, 1));
+    secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
+    secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
+    memcpy(data->data, init_x, 32);
+    memcpy(data->data + 32, init_y, 32);
+}
+
+void bench_scalar_add(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000000; i++) {
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_scalar_negate(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000000; i++) {
+        secp256k1_scalar_negate(&data->scalar_x, &data->scalar_x);
+    }
+}
+
+void bench_scalar_sqr(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_scalar_sqr(&data->scalar_x, &data->scalar_x);
+    }
+}
+
+void bench_scalar_mul(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_scalar_mul(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+#ifdef USE_ENDOMORPHISM
+void bench_scalar_split(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_scalar l, r;
+        secp256k1_scalar_split_lambda(&l, &r, &data->scalar_x);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+#endif
+
+void bench_scalar_inverse(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000; i++) {
+        secp256k1_scalar_inverse(&data->scalar_x, &data->scalar_x);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_scalar_inverse_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000; i++) {
+        secp256k1_scalar_inverse_var(&data->scalar_x, &data->scalar_x);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_field_normalize(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000000; i++) {
+        secp256k1_fe_normalize(&data->fe_x);
+    }
+}
+
+void bench_field_normalize_weak(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 2000000; i++) {
+        secp256k1_fe_normalize_weak(&data->fe_x);
+    }
+}
+
+void bench_field_mul(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_fe_mul(&data->fe_x, &data->fe_x, &data->fe_y);
+    }
+}
+
+void bench_field_sqr(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_fe_sqr(&data->fe_x, &data->fe_x);
+    }
+}
+
+void bench_field_inverse(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_fe_inv(&data->fe_x, &data->fe_x);
+        secp256k1_fe_add(&data->fe_x, &data->fe_y);
+    }
+}
+
+void bench_field_inverse_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_fe_inv_var(&data->fe_x, &data->fe_x);
+        secp256k1_fe_add(&data->fe_x, &data->fe_y);
+    }
+}
+
+void bench_field_sqrt(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_fe_sqrt(&data->fe_x, &data->fe_x);
+        secp256k1_fe_add(&data->fe_x, &data->fe_y);
+    }
+}
+
+void bench_group_double_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL);
+    }
+}
+
+void bench_group_add_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL);
+    }
+}
+
+void bench_group_add_affine(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_gej_add_ge(&data->gej_x, &data->gej_x, &data->ge_y);
+    }
+}
+
+void bench_group_add_affine_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL);
+    }
+}
+
+void bench_group_jacobi_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_gej_has_quad_y_var(&data->gej_x);
+    }
+}
+
+void bench_ecmult_wnaf(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_wnaf_const(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+
+void bench_sha256(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+    secp256k1_sha256_t sha;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, data->data, 32);
+        secp256k1_sha256_finalize(&sha, data->data);
+    }
+}
+
+void bench_hmac_sha256(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+    secp256k1_hmac_sha256_t hmac;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_hmac_sha256_initialize(&hmac, data->data, 32);
+        secp256k1_hmac_sha256_write(&hmac, data->data, 32);
+        secp256k1_hmac_sha256_finalize(&hmac, data->data);
+    }
+}
+
+void bench_rfc6979_hmac_sha256(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+    secp256k1_rfc6979_hmac_sha256_t rng;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
+    }
+}
+
+void bench_context_verify(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 20; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
+    }
+}
+
+void bench_context_sign(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 200; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
+    }
+}
+
+#ifndef USE_NUM_NONE
+void bench_num_jacobi(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+    secp256k1_num nx, norder;
+
+    secp256k1_scalar_get_num(&nx, &data->scalar_x);
+    secp256k1_scalar_order_get_num(&norder);
+    secp256k1_scalar_get_num(&norder, &data->scalar_y);
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_num_jacobi(&nx, &norder);
+    }
+}
+#endif
+
+int have_flag(int argc, char** argv, char *flag) {
+    char** argm = argv + argc;
+    argv++;
+    if (argv == argm) {
+        return 1;
+    }
+    while (argv != NULL && argv != argm) {
+        if (strcmp(*argv, flag) == 0) {
+            return 1;
+        }
+        argv++;
+    }
+    return 0;
+}
+
+int main(int argc, char **argv) {
+    bench_inv_t data;
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, 2000000);
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, 2000000);
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, 200000);
+#ifdef USE_ENDOMORPHISM
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, 20000);
+#endif
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000);
+    if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000);
+
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, 2000000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, 2000000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, 200000);
+    if (have_flag(argc, argv, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
+
+#ifndef USE_NUM_NONE
+    if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, 200000);
+#endif
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_recover.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_recover.c
new file mode 100644
index 000000000..6489378cc
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_recover.c
@@ -0,0 +1,60 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_recovery.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    unsigned char sig[64];
+} bench_recover_t;
+
+void bench_recover(void* arg) {
+    int i;
+    bench_recover_t *data = (bench_recover_t*)arg;
+    secp256k1_pubkey pubkey;
+    unsigned char pubkeyc[33];
+
+    for (i = 0; i < 20000; i++) {
+        int j;
+        size_t pubkeylen = 33;
+        secp256k1_ecdsa_recoverable_signature sig;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2));
+        CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
+        for (j = 0; j < 32; j++) {
+            data->sig[j + 32] = data->msg[j];    /* Move former message to S. */
+            data->msg[j] = data->sig[j];         /* Move former R to message. */
+            data->sig[j] = pubkeyc[j + 1];       /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
+        }
+    }
+}
+
+void bench_recover_setup(void* arg) {
+    int i;
+    bench_recover_t *data = (bench_recover_t*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (i = 0; i < 64; i++) {
+        data->sig[i] = 65 + i;
+    }
+}
+
+int main(void) {
+    bench_recover_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+
+    run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_schnorr_verify.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_schnorr_verify.c
new file mode 100644
index 000000000..5f137dda2
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_schnorr_verify.c
@@ -0,0 +1,73 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_schnorr.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    unsigned char key[32];
+    unsigned char sig[64];
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+} benchmark_schnorr_sig_t;
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    benchmark_schnorr_sig_t sigs[64];
+    int numsigs;
+} benchmark_schnorr_verify_t;
+
+static void benchmark_schnorr_init(void* arg) {
+    int i, k;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (k = 0; k < data->numsigs; k++) {
+        secp256k1_pubkey pubkey;
+        for (i = 0; i < 32; i++) {
+            data->sigs[k].key[i] = 33 + i + k;
+        }
+        secp256k1_schnorr_sign(data->ctx, data->sigs[k].sig, data->msg, data->sigs[k].key, NULL, NULL);
+        data->sigs[k].pubkeylen = 33;
+        CHECK(secp256k1_ec_pubkey_create(data->ctx, &pubkey, data->sigs[k].key));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
+    }
+}
+
+static void benchmark_schnorr_verify(void* arg) {
+    int i;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 20000 / data->numsigs; i++) {
+        secp256k1_pubkey pubkey;
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->sigs[0].pubkey, data->sigs[0].pubkeylen));
+        CHECK(secp256k1_schnorr_verify(data->ctx, data->sigs[0].sig, data->msg, &pubkey) == ((i & 0xFF) == 0));
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+    }
+}
+
+
+
+int main(void) {
+    benchmark_schnorr_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    data.numsigs = 1;
+    run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_sign.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_sign.c
new file mode 100644
index 000000000..ed7224d75
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_sign.c
@@ -0,0 +1,56 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include "include/secp256k1.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context* ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+} bench_sign_t;
+
+static void bench_sign_setup(void* arg) {
+    int i;
+    bench_sign_t *data = (bench_sign_t*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = i + 1;
+    }
+    for (i = 0; i < 32; i++) {
+        data->key[i] = i + 65;
+    }
+}
+
+static void bench_sign(void* arg) {
+    int i;
+    bench_sign_t *data = (bench_sign_t*)arg;
+
+    unsigned char sig[74];
+    for (i = 0; i < 20000; i++) {
+        size_t siglen = 74;
+        int j;
+        secp256k1_ecdsa_signature signature;
+        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
+        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
+        for (j = 0; j < 32; j++) {
+            data->msg[j] = sig[j];
+            data->key[j] = sig[j + 32];
+        }
+    }
+}
+
+int main(void) {
+    bench_sign_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+
+    run_benchmark("ecdsa_sign", bench_sign, bench_sign_setup, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_verify.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_verify.c
new file mode 100644
index 000000000..418defa0a
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/bench_verify.c
@@ -0,0 +1,112 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "util.h"
+#include "bench.h"
+
+#ifdef ENABLE_OPENSSL_TESTS
+#include <openssl/bn.h>
+#include <openssl/ecdsa.h>
+#include <openssl/obj_mac.h>
+#endif
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    unsigned char key[32];
+    unsigned char sig[72];
+    size_t siglen;
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+#ifdef ENABLE_OPENSSL_TESTS
+    EC_GROUP* ec_group;
+#endif
+} benchmark_verify_t;
+
+static void benchmark_verify(void* arg) {
+    int i;
+    benchmark_verify_t* data = (benchmark_verify_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_pubkey pubkey;
+        secp256k1_ecdsa_signature sig;
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
+        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+    }
+}
+
+#ifdef ENABLE_OPENSSL_TESTS
+static void benchmark_verify_openssl(void* arg) {
+    int i;
+    benchmark_verify_t* data = (benchmark_verify_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+        {
+            EC_KEY *pkey = EC_KEY_new();
+            const unsigned char *pubkey = &data->pubkey[0];
+            int result;
+
+            CHECK(pkey != NULL);
+            result = EC_KEY_set_group(pkey, data->ec_group);
+            CHECK(result);
+            result = (o2i_ECPublicKey(&pkey, &pubkey, data->pubkeylen)) != NULL;
+            CHECK(result);
+            result = ECDSA_verify(0, &data->msg[0], sizeof(data->msg), &data->sig[0], data->siglen, pkey) == (i == 0);
+            CHECK(result);
+            EC_KEY_free(pkey);
+        }
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+    }
+}
+#endif
+
+int main(void) {
+    int i;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    benchmark_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    for (i = 0; i < 32; i++) {
+        data.msg[i] = 1 + i;
+    }
+    for (i = 0; i < 32; i++) {
+        data.key[i] = 33 + i;
+    }
+    data.siglen = 72;
+    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
+    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
+    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
+    data.pubkeylen = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+
+    run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, 20000);
+#ifdef ENABLE_OPENSSL_TESTS
+    data.ec_group = EC_GROUP_new_by_curve_name(NID_secp256k1);
+    run_benchmark("ecdsa_verify_openssl", benchmark_verify_openssl, NULL, NULL, &data, 10, 20000);
+    EC_GROUP_free(data.ec_group);
+#endif
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa.h
new file mode 100644
index 000000000..54ae101b9
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa.h
@@ -0,0 +1,21 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECDSA_
+#define _SECP256K1_ECDSA_
+
+#include <stddef.h>
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult.h"
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h
new file mode 100644
index 000000000..453bb1188
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h
@@ -0,0 +1,315 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+
+#ifndef _SECP256K1_ECDSA_IMPL_H_
+#define _SECP256K1_ECDSA_IMPL_H_
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+#include "ecdsa.h"
+
+/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
+ *  sage: for t in xrange(1023, -1, -1):
+ *     ..   p = 2**256 - 2**32 - t
+ *     ..   if p.is_prime():
+ *     ..     print '%x'%p
+ *     ..     break
+ *   'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
+ *  sage: a = 0
+ *  sage: b = 7
+ *  sage: F = FiniteField (p)
+ *  sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
+ *   'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+    0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+    0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
+);
+
+/** Difference between field and order, values 'p' and 'n' values defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ *  sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+ *  sage: a = 0
+ *  sage: b = 7
+ *  sage: F = FiniteField (p)
+ *  sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
+ *   '14551231950b75fc4402da1722fc9baee'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
+);
+
+static int secp256k1_der_read_len(const unsigned char **sigp, const unsigned char *sigend) {
+    int lenleft, b1;
+    size_t ret = 0;
+    if (*sigp >= sigend) {
+        return -1;
+    }
+    b1 = *((*sigp)++);
+    if (b1 == 0xFF) {
+        /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */
+        return -1;
+    }
+    if ((b1 & 0x80) == 0) {
+        /* X.690-0207 8.1.3.4 short form length octets */
+        return b1;
+    }
+    if (b1 == 0x80) {
+        /* Indefinite length is not allowed in DER. */
+        return -1;
+    }
+    /* X.690-207 8.1.3.5 long form length octets */
+    lenleft = b1 & 0x7F;
+    if (lenleft > sigend - *sigp) {
+        return -1;
+    }
+    if (**sigp == 0) {
+        /* Not the shortest possible length encoding. */
+        return -1;
+    }
+    if ((size_t)lenleft > sizeof(size_t)) {
+        /* The resulting length would exceed the range of a size_t, so
+         * certainly longer than the passed array size.
+         */
+        return -1;
+    }
+    while (lenleft > 0) {
+        if ((ret >> ((sizeof(size_t) - 1) * 8)) != 0) {
+        }
+        ret = (ret << 8) | **sigp;
+        if (ret + lenleft > (size_t)(sigend - *sigp)) {
+            /* Result exceeds the length of the passed array. */
+            return -1;
+        }
+        (*sigp)++;
+        lenleft--;
+    }
+    if (ret < 128) {
+        /* Not the shortest possible length encoding. */
+        return -1;
+    }
+    return ret;
+}
+
+static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) {
+    int overflow = 0;
+    unsigned char ra[32] = {0};
+    int rlen;
+
+    if (*sig == sigend || **sig != 0x02) {
+        /* Not a primitive integer (X.690-0207 8.3.1). */
+        return 0;
+    }
+    (*sig)++;
+    rlen = secp256k1_der_read_len(sig, sigend);
+    if (rlen <= 0 || (*sig) + rlen > sigend) {
+        /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1).  */
+        return 0;
+    }
+    if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) {
+        /* Excessive 0x00 padding. */
+        return 0;
+    }
+    if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) {
+        /* Excessive 0xFF padding. */
+        return 0;
+    }
+    if ((**sig & 0x80) == 0x80) {
+        /* Negative. */
+        overflow = 1;
+    }
+    while (rlen > 0 && **sig == 0) {
+        /* Skip leading zero bytes */
+        rlen--;
+        (*sig)++;
+    }
+    if (rlen > 32) {
+        overflow = 1;
+    }
+    if (!overflow) {
+        memcpy(ra + 32 - rlen, *sig, rlen);
+        secp256k1_scalar_set_b32(r, ra, &overflow);
+    }
+    if (overflow) {
+        secp256k1_scalar_set_int(r, 0);
+    }
+    (*sig) += rlen;
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
+    const unsigned char *sigend = sig + size;
+    int rlen;
+    if (sig == sigend || *(sig++) != 0x30) {
+        /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */
+        return 0;
+    }
+    rlen = secp256k1_der_read_len(&sig, sigend);
+    if (rlen < 0 || sig + rlen > sigend) {
+        /* Tuple exceeds bounds */
+        return 0;
+    }
+    if (sig + rlen != sigend) {
+        /* Garbage after tuple. */
+        return 0;
+    }
+
+    if (!secp256k1_der_parse_integer(rr, &sig, sigend)) {
+        return 0;
+    }
+    if (!secp256k1_der_parse_integer(rs, &sig, sigend)) {
+        return 0;
+    }
+
+    if (sig != sigend) {
+        /* Trailing garbage inside tuple. */
+        return 0;
+    }
+
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
+    unsigned char r[33] = {0}, s[33] = {0};
+    unsigned char *rp = r, *sp = s;
+    size_t lenR = 33, lenS = 33;
+    secp256k1_scalar_get_b32(&r[1], ar);
+    secp256k1_scalar_get_b32(&s[1], as);
+    while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
+    while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
+    if (*size < 6+lenS+lenR) {
+        *size = 6 + lenS + lenR;
+        return 0;
+    }
+    *size = 6 + lenS + lenR;
+    sig[0] = 0x30;
+    sig[1] = 4 + lenS + lenR;
+    sig[2] = 0x02;
+    sig[3] = lenR;
+    memcpy(sig+4, rp, lenR);
+    sig[4+lenR] = 0x02;
+    sig[5+lenR] = lenS;
+    memcpy(sig+lenR+6, sp, lenS);
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
+    unsigned char c[32];
+    secp256k1_scalar sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
+    secp256k1_fe xr;
+#endif
+    secp256k1_gej pubkeyj;
+    secp256k1_gej pr;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_inverse_var(&sn, sigs);
+    secp256k1_scalar_mul(&u1, &sn, message);
+    secp256k1_scalar_mul(&u2, &sn, sigr);
+    secp256k1_gej_set_ge(&pubkeyj, pubkey);
+    secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
+    if (secp256k1_gej_is_infinity(&pr)) {
+        return 0;
+    }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+    secp256k1_scalar computed_r;
+    secp256k1_ge pr_ge;
+    secp256k1_ge_set_gej(&pr_ge, &pr);
+    secp256k1_fe_normalize(&pr_ge.x);
+
+    secp256k1_fe_get_b32(c, &pr_ge.x);
+    secp256k1_scalar_set_b32(&computed_r, c, NULL);
+    return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
+    secp256k1_scalar_get_b32(c, sigr);
+    secp256k1_fe_set_b32(&xr, c);
+
+    /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
+     *  in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
+     *  compute the remainder modulo n, and compare it to xr. However:
+     *
+     *        xr == X(pr) mod n
+     *    <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
+     *    [Since 2 * n > p, h can only be 0 or 1]
+     *    <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
+     *    [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
+     *    <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
+     *    [Multiplying both sides of the equations by pr.z^2 mod p]
+     *    <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
+     *
+     *  Thus, we can avoid the inversion, but we have to check both cases separately.
+     *  secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
+     */
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+        /* xr + n >= p, so we can skip testing the second case. */
+        return 0;
+    }
+    secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    return 0;
+#endif
+}
+
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
+    unsigned char b[32];
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    secp256k1_scalar n;
+    int overflow = 0;
+
+    secp256k1_ecmult_gen(ctx, &rp, nonce);
+    secp256k1_ge_set_gej(&r, &rp);
+    secp256k1_fe_normalize(&r.x);
+    secp256k1_fe_normalize(&r.y);
+    secp256k1_fe_get_b32(b, &r.x);
+    secp256k1_scalar_set_b32(sigr, b, &overflow);
+    /* These two conditions should be checked before calling */
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr));
+    VERIFY_CHECK(overflow == 0);
+
+    if (recid) {
+        /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
+         * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
+         */
+        *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
+    }
+    secp256k1_scalar_mul(&n, sigr, seckey);
+    secp256k1_scalar_add(&n, &n, message);
+    secp256k1_scalar_inverse(sigs, nonce);
+    secp256k1_scalar_mul(sigs, sigs, &n);
+    secp256k1_scalar_clear(&n);
+    secp256k1_gej_clear(&rp);
+    secp256k1_ge_clear(&r);
+    if (secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+    if (secp256k1_scalar_is_high(sigs)) {
+        secp256k1_scalar_negate(sigs, sigs);
+        if (recid) {
+            *recid ^= 1;
+        }
+    }
+    return 1;
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey.h
new file mode 100644
index 000000000..42739a3be
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey.h
@@ -0,0 +1,25 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECKEY_
+#define _SECP256K1_ECKEY_
+
+#include <stddef.h>
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed);
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey_impl.h
new file mode 100644
index 000000000..ce38071ac
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/eckey_impl.h
@@ -0,0 +1,99 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECKEY_IMPL_H_
+#define _SECP256K1_ECKEY_IMPL_H_
+
+#include "eckey.h"
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
+    if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
+        secp256k1_fe x;
+        return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == 0x03);
+    } else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
+        secp256k1_fe x, y;
+        if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
+            return 0;
+        }
+        secp256k1_ge_set_xy(elem, &x, &y);
+        if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07)) {
+            return 0;
+        }
+        return secp256k1_ge_is_valid_var(elem);
+    } else {
+        return 0;
+    }
+}
+
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) {
+    if (secp256k1_ge_is_infinity(elem)) {
+        return 0;
+    }
+    secp256k1_fe_normalize_var(&elem->x);
+    secp256k1_fe_normalize_var(&elem->y);
+    secp256k1_fe_get_b32(&pub[1], &elem->x);
+    if (compressed) {
+        *size = 33;
+        pub[0] = 0x02 | (secp256k1_fe_is_odd(&elem->y) ? 0x01 : 0x00);
+    } else {
+        *size = 65;
+        pub[0] = 0x04;
+        secp256k1_fe_get_b32(&pub[33], &elem->y);
+    }
+    return 1;
+}
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar_add(key, key, tweak);
+    if (secp256k1_scalar_is_zero(key)) {
+        return 0;
+    }
+    return 1;
+}
+
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    secp256k1_scalar one;
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_scalar_set_int(&one, 1);
+    secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
+
+    if (secp256k1_gej_is_infinity(&pt)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    if (secp256k1_scalar_is_zero(tweak)) {
+        return 0;
+    }
+
+    secp256k1_scalar_mul(key, key, tweak);
+    return 1;
+}
+
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar zero;
+    secp256k1_gej pt;
+    if (secp256k1_scalar_is_zero(tweak)) {
+        return 0;
+    }
+
+    secp256k1_scalar_set_int(&zero, 0);
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero);
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult.h
new file mode 100644
index 000000000..20484134f
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult.h
@@ -0,0 +1,31 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_
+#define _SECP256K1_ECMULT_
+
+#include "num.h"
+#include "group.h"
+
+typedef struct {
+    /* For accelerating the computation of a*P + b*G: */
+    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
+#endif
+} secp256k1_ecmult_context;
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
+
+/** Double multiply: R = na*A + ng*G */
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const.h
new file mode 100644
index 000000000..2b0097655
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const.h
@@ -0,0 +1,15 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_
+#define _SECP256K1_ECMULT_CONST_
+
+#include "scalar.h"
+#include "group.h"
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const_impl.h
new file mode 100644
index 000000000..0db314c48
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_const_impl.h
@@ -0,0 +1,239 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_IMPL_
+#define _SECP256K1_ECMULT_CONST_IMPL_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+#ifdef USE_ENDOMORPHISM
+    #define WNAF_BITS 128
+#else
+    #define WNAF_BITS 256
+#endif
+#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+    int m; \
+    int abs_n = (n) * (((n) > 0) * 2 - 1); \
+    int idx_n = abs_n / 2; \
+    secp256k1_fe neg_y; \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+    for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+        /* This loop is used to avoid secret data in array indices. See
+         * the comment in ecmult_gen_impl.h for rationale. */ \
+        secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+        secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+    } \
+    (r)->infinity = 0; \
+    secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+    secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^{wi} * wnaf[i], i=0..return_val)
+ *  with the following guarantees:
+ *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ *  - each wnaf[i] is nonzero
+ *  - the number of words set is returned; this is always (WNAF_BITS + w - 1) / w
+ *
+ *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
+    int global_sign;
+    int skew = 0;
+    int word = 0;
+
+    /* 1 2 3 */
+    int u_last;
+    int u;
+
+    int flip;
+    int bit;
+    secp256k1_scalar neg_s;
+    int not_neg_one;
+    /* Note that we cannot handle even numbers by negating them to be odd, as is
+     * done in other implementations, since if our scalars were specified to have
+     * width < 256 for performance reasons, their negations would have width 256
+     * and we'd lose any performance benefit. Instead, we use a technique from
+     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+     * or 2 (for odd) to the number we are encoding, returning a skew value indicating
+     * this, and having the caller compensate after doing the multiplication. */
+
+    /* Negative numbers will be negated to keep their bit representation below the maximum width */
+    flip = secp256k1_scalar_is_high(&s);
+    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+    bit = flip ^ !secp256k1_scalar_is_even(&s);
+    /* We check for negative one, since adding 2 to it will cause an overflow */
+    secp256k1_scalar_negate(&neg_s, &s);
+    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+     * that we added two to it and flipped it. In fact for -1 these operations are
+     * identical. We only flipped, but since skewing is required (in the sense that
+     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+     * our flags to claim that we only skewed. */
+    global_sign = secp256k1_scalar_cond_negate(&s, flip);
+    global_sign *= not_neg_one * 2 - 1;
+    skew = 1 << bit;
+
+    /* 4 */
+    u_last = secp256k1_scalar_shr_int(&s, w);
+    while (word * w < WNAF_BITS) {
+        int sign;
+        int even;
+
+        /* 4.1 4.4 */
+        u = secp256k1_scalar_shr_int(&s, w);
+        /* 4.2 */
+        even = ((u & 1) == 0);
+        sign = 2 * (u_last > 0) - 1;
+        u += sign * even;
+        u_last -= sign * even * (1 << w);
+
+        /* 4.3, adapted for global sign change */
+        wnaf[word++] = u_last * global_sign;
+
+        u_last = u;
+    }
+    wnaf[word] = u * global_sign;
+
+    VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+    VERIFY_CHECK(word == WNAF_SIZE(w));
+    return skew;
+}
+
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+
+    int skew_1;
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int skew_lam;
+    secp256k1_scalar q_1, q_lam;
+#endif
+
+    int i;
+    secp256k1_scalar sc = *scalar;
+
+    /* build wnaf representation for q. */
+#ifdef USE_ENDOMORPHISM
+    /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+    skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1);
+    skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
+#else
+    skew_1   = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1);
+#endif
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_fe_normalize_weak(&pre_a[i].y);
+    }
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+#endif
+
+    /* first loop iteration (separated out so we can directly set r, rather
+     * than having it start at infinity, get doubled several times, then have
+     * its new value added to it) */
+    i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+    i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+    secp256k1_gej_add_ge(r, r, &tmpa);
+#endif
+    /* remaining loop iterations */
+    for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
+        int n;
+        int j;
+        for (j = 0; j < WINDOW_A - 1; ++j) {
+            secp256k1_gej_double_nonzero(r, r, NULL);
+        }
+
+        n = wnaf_1[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+        n = wnaf_lam[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#endif
+    }
+
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
+
+    {
+        /* Correct for wNAF skew */
+        secp256k1_ge correction = *a;
+        secp256k1_ge_storage correction_1_stor;
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_storage correction_lam_stor;
+#endif
+        secp256k1_ge_storage a2_stor;
+        secp256k1_gej tmpj;
+        secp256k1_gej_set_ge(&tmpj, &correction);
+        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+        secp256k1_ge_set_gej(&correction, &tmpj);
+        secp256k1_ge_to_storage(&correction_1_stor, a);
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_to_storage(&correction_lam_stor, a);
+#endif
+        secp256k1_ge_to_storage(&a2_stor, &correction);
+
+        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+#endif
+
+        /* Apply the correction */
+        secp256k1_ge_from_storage(&correction, &correction_1_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_ge_mul_lambda(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+#endif
+    }
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen.h
new file mode 100644
index 000000000..eb2cc9ead
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen.h
@@ -0,0 +1,43 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_GEN_
+#define _SECP256K1_ECMULT_GEN_
+
+#include "scalar.h"
+#include "group.h"
+
+typedef struct {
+    /* For accelerating the computation of a*G:
+     * To harden against timing attacks, use the following mechanism:
+     * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
+     * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
+     *   * U_i = U * 2^i (for i=0..62)
+     *   * U_i = U * (1-2^63) (for i=63)
+     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
+     * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
+     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
+     * None of the resulting prec group elements have a known scalar, and neither do any of
+     * the intermediate sums while computing a*G.
+     */
+    secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
+    secp256k1_scalar blind;
+    secp256k1_gej initial;
+} secp256k1_ecmult_gen_context;
+
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
+
+/** Multiply with the generator: R = a*G */
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
+
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen_impl.h
new file mode 100644
index 000000000..35f254607
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_gen_impl.h
@@ -0,0 +1,210 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
+#define _SECP256K1_ECMULT_GEN_IMPL_H_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_gen.h"
+#include "hash_impl.h"
+#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
+#include "ecmult_static_context.h"
+#endif
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    secp256k1_ge prec[1024];
+    secp256k1_gej gj;
+    secp256k1_gej nums_gej;
+    int i, j;
+#endif
+
+    if (ctx->prec != NULL) {
+        return;
+    }
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+
+    /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
+    {
+        static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
+        secp256k1_fe nums_x;
+        secp256k1_ge nums_ge;
+        int r;
+        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+        (void)r;
+        VERIFY_CHECK(r);
+        r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
+        (void)r;
+        VERIFY_CHECK(r);
+        secp256k1_gej_set_ge(&nums_gej, &nums_ge);
+        /* Add G to make the bits in x uniformly distributed. */
+        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
+    }
+
+    /* compute prec. */
+    {
+        secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
+        secp256k1_gej gbase;
+        secp256k1_gej numsbase;
+        gbase = gj; /* 16^j * G */
+        numsbase = nums_gej; /* 2^j * nums. */
+        for (j = 0; j < 64; j++) {
+            /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
+            precj[j*16] = numsbase;
+            for (i = 1; i < 16; i++) {
+                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
+            }
+            /* Multiply gbase by 16. */
+            for (i = 0; i < 4; i++) {
+                secp256k1_gej_double_var(&gbase, &gbase, NULL);
+            }
+            /* Multiply numbase by 2. */
+            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
+            if (j == 62) {
+                /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
+                secp256k1_gej_neg(&numsbase, &numsbase);
+                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
+            }
+        }
+        secp256k1_ge_set_all_gej_var(prec, precj, 1024, cb);
+    }
+    for (j = 0; j < 64; j++) {
+        for (i = 0; i < 16; i++) {
+            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
+        }
+    }
+#else
+    (void)cb;
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
+#endif
+    secp256k1_ecmult_gen_blind(ctx, NULL);
+}
+
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
+    return ctx->prec != NULL;
+}
+
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
+    if (src->prec == NULL) {
+        dst->prec = NULL;
+    } else {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+        dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
+        memcpy(dst->prec, src->prec, sizeof(*dst->prec));
+#else
+        (void)cb;
+        dst->prec = src->prec;
+#endif
+        dst->initial = src->initial;
+        dst->blind = src->blind;
+    }
+}
+
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    free(ctx->prec);
+#endif
+    secp256k1_scalar_clear(&ctx->blind);
+    secp256k1_gej_clear(&ctx->initial);
+    ctx->prec = NULL;
+}
+
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    secp256k1_ge add;
+    secp256k1_ge_storage adds;
+    secp256k1_scalar gnb;
+    int bits;
+    int i, j;
+    memset(&adds, 0, sizeof(adds));
+    *r = ctx->initial;
+    /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
+    secp256k1_scalar_add(&gnb, gn, &ctx->blind);
+    add.infinity = 0;
+    for (j = 0; j < 64; j++) {
+        bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
+        for (i = 0; i < 16; i++) {
+            /** This uses a conditional move to avoid any secret data in array indexes.
+             *   _Any_ use of secret indexes has been demonstrated to result in timing
+             *   sidechannels, even when the cache-line access patterns are uniform.
+             *  See also:
+             *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
+             *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
+             *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
+             *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
+             *    (http://www.tau.ac.il/~tromer/papers/cache.pdf)
+             */
+            secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
+        }
+        secp256k1_ge_from_storage(&add, &adds);
+        secp256k1_gej_add_ge(r, r, &add);
+    }
+    bits = 0;
+    secp256k1_ge_clear(&add);
+    secp256k1_scalar_clear(&gnb);
+}
+
+/* Setup blinding values for secp256k1_ecmult_gen. */
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+    secp256k1_scalar b;
+    secp256k1_gej gb;
+    secp256k1_fe s;
+    unsigned char nonce32[32];
+    secp256k1_rfc6979_hmac_sha256_t rng;
+    int retry;
+    unsigned char keydata[64] = {0};
+    if (seed32 == NULL) {
+        /* When seed is NULL, reset the initial point and blinding value. */
+        secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
+        secp256k1_gej_neg(&ctx->initial, &ctx->initial);
+        secp256k1_scalar_set_int(&ctx->blind, 1);
+    }
+    /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
+    secp256k1_scalar_get_b32(nonce32, &ctx->blind);
+    /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
+     *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
+     *   asking the caller for blinding values directly and expecting them to retry on failure.
+     */
+    memcpy(keydata, nonce32, 32);
+    if (seed32 != NULL) {
+        memcpy(keydata + 32, seed32, 32);
+    }
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+    memset(keydata, 0, sizeof(keydata));
+    /* Retry for out of range results to achieve uniformity. */
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        retry = !secp256k1_fe_set_b32(&s, nonce32);
+        retry |= secp256k1_fe_is_zero(&s);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
+    /* Randomize the projection to defend against multiplier sidechannels. */
+    secp256k1_gej_rescale(&ctx->initial, &s);
+    secp256k1_fe_clear(&s);
+    do {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+        secp256k1_scalar_set_b32(&b, nonce32, &retry);
+        /* A blinding value of 0 works, but would undermine the projection hardening. */
+        retry |= secp256k1_scalar_is_zero(&b);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+    memset(nonce32, 0, 32);
+    secp256k1_ecmult_gen(ctx, &gb, &b);
+    secp256k1_scalar_negate(&b, &b);
+    ctx->blind = b;
+    ctx->initial = gb;
+    secp256k1_scalar_clear(&b);
+    secp256k1_gej_clear(&gb);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_impl.h
new file mode 100644
index 000000000..4e40104ad
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/ecmult_impl.h
@@ -0,0 +1,406 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_IMPL_H_
+#define _SECP256K1_ECMULT_IMPL_H_
+
+#include <string.h>
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to lower these values for exhaustive tests because
+ * the tables cannot have infinities in them (this breaks the
+ * affine-isomorphism stuff which tracks z-ratios) */
+#  if EXHAUSTIVE_TEST_ORDER > 128
+#    define WINDOW_A 5
+#    define WINDOW_G 8
+#  elif EXHAUSTIVE_TEST_ORDER > 8
+#    define WINDOW_A 4
+#    define WINDOW_G 4
+#  else
+#    define WINDOW_A 2
+#    define WINDOW_G 2
+#  endif
+#else
+/* optimal for 128-bit and 256-bit exponents. */
+#define WINDOW_A 5
+/** larger numbers may result in slightly better performance, at the cost of
+    exponentially larger precomputed tables. */
+#ifdef USE_ENDOMORPHISM
+/** Two tables for window size 15: 1.375 MiB. */
+#define WINDOW_G 15
+#else
+/** One table for window size 16: 1.375 MiB. */
+#define WINDOW_G 16
+#endif
+#endif
+
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
+
+/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
+ *  the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
+ *  contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
+ *  Prej's Z values are undefined, except for the last value.
+ */
+static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
+    secp256k1_gej d;
+    secp256k1_ge a_ge, d_ge;
+    int i;
+
+    VERIFY_CHECK(!a->infinity);
+
+    secp256k1_gej_double_var(&d, a, NULL);
+
+    /*
+     * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
+     * of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
+     */
+    d_ge.x = d.x;
+    d_ge.y = d.y;
+    d_ge.infinity = 0;
+
+    secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
+    prej[0].x = a_ge.x;
+    prej[0].y = a_ge.y;
+    prej[0].z = a->z;
+    prej[0].infinity = 0;
+
+    zr[0] = d.z;
+    for (i = 1; i < n; i++) {
+        secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
+    }
+
+    /*
+     * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
+     * the final point's z coordinate is actually used though, so just update that.
+     */
+    secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
+}
+
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ *  There are two versions of this function:
+ *  - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
+ *    resulting point set to a single constant Z denominator, stores the X and Y
+ *    coordinates as ge_storage points in pre, and stores the global Z in rz.
+ *    It only operates on tables sized for WINDOW_A wnaf multiples.
+ *  - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
+ *    resulting point set to actually affine points, and stores those in pre.
+ *    It operates on tables of any size, but uses heap-allocated temporaries.
+ *
+ *  To compute a*P + b*G, we compute a table for P using the first function,
+ *  and for G using the second (which requires an inverse, but it only needs to
+ *  happen once).
+ */
+static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+    secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
+    /* Bring them to the same Z denominator. */
+    secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
+}
+
+static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
+    secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
+    secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
+    secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
+    int i;
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
+    /* Convert them in batch to affine coordinates. */
+    secp256k1_ge_set_table_gej_var(prea, prej, zr, n);
+    /* Convert them to compact storage form. */
+    for (i = 0; i < n; i++) {
+        secp256k1_ge_to_storage(&pre[i], &prea[i]);
+    }
+
+    free(prea);
+    free(prej);
+    free(zr);
+}
+
+/** The following two macro retrieves a particular odd multiple from a table
+ *  of precomputed multiples. */
+#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    if ((n) > 0) { \
+        *(r) = (pre)[((n)-1)/2]; \
+    } else { \
+        secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
+    } \
+} while(0)
+
+#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    if ((n) > 0) { \
+        secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
+    } else { \
+        secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
+        secp256k1_ge_neg((r), (r)); \
+    } \
+} while(0)
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
+    ctx->pre_g = NULL;
+#ifdef USE_ENDOMORPHISM
+    ctx->pre_g_128 = NULL;
+#endif
+}
+
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
+    secp256k1_gej gj;
+
+    if (ctx->pre_g != NULL) {
+        return;
+    }
+
+    /* get the generator */
+    secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
+
+    ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+
+    /* precompute the tables with odd multiples */
+    secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
+
+#ifdef USE_ENDOMORPHISM
+    {
+        secp256k1_gej g_128j;
+        int i;
+
+        ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+
+        /* calculate 2^128*generator */
+        g_128j = gj;
+        for (i = 0; i < 128; i++) {
+            secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
+        }
+        secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
+    }
+#endif
+}
+
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
+    if (src->pre_g == NULL) {
+        dst->pre_g = NULL;
+    } else {
+        size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
+        dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
+        memcpy(dst->pre_g, src->pre_g, size);
+    }
+#ifdef USE_ENDOMORPHISM
+    if (src->pre_g_128 == NULL) {
+        dst->pre_g_128 = NULL;
+    } else {
+        size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
+        dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
+        memcpy(dst->pre_g_128, src->pre_g_128, size);
+    }
+#endif
+}
+
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
+    return ctx->pre_g != NULL;
+}
+
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
+    free(ctx->pre_g);
+#ifdef USE_ENDOMORPHISM
+    free(ctx->pre_g_128);
+#endif
+    secp256k1_ecmult_context_init(ctx);
+}
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
+ *  with the following guarantees:
+ *  - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
+ *  - two non-zero entries in wnaf are separated by at least w-1 zeroes.
+ *  - the number of set values in wnaf is returned. This number is at most 256, and at most one more
+ *    than the number of bits in the (absolute value) of the input.
+ */
+static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
+    secp256k1_scalar s = *a;
+    int last_set_bit = -1;
+    int bit = 0;
+    int sign = 1;
+    int carry = 0;
+
+    VERIFY_CHECK(wnaf != NULL);
+    VERIFY_CHECK(0 <= len && len <= 256);
+    VERIFY_CHECK(a != NULL);
+    VERIFY_CHECK(2 <= w && w <= 31);
+
+    memset(wnaf, 0, len * sizeof(wnaf[0]));
+
+    if (secp256k1_scalar_get_bits(&s, 255, 1)) {
+        secp256k1_scalar_negate(&s, &s);
+        sign = -1;
+    }
+
+    while (bit < len) {
+        int now;
+        int word;
+        if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
+            bit++;
+            continue;
+        }
+
+        now = w;
+        if (now > len - bit) {
+            now = len - bit;
+        }
+
+        word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
+
+        carry = (word >> (w-1)) & 1;
+        word -= carry << w;
+
+        wnaf[bit] = sign * word;
+        last_set_bit = bit;
+
+        bit += now;
+    }
+#ifdef VERIFY
+    CHECK(carry == 0);
+    while (bit < 256) {
+        CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
+    } 
+#endif
+    return last_set_bit + 1;
+}
+
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_scalar na_1, na_lam;
+    /* Splitted G factors. */
+    secp256k1_scalar ng_1, ng_128;
+    int wnaf_na_1[130];
+    int wnaf_na_lam[130];
+    int bits_na_1;
+    int bits_na_lam;
+    int wnaf_ng_1[129];
+    int bits_ng_1;
+    int wnaf_ng_128[129];
+    int bits_ng_128;
+#else
+    int wnaf_na[256];
+    int bits_na;
+    int wnaf_ng[256];
+    int bits_ng;
+#endif
+    int i;
+    int bits;
+
+#ifdef USE_ENDOMORPHISM
+    /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&na_1, &na_lam, na);
+
+    /* build wnaf representation for na_1 and na_lam. */
+    bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   130, &na_1,   WINDOW_A);
+    bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
+    VERIFY_CHECK(bits_na_1 <= 130);
+    VERIFY_CHECK(bits_na_lam <= 130);
+    bits = bits_na_1;
+    if (bits_na_lam > bits) {
+        bits = bits_na_lam;
+    }
+#else
+    /* build wnaf representation for na. */
+    bits_na     = secp256k1_ecmult_wnaf(wnaf_na,     256, na,      WINDOW_A);
+    bits = bits_na;
+#endif
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     * The exception is the precomputed G table points, which are actually
+     * affine. Compared to the base used for other points, they have a Z ratio
+     * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+     * isomorphism to efficiently add with a known Z inverse.
+     */
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
+
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+
+    /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
+    secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
+
+    /* Build wnaf representation for ng_1 and ng_128 */
+    bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   129, &ng_1,   WINDOW_G);
+    bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
+    if (bits_ng_1 > bits) {
+        bits = bits_ng_1;
+    }
+    if (bits_ng_128 > bits) {
+        bits = bits_ng_128;
+    }
+#else
+    bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     256, ng,      WINDOW_G);
+    if (bits_ng > bits) {
+        bits = bits_ng;
+    }
+#endif
+
+    secp256k1_gej_set_infinity(r);
+
+    for (i = bits - 1; i >= 0; i--) {
+        int n;
+        secp256k1_gej_double_var(r, r, NULL);
+#ifdef USE_ENDOMORPHISM
+        if (i < bits_na_1 && (n = wnaf_na_1[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+        if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+#else
+        if (i < bits_na && (n = wnaf_na[i])) {
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+        }
+        if (i < bits_ng && (n = wnaf_ng[i])) {
+            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+#endif
+    }
+
+    if (!r->infinity) {
+        secp256k1_fe_mul(&r->z, &r->z, &Z);
+    }
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field.h
new file mode 100644
index 000000000..bbb1ee866
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field.h
@@ -0,0 +1,132 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_
+#define _SECP256K1_FIELD_
+
+/** Field element module.
+ *
+ *  Field elements can be represented in several ways, but code accessing
+ *  it (and implementations) need to take certain properties into account:
+ *  - Each field element can be normalized or not.
+ *  - Each field element has a magnitude, which represents how far away
+ *    its representation is away from normalization. Normalized elements
+ *    always have a magnitude of 1, but a magnitude of 1 doesn't imply
+ *    normality.
+ */
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(USE_FIELD_10X26)
+#include "field_10x26.h"
+#elif defined(USE_FIELD_5X52)
+#include "field_5x52.h"
+#else
+#error "Please select field implementation"
+#endif
+
+#include "util.h"
+
+/** Normalize a field element. */
+static void secp256k1_fe_normalize(secp256k1_fe *r);
+
+/** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
+
+/** Normalize a field element, without constant-time guarantee. */
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
+
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ *  implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
+
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ *  implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
+
+/** Set a field element equal to a small integer. Resulting field element is normalized. */
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
+
+/** Sets a field element equal to zero, initializing all fields. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
+
+/** Verify whether a field element is zero. Requires the input to be normalized. */
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
+
+/** Check the "oddness" of a field element. Requires the input to be normalized. */
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
+
+/** Compare two field elements. Requires magnitude-1 inputs. */
+static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Same as secp256k1_fe_equal, but may be variable time. */
+static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Compare two field elements. Requires both inputs to be normalized */
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
+
+/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
+ *  as an argument. The magnitude of the output is one higher. */
+static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
+
+/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
+ *  small integer. */
+static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
+
+/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
+ *  The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
+
+/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
+ *  The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** If a has a square root, it is computed in r and 1 is returned. If a does not
+ *  have a square root, the root of its negation is computed and 0 is returned.
+ *  The input's magnitude can be at most 8. The output magnitude is 1 (but not
+ *  guaranteed to be normalized). The result in r will always be a square
+ *  itself. */
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Checks whether a field element is a quadratic residue. */
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a);
+
+/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
+ *  at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
+ *  at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
+ *  outputs must not overlap in memory. */
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len);
+
+/** Convert a field element to the storage type. */
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
+
+/** Convert a field element back from the storage type. */
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26.h
new file mode 100644
index 000000000..61ee1e096
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26.h
@@ -0,0 +1,47 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_REPR_
+#define _SECP256K1_FIELD_REPR_
+
+#include <stdint.h>
+
+typedef struct {
+    /* X = sum(i=0..9, elem[i]*2^26) mod n */
+    uint32_t n[10];
+#ifdef VERIFY
+    int magnitude;
+    int normalized;
+#endif
+} secp256k1_fe;
+
+/* Unpacks a constant into a overlapping multi-limbed FE element. */
+#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
+    (d0) & 0x3FFFFFFUL, \
+    (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
+    (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
+    (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
+    (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
+    (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
+    (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
+    (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
+    (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
+    (((uint32_t)d7) >> 10) \
+}
+
+#ifdef VERIFY
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
+#else
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
+#endif
+
+typedef struct {
+    uint32_t n[8];
+} secp256k1_fe_storage;
+
+#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
+#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26_impl.h
new file mode 100644
index 000000000..5fb092f1b
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_10x26_impl.h
@@ -0,0 +1,1140 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
+#define _SECP256K1_FIELD_REPR_IMPL_H_
+
+#include "util.h"
+#include "num.h"
+#include "field.h"
+
+#ifdef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
+    const uint32_t *d = a->n;
+    int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
+    r &= (d[0] <= 0x3FFFFFFUL * m);
+    r &= (d[1] <= 0x3FFFFFFUL * m);
+    r &= (d[2] <= 0x3FFFFFFUL * m);
+    r &= (d[3] <= 0x3FFFFFFUL * m);
+    r &= (d[4] <= 0x3FFFFFFUL * m);
+    r &= (d[5] <= 0x3FFFFFFUL * m);
+    r &= (d[6] <= 0x3FFFFFFUL * m);
+    r &= (d[7] <= 0x3FFFFFFUL * m);
+    r &= (d[8] <= 0x3FFFFFFUL * m);
+    r &= (d[9] <= 0x03FFFFFUL * m);
+    r &= (a->magnitude >= 0);
+    r &= (a->magnitude <= 32);
+    if (a->normalized) {
+        r &= (a->magnitude <= 1);
+        if (r && (d[9] == 0x03FFFFFUL)) {
+            uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
+            if (mid == 0x3FFFFFFUL) {
+                r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
+            }
+        }
+    }
+    VERIFY_CHECK(r == 1);
+}
+#endif
+
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
+    uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
+             t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
+
+    /* Reduce t9 at the start so there will be at most a single carry from the first pass */
+    uint32_t m;
+    uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
+
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
+        & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
+
+    /* Apply the final reduction (for constant-time behaviour, we do it always) */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
+
+    /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
+    VERIFY_CHECK(t9 >> 22 == x);
+
+    /* Mask off the possible multiple of 2^256 from the final reduction */
+    t9 &= 0x03FFFFFUL;
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+    r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+    uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
+             t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
+
+    /* Reduce t9 at the start so there will be at most a single carry from the first pass */
+    uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
+
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+    r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+    uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
+             t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
+
+    /* Reduce t9 at the start so there will be at most a single carry from the first pass */
+    uint32_t m;
+    uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
+
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
+        & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
+
+    if (x) {
+        t0 += 0x3D1UL; t1 += (x << 6);
+        t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
+        t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
+        t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
+        t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
+        t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
+        t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
+        t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
+        t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
+        t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
+
+        /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
+        VERIFY_CHECK(t9 >> 22 == x);
+
+        /* Mask off the possible multiple of 2^256 from the final reduction */
+        t9 &= 0x03FFFFFUL;
+    }
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+    r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
+    uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
+             t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint32_t z0, z1;
+
+    /* Reduce t9 at the start so there will be at most a single carry from the first pass */
+    uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL; t1 += (x << 6);
+    t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0  = t0; z1  = t0 ^ 0x3D0UL;
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
+                                         z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
+
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
+    return (z0 == 0) | (z1 == 0x3FFFFFFUL);
+}
+
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
+    uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
+    uint32_t z0, z1;
+    uint32_t x;
+
+    t0 = r->n[0];
+    t9 = r->n[9];
+
+    /* Reduce t9 at the start so there will be at most a single carry from the first pass */
+    x = t9 >> 22;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x3D1UL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    z0 = t0 & 0x3FFFFFFUL;
+    z1 = z0 ^ 0x3D0UL;
+
+    /* Fast return path should catch the majority of cases */
+    if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
+        return 0;
+    }
+
+    t1 = r->n[1];
+    t2 = r->n[2];
+    t3 = r->n[3];
+    t4 = r->n[4];
+    t5 = r->n[5];
+    t6 = r->n[6];
+    t7 = r->n[7];
+    t8 = r->n[8];
+
+    t9 &= 0x03FFFFFUL;
+    t1 += (x << 6);
+
+    t1 += (t0 >> 26);
+    t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
+    t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
+    t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
+    t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
+    t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
+    t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
+    t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
+                                         z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
+
+    /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t9 >> 23 == 0);
+
+    return (z0 == 0) | (z1 == 0x3FFFFFFUL);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    r->n[0] = a;
+    r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+    const uint32_t *t = a->n;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return a->n[0] & 1;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+    int i;
+#ifdef VERIFY
+    a->magnitude = 0;
+    a->normalized = 1;
+#endif
+    for (i=0; i<10; i++) {
+        a->n[i] = 0;
+    }
+}
+
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    int i;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    VERIFY_CHECK(b->normalized);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+#endif
+    for (i = 9; i >= 0; i--) {
+        if (a->n[i] > b->n[i]) {
+            return 1;
+        }
+        if (a->n[i] < b->n[i]) {
+            return -1;
+        }
+    }
+    return 0;
+}
+
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
+    int i;
+    r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+    r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
+    for (i=0; i<32; i++) {
+        int j;
+        for (j=0; j<4; j++) {
+            int limb = (8*i+2*j)/26;
+            int shift = (8*i+2*j)%26;
+            r->n[limb] |= (uint32_t)((a[31-i] >> (2*j)) & 0x3) << shift;
+        }
+    }
+    if (r->n[9] == 0x3FFFFFUL && (r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL && (r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL) {
+        return 0;
+    }
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+    return 1;
+}
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
+    int i;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    for (i=0; i<32; i++) {
+        int j;
+        int c = 0;
+        for (j=0; j<4; j++) {
+            int limb = (8*i+2*j)/26;
+            int shift = (8*i+2*j)%26;
+            c |= ((a->n[limb] >> shift) & 0x3) << (2 * j);
+        }
+        r[31-i] = c;
+    }
+}
+
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= m);
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
+    r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
+    r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
+    r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
+    r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
+    r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
+    r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
+    r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
+    r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
+    r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
+#ifdef VERIFY
+    r->magnitude = m + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+    r->n[0] *= a;
+    r->n[1] *= a;
+    r->n[2] *= a;
+    r->n[3] *= a;
+    r->n[4] *= a;
+    r->n[5] *= a;
+    r->n[6] *= a;
+    r->n[7] *= a;
+    r->n[8] *= a;
+    r->n[9] *= a;
+#ifdef VERIFY
+    r->magnitude *= a;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] += a->n[0];
+    r->n[1] += a->n[1];
+    r->n[2] += a->n[2];
+    r->n[3] += a->n[3];
+    r->n[4] += a->n[4];
+    r->n[5] += a->n[5];
+    r->n[6] += a->n[6];
+    r->n[7] += a->n[7];
+    r->n[8] += a->n[8];
+    r->n[9] += a->n[9];
+#ifdef VERIFY
+    r->magnitude += a->magnitude;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+#if defined(USE_EXTERNAL_ASM)
+
+/* External assembler implementation */
+void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
+void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
+
+#else
+
+#ifdef VERIFY
+#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
+#else
+#define VERIFY_BITS(x, n) do { } while(0)
+#endif
+
+SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
+    uint64_t c, d;
+    uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
+    uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
+    const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
+
+    VERIFY_BITS(a[0], 30);
+    VERIFY_BITS(a[1], 30);
+    VERIFY_BITS(a[2], 30);
+    VERIFY_BITS(a[3], 30);
+    VERIFY_BITS(a[4], 30);
+    VERIFY_BITS(a[5], 30);
+    VERIFY_BITS(a[6], 30);
+    VERIFY_BITS(a[7], 30);
+    VERIFY_BITS(a[8], 30);
+    VERIFY_BITS(a[9], 26);
+    VERIFY_BITS(b[0], 30);
+    VERIFY_BITS(b[1], 30);
+    VERIFY_BITS(b[2], 30);
+    VERIFY_BITS(b[3], 30);
+    VERIFY_BITS(b[4], 30);
+    VERIFY_BITS(b[5], 30);
+    VERIFY_BITS(b[6], 30);
+    VERIFY_BITS(b[7], 30);
+    VERIFY_BITS(b[8], 30);
+    VERIFY_BITS(b[9], 26);
+
+    /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0].
+     */
+
+    d  = (uint64_t)a[0] * b[9]
+       + (uint64_t)a[1] * b[8]
+       + (uint64_t)a[2] * b[7]
+       + (uint64_t)a[3] * b[6]
+       + (uint64_t)a[4] * b[5]
+       + (uint64_t)a[5] * b[4]
+       + (uint64_t)a[6] * b[3]
+       + (uint64_t)a[7] * b[2]
+       + (uint64_t)a[8] * b[1]
+       + (uint64_t)a[9] * b[0];
+    /* VERIFY_BITS(d, 64); */
+    /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
+    t9 = d & M; d >>= 26;
+    VERIFY_BITS(t9, 26);
+    VERIFY_BITS(d, 38);
+    /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
+
+    c  = (uint64_t)a[0] * b[0];
+    VERIFY_BITS(c, 60);
+    /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
+    d += (uint64_t)a[1] * b[9]
+       + (uint64_t)a[2] * b[8]
+       + (uint64_t)a[3] * b[7]
+       + (uint64_t)a[4] * b[6]
+       + (uint64_t)a[5] * b[5]
+       + (uint64_t)a[6] * b[4]
+       + (uint64_t)a[7] * b[3]
+       + (uint64_t)a[8] * b[2]
+       + (uint64_t)a[9] * b[1];
+    VERIFY_BITS(d, 63);
+    /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    u0 = d & M; d >>= 26; c += u0 * R0;
+    VERIFY_BITS(u0, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 61);
+    /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    t0 = c & M; c >>= 26; c += u0 * R1;
+    VERIFY_BITS(t0, 26);
+    VERIFY_BITS(c, 37);
+    /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+
+    c += (uint64_t)a[0] * b[1]
+       + (uint64_t)a[1] * b[0];
+    VERIFY_BITS(c, 62);
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    d += (uint64_t)a[2] * b[9]
+       + (uint64_t)a[3] * b[8]
+       + (uint64_t)a[4] * b[7]
+       + (uint64_t)a[5] * b[6]
+       + (uint64_t)a[6] * b[5]
+       + (uint64_t)a[7] * b[4]
+       + (uint64_t)a[8] * b[3]
+       + (uint64_t)a[9] * b[2];
+    VERIFY_BITS(d, 63);
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    u1 = d & M; d >>= 26; c += u1 * R0;
+    VERIFY_BITS(u1, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 63);
+    /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    t1 = c & M; c >>= 26; c += u1 * R1;
+    VERIFY_BITS(t1, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+
+    c += (uint64_t)a[0] * b[2]
+       + (uint64_t)a[1] * b[1]
+       + (uint64_t)a[2] * b[0];
+    VERIFY_BITS(c, 62);
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    d += (uint64_t)a[3] * b[9]
+       + (uint64_t)a[4] * b[8]
+       + (uint64_t)a[5] * b[7]
+       + (uint64_t)a[6] * b[6]
+       + (uint64_t)a[7] * b[5]
+       + (uint64_t)a[8] * b[4]
+       + (uint64_t)a[9] * b[3];
+    VERIFY_BITS(d, 63);
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    u2 = d & M; d >>= 26; c += u2 * R0;
+    VERIFY_BITS(u2, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 63);
+    /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    t2 = c & M; c >>= 26; c += u2 * R1;
+    VERIFY_BITS(t2, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[3]
+       + (uint64_t)a[1] * b[2]
+       + (uint64_t)a[2] * b[1]
+       + (uint64_t)a[3] * b[0];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    d += (uint64_t)a[4] * b[9]
+       + (uint64_t)a[5] * b[8]
+       + (uint64_t)a[6] * b[7]
+       + (uint64_t)a[7] * b[6]
+       + (uint64_t)a[8] * b[5]
+       + (uint64_t)a[9] * b[4];
+    VERIFY_BITS(d, 63);
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    u3 = d & M; d >>= 26; c += u3 * R0;
+    VERIFY_BITS(u3, 26);
+    VERIFY_BITS(d, 37);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    t3 = c & M; c >>= 26; c += u3 * R1;
+    VERIFY_BITS(t3, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[4]
+       + (uint64_t)a[1] * b[3]
+       + (uint64_t)a[2] * b[2]
+       + (uint64_t)a[3] * b[1]
+       + (uint64_t)a[4] * b[0];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[5] * b[9]
+       + (uint64_t)a[6] * b[8]
+       + (uint64_t)a[7] * b[7]
+       + (uint64_t)a[8] * b[6]
+       + (uint64_t)a[9] * b[5];
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    u4 = d & M; d >>= 26; c += u4 * R0;
+    VERIFY_BITS(u4, 26);
+    VERIFY_BITS(d, 36);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    t4 = c & M; c >>= 26; c += u4 * R1;
+    VERIFY_BITS(t4, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[5]
+       + (uint64_t)a[1] * b[4]
+       + (uint64_t)a[2] * b[3]
+       + (uint64_t)a[3] * b[2]
+       + (uint64_t)a[4] * b[1]
+       + (uint64_t)a[5] * b[0];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[6] * b[9]
+       + (uint64_t)a[7] * b[8]
+       + (uint64_t)a[8] * b[7]
+       + (uint64_t)a[9] * b[6];
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    u5 = d & M; d >>= 26; c += u5 * R0;
+    VERIFY_BITS(u5, 26);
+    VERIFY_BITS(d, 36);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    t5 = c & M; c >>= 26; c += u5 * R1;
+    VERIFY_BITS(t5, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[6]
+       + (uint64_t)a[1] * b[5]
+       + (uint64_t)a[2] * b[4]
+       + (uint64_t)a[3] * b[3]
+       + (uint64_t)a[4] * b[2]
+       + (uint64_t)a[5] * b[1]
+       + (uint64_t)a[6] * b[0];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[7] * b[9]
+       + (uint64_t)a[8] * b[8]
+       + (uint64_t)a[9] * b[7];
+    VERIFY_BITS(d, 61);
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    u6 = d & M; d >>= 26; c += u6 * R0;
+    VERIFY_BITS(u6, 26);
+    VERIFY_BITS(d, 35);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    t6 = c & M; c >>= 26; c += u6 * R1;
+    VERIFY_BITS(t6, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[7]
+       + (uint64_t)a[1] * b[6]
+       + (uint64_t)a[2] * b[5]
+       + (uint64_t)a[3] * b[4]
+       + (uint64_t)a[4] * b[3]
+       + (uint64_t)a[5] * b[2]
+       + (uint64_t)a[6] * b[1]
+       + (uint64_t)a[7] * b[0];
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x8000007C00000007ULL);
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[8] * b[9]
+       + (uint64_t)a[9] * b[8];
+    VERIFY_BITS(d, 58);
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    u7 = d & M; d >>= 26; c += u7 * R0;
+    VERIFY_BITS(u7, 26);
+    VERIFY_BITS(d, 32);
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
+    /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    t7 = c & M; c >>= 26; c += u7 * R1;
+    VERIFY_BITS(t7, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)a[0] * b[8]
+       + (uint64_t)a[1] * b[7]
+       + (uint64_t)a[2] * b[6]
+       + (uint64_t)a[3] * b[5]
+       + (uint64_t)a[4] * b[4]
+       + (uint64_t)a[5] * b[3]
+       + (uint64_t)a[6] * b[2]
+       + (uint64_t)a[7] * b[1]
+       + (uint64_t)a[8] * b[0];
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x9000007B80000008ULL);
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[9] * b[9];
+    VERIFY_BITS(d, 57);
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    u8 = d & M; d >>= 26; c += u8 * R0;
+    VERIFY_BITS(u8, 26);
+    VERIFY_BITS(d, 31);
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    r[3] = t3;
+    VERIFY_BITS(r[3], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = t4;
+    VERIFY_BITS(r[4], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[5] = t5;
+    VERIFY_BITS(r[5], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[6] = t6;
+    VERIFY_BITS(r[6], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[7] = t7;
+    VERIFY_BITS(r[7], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    r[8] = c & M; c >>= 26; c += u8 * R1;
+    VERIFY_BITS(r[8], 26);
+    VERIFY_BITS(c, 39);
+    /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += d * R0 + t9;
+    VERIFY_BITS(c, 45);
+    /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
+    VERIFY_BITS(r[9], 22);
+    VERIFY_BITS(c, 46);
+    /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    d    = c * (R0 >> 4) + t0;
+    VERIFY_BITS(d, 56);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[0] = d & M; d >>= 26;
+    VERIFY_BITS(r[0], 26);
+    VERIFY_BITS(d, 30);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d   += c * (R1 >> 4) + t1;
+    VERIFY_BITS(d, 53);
+    VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[1] = d & M; d >>= 26;
+    VERIFY_BITS(r[1], 26);
+    VERIFY_BITS(d, 27);
+    VERIFY_CHECK(d <= 0x4000000ULL);
+    /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d   += t2;
+    VERIFY_BITS(d, 27);
+    /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = d;
+    VERIFY_BITS(r[2], 27);
+    /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
+    uint64_t c, d;
+    uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
+    uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
+    const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
+
+    VERIFY_BITS(a[0], 30);
+    VERIFY_BITS(a[1], 30);
+    VERIFY_BITS(a[2], 30);
+    VERIFY_BITS(a[3], 30);
+    VERIFY_BITS(a[4], 30);
+    VERIFY_BITS(a[5], 30);
+    VERIFY_BITS(a[6], 30);
+    VERIFY_BITS(a[7], 30);
+    VERIFY_BITS(a[8], 30);
+    VERIFY_BITS(a[9], 26);
+
+    /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*a[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0].
+     */
+
+    d  = (uint64_t)(a[0]*2) * a[9]
+       + (uint64_t)(a[1]*2) * a[8]
+       + (uint64_t)(a[2]*2) * a[7]
+       + (uint64_t)(a[3]*2) * a[6]
+       + (uint64_t)(a[4]*2) * a[5];
+    /* VERIFY_BITS(d, 64); */
+    /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
+    t9 = d & M; d >>= 26;
+    VERIFY_BITS(t9, 26);
+    VERIFY_BITS(d, 38);
+    /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
+
+    c  = (uint64_t)a[0] * a[0];
+    VERIFY_BITS(c, 60);
+    /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
+    d += (uint64_t)(a[1]*2) * a[9]
+       + (uint64_t)(a[2]*2) * a[8]
+       + (uint64_t)(a[3]*2) * a[7]
+       + (uint64_t)(a[4]*2) * a[6]
+       + (uint64_t)a[5] * a[5];
+    VERIFY_BITS(d, 63);
+    /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    u0 = d & M; d >>= 26; c += u0 * R0;
+    VERIFY_BITS(u0, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 61);
+    /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    t0 = c & M; c >>= 26; c += u0 * R1;
+    VERIFY_BITS(t0, 26);
+    VERIFY_BITS(c, 37);
+    /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[1];
+    VERIFY_BITS(c, 62);
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    d += (uint64_t)(a[2]*2) * a[9]
+       + (uint64_t)(a[3]*2) * a[8]
+       + (uint64_t)(a[4]*2) * a[7]
+       + (uint64_t)(a[5]*2) * a[6];
+    VERIFY_BITS(d, 63);
+    /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    u1 = d & M; d >>= 26; c += u1 * R0;
+    VERIFY_BITS(u1, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 63);
+    /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    t1 = c & M; c >>= 26; c += u1 * R1;
+    VERIFY_BITS(t1, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[2]
+       + (uint64_t)a[1] * a[1];
+    VERIFY_BITS(c, 62);
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    d += (uint64_t)(a[3]*2) * a[9]
+       + (uint64_t)(a[4]*2) * a[8]
+       + (uint64_t)(a[5]*2) * a[7]
+       + (uint64_t)a[6] * a[6];
+    VERIFY_BITS(d, 63);
+    /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    u2 = d & M; d >>= 26; c += u2 * R0;
+    VERIFY_BITS(u2, 26);
+    VERIFY_BITS(d, 37);
+    VERIFY_BITS(c, 63);
+    /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    t2 = c & M; c >>= 26; c += u2 * R1;
+    VERIFY_BITS(t2, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[3]
+       + (uint64_t)(a[1]*2) * a[2];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    d += (uint64_t)(a[4]*2) * a[9]
+       + (uint64_t)(a[5]*2) * a[8]
+       + (uint64_t)(a[6]*2) * a[7];
+    VERIFY_BITS(d, 63);
+    /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    u3 = d & M; d >>= 26; c += u3 * R0;
+    VERIFY_BITS(u3, 26);
+    VERIFY_BITS(d, 37);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    t3 = c & M; c >>= 26; c += u3 * R1;
+    VERIFY_BITS(t3, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[4]
+       + (uint64_t)(a[1]*2) * a[3]
+       + (uint64_t)a[2] * a[2];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    d += (uint64_t)(a[5]*2) * a[9]
+       + (uint64_t)(a[6]*2) * a[8]
+       + (uint64_t)a[7] * a[7];
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    u4 = d & M; d >>= 26; c += u4 * R0;
+    VERIFY_BITS(u4, 26);
+    VERIFY_BITS(d, 36);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    t4 = c & M; c >>= 26; c += u4 * R1;
+    VERIFY_BITS(t4, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[5]
+       + (uint64_t)(a[1]*2) * a[4]
+       + (uint64_t)(a[2]*2) * a[3];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)(a[6]*2) * a[9]
+       + (uint64_t)(a[7]*2) * a[8];
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    u5 = d & M; d >>= 26; c += u5 * R0;
+    VERIFY_BITS(u5, 26);
+    VERIFY_BITS(d, 36);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    t5 = c & M; c >>= 26; c += u5 * R1;
+    VERIFY_BITS(t5, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[6]
+       + (uint64_t)(a[1]*2) * a[5]
+       + (uint64_t)(a[2]*2) * a[4]
+       + (uint64_t)a[3] * a[3];
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)(a[7]*2) * a[9]
+       + (uint64_t)a[8] * a[8];
+    VERIFY_BITS(d, 61);
+    /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    u6 = d & M; d >>= 26; c += u6 * R0;
+    VERIFY_BITS(u6, 26);
+    VERIFY_BITS(d, 35);
+    /* VERIFY_BITS(c, 64); */
+    /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    t6 = c & M; c >>= 26; c += u6 * R1;
+    VERIFY_BITS(t6, 26);
+    VERIFY_BITS(c, 39);
+    /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[7]
+       + (uint64_t)(a[1]*2) * a[6]
+       + (uint64_t)(a[2]*2) * a[5]
+       + (uint64_t)(a[3]*2) * a[4];
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x8000007C00000007ULL);
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)(a[8]*2) * a[9];
+    VERIFY_BITS(d, 58);
+    /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    u7 = d & M; d >>= 26; c += u7 * R0;
+    VERIFY_BITS(u7, 26);
+    VERIFY_BITS(d, 32);
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
+    /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    t7 = c & M; c >>= 26; c += u7 * R1;
+    VERIFY_BITS(t7, 26);
+    VERIFY_BITS(c, 38);
+    /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    c += (uint64_t)(a[0]*2) * a[8]
+       + (uint64_t)(a[1]*2) * a[7]
+       + (uint64_t)(a[2]*2) * a[6]
+       + (uint64_t)(a[3]*2) * a[5]
+       + (uint64_t)a[4] * a[4];
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x9000007B80000008ULL);
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint64_t)a[9] * a[9];
+    VERIFY_BITS(d, 57);
+    /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    u8 = d & M; d >>= 26; c += u8 * R0;
+    VERIFY_BITS(u8, 26);
+    VERIFY_BITS(d, 31);
+    /* VERIFY_BITS(c, 64); */
+    VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    r[3] = t3;
+    VERIFY_BITS(r[3], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = t4;
+    VERIFY_BITS(r[4], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[5] = t5;
+    VERIFY_BITS(r[5], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[6] = t6;
+    VERIFY_BITS(r[6], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[7] = t7;
+    VERIFY_BITS(r[7], 26);
+    /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    r[8] = c & M; c >>= 26; c += u8 * R1;
+    VERIFY_BITS(r[8], 26);
+    VERIFY_BITS(c, 39);
+    /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += d * R0 + t9;
+    VERIFY_BITS(c, 45);
+    /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
+    VERIFY_BITS(r[9], 22);
+    VERIFY_BITS(c, 46);
+    /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    d    = c * (R0 >> 4) + t0;
+    VERIFY_BITS(d, 56);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[0] = d & M; d >>= 26;
+    VERIFY_BITS(r[0], 26);
+    VERIFY_BITS(d, 30);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d   += c * (R1 >> 4) + t1;
+    VERIFY_BITS(d, 53);
+    VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
+    /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[1] = d & M; d >>= 26;
+    VERIFY_BITS(r[1], 26);
+    VERIFY_BITS(d, 27);
+    VERIFY_CHECK(d <= 0x4000000ULL);
+    /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    d   += t2;
+    VERIFY_BITS(d, 27);
+    /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = d;
+    VERIFY_BITS(r[2], 27);
+    /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+#endif
+
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    VERIFY_CHECK(b->magnitude <= 8);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(r != b);
+#endif
+    secp256k1_fe_mul_inner(r->n, a->n, b->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    secp256k1_fe_verify(a);
+#endif
+    secp256k1_fe_sqr_inner(r->n, a->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint32_t mask0, mask1;
+    mask0 = flag + ~((uint32_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+    r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
+    r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
+    r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
+    r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
+    r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
+#ifdef VERIFY
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
+    uint32_t mask0, mask1;
+    mask0 = flag + ~((uint32_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+    r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
+    r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
+    r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
+}
+
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+#endif
+    r->n[0] = a->n[0] | a->n[1] << 26;
+    r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
+    r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
+    r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
+    r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
+    r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
+    r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
+    r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
+}
+
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    r->n[0] = a->n[0] & 0x3FFFFFFUL;
+    r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
+    r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
+    r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
+    r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
+    r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
+    r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
+    r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
+    r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
+    r->n[9] = a->n[7] >> 10;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+#endif
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52.h
new file mode 100644
index 000000000..8e69a560d
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52.h
@@ -0,0 +1,47 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_REPR_
+#define _SECP256K1_FIELD_REPR_
+
+#include <stdint.h>
+
+typedef struct {
+    /* X = sum(i=0..4, elem[i]*2^52) mod n */
+    uint64_t n[5];
+#ifdef VERIFY
+    int magnitude;
+    int normalized;
+#endif
+} secp256k1_fe;
+
+/* Unpacks a constant into a overlapping multi-limbed FE element. */
+#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
+    (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
+    ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
+    ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
+    ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
+    ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
+}
+
+#ifdef VERIFY
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
+#else
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
+#endif
+
+typedef struct {
+    uint64_t n[4];
+} secp256k1_fe_storage;
+
+#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
+    (d0) | (((uint64_t)(d1)) << 32), \
+    (d2) | (((uint64_t)(d3)) << 32), \
+    (d4) | (((uint64_t)(d5)) << 32), \
+    (d6) | (((uint64_t)(d7)) << 32) \
+}}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_asm_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_asm_impl.h
new file mode 100644
index 000000000..98cc004bf
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_asm_impl.h
@@ -0,0 +1,502 @@
+/**********************************************************************
+ * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille               *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/**
+ * Changelog:
+ * - March 2013, Diederik Huys:    original version
+ * - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm
+ * - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly
+ */
+
+#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
+#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
+
+SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
+/**
+ * Registers: rdx:rax = multiplication accumulator
+ *            r9:r8   = c
+ *            r15:rcx = d
+ *            r10-r14 = a0-a4
+ *            rbx     = b
+ *            rdi     = r
+ *            rsi     = a / t?
+ */
+  uint64_t tmp1, tmp2, tmp3;
+__asm__ __volatile__(
+    "movq 0(%%rsi),%%r10\n"
+    "movq 8(%%rsi),%%r11\n"
+    "movq 16(%%rsi),%%r12\n"
+    "movq 24(%%rsi),%%r13\n"
+    "movq 32(%%rsi),%%r14\n"
+
+    /* d += a3 * b0 */
+    "movq 0(%%rbx),%%rax\n"
+    "mulq %%r13\n"
+    "movq %%rax,%%rcx\n"
+    "movq %%rdx,%%r15\n"
+    /* d += a2 * b1 */
+    "movq 8(%%rbx),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a1 * b2 */
+    "movq 16(%%rbx),%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d = a0 * b3 */
+    "movq 24(%%rbx),%%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* c = a4 * b4 */
+    "movq 32(%%rbx),%%rax\n"
+    "mulq %%r14\n"
+    "movq %%rax,%%r8\n"
+    "movq %%rdx,%%r9\n"
+    /* d += (c & M) * R */
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* c >>= 52 (%%r8 only) */
+    "shrdq $52,%%r9,%%r8\n"
+    /* t3 (tmp1) = d & M */
+    "movq %%rcx,%%rsi\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rsi\n"
+    "movq %%rsi,%q1\n"
+    /* d >>= 52 */
+    "shrdq $52,%%r15,%%rcx\n"
+    "xorq %%r15,%%r15\n"
+    /* d += a4 * b0 */
+    "movq 0(%%rbx),%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a3 * b1 */
+    "movq 8(%%rbx),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a2 * b2 */
+    "movq 16(%%rbx),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a1 * b3 */
+    "movq 24(%%rbx),%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a0 * b4 */
+    "movq 32(%%rbx),%%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += c * R */
+    "movq %%r8,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* t4 = d & M (%%rsi) */
+    "movq %%rcx,%%rsi\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rsi\n"
+    /* d >>= 52 */
+    "shrdq $52,%%r15,%%rcx\n"
+    "xorq %%r15,%%r15\n"
+    /* tx = t4 >> 48 (tmp3) */
+    "movq %%rsi,%%rax\n"
+    "shrq $48,%%rax\n"
+    "movq %%rax,%q3\n"
+    /* t4 &= (M >> 4) (tmp2) */
+    "movq $0xffffffffffff,%%rax\n"
+    "andq %%rax,%%rsi\n"
+    "movq %%rsi,%q2\n"
+    /* c = a0 * b0 */
+    "movq 0(%%rbx),%%rax\n"
+    "mulq %%r10\n"
+    "movq %%rax,%%r8\n"
+    "movq %%rdx,%%r9\n"
+    /* d += a4 * b1 */
+    "movq 8(%%rbx),%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a3 * b2 */
+    "movq 16(%%rbx),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a2 * b3 */
+    "movq 24(%%rbx),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a1 * b4 */
+    "movq 32(%%rbx),%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* u0 = d & M (%%rsi) */
+    "movq %%rcx,%%rsi\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rsi\n"
+    /* d >>= 52 */
+    "shrdq $52,%%r15,%%rcx\n"
+    "xorq %%r15,%%r15\n"
+    /* u0 = (u0 << 4) | tx (%%rsi) */
+    "shlq $4,%%rsi\n"
+    "movq %q3,%%rax\n"
+    "orq %%rax,%%rsi\n"
+    /* c += u0 * (R >> 4) */
+    "movq $0x1000003d1,%%rax\n"
+    "mulq %%rsi\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* r[0] = c & M */
+    "movq %%r8,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq %%rax,0(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* c += a1 * b0 */
+    "movq 0(%%rbx),%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* c += a0 * b1 */
+    "movq 8(%%rbx),%%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d += a4 * b2 */
+    "movq 16(%%rbx),%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a3 * b3 */
+    "movq 24(%%rbx),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a2 * b4 */
+    "movq 32(%%rbx),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* c += (d & M) * R */
+    "movq %%rcx,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d >>= 52 */
+    "shrdq $52,%%r15,%%rcx\n"
+    "xorq %%r15,%%r15\n"
+    /* r[1] = c & M */
+    "movq %%r8,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq %%rax,8(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* c += a2 * b0 */
+    "movq 0(%%rbx),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* c += a1 * b1 */
+    "movq 8(%%rbx),%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* c += a0 * b2 (last use of %%r10 = a0) */
+    "movq 16(%%rbx),%%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */
+    "movq %q2,%%rsi\n"
+    "movq %q1,%%r10\n"
+    /* d += a4 * b3 */
+    "movq 24(%%rbx),%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* d += a3 * b4 */
+    "movq 32(%%rbx),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rcx\n"
+    "adcq %%rdx,%%r15\n"
+    /* c += (d & M) * R */
+    "movq %%rcx,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d >>= 52 (%%rcx only) */
+    "shrdq $52,%%r15,%%rcx\n"
+    /* r[2] = c & M */
+    "movq %%r8,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq %%rax,16(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* c += t3 */
+    "addq %%r10,%%r8\n"
+    /* c += d * R */
+    "movq %%rcx,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* r[3] = c & M */
+    "movq %%r8,%%rax\n"
+    "movq $0xfffffffffffff,%%rdx\n"
+    "andq %%rdx,%%rax\n"
+    "movq %%rax,24(%%rdi)\n"
+    /* c >>= 52 (%%r8 only) */
+    "shrdq $52,%%r9,%%r8\n"
+    /* c += t4 (%%r8 only) */
+    "addq %%rsi,%%r8\n"
+    /* r[4] = c */
+    "movq %%r8,32(%%rdi)\n"
+: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
+: "b"(b), "D"(r)
+: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
+);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
+/**
+ * Registers: rdx:rax = multiplication accumulator
+ *            r9:r8   = c
+ *            rcx:rbx = d
+ *            r10-r14 = a0-a4
+ *            r15     = M (0xfffffffffffff)
+ *            rdi     = r
+ *            rsi     = a / t?
+ */
+  uint64_t tmp1, tmp2, tmp3;
+__asm__ __volatile__(
+    "movq 0(%%rsi),%%r10\n"
+    "movq 8(%%rsi),%%r11\n"
+    "movq 16(%%rsi),%%r12\n"
+    "movq 24(%%rsi),%%r13\n"
+    "movq 32(%%rsi),%%r14\n"
+    "movq $0xfffffffffffff,%%r15\n"
+
+    /* d = (a0*2) * a3 */
+    "leaq (%%r10,%%r10,1),%%rax\n"
+    "mulq %%r13\n"
+    "movq %%rax,%%rbx\n"
+    "movq %%rdx,%%rcx\n"
+    /* d += (a1*2) * a2 */
+    "leaq (%%r11,%%r11,1),%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* c = a4 * a4 */
+    "movq %%r14,%%rax\n"
+    "mulq %%r14\n"
+    "movq %%rax,%%r8\n"
+    "movq %%rdx,%%r9\n"
+    /* d += (c & M) * R */
+    "andq %%r15,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* c >>= 52 (%%r8 only) */
+    "shrdq $52,%%r9,%%r8\n"
+    /* t3 (tmp1) = d & M */
+    "movq %%rbx,%%rsi\n"
+    "andq %%r15,%%rsi\n"
+    "movq %%rsi,%q1\n"
+    /* d >>= 52 */
+    "shrdq $52,%%rcx,%%rbx\n"
+    "xorq %%rcx,%%rcx\n"
+    /* a4 *= 2 */
+    "addq %%r14,%%r14\n"
+    /* d += a0 * a4 */
+    "movq %%r10,%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* d+= (a1*2) * a3 */
+    "leaq (%%r11,%%r11,1),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* d += a2 * a2 */
+    "movq %%r12,%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* d += c * R */
+    "movq %%r8,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* t4 = d & M (%%rsi) */
+    "movq %%rbx,%%rsi\n"
+    "andq %%r15,%%rsi\n"
+    /* d >>= 52 */
+    "shrdq $52,%%rcx,%%rbx\n"
+    "xorq %%rcx,%%rcx\n"
+    /* tx = t4 >> 48 (tmp3) */
+    "movq %%rsi,%%rax\n"
+    "shrq $48,%%rax\n"
+    "movq %%rax,%q3\n"
+    /* t4 &= (M >> 4) (tmp2) */
+    "movq $0xffffffffffff,%%rax\n"
+    "andq %%rax,%%rsi\n"
+    "movq %%rsi,%q2\n"
+    /* c = a0 * a0 */
+    "movq %%r10,%%rax\n"
+    "mulq %%r10\n"
+    "movq %%rax,%%r8\n"
+    "movq %%rdx,%%r9\n"
+    /* d += a1 * a4 */
+    "movq %%r11,%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* d += (a2*2) * a3 */
+    "leaq (%%r12,%%r12,1),%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* u0 = d & M (%%rsi) */
+    "movq %%rbx,%%rsi\n"
+    "andq %%r15,%%rsi\n"
+    /* d >>= 52 */
+    "shrdq $52,%%rcx,%%rbx\n"
+    "xorq %%rcx,%%rcx\n"
+    /* u0 = (u0 << 4) | tx (%%rsi) */
+    "shlq $4,%%rsi\n"
+    "movq %q3,%%rax\n"
+    "orq %%rax,%%rsi\n"
+    /* c += u0 * (R >> 4) */
+    "movq $0x1000003d1,%%rax\n"
+    "mulq %%rsi\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* r[0] = c & M */
+    "movq %%r8,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq %%rax,0(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* a0 *= 2 */
+    "addq %%r10,%%r10\n"
+    /* c += a0 * a1 */
+    "movq %%r10,%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d += a2 * a4 */
+    "movq %%r12,%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* d += a3 * a3 */
+    "movq %%r13,%%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* c += (d & M) * R */
+    "movq %%rbx,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d >>= 52 */
+    "shrdq $52,%%rcx,%%rbx\n"
+    "xorq %%rcx,%%rcx\n"
+    /* r[1] = c & M */
+    "movq %%r8,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq %%rax,8(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* c += a0 * a2 (last use of %%r10) */
+    "movq %%r10,%%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */
+    "movq %q2,%%rsi\n"
+    "movq %q1,%%r10\n"
+    /* c += a1 * a1 */
+    "movq %%r11,%%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d += a3 * a4 */
+    "movq %%r13,%%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax,%%rbx\n"
+    "adcq %%rdx,%%rcx\n"
+    /* c += (d & M) * R */
+    "movq %%rbx,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* d >>= 52 (%%rbx only) */
+    "shrdq $52,%%rcx,%%rbx\n"
+    /* r[2] = c & M */
+    "movq %%r8,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq %%rax,16(%%rdi)\n"
+    /* c >>= 52 */
+    "shrdq $52,%%r9,%%r8\n"
+    "xorq %%r9,%%r9\n"
+    /* c += t3 */
+    "addq %%r10,%%r8\n"
+    /* c += d * R */
+    "movq %%rbx,%%rax\n"
+    "movq $0x1000003d10,%%rdx\n"
+    "mulq %%rdx\n"
+    "addq %%rax,%%r8\n"
+    "adcq %%rdx,%%r9\n"
+    /* r[3] = c & M */
+    "movq %%r8,%%rax\n"
+    "andq %%r15,%%rax\n"
+    "movq %%rax,24(%%rdi)\n"
+    /* c >>= 52 (%%r8 only) */
+    "shrdq $52,%%r9,%%r8\n"
+    /* c += t4 (%%r8 only) */
+    "addq %%rsi,%%r8\n"
+    /* r[4] = c */
+    "movq %%r8,32(%%rdi)\n"
+: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
+: "D"(r)
+: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
+);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h
new file mode 100644
index 000000000..dd88f38c7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h
@@ -0,0 +1,451 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
+#define _SECP256K1_FIELD_REPR_IMPL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "util.h"
+#include "num.h"
+#include "field.h"
+
+#if defined(USE_ASM_X86_64)
+#include "field_5x52_asm_impl.h"
+#else
+#include "field_5x52_int128_impl.h"
+#endif
+
+/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
+ *  represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
+ *  each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
+ *  is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
+ *  accept any input with magnitude at most M, and have different rules for propagating magnitude to their
+ *  output.
+ */
+
+#ifdef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
+    const uint64_t *d = a->n;
+    int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
+   /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
+    r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
+    r &= (a->magnitude >= 0);
+    r &= (a->magnitude <= 2048);
+    if (a->normalized) {
+        r &= (a->magnitude <= 1);
+        if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+            r &= (d[0] < 0xFFFFEFFFFFC2FULL);
+        }
+    }
+    VERIFY_CHECK(r == 1);
+}
+#endif
+
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    /* Apply the final reduction (for constant-time behaviour, we do it always) */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+    VERIFY_CHECK(t4 >> 48 == x);
+
+    /* Mask off the possible multiple of 2^256 from the final reduction */
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    if (x) {
+        t0 += 0x1000003D1ULL;
+        t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+        t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+        t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+        t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+        /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+        VERIFY_CHECK(t4 >> 48 == x);
+
+        /* Mask off the possible multiple of 2^256 from the final reduction */
+        t4 &= 0x0FFFFFFFFFFFFULL;
+    }
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint64_t z0, z1;
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0  = t0; z1  = t0 ^ 0x1000003D0ULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
+    uint64_t t0, t1, t2, t3, t4;
+    uint64_t z0, z1;
+    uint64_t x;
+
+    t0 = r->n[0];
+    t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    x = t4 >> 48;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    z0 = t0 & 0xFFFFFFFFFFFFFULL;
+    z1 = z0 ^ 0x1000003D0ULL;
+
+    /* Fast return path should catch the majority of cases */
+    if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
+        return 0;
+    }
+
+    t1 = r->n[1];
+    t2 = r->n[2];
+    t3 = r->n[3];
+
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    t1 += (t0 >> 52);
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    r->n[0] = a;
+    r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+    const uint64_t *t = a->n;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    return a->n[0] & 1;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+    int i;
+#ifdef VERIFY
+    a->magnitude = 0;
+    a->normalized = 1;
+#endif
+    for (i=0; i<5; i++) {
+        a->n[i] = 0;
+    }
+}
+
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    int i;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    VERIFY_CHECK(b->normalized);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+#endif
+    for (i = 4; i >= 0; i--) {
+        if (a->n[i] > b->n[i]) {
+            return 1;
+        }
+        if (a->n[i] < b->n[i]) {
+            return -1;
+        }
+    }
+    return 0;
+}
+
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
+    int i;
+    r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+    for (i=0; i<32; i++) {
+        int j;
+        for (j=0; j<2; j++) {
+            int limb = (8*i+4*j)/52;
+            int shift = (8*i+4*j)%52;
+            r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
+        }
+    }
+    if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
+        return 0;
+    }
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+#endif
+    return 1;
+}
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
+    int i;
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_verify(a);
+#endif
+    for (i=0; i<32; i++) {
+        int j;
+        int c = 0;
+        for (j=0; j<2; j++) {
+            int limb = (8*i+4*j)/52;
+            int shift = (8*i+4*j)%52;
+            c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
+        }
+        r[31-i] = c;
+    }
+}
+
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= m);
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
+    r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
+    r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
+    r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
+    r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
+#ifdef VERIFY
+    r->magnitude = m + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+    r->n[0] *= a;
+    r->n[1] *= a;
+    r->n[2] *= a;
+    r->n[3] *= a;
+    r->n[4] *= a;
+#ifdef VERIFY
+    r->magnitude *= a;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    secp256k1_fe_verify(a);
+#endif
+    r->n[0] += a->n[0];
+    r->n[1] += a->n[1];
+    r->n[2] += a->n[2];
+    r->n[3] += a->n[3];
+    r->n[4] += a->n[4];
+#ifdef VERIFY
+    r->magnitude += a->magnitude;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    VERIFY_CHECK(b->magnitude <= 8);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(r != b);
+#endif
+    secp256k1_fe_mul_inner(r->n, a->n, b->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->magnitude <= 8);
+    secp256k1_fe_verify(a);
+#endif
+    secp256k1_fe_sqr_inner(r->n, a->n);
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint64_t mask0, mask1;
+    mask0 = flag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+#ifdef VERIFY
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
+#endif
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
+    uint64_t mask0, mask1;
+    mask0 = flag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+}
+
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+#ifdef VERIFY
+    VERIFY_CHECK(a->normalized);
+#endif
+    r->n[0] = a->n[0] | a->n[1] << 52;
+    r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
+    r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
+    r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
+}
+
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
+    r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
+    r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
+    r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
+    r->n[4] = a->n[3] >> 16;
+#ifdef VERIFY
+    r->magnitude = 1;
+    r->normalized = 1;
+#endif
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_int128_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_int128_impl.h
new file mode 100644
index 000000000..0bf22bdd3
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_5x52_int128_impl.h
@@ -0,0 +1,277 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
+#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
+
+#include <stdint.h>
+
+#ifdef VERIFY
+#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
+#else
+#define VERIFY_BITS(x, n) do { } while(0)
+#endif
+
+SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
+    uint128_t c, d;
+    uint64_t t3, t4, tx, u0;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+    VERIFY_BITS(b[0], 56);
+    VERIFY_BITS(b[1], 56);
+    VERIFY_BITS(b[2], 56);
+    VERIFY_BITS(b[3], 56);
+    VERIFY_BITS(b[4], 52);
+    VERIFY_CHECK(r != b);
+
+    /*  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    d  = (uint128_t)a0 * b[3]
+       + (uint128_t)a1 * b[2]
+       + (uint128_t)a2 * b[1]
+       + (uint128_t)a3 * b[0];
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    c  = (uint128_t)a4 * b[4];
+    VERIFY_BITS(c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    d += (c & M) * R; c >>= 52;
+    VERIFY_BITS(d, 115);
+    VERIFY_BITS(c, 60);
+    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = d & M; d >>= 52;
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS(d, 63);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    d += (uint128_t)a0 * b[4]
+       + (uint128_t)a1 * b[3]
+       + (uint128_t)a2 * b[2]
+       + (uint128_t)a3 * b[1]
+       + (uint128_t)a4 * b[0];
+    VERIFY_BITS(d, 115);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    d += c * R;
+    VERIFY_BITS(d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = d & M; d >>= 52;
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS(d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    c  = (uint128_t)a0 * b[0];
+    VERIFY_BITS(c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    d += (uint128_t)a1 * b[4]
+       + (uint128_t)a2 * b[3]
+       + (uint128_t)a3 * b[2]
+       + (uint128_t)a4 * b[1];
+    VERIFY_BITS(d, 115);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = d & M; d >>= 52;
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS(d, 63);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    c += (uint128_t)u0 * (R >> 4);
+    VERIFY_BITS(c, 115);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = c & M; c >>= 52;
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS(c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    c += (uint128_t)a0 * b[1]
+       + (uint128_t)a1 * b[0];
+    VERIFY_BITS(c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    d += (uint128_t)a2 * b[4]
+       + (uint128_t)a3 * b[3]
+       + (uint128_t)a4 * b[2];
+    VERIFY_BITS(d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = c & M; c >>= 52;
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    c += (uint128_t)a0 * b[2]
+       + (uint128_t)a1 * b[1]
+       + (uint128_t)a2 * b[0];
+    VERIFY_BITS(c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint128_t)a3 * b[4]
+       + (uint128_t)a4 * b[3];
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = c & M; c >>= 52;
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += d * R + t3;
+    VERIFY_BITS(c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = c & M; c >>= 52;
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS(c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += t4;
+    VERIFY_BITS(c, 49);
+    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = c;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
+    uint128_t c, d;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    int64_t t3, t4, tx, u0;
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+
+    /**  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*a[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    d  = (uint128_t)(a0*2) * a3
+       + (uint128_t)(a1*2) * a2;
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    c  = (uint128_t)a4 * a4;
+    VERIFY_BITS(c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    d += (c & M) * R; c >>= 52;
+    VERIFY_BITS(d, 115);
+    VERIFY_BITS(c, 60);
+    /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = d & M; d >>= 52;
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS(d, 63);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    a4 *= 2;
+    d += (uint128_t)a0 * a4
+       + (uint128_t)(a1*2) * a3
+       + (uint128_t)a2 * a2;
+    VERIFY_BITS(d, 115);
+    /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    d += c * R;
+    VERIFY_BITS(d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = d & M; d >>= 52;
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS(d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    c  = (uint128_t)a0 * a0;
+    VERIFY_BITS(c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    d += (uint128_t)a1 * a4
+       + (uint128_t)(a2*2) * a3;
+    VERIFY_BITS(d, 114);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = d & M; d >>= 52;
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS(d, 62);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    c += (uint128_t)u0 * (R >> 4);
+    VERIFY_BITS(c, 113);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = c & M; c >>= 52;
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS(c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    a0 *= 2;
+    c += (uint128_t)a0 * a1;
+    VERIFY_BITS(c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    d += (uint128_t)a2 * a4
+       + (uint128_t)a3 * a3;
+    VERIFY_BITS(d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = c & M; c >>= 52;
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    c += (uint128_t)a0 * a2
+       + (uint128_t)a1 * a1;
+    VERIFY_BITS(c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (uint128_t)a3 * a4;
+    VERIFY_BITS(d, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c += (d & M) * R; d >>= 52;
+    VERIFY_BITS(c, 115);
+    VERIFY_BITS(d, 62);
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = c & M; c >>= 52;
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS(c, 63);
+    /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    c   += d * R + t3;
+    VERIFY_BITS(c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = c & M; c >>= 52;
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS(c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    c   += t4;
+    VERIFY_BITS(c, 49);
+    /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = c;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_impl.h
new file mode 100644
index 000000000..5127b279b
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/field_impl.h
@@ -0,0 +1,315 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_IMPL_H_
+#define _SECP256K1_FIELD_IMPL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "util.h"
+
+#if defined(USE_FIELD_10X26)
+#include "field_10x26_impl.h"
+#elif defined(USE_FIELD_5X52)
+#include "field_5x52_impl.h"
+#else
+#error "Please select field implementation"
+#endif
+
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero(&na);
+}
+
+SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero_var(&na);
+}
+
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
+    /** Given that p is congruent to 3 mod 4, we can compute the square root of
+     *  a mod p as the (p+1)/4'th power of a.
+     *
+     *  As (p+1)/4 is an even number, it will have the same result for a and for
+     *  (-a). Only one of these two numbers actually has a square root however,
+     *  so we test at the end by squaring and comparing to the input.
+     *  Also because (p+1)/4 is an even number, the computed square root is
+     *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
+     */
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+    int j;
+
+    /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
+     *  { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+     *  1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+     */
+
+    secp256k1_fe_sqr(&x2, a);
+    secp256k1_fe_mul(&x2, &x2, a);
+
+    secp256k1_fe_sqr(&x3, &x2);
+    secp256k1_fe_mul(&x3, &x3, a);
+
+    x6 = x3;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x6, &x6);
+    }
+    secp256k1_fe_mul(&x6, &x6, &x3);
+
+    x9 = x6;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x9, &x9);
+    }
+    secp256k1_fe_mul(&x9, &x9, &x3);
+
+    x11 = x9;
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&x11, &x11);
+    }
+    secp256k1_fe_mul(&x11, &x11, &x2);
+
+    x22 = x11;
+    for (j=0; j<11; j++) {
+        secp256k1_fe_sqr(&x22, &x22);
+    }
+    secp256k1_fe_mul(&x22, &x22, &x11);
+
+    x44 = x22;
+    for (j=0; j<22; j++) {
+        secp256k1_fe_sqr(&x44, &x44);
+    }
+    secp256k1_fe_mul(&x44, &x44, &x22);
+
+    x88 = x44;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x88, &x88);
+    }
+    secp256k1_fe_mul(&x88, &x88, &x44);
+
+    x176 = x88;
+    for (j=0; j<88; j++) {
+        secp256k1_fe_sqr(&x176, &x176);
+    }
+    secp256k1_fe_mul(&x176, &x176, &x88);
+
+    x220 = x176;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x220, &x220);
+    }
+    secp256k1_fe_mul(&x220, &x220, &x44);
+
+    x223 = x220;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x223, &x223);
+    }
+    secp256k1_fe_mul(&x223, &x223, &x3);
+
+    /* The final result is then assembled using a sliding window over the blocks. */
+
+    t1 = x223;
+    for (j=0; j<23; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x22);
+    for (j=0; j<6; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x2);
+    secp256k1_fe_sqr(&t1, &t1);
+    secp256k1_fe_sqr(r, &t1);
+
+    /* Check that a square root was actually calculated */
+
+    secp256k1_fe_sqr(&t1, r);
+    return secp256k1_fe_equal(&t1, a);
+}
+
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+    int j;
+
+    /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
+     *  { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+     *  [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+     */
+
+    secp256k1_fe_sqr(&x2, a);
+    secp256k1_fe_mul(&x2, &x2, a);
+
+    secp256k1_fe_sqr(&x3, &x2);
+    secp256k1_fe_mul(&x3, &x3, a);
+
+    x6 = x3;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x6, &x6);
+    }
+    secp256k1_fe_mul(&x6, &x6, &x3);
+
+    x9 = x6;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x9, &x9);
+    }
+    secp256k1_fe_mul(&x9, &x9, &x3);
+
+    x11 = x9;
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&x11, &x11);
+    }
+    secp256k1_fe_mul(&x11, &x11, &x2);
+
+    x22 = x11;
+    for (j=0; j<11; j++) {
+        secp256k1_fe_sqr(&x22, &x22);
+    }
+    secp256k1_fe_mul(&x22, &x22, &x11);
+
+    x44 = x22;
+    for (j=0; j<22; j++) {
+        secp256k1_fe_sqr(&x44, &x44);
+    }
+    secp256k1_fe_mul(&x44, &x44, &x22);
+
+    x88 = x44;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x88, &x88);
+    }
+    secp256k1_fe_mul(&x88, &x88, &x44);
+
+    x176 = x88;
+    for (j=0; j<88; j++) {
+        secp256k1_fe_sqr(&x176, &x176);
+    }
+    secp256k1_fe_mul(&x176, &x176, &x88);
+
+    x220 = x176;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x220, &x220);
+    }
+    secp256k1_fe_mul(&x220, &x220, &x44);
+
+    x223 = x220;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x223, &x223);
+    }
+    secp256k1_fe_mul(&x223, &x223, &x3);
+
+    /* The final result is then assembled using a sliding window over the blocks. */
+
+    t1 = x223;
+    for (j=0; j<23; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x22);
+    for (j=0; j<5; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, a);
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x2);
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(r, a, &t1);
+}
+
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
+#if defined(USE_FIELD_INV_BUILTIN)
+    secp256k1_fe_inv(r, a);
+#elif defined(USE_FIELD_INV_NUM)
+    secp256k1_num n, m;
+    static const secp256k1_fe negone = SECP256K1_FE_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
+    );
+    /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    static const unsigned char prime[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+    };
+    unsigned char b[32];
+    int res;
+    secp256k1_fe c = *a;
+    secp256k1_fe_normalize_var(&c);
+    secp256k1_fe_get_b32(b, &c);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_num_set_bin(&m, prime, 32);
+    secp256k1_num_mod_inverse(&n, &n, &m);
+    secp256k1_num_get_bin(b, 32, &n);
+    res = secp256k1_fe_set_b32(r, b);
+    (void)res;
+    VERIFY_CHECK(res);
+    /* Verify the result is the (unique) valid inverse using non-GMP code. */
+    secp256k1_fe_mul(&c, &c, r);
+    secp256k1_fe_add(&c, &negone);
+    CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
+#else
+#error "Please select field inverse implementation"
+#endif
+}
+
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
+    secp256k1_fe u;
+    size_t i;
+    if (len < 1) {
+        return;
+    }
+
+    VERIFY_CHECK((r + len <= a) || (a + len <= r));
+
+    r[0] = a[0];
+
+    i = 0;
+    while (++i < len) {
+        secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]);
+    }
+
+    secp256k1_fe_inv_var(&u, &r[--i]);
+
+    while (i > 0) {
+        size_t j = i--;
+        secp256k1_fe_mul(&r[j], &r[i], &u);
+        secp256k1_fe_mul(&u, &u, &a[j]);
+    }
+
+    r[0] = u;
+}
+
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
+#ifndef USE_NUM_NONE
+    unsigned char b[32];
+    secp256k1_num n;
+    secp256k1_num m;
+    /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    static const unsigned char prime[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+    };
+
+    secp256k1_fe c = *a;
+    secp256k1_fe_normalize_var(&c);
+    secp256k1_fe_get_b32(b, &c);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_num_set_bin(&m, prime, 32);
+    return secp256k1_num_jacobi(&n, &m) >= 0;
+#else
+    secp256k1_fe r;
+    return secp256k1_fe_sqrt(&r, a);
+#endif
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/gen_context.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/gen_context.c
new file mode 100644
index 000000000..1835fd491
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/gen_context.c
@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields           *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#define USE_BASIC_CONFIG 1
+
+#include "basic-config.h"
+#include "include/secp256k1.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_gen_impl.h"
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+int main(int argc, char **argv) {
+    secp256k1_ecmult_gen_context ctx;
+    int inner;
+    int outer;
+    FILE* fp;
+
+    (void)argc;
+    (void)argv;
+
+    fp = fopen("src/ecmult_static_context.h","w");
+    if (fp == NULL) {
+        fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n");
+        return -1;
+    }
+    
+    fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#include \"group.h\"\n");
+    fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
+    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = {\n");
+
+    secp256k1_ecmult_gen_context_init(&ctx);
+    secp256k1_ecmult_gen_context_build(&ctx, &default_error_callback);
+    for(outer = 0; outer != 64; outer++) {
+        fprintf(fp,"{\n");
+        for(inner = 0; inner != 16; inner++) {
+            fprintf(fp,"    SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
+            if (inner != 15) {
+                fprintf(fp,",\n");
+            } else {
+                fprintf(fp,"\n");
+            }
+        }
+        if (outer != 63) {
+            fprintf(fp,"},\n");
+        } else {
+            fprintf(fp,"}\n");
+        }
+    }
+    fprintf(fp,"};\n");
+    secp256k1_ecmult_gen_context_clear(&ctx);
+    
+    fprintf(fp, "#undef SC\n");
+    fprintf(fp, "#endif\n");
+    fclose(fp);
+    
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group.h
new file mode 100644
index 000000000..4957b248f
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group.h
@@ -0,0 +1,144 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_GROUP_
+#define _SECP256K1_GROUP_
+
+#include "num.h"
+#include "field.h"
+
+/** A group element of the secp256k1 curve, in affine coordinates. */
+typedef struct {
+    secp256k1_fe x;
+    secp256k1_fe y;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_ge;
+
+#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
+#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+/** A group element of the secp256k1 curve, in jacobian coordinates. */
+typedef struct {
+    secp256k1_fe x; /* actual X: x/z^2 */
+    secp256k1_fe y; /* actual Y: y/z^3 */
+    secp256k1_fe z;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_gej;
+
+#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
+#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+typedef struct {
+    secp256k1_fe_storage x;
+    secp256k1_fe_storage y;
+} secp256k1_ge_storage;
+
+#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
+
+#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
+
+/** Set a group element equal to the point with given X and Y coordinates */
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (affine) equal to the point with the given X coordinate
+ *  and a Y coordinate that is a quadratic residue modulo p. The return value
+ *  is true iff a coordinate with the given X coordinate exists.
+ */
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x);
+
+/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
+ *  for Y. Return value indicates whether the result is valid. */
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
+
+/** Check whether a group element is valid (i.e., on the curve). */
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates */
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
+
+/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb);
+
+/** Set a batch of group elements equal to the inputs given in jacobian
+ *  coordinates (with known z-ratios). zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len);
+
+/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
+ *  the same global z "denominator". zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
+ *  coordinates of the result are stored in r, the common z coordinate is
+ *  stored in globalz. */
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
+
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej *r);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
+
+/** Compare the X coordinate of a group element (jacobian). */
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
+
+/** Check whether a group element's y coordinate is a quadratic residue. */
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
+ * a may not be zero. Constant time. */
+static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
+    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
+    guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
+
+#ifdef USE_ENDOMORPHISM
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
+#endif
+
+/** Clear a secp256k1_gej to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej *r);
+
+/** Clear a secp256k1_ge to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge *r);
+
+/** Convert a group element to the storage type. */
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
+
+/** Convert a group element back from the storage type. */
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
+
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
+
+/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group_impl.h
new file mode 100644
index 000000000..7d723532f
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/group_impl.h
@@ -0,0 +1,700 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_GROUP_IMPL_H_
+#define _SECP256K1_GROUP_IMPL_H_
+
+#include "num.h"
+#include "field.h"
+#include "group.h"
+
+/* These points can be generated in sage as follows:
+ *
+ * 0. Setup a worksheet with the following parameters.
+ *   b = 4  # whatever CURVE_B will be set to
+ *   F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+ *   C = EllipticCurve ([F (0), F (b)])
+ *
+ * 1. Determine all the small orders available to you. (If there are
+ *    no satisfactory ones, go back and change b.)
+ *   print C.order().factor(limit=1000)
+ *
+ * 2. Choose an order as one of the prime factors listed in the above step.
+ *    (You can also multiply some to get a composite order, though the
+ *    tests will crash trying to invert scalars during signing.) We take a
+ *    random point and scale it to drop its order to the desired value.
+ *    There is some probability this won't work; just try again.
+ *   order = 199
+ *   P = C.random_point()
+ *   P = (int(P.order()) / int(order)) * P
+ *   assert(P.order() == order)
+ *
+ * 3. Print the values. You'll need to use a vim macro or something to
+ *    split the hex output into 4-byte chunks.
+ *   print "%x %x" % P.xy()
+ */
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#  if EXHAUSTIVE_TEST_ORDER == 199
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
+    0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
+    0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
+    0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
+);
+
+const int CURVE_B = 4;
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
+    0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
+    0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
+    0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
+);
+const int CURVE_B = 2;
+#  else
+#    error No known generator for the specified exhaustive test group order.
+#  endif
+#else
+/** Generator for secp256k1, value 'g' defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ */
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
+    0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
+    0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
+    0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
+);
+
+const int CURVE_B = 7;
+#endif
+
+static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
+    secp256k1_fe zi2;
+    secp256k1_fe zi3;
+    secp256k1_fe_sqr(&zi2, zi);
+    secp256k1_fe_mul(&zi3, &zi2, zi);
+    secp256k1_fe_mul(&r->x, &a->x, &zi2);
+    secp256k1_fe_mul(&r->y, &a->y, &zi3);
+    r->infinity = a->infinity;
+}
+
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
+    r->infinity = 0;
+    r->x = *x;
+    r->y = *y;
+}
+
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
+    return a->infinity;
+}
+
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
+    *r = *a;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    secp256k1_fe_inv(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
+    r->infinity = a->infinity;
+    if (a->infinity) {
+        return;
+    }
+    secp256k1_fe_inv_var(&a->z, &a->z);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_mul(&z3, &a->z, &z2);
+    secp256k1_fe_mul(&a->x, &a->x, &z2);
+    secp256k1_fe_mul(&a->y, &a->y, &z3);
+    secp256k1_fe_set_int(&a->z, 1);
+    r->x = a->x;
+    r->y = a->y;
+}
+
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb) {
+    secp256k1_fe *az;
+    secp256k1_fe *azi;
+    size_t i;
+    size_t count = 0;
+    az = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * len);
+    for (i = 0; i < len; i++) {
+        if (!a[i].infinity) {
+            az[count++] = a[i].z;
+        }
+    }
+
+    azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
+    secp256k1_fe_inv_all_var(azi, az, count);
+    free(az);
+
+    count = 0;
+    for (i = 0; i < len; i++) {
+        r[i].infinity = a[i].infinity;
+        if (!a[i].infinity) {
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &azi[count++]);
+        }
+    }
+    free(azi);
+}
+
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len) {
+    size_t i = len - 1;
+    secp256k1_fe zi;
+
+    if (len > 0) {
+        /* Compute the inverse of the last z coordinate, and use it to compute the last affine output. */
+        secp256k1_fe_inv(&zi, &a[i].z);
+        secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+
+        /* Work out way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            secp256k1_fe_mul(&zi, &zi, &zr[i]);
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+        }
+    }
+}
+
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zs;
+
+    if (len > 0) {
+        /* The z of the final point gives us the "global Z" for the table. */
+        r[i].x = a[i].x;
+        r[i].y = a[i].y;
+        *globalz = a[i].z;
+        r[i].infinity = 0;
+        zs = zr[i];
+
+        /* Work our way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            if (i != len - 1) {
+                secp256k1_fe_mul(&zs, &zs, &zr[i]);
+            }
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
+        }
+    }
+}
+
+static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
+    r->infinity = 1;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_gej_clear(secp256k1_gej *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_clear(secp256k1_ge *r) {
+    r->infinity = 0;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+}
+
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
+    secp256k1_fe x2, x3, c;
+    r->x = *x;
+    secp256k1_fe_sqr(&x2, x);
+    secp256k1_fe_mul(&x3, x, &x2);
+    r->infinity = 0;
+    secp256k1_fe_set_int(&c, CURVE_B);
+    secp256k1_fe_add(&c, &x3);
+    return secp256k1_fe_sqrt(&r->y, &c);
+}
+
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
+    if (!secp256k1_ge_set_xquad(r, x)) {
+        return 0;
+    }
+    secp256k1_fe_normalize_var(&r->y);
+    if (secp256k1_fe_is_odd(&r->y) != odd) {
+        secp256k1_fe_negate(&r->y, &r->y, 1);
+    }
+    return 1;
+
+}
+
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
+   r->infinity = a->infinity;
+   r->x = a->x;
+   r->y = a->y;
+   secp256k1_fe_set_int(&r->z, 1);
+}
+
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
+    secp256k1_fe r, r2;
+    VERIFY_CHECK(!a->infinity);
+    secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
+    r2 = a->x; secp256k1_fe_normalize_weak(&r2);
+    return secp256k1_fe_equal_var(&r, &r2);
+}
+
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
+    r->infinity = a->infinity;
+    r->x = a->x;
+    r->y = a->y;
+    r->z = a->z;
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
+    return a->infinity;
+}
+
+static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
+    secp256k1_fe y2, x3, z2, z6;
+    if (a->infinity) {
+        return 0;
+    }
+    /** y^2 = x^3 + 7
+     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
+     *  Y^2 / Z^6 = X^3 / Z^6 + 7
+     *  Y^2 = X^3 + 7*Z^6
+     */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_sqr(&z2, &a->z);
+    secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
+    secp256k1_fe_mul_int(&z6, CURVE_B);
+    secp256k1_fe_add(&x3, &z6);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
+    secp256k1_fe y2, x3, c;
+    if (a->infinity) {
+        return 0;
+    }
+    /* y^2 = x^3 + 7 */
+    secp256k1_fe_sqr(&y2, &a->y);
+    secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
+    secp256k1_fe_set_int(&c, CURVE_B);
+    secp256k1_fe_add(&x3, &c);
+    secp256k1_fe_normalize_weak(&x3);
+    return secp256k1_fe_equal_var(&y2, &x3);
+}
+
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
+     *
+     * Note that there is an implementation described at
+     *     https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+     * which trades a multiply for a square, but in practice this is actually slower,
+     * mainly because it requires more normalizations.
+     */
+    secp256k1_fe t1,t2,t3,t4;
+    /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
+     *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
+     *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
+     *
+     *  Having said this, if this function receives a point on a sextic twist, e.g. by
+     *  a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
+     *  since -6 does have a cube root mod p. For this point, this function will not set
+     *  the infinity flag even though the point doubles to infinity, and the result
+     *  point will be gibberish (z = 0 but infinity = 0).
+     */
+    r->infinity = a->infinity;
+    if (r->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        return;
+    }
+
+    if (rzr != NULL) {
+        *rzr = a->y;
+        secp256k1_fe_normalize_weak(rzr);
+        secp256k1_fe_mul_int(rzr, 2);
+    }
+
+    secp256k1_fe_mul(&r->z, &a->z, &a->y);
+    secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
+    secp256k1_fe_sqr(&t1, &a->x);
+    secp256k1_fe_mul_int(&t1, 3);         /* T1 = 3*X^2 (3) */
+    secp256k1_fe_sqr(&t2, &t1);           /* T2 = 9*X^4 (1) */
+    secp256k1_fe_sqr(&t3, &a->y);
+    secp256k1_fe_mul_int(&t3, 2);         /* T3 = 2*Y^2 (2) */
+    secp256k1_fe_sqr(&t4, &t3);
+    secp256k1_fe_mul_int(&t4, 2);         /* T4 = 8*Y^4 (2) */
+    secp256k1_fe_mul(&t3, &t3, &a->x);    /* T3 = 2*X*Y^2 (1) */
+    r->x = t3;
+    secp256k1_fe_mul_int(&r->x, 4);       /* X' = 8*X*Y^2 (4) */
+    secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
+    secp256k1_fe_add(&r->x, &t2);         /* X' = 9*X^4 - 8*X*Y^2 (6) */
+    secp256k1_fe_negate(&t2, &t2, 1);     /* T2 = -9*X^4 (2) */
+    secp256k1_fe_mul_int(&t3, 6);         /* T3 = 12*X*Y^2 (6) */
+    secp256k1_fe_add(&t3, &t2);           /* T3 = 12*X*Y^2 - 9*X^4 (8) */
+    secp256k1_fe_mul(&r->y, &t1, &t3);    /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
+    secp256k1_fe_negate(&t2, &t4, 2);     /* T2 = -8*Y^4 (3) */
+    secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
+}
+
+static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
+    secp256k1_gej_double_var(r, a, rzr);
+}
+
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
+    /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        *r = *b;
+        return;
+    }
+
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+
+    r->infinity = 0;
+    secp256k1_fe_sqr(&z22, &b->z);
+    secp256k1_fe_sqr(&z12, &a->z);
+    secp256k1_fe_mul(&u1, &a->x, &z22);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    secp256k1_fe_mul(&h, &h, &b->z);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
+    /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
+        secp256k1_gej_set_ge(r, b);
+        return;
+    }
+    if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
+        *r = *a;
+        return;
+    }
+    r->infinity = 0;
+
+    secp256k1_fe_sqr(&z12, &a->z);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
+    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
+    if (a->infinity) {
+        secp256k1_fe bzinv2, bzinv3;
+        r->infinity = b->infinity;
+        secp256k1_fe_sqr(&bzinv2, bzinv);
+        secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
+        secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
+        secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
+        secp256k1_fe_set_int(&r->z, 1);
+        return;
+    }
+    r->infinity = 0;
+
+    /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
+     *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
+     *  by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
+     *  This means that (rx,ry,rz) can be calculated as
+     *  (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
+     *  The variable az below holds the modified Z coordinate for a, which is used
+     *  for the computation of rx and ry, but not for rz.
+     */
+    secp256k1_fe_mul(&az, &a->z, bzinv);
+
+    secp256k1_fe_sqr(&z12, &az);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, NULL);
+        } else {
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
+    /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
+    static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
+    secp256k1_fe m_alt, rr_alt;
+    int infinity, degenerate;
+    VERIFY_CHECK(!b->infinity);
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+
+    /** In:
+     *    Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
+     *    In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
+     *  we find as solution for a unified addition/doubling formula:
+     *    lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
+     *    x3 = lambda^2 - (x1 + x2)
+     *    2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
+     *
+     *  Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
+     *    U1 = X1*Z2^2, U2 = X2*Z1^2
+     *    S1 = Y1*Z2^3, S2 = Y2*Z1^3
+     *    Z = Z1*Z2
+     *    T = U1+U2
+     *    M = S1+S2
+     *    Q = T*M^2
+     *    R = T^2-U1*U2
+     *    X3 = 4*(R^2-Q)
+     *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
+     *    Z3 = 2*M*Z
+     *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
+     *
+     *  This formula has the benefit of being the same for both addition
+     *  of distinct points and doubling. However, it breaks down in the
+     *  case that either point is infinity, or that y1 = -y2. We handle
+     *  these cases in the following ways:
+     *
+     *    - If b is infinity we simply bail by means of a VERIFY_CHECK.
+     *
+     *    - If a is infinity, we detect this, and at the end of the
+     *      computation replace the result (which will be meaningless,
+     *      but we compute to be constant-time) with b.x : b.y : 1.
+     *
+     *    - If a = -b, we have y1 = -y2, which is a degenerate case.
+     *      But here the answer is infinity, so we simply set the
+     *      infinity flag of the result, overriding the computed values
+     *      without even needing to cmov.
+     *
+     *    - If y1 = -y2 but x1 != x2, which does occur thanks to certain
+     *      properties of our curve (specifically, 1 has nontrivial cube
+     *      roots in our field, and the curve equation has no x coefficient)
+     *      then the answer is not infinity but also not given by the above
+     *      equation. In this case, we cmov in place an alternate expression
+     *      for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
+     *      expressions for lambda are defined, they are equal, and can be
+     *      obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
+     *      then substitution of x^3 + 7 for y^2 (using the curve equation).
+     *      For all pairs of nonzero points (a, b) at least one is defined,
+     *      so this covers everything.
+     */
+
+    secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
+    secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
+    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z1^2 (1) */
+    secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
+    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
+    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
+    secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
+    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 */
+    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (2) */
+    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (3) */
+    /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
+     *  case that Z = z1z2 = 0, and this is special-cased later on). */
+    degenerate = secp256k1_fe_normalizes_to_zero(&m) &
+                 secp256k1_fe_normalizes_to_zero(&rr);
+    /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
+     * This means either x1 == beta*x2 or beta*x1 == x2, where beta is
+     * a nontrivial cube root of one. In either case, an alternate
+     * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
+     * so we set R/M equal to this. */
+    rr_alt = s1;
+    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
+    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 */
+
+    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
+    secp256k1_fe_cmov(&m_alt, &m, !degenerate);
+    /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
+     * From here on out Ralt and Malt represent the numerator
+     * and denominator of lambda; R and M represent the explicit
+     * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
+    secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
+    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*Malt^2 (1) */
+    /* These two lines use the observation that either M == Malt or M == 0,
+     * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
+     * zero (which is "computed" by cmov). So the cost is one squaring
+     * versus two multiplications. */
+    secp256k1_fe_sqr(&n, &n);
+    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
+    secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
+    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Malt*Z (1) */
+    infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
+    secp256k1_fe_mul_int(&r->z, 2);                     /* r->z = Z3 = 2*Malt*Z (2) */
+    secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2-Q (3) */
+    secp256k1_fe_normalize_weak(&t);
+    r->x = t;                                           /* r->x = Ralt^2-Q (1) */
+    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*x3 (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = 2*x3 - Q: (4) */
+    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*x3 - Q) (1) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
+    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
+    secp256k1_fe_normalize_weak(&r->y);
+    secp256k1_fe_mul_int(&r->x, 4);                     /* r->x = X3 = 4*(Ralt^2-Q) */
+    secp256k1_fe_mul_int(&r->y, 4);                     /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
+
+    /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
+    secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
+    secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
+    secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
+    r->infinity = infinity;
+}
+
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
+    /* Operations: 4 mul, 1 sqr */
+    secp256k1_fe zz;
+    VERIFY_CHECK(!secp256k1_fe_is_zero(s));
+    secp256k1_fe_sqr(&zz, s);
+    secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
+    secp256k1_fe_mul(&r->y, &r->y, &zz);
+    secp256k1_fe_mul(&r->y, &r->y, s);                  /* r->y *= s^3 */
+    secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
+}
+
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
+    secp256k1_fe x, y;
+    VERIFY_CHECK(!a->infinity);
+    x = a->x;
+    secp256k1_fe_normalize(&x);
+    y = a->y;
+    secp256k1_fe_normalize(&y);
+    secp256k1_fe_to_storage(&r->x, &x);
+    secp256k1_fe_to_storage(&r->y, &y);
+}
+
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
+    secp256k1_fe_from_storage(&r->x, &a->x);
+    secp256k1_fe_from_storage(&r->y, &a->y);
+    r->infinity = 0;
+}
+
+static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
+    secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
+    secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
+    static const secp256k1_fe beta = SECP256K1_FE_CONST(
+        0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
+        0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
+    );
+    *r = *a;
+    secp256k1_fe_mul(&r->x, &r->x, &beta);
+}
+#endif
+
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
+    secp256k1_fe yz;
+
+    if (a->infinity) {
+        return 0;
+    }
+
+    /* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as
+     * that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z
+       is */
+    secp256k1_fe_mul(&yz, &a->y, &a->z);
+    return secp256k1_fe_is_quad_var(&yz);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash.h
new file mode 100644
index 000000000..fca98cab9
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash.h
@@ -0,0 +1,41 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_HASH_
+#define _SECP256K1_HASH_
+
+#include <stdlib.h>
+#include <stdint.h>
+
+typedef struct {
+    uint32_t s[8];
+    uint32_t buf[16]; /* In big endian */
+    size_t bytes;
+} secp256k1_sha256_t;
+
+static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash);
+static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t size);
+static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32);
+
+typedef struct {
+    secp256k1_sha256_t inner, outer;
+} secp256k1_hmac_sha256_t;
+
+static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t size);
+static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size);
+static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32);
+
+typedef struct {
+    unsigned char v[32];
+    unsigned char k[32];
+    int retry;
+} secp256k1_rfc6979_hmac_sha256_t;
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen);
+static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen);
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash_impl.h
new file mode 100644
index 000000000..b47e65f83
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/hash_impl.h
@@ -0,0 +1,281 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_HASH_IMPL_H_
+#define _SECP256K1_HASH_IMPL_H_
+
+#include "hash.h"
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+
+#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z))))
+#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y))))
+#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10))
+#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7))
+#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3))
+#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10))
+
+#define Round(a,b,c,d,e,f,g,h,k,w) do { \
+    uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \
+    uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \
+    (d) += t1; \
+    (h) = t1 + t2; \
+} while(0)
+
+#ifdef WORDS_BIGENDIAN
+#define BE32(x) (x)
+#else
+#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
+#endif
+
+static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash) {
+    hash->s[0] = 0x6a09e667ul;
+    hash->s[1] = 0xbb67ae85ul;
+    hash->s[2] = 0x3c6ef372ul;
+    hash->s[3] = 0xa54ff53aul;
+    hash->s[4] = 0x510e527ful;
+    hash->s[5] = 0x9b05688cul;
+    hash->s[6] = 0x1f83d9abul;
+    hash->s[7] = 0x5be0cd19ul;
+    hash->bytes = 0;
+}
+
+/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
+static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) {
+    uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
+    uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
+
+    Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0]));
+    Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1]));
+    Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2]));
+    Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3]));
+    Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4]));
+    Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5]));
+    Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6]));
+    Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7]));
+    Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8]));
+    Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9]));
+    Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10]));
+    Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11]));
+    Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12]));
+    Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13]));
+    Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14]));
+    Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15]));
+
+    Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0));
+
+    s[0] += a;
+    s[1] += b;
+    s[2] += c;
+    s[3] += d;
+    s[4] += e;
+    s[5] += f;
+    s[6] += g;
+    s[7] += h;
+}
+
+static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t len) {
+    size_t bufsize = hash->bytes & 0x3F;
+    hash->bytes += len;
+    while (bufsize + len >= 64) {
+        /* Fill the buffer, and process it. */
+        memcpy(((unsigned char*)hash->buf) + bufsize, data, 64 - bufsize);
+        data += 64 - bufsize;
+        len -= 64 - bufsize;
+        secp256k1_sha256_transform(hash->s, hash->buf);
+        bufsize = 0;
+    }
+    if (len) {
+        /* Fill the buffer with what remains. */
+        memcpy(((unsigned char*)hash->buf) + bufsize, data, len);
+    }
+}
+
+static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32) {
+    static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
+    uint32_t sizedesc[2];
+    uint32_t out[8];
+    int i = 0;
+    sizedesc[0] = BE32(hash->bytes >> 29);
+    sizedesc[1] = BE32(hash->bytes << 3);
+    secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
+    secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8);
+    for (i = 0; i < 8; i++) {
+        out[i] = BE32(hash->s[i]);
+        hash->s[i] = 0;
+    }
+    memcpy(out32, (const unsigned char*)out, 32);
+}
+
+static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t keylen) {
+    int n;
+    unsigned char rkey[64];
+    if (keylen <= 64) {
+        memcpy(rkey, key, keylen);
+        memset(rkey + keylen, 0, 64 - keylen);
+    } else {
+        secp256k1_sha256_t sha256;
+        secp256k1_sha256_initialize(&sha256);
+        secp256k1_sha256_write(&sha256, key, keylen);
+        secp256k1_sha256_finalize(&sha256, rkey);
+        memset(rkey + 32, 0, 32);
+    }
+
+    secp256k1_sha256_initialize(&hash->outer);
+    for (n = 0; n < 64; n++) {
+        rkey[n] ^= 0x5c;
+    }
+    secp256k1_sha256_write(&hash->outer, rkey, 64);
+
+    secp256k1_sha256_initialize(&hash->inner);
+    for (n = 0; n < 64; n++) {
+        rkey[n] ^= 0x5c ^ 0x36;
+    }
+    secp256k1_sha256_write(&hash->inner, rkey, 64);
+    memset(rkey, 0, 64);
+}
+
+static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size) {
+    secp256k1_sha256_write(&hash->inner, data, size);
+}
+
+static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32) {
+    unsigned char temp[32];
+    secp256k1_sha256_finalize(&hash->inner, temp);
+    secp256k1_sha256_write(&hash->outer, temp, 32);
+    memset(temp, 0, 32);
+    secp256k1_sha256_finalize(&hash->outer, out32);
+}
+
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen) {
+    secp256k1_hmac_sha256_t hmac;
+    static const unsigned char zero[1] = {0x00};
+    static const unsigned char one[1] = {0x01};
+
+    memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */
+    memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
+
+    /* RFC6979 3.2.d. */
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(&hmac, zero, 1);
+    secp256k1_hmac_sha256_write(&hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+
+    /* RFC6979 3.2.f. */
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(&hmac, one, 1);
+    secp256k1_hmac_sha256_write(&hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    rng->retry = 0;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen) {
+    /* RFC6979 3.2.h. */
+    static const unsigned char zero[1] = {0x00};
+    if (rng->retry) {
+        secp256k1_hmac_sha256_t hmac;
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_write(&hmac, zero, 1);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->k);
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+    }
+
+    while (outlen > 0) {
+        secp256k1_hmac_sha256_t hmac;
+        int now = outlen;
+        secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(&hmac, rng->v);
+        if (now > 32) {
+            now = 32;
+        }
+        memcpy(out, rng->v, now);
+        out += now;
+        outlen -= now;
+    }
+
+    rng->retry = 1;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng) {
+    memset(rng->k, 0, 32);
+    memset(rng->v, 0, 32);
+    rng->retry = 0;
+}
+
+#undef BE32
+#undef Round
+#undef sigma1
+#undef sigma0
+#undef Sigma1
+#undef Sigma0
+#undef Maj
+#undef Ch
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1.java b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1.java
new file mode 100644
index 000000000..1c67802fb
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1.java
@@ -0,0 +1,446 @@
+/*
+ * Copyright 2013 Google Inc.
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.bitcoin;
+
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+
+import java.math.BigInteger;
+import com.google.common.base.Preconditions;
+import java.util.concurrent.locks.Lock;
+import java.util.concurrent.locks.ReentrantReadWriteLock;
+import static org.bitcoin.NativeSecp256k1Util.*;
+
+/**
+ * <p>This class holds native methods to handle ECDSA verification.</p>
+ *
+ * <p>You can find an example library that can be used for this at https://github.com/bitcoin/secp256k1</p>
+ *
+ * <p>To build secp256k1 for use with bitcoinj, run
+ * `./configure --enable-jni --enable-experimental --enable-module-ecdh`
+ * and `make` then copy `.libs/libsecp256k1.so` to your system library path
+ * or point the JVM to the folder containing it with -Djava.library.path
+ * </p>
+ */
+public class NativeSecp256k1 {
+
+    private static final ReentrantReadWriteLock rwl = new ReentrantReadWriteLock();
+    private static final Lock r = rwl.readLock();
+    private static final Lock w = rwl.writeLock();
+    private static ThreadLocal<ByteBuffer> nativeECDSABuffer = new ThreadLocal<ByteBuffer>();
+    /**
+     * Verifies the given secp256k1 signature in native code.
+     * Calling when enabled == false is undefined (probably library not loaded)
+     *
+     * @param data The data which was signed, must be exactly 32 bytes
+     * @param signature The signature
+     * @param pub The public key which did the signing
+     */
+    public static boolean verify(byte[] data, byte[] signature, byte[] pub) throws AssertFailException{
+        Preconditions.checkArgument(data.length == 32 && signature.length <= 520 && pub.length <= 520);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < 520) {
+            byteBuff = ByteBuffer.allocateDirect(520);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(data);
+        byteBuff.put(signature);
+        byteBuff.put(pub);
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          return secp256k1_ecdsa_verify(byteBuff, Secp256k1Context.getContext(), signature.length, pub.length) == 1;
+        } finally {
+          r.unlock();
+        }
+    }
+
+    /**
+     * libsecp256k1 Create an ECDSA signature.
+     *
+     * @param data Message hash, 32 bytes
+     * @param key Secret key, 32 bytes
+     *
+     * Return values
+     * @param sig byte array of signature
+     */
+    public static byte[] sign(byte[] data, byte[] sec) throws AssertFailException{
+        Preconditions.checkArgument(data.length == 32 && sec.length <= 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < 32 + 32) {
+            byteBuff = ByteBuffer.allocateDirect(32 + 32);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(data);
+        byteBuff.put(sec);
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          retByteArray = secp256k1_ecdsa_sign(byteBuff, Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] sigArr = retByteArray[0];
+        int sigLen = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(sigArr.length, sigLen, "Got bad signature length.");
+
+        return retVal == 0 ? new byte[0] : sigArr;
+    }
+
+    /**
+     * libsecp256k1 Seckey Verify - returns 1 if valid, 0 if invalid
+     *
+     * @param seckey ECDSA Secret key, 32 bytes
+     */
+    public static boolean secKeyVerify(byte[] seckey) {
+        Preconditions.checkArgument(seckey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seckey.length) {
+            byteBuff = ByteBuffer.allocateDirect(seckey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+
+        r.lock();
+        try {
+          return secp256k1_ec_seckey_verify(byteBuff,Secp256k1Context.getContext()) == 1;
+        } finally {
+          r.unlock();
+        }
+    }
+
+
+    /**
+     * libsecp256k1 Compute Pubkey - computes public key from secret key
+     *
+     * @param seckey ECDSA Secret key, 32 bytes
+     *
+     * Return values
+     * @param pubkey ECDSA Public key, 33 or 65 bytes
+     */
+    //TODO add a 'compressed' arg
+    public static byte[] computePubkey(byte[] seckey) throws AssertFailException{
+        Preconditions.checkArgument(seckey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seckey.length) {
+            byteBuff = ByteBuffer.allocateDirect(seckey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          retByteArray = secp256k1_ec_pubkey_create(byteBuff, Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+        int pubLen = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        return retVal == 0 ? new byte[0]: pubArr;
+    }
+
+    /**
+     * libsecp256k1 Cleanup - This destroys the secp256k1 context object
+     * This should be called at the end of the program for proper cleanup of the context.
+     */
+    public static synchronized void cleanup() {
+        w.lock();
+        try {
+          secp256k1_destroy_context(Secp256k1Context.getContext());
+        } finally {
+          w.unlock();
+        }
+    }
+
+    public static long cloneContext() {
+       r.lock();
+       try {
+        return secp256k1_ctx_clone(Secp256k1Context.getContext());
+       } finally { r.unlock(); }
+    }
+
+    /**
+     * libsecp256k1 PrivKey Tweak-Mul - Tweak privkey by multiplying to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param seckey 32-byte seckey
+     */
+    public static byte[] privKeyTweakMul(byte[] privkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(privkey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < privkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(privkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(privkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_privkey_tweak_mul(byteBuff,Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] privArr = retByteArray[0];
+
+        int privLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(privArr.length, privLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return privArr;
+    }
+
+    /**
+     * libsecp256k1 PrivKey Tweak-Add - Tweak privkey by adding to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param seckey 32-byte seckey
+     */
+    public static byte[] privKeyTweakAdd(byte[] privkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(privkey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < privkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(privkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(privkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_privkey_tweak_add(byteBuff,Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] privArr = retByteArray[0];
+
+        int privLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(privArr.length, privLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return privArr;
+    }
+
+    /**
+     * libsecp256k1 PubKey Tweak-Add - Tweak pubkey by adding to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param pubkey 32-byte seckey
+     */
+    public static byte[] pubKeyTweakAdd(byte[] pubkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(pubkey.length == 33 || pubkey.length == 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < pubkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(pubkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(pubkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_pubkey_tweak_add(byteBuff,Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+
+        int pubLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return pubArr;
+    }
+
+    /**
+     * libsecp256k1 PubKey Tweak-Mul - Tweak pubkey by multiplying to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param pubkey 32-byte seckey
+     */
+    public static byte[] pubKeyTweakMul(byte[] pubkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(pubkey.length == 33 || pubkey.length == 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < pubkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(pubkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(pubkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_pubkey_tweak_mul(byteBuff,Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+
+        int pubLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return pubArr;
+    }
+
+    /**
+     * libsecp256k1 create ECDH secret - constant time ECDH calculation
+     *
+     * @param seckey byte array of secret key used in exponentiaion
+     * @param pubkey byte array of public key used in exponentiaion
+     */
+    public static byte[] createECDHSecret(byte[] seckey, byte[] pubkey) throws AssertFailException{
+        Preconditions.checkArgument(seckey.length <= 32 && pubkey.length <= 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < 32 + pubkey.length) {
+            byteBuff = ByteBuffer.allocateDirect(32 + pubkey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+        byteBuff.put(pubkey);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_ecdh(byteBuff, Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] resArr = retByteArray[0];
+        int retVal = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+
+        assertEquals(resArr.length, 32, "Got bad result length.");
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return resArr;
+    }
+
+    /**
+     * libsecp256k1 randomize - updates the context randomization
+     *
+     * @param seed 32-byte random seed
+     */
+    public static synchronized boolean randomize(byte[] seed) throws AssertFailException{
+        Preconditions.checkArgument(seed.length == 32 || seed == null);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seed.length) {
+            byteBuff = ByteBuffer.allocateDirect(seed.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seed);
+
+        w.lock();
+        try {
+          return secp256k1_context_randomize(byteBuff, Secp256k1Context.getContext()) == 1;
+        } finally {
+          w.unlock();
+        }
+    }
+
+    private static native long secp256k1_ctx_clone(long context);
+
+    private static native int secp256k1_context_randomize(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_privkey_tweak_add(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_privkey_tweak_mul(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_pubkey_tweak_add(ByteBuffer byteBuff, long context, int pubLen);
+
+    private static native byte[][] secp256k1_pubkey_tweak_mul(ByteBuffer byteBuff, long context, int pubLen);
+
+    private static native void secp256k1_destroy_context(long context);
+
+    private static native int secp256k1_ecdsa_verify(ByteBuffer byteBuff, long context, int sigLen, int pubLen);
+
+    private static native byte[][] secp256k1_ecdsa_sign(ByteBuffer byteBuff, long context);
+
+    private static native int secp256k1_ec_seckey_verify(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_ec_pubkey_create(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_ec_pubkey_parse(ByteBuffer byteBuff, long context, int inputLen);
+
+    private static native byte[][] secp256k1_ecdh(ByteBuffer byteBuff, long context, int inputLen);
+
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java
new file mode 100644
index 000000000..c00d08899
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java
@@ -0,0 +1,226 @@
+package org.bitcoin;
+
+import com.google.common.io.BaseEncoding;
+import java.util.Arrays;
+import java.math.BigInteger;
+import javax.xml.bind.DatatypeConverter;
+import static org.bitcoin.NativeSecp256k1Util.*;
+
+/**
+ * This class holds test cases defined for testing this library.
+ */
+public class NativeSecp256k1Test {
+
+    //TODO improve comments/add more tests
+    /**
+      * This tests verify() for a valid signature
+      */
+    public static void testVerifyPos() throws AssertFailException{
+        boolean result = false;
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sig = BaseEncoding.base16().lowerCase().decode("3044022079BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F817980220294F14E883B3F525B5367756C2A11EF6CF84B730B36C17CB0C56F0AAB2C98589".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        result = NativeSecp256k1.verify( data, sig, pub);
+        assertEquals( result, true , "testVerifyPos");
+    }
+
+    /**
+      * This tests verify() for a non-valid signature
+      */
+    public static void testVerifyNeg() throws AssertFailException{
+        boolean result = false;
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A91".toLowerCase()); //sha256hash of "testing"
+        byte[] sig = BaseEncoding.base16().lowerCase().decode("3044022079BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F817980220294F14E883B3F525B5367756C2A11EF6CF84B730B36C17CB0C56F0AAB2C98589".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        result = NativeSecp256k1.verify( data, sig, pub);
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, false , "testVerifyNeg");
+    }
+
+    /**
+      * This tests secret key verify() for a valid secretkey
+      */
+    public static void testSecKeyVerifyPos() throws AssertFailException{
+        boolean result = false;
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        result = NativeSecp256k1.secKeyVerify( sec );
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, true , "testSecKeyVerifyPos");
+    }
+
+    /**
+      * This tests secret key verify() for a invalid secretkey
+      */
+    public static void testSecKeyVerifyNeg() throws AssertFailException{
+        boolean result = false;
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+        result = NativeSecp256k1.secKeyVerify( sec );
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, false , "testSecKeyVerifyNeg");
+    }
+
+    /**
+      * This tests public key create() for a valid secretkey
+      */
+    public static void testPubKeyCreatePos() throws AssertFailException{
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.computePubkey( sec);
+        String pubkeyString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( pubkeyString , "04C591A8FF19AC9C4E4E5793673B83123437E975285E7B442F4EE2654DFFCA5E2D2103ED494718C697AC9AEBCFD19612E224DB46661011863ED2FC54E71861E2A6" , "testPubKeyCreatePos");
+    }
+
+    /**
+      * This tests public key create() for a invalid secretkey
+      */
+    public static void testPubKeyCreateNeg() throws AssertFailException{
+       byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+       byte[] resultArr = NativeSecp256k1.computePubkey( sec);
+       String pubkeyString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+       assertEquals( pubkeyString, "" , "testPubKeyCreateNeg");
+    }
+
+    /**
+      * This tests sign() for a valid secretkey
+      */
+    public static void testSignPos() throws AssertFailException{
+
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.sign(data, sec);
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString, "30440220182A108E1448DC8F1FB467D06A0F3BB8EA0533584CB954EF8DA112F1D60E39A202201C66F36DA211C087F3AF88B50EDF4F9BDAA6CF5FD6817E74DCA34DB12390C6E9" , "testSignPos");
+    }
+
+    /**
+      * This tests sign() for a invalid secretkey
+      */
+    public static void testSignNeg() throws AssertFailException{
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.sign(data, sec);
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString, "" , "testSignNeg");
+    }
+
+    /**
+      * This tests private key tweak-add
+      */
+    public static void testPrivKeyTweakAdd_1() throws AssertFailException {
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.privKeyTweakAdd( sec , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "A168571E189E6F9A7E2D657A4B53AE99B909F7E712D1C23CED28093CD57C88F3" , "testPrivKeyAdd_1");
+    }
+
+    /**
+      * This tests private key tweak-mul
+      */
+    public static void testPrivKeyTweakMul_1() throws AssertFailException {
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.privKeyTweakMul( sec , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "97F8184235F101550F3C71C927507651BD3F1CDB4A5A33B8986ACF0DEE20FFFC" , "testPrivKeyMul_1");
+    }
+
+    /**
+      * This tests private key tweak-add uncompressed
+      */
+    public static void testPrivKeyTweakAdd_2() throws AssertFailException {
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.pubKeyTweakAdd( pub , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "0411C6790F4B663CCE607BAAE08C43557EDC1A4D11D88DFCB3D841D0C6A941AF525A268E2A863C148555C48FB5FBA368E88718A46E205FABC3DBA2CCFFAB0796EF" , "testPrivKeyAdd_2");
+    }
+
+    /**
+      * This tests private key tweak-mul uncompressed
+      */
+    public static void testPrivKeyTweakMul_2() throws AssertFailException {
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.pubKeyTweakMul( pub , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "04E0FE6FE55EBCA626B98A807F6CAF654139E14E5E3698F01A9A658E21DC1D2791EC060D4F412A794D5370F672BC94B722640B5F76914151CFCA6E712CA48CC589" , "testPrivKeyMul_2");
+    }
+
+    /**
+      * This tests seed randomization
+      */
+    public static void testRandomize() throws AssertFailException {
+        byte[] seed = BaseEncoding.base16().lowerCase().decode("A441B15FE9A3CF56661190A0B93B9DEC7D04127288CC87250967CF3B52894D11".toLowerCase()); //sha256hash of "random"
+        boolean result = NativeSecp256k1.randomize(seed);
+        assertEquals( result, true, "testRandomize");
+    }
+
+    public static void testCreateECDHSecret() throws AssertFailException{
+
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.createECDHSecret(sec, pub);
+        String ecdhString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( ecdhString, "2A2A67007A926E6594AF3EB564FC74005B37A9C8AEF2033C4552051B5C87F043" , "testCreateECDHSecret");
+    }
+
+    public static void main(String[] args) throws AssertFailException{
+
+
+        System.out.println("\n libsecp256k1 enabled: " + Secp256k1Context.isEnabled() + "\n");
+
+        assertEquals( Secp256k1Context.isEnabled(), true, "isEnabled" );
+
+        //Test verify() success/fail
+        testVerifyPos();
+        testVerifyNeg();
+
+        //Test secKeyVerify() success/fail
+        testSecKeyVerifyPos();
+        testSecKeyVerifyNeg();
+
+        //Test computePubkey() success/fail
+        testPubKeyCreatePos();
+        testPubKeyCreateNeg();
+
+        //Test sign() success/fail
+        testSignPos();
+        testSignNeg();
+
+        //Test privKeyTweakAdd() 1
+        testPrivKeyTweakAdd_1();
+
+        //Test privKeyTweakMul() 2
+        testPrivKeyTweakMul_1();
+
+        //Test privKeyTweakAdd() 3
+        testPrivKeyTweakAdd_2();
+
+        //Test privKeyTweakMul() 4
+        testPrivKeyTweakMul_2();
+
+        //Test randomize()
+        testRandomize();
+
+        //Test ECDH
+        testCreateECDHSecret();
+
+        NativeSecp256k1.cleanup();
+
+        System.out.println(" All tests passed." );
+
+    }
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java
new file mode 100644
index 000000000..04732ba04
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java
@@ -0,0 +1,45 @@
+/*
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.bitcoin;
+
+public class NativeSecp256k1Util{
+
+    public static void assertEquals( int val, int val2, String message ) throws AssertFailException{
+      if( val != val2 )
+        throw new AssertFailException("FAIL: " + message);
+    }
+
+    public static void assertEquals( boolean val, boolean val2, String message ) throws AssertFailException{
+      if( val != val2 )
+        throw new AssertFailException("FAIL: " + message);
+      else
+        System.out.println("PASS: " + message);
+    }
+
+    public static void assertEquals( String val, String val2, String message ) throws AssertFailException{
+      if( !val.equals(val2) )
+        throw new AssertFailException("FAIL: " + message);
+      else
+        System.out.println("PASS: " + message);
+    }
+
+    public static class AssertFailException extends Exception {
+      public AssertFailException(String message) {
+        super( message );
+      }
+    }
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/Secp256k1Context.java b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/Secp256k1Context.java
new file mode 100644
index 000000000..216c986a8
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org/bitcoin/Secp256k1Context.java
@@ -0,0 +1,51 @@
+/*
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.bitcoin;
+
+/**
+ * This class holds the context reference used in native methods 
+ * to handle ECDSA operations.
+ */
+public class Secp256k1Context {
+  private static final boolean enabled; //true if the library is loaded
+  private static final long context; //ref to pointer to context obj
+
+  static { //static initializer
+      boolean isEnabled = true;
+      long contextRef = -1;
+      try {
+          System.loadLibrary("secp256k1");
+          contextRef = secp256k1_init_context();
+      } catch (UnsatisfiedLinkError e) {
+          System.out.println("UnsatisfiedLinkError: " + e.toString());
+          isEnabled = false;
+      }
+      enabled = isEnabled;
+      context = contextRef;
+  }
+
+  public static boolean isEnabled() {
+     return enabled;
+  }
+
+  public static long getContext() {
+     if(!enabled) return -1; //sanity check
+     return context;
+  }
+
+  private static native long secp256k1_init_context();
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.c
new file mode 100644
index 000000000..bcef7b32c
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.c
@@ -0,0 +1,377 @@
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+#include "org_bitcoin_NativeSecp256k1.h"
+#include "include/secp256k1.h"
+#include "include/secp256k1_ecdh.h"
+#include "include/secp256k1_recovery.h"
+
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ctx_1clone
+  (JNIEnv* env, jclass classObject, jlong ctx_l)
+{
+  const secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  jlong ctx_clone_l = (uintptr_t) secp256k1_context_clone(ctx);
+
+  (void)classObject;(void)env;
+
+  return ctx_clone_l;
+
+}
+
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1context_1randomize
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  const unsigned char* seed = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  (void)classObject;
+
+  return secp256k1_context_randomize(ctx, seed);
+
+}
+
+SECP256K1_API void JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1destroy_1context
+  (JNIEnv* env, jclass classObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  secp256k1_context_destroy(ctx);
+
+  (void)classObject;(void)env;
+}
+
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint siglen, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* sigdata = {  (unsigned char*) (data + 32) };
+  const unsigned char* pubdata = { (unsigned char*) (data + siglen + 32) };
+
+  secp256k1_ecdsa_signature sig;
+  secp256k1_pubkey pubkey;
+
+  int ret = secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigdata, siglen);
+
+  if( ret ) {
+    ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pubdata, publen);
+
+    if( ret ) {
+      ret = secp256k1_ecdsa_verify(ctx, &sig, data, &pubkey);
+    }
+  }
+
+  (void)classObject;
+
+  return ret;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1sign
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  unsigned char* secKey = (unsigned char*) (data + 32);
+
+  jobjectArray retArray;
+  jbyteArray sigArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  secp256k1_ecdsa_signature sig[72];
+
+  int ret = secp256k1_ecdsa_sign(ctx, sig, data, secKey, NULL, NULL );
+
+  unsigned char outputSer[72];
+  size_t outputLen = 72;
+
+  if( ret ) {
+    int ret2 = secp256k1_ecdsa_signature_serialize_der(ctx,outputSer, &outputLen, sig ); (void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  sigArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, sigArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, sigArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1seckey_1verify
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* secKey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  (void)classObject;
+
+  return secp256k1_ec_seckey_verify(ctx, secKey);
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1create
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  const unsigned char* secKey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  secp256k1_pubkey pubkey;
+
+  jobjectArray retArray;
+  jbyteArray pubkeyArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int ret = secp256k1_ec_pubkey_create(ctx, &pubkey, secKey);
+
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubkeyArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubkeyArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubkeyArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1add
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* privkey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (privkey + 32);
+
+  jobjectArray retArray;
+  jbyteArray privArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int privkeylen = 32;
+
+  int ret = secp256k1_ec_privkey_tweak_add(ctx, privkey, tweak);
+
+  intsarray[0] = privkeylen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  privArray = (*env)->NewByteArray(env, privkeylen);
+  (*env)->SetByteArrayRegion(env, privArray, 0, privkeylen, (jbyte*)privkey);
+  (*env)->SetObjectArrayElement(env, retArray, 0, privArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1mul
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* privkey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (privkey + 32);
+
+  jobjectArray retArray;
+  jbyteArray privArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int privkeylen = 32;
+
+  int ret = secp256k1_ec_privkey_tweak_mul(ctx, privkey, tweak);
+
+  intsarray[0] = privkeylen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  privArray = (*env)->NewByteArray(env, privkeylen);
+  (*env)->SetByteArrayRegion(env, privArray, 0, privkeylen, (jbyte*)privkey);
+  (*env)->SetObjectArrayElement(env, retArray, 0, privArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1add
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+/*  secp256k1_pubkey* pubkey = (secp256k1_pubkey*) (*env)->GetDirectBufferAddress(env, byteBufferObject);*/
+  unsigned char* pkey = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (pkey + publen);
+
+  jobjectArray retArray;
+  jbyteArray pubArray, intsByteArray;
+  unsigned char intsarray[2];
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  secp256k1_pubkey pubkey;
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pkey, publen);
+
+  if( ret ) {
+    ret = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, tweak);
+  }
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1mul
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* pkey = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (pkey + publen);
+
+  jobjectArray retArray;
+  jbyteArray pubArray, intsByteArray;
+  unsigned char intsarray[2];
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  secp256k1_pubkey pubkey;
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pkey, publen);
+
+  if ( ret ) {
+    ret = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, tweak);
+  }
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1pubkey_1combine
+  (JNIEnv * env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint numkeys)
+{
+  (void)classObject;(void)env;(void)byteBufferObject;(void)ctx_l;(void)numkeys;
+
+  return 0;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdh
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  const unsigned char* secdata = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* pubdata = (const unsigned char*) (secdata + 32);
+
+  jobjectArray retArray;
+  jbyteArray outArray, intsByteArray;
+  unsigned char intsarray[1];
+  secp256k1_pubkey pubkey;
+  unsigned char nonce_res[32];
+  size_t outputLen = 32;
+
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pubdata, publen);
+
+  if (ret) {
+    ret = secp256k1_ecdh(
+      ctx,
+      nonce_res,
+      &pubkey,
+      secdata
+    );
+  }
+
+  intsarray[0] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  outArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, outArray, 0, 32, (jbyte*)nonce_res);
+  (*env)->SetObjectArrayElement(env, retArray, 0, outArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 1);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 1, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.h
new file mode 100644
index 000000000..fe613c9e9
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_NativeSecp256k1.h
@@ -0,0 +1,119 @@
+/* DO NOT EDIT THIS FILE - it is machine generated */
+#include <jni.h>
+#include "include/secp256k1.h"
+/* Header for class org_bitcoin_NativeSecp256k1 */
+
+#ifndef _Included_org_bitcoin_NativeSecp256k1
+#define _Included_org_bitcoin_NativeSecp256k1
+#ifdef __cplusplus
+extern "C" {
+#endif
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ctx_clone
+ * Signature: (J)J
+ */
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ctx_1clone
+  (JNIEnv *, jclass, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_context_randomize
+ * Signature: (Ljava/nio/ByteBuffer;J)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1context_1randomize
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_privkey_tweak_add
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1add
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_privkey_tweak_mul
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1mul
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_pubkey_tweak_add
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1add
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_pubkey_tweak_mul
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1mul
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_destroy_context
+ * Signature: (J)V
+ */
+SECP256K1_API void JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1destroy_1context
+  (JNIEnv *, jclass, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ecdsa_verify
+ * Signature: (Ljava/nio/ByteBuffer;JII)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
+  (JNIEnv *, jclass, jobject, jlong, jint, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ecdsa_sign
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1sign
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_seckey_verify
+ * Signature: (Ljava/nio/ByteBuffer;J)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1seckey_1verify
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_pubkey_create
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1create
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_pubkey_parse
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1parse
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ecdh
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdh
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen);
+
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.c
new file mode 100644
index 000000000..a52939e7e
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.c
@@ -0,0 +1,15 @@
+#include <stdlib.h>
+#include <stdint.h>
+#include "org_bitcoin_Secp256k1Context.h"
+#include "include/secp256k1.h"
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_Secp256k1Context_secp256k1_1init_1context
+  (JNIEnv* env, jclass classObject)
+{
+  secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+  (void)classObject;(void)env;
+
+  return (uintptr_t)ctx;
+}
+
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.h
new file mode 100644
index 000000000..0d2bc84b7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/java/org_bitcoin_Secp256k1Context.h
@@ -0,0 +1,22 @@
+/* DO NOT EDIT THIS FILE - it is machine generated */
+#include <jni.h>
+#include "include/secp256k1.h"
+/* Header for class org_bitcoin_Secp256k1Context */
+
+#ifndef _Included_org_bitcoin_Secp256k1Context
+#define _Included_org_bitcoin_Secp256k1Context
+#ifdef __cplusplus
+extern "C" {
+#endif
+/*
+ * Class:     org_bitcoin_Secp256k1Context
+ * Method:    secp256k1_init_context
+ * Signature: ()J
+ */
+SECP256K1_API jlong JNICALL Java_org_bitcoin_Secp256k1Context_secp256k1_1init_1context
+  (JNIEnv *, jclass);
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/Makefile.am.include b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/Makefile.am.include
new file mode 100644
index 000000000..e3088b469
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/Makefile.am.include
@@ -0,0 +1,8 @@
+include_HEADERS += include/secp256k1_ecdh.h
+noinst_HEADERS += src/modules/ecdh/main_impl.h
+noinst_HEADERS += src/modules/ecdh/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_ecdh
+bench_ecdh_SOURCES = src/bench_ecdh.c
+bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
+endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h
new file mode 100644
index 000000000..9e30fb73d
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h
@@ -0,0 +1,54 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_MAIN_
+#define _SECP256K1_MODULE_ECDH_MAIN_
+
+#include "include/secp256k1_ecdh.h"
+#include "ecmult_const_impl.h"
+
+int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const secp256k1_pubkey *point, const unsigned char *scalar) {
+    int ret = 0;
+    int overflow = 0;
+    secp256k1_gej res;
+    secp256k1_ge pt;
+    secp256k1_scalar s;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(result != NULL);
+    ARG_CHECK(point != NULL);
+    ARG_CHECK(scalar != NULL);
+
+    secp256k1_pubkey_load(ctx, &pt, point);
+    secp256k1_scalar_set_b32(&s, scalar, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&s)) {
+        ret = 0;
+    } else {
+        unsigned char x[32];
+        unsigned char y[1];
+        secp256k1_sha256_t sha;
+
+        secp256k1_ecmult_const(&res, &pt, &s);
+        secp256k1_ge_set_gej(&pt, &res);
+        /* Compute a hash of the point in compressed form
+         * Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not
+         * expect its output to be secret and has a timing sidechannel. */
+        secp256k1_fe_normalize(&pt.x);
+        secp256k1_fe_normalize(&pt.y);
+        secp256k1_fe_get_b32(x, &pt.x);
+        y[0] = 0x02 | secp256k1_fe_is_odd(&pt.y);
+
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, y, sizeof(y));
+        secp256k1_sha256_write(&sha, x, sizeof(x));
+        secp256k1_sha256_finalize(&sha, result);
+        ret = 1;
+    }
+
+    secp256k1_scalar_clear(&s);
+    return ret;
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h
new file mode 100644
index 000000000..85a5d0a9a
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h
@@ -0,0 +1,105 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_TESTS_
+#define _SECP256K1_MODULE_ECDH_TESTS_
+
+void test_ecdh_api(void) {
+    /* Setup context that just counts errors */
+    secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_pubkey point;
+    unsigned char res[32];
+    unsigned char s_one[32] = { 0 };
+    int32_t ecount = 0;
+    s_one[31] = 1;
+
+    secp256k1_context_set_error_callback(tctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(tctx, counting_illegal_callback_fn, &ecount);
+    CHECK(secp256k1_ec_pubkey_create(tctx, &point, s_one) == 1);
+
+    /* Check all NULLs are detected */
+    CHECK(secp256k1_ecdh(tctx, res, &point, s_one) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ecdh(tctx, NULL, &point, s_one) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdh(tctx, res, NULL, s_one) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdh(tctx, res, &point, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdh(tctx, res, &point, s_one) == 1);
+    CHECK(ecount == 3);
+
+    /* Cleanup */
+    secp256k1_context_destroy(tctx);
+}
+
+void test_ecdh_generator_basepoint(void) {
+    unsigned char s_one[32] = { 0 };
+    secp256k1_pubkey point[2];
+    int i;
+
+    s_one[31] = 1;
+    /* Check against pubkey creation when the basepoint is the generator */
+    for (i = 0; i < 100; ++i) {
+        secp256k1_sha256_t sha;
+        unsigned char s_b32[32];
+        unsigned char output_ecdh[32];
+        unsigned char output_ser[32];
+        unsigned char point_ser[33];
+        size_t point_ser_len = sizeof(point_ser);
+        secp256k1_scalar s;
+
+        random_scalar_order(&s);
+        secp256k1_scalar_get_b32(s_b32, &s);
+
+        /* compute using ECDH function */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[0], s_one) == 1);
+        CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32) == 1);
+        /* compute "explicitly" */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[1], s_b32) == 1);
+        CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
+        CHECK(point_ser_len == sizeof(point_ser));
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, point_ser, point_ser_len);
+        secp256k1_sha256_finalize(&sha, output_ser);
+        /* compare */
+        CHECK(memcmp(output_ecdh, output_ser, sizeof(output_ser)) == 0);
+    }
+}
+
+void test_bad_scalar(void) {
+    unsigned char s_zero[32] = { 0 };
+    unsigned char s_overflow[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+    };
+    unsigned char s_rand[32] = { 0 };
+    unsigned char output[32];
+    secp256k1_scalar rand;
+    secp256k1_pubkey point;
+
+    /* Create random point */
+    random_scalar_order(&rand);
+    secp256k1_scalar_get_b32(s_rand, &rand);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_rand) == 1);
+
+    /* Try to multiply it by bad values */
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_zero) == 0);
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 0);
+    /* ...and a good one */
+    s_overflow[31] -= 1;
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 1);
+}
+
+void run_ecdh_tests(void) {
+    test_ecdh_api();
+    test_ecdh_generator_basepoint();
+    test_bad_scalar();
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/Makefile.am.include b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/Makefile.am.include
new file mode 100644
index 000000000..bf23c26e7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/Makefile.am.include
@@ -0,0 +1,8 @@
+include_HEADERS += include/secp256k1_recovery.h
+noinst_HEADERS += src/modules/recovery/main_impl.h
+noinst_HEADERS += src/modules/recovery/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_recover
+bench_recover_SOURCES = src/bench_recover.c
+bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
+endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/main_impl.h
new file mode 100755
index 000000000..c6fbe2398
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/main_impl.h
@@ -0,0 +1,193 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_MAIN_
+#define _SECP256K1_MODULE_RECOVERY_MAIN_
+
+#include "include/secp256k1_recovery.h"
+
+static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+    *recid = sig->data[64];
+}
+
+static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+    sig->data[64] = recid;
+}
+
+int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) {
+    secp256k1_scalar r, s;
+    int ret = 1;
+    int overflow = 0;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+    ARG_CHECK(recid >= 0 && recid <= 3);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid);
+    } else {
+        memset(sig, 0, sizeof(*sig));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(recid != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) {
+    secp256k1_scalar r, s;
+    int recid;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin);
+    secp256k1_ecdsa_signature_save(sig, &r, &s);
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
+    unsigned char brx[32];
+    secp256k1_fe fx;
+    secp256k1_ge x;
+    secp256k1_gej xj;
+    secp256k1_scalar rn, u1, u2;
+    secp256k1_gej qj;
+    int r;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_get_b32(brx, sigr);
+    r = secp256k1_fe_set_b32(&fx, brx);
+    (void)r;
+    VERIFY_CHECK(r); /* brx comes from a scalar, so is less than the order; certainly less than p */
+    if (recid & 2) {
+        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+            return 0;
+        }
+        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
+    }
+    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&xj, &x);
+    secp256k1_scalar_inverse_var(&rn, sigr);
+    secp256k1_scalar_mul(&u1, &rn, message);
+    secp256k1_scalar_negate(&u1, &u1);
+    secp256k1_scalar_mul(&u2, &rn, sigs);
+    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
+    secp256k1_ge_set_gej_var(pubkey, &qj);
+    return !secp256k1_gej_is_infinity(&qj);
+}
+
+int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int recid;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        memset(nonce32, 0, 32);
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    int recid;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
+    VERIFY_CHECK(recid >= 0 && recid < 4);  /* should have been caught in parse_compact */
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
+        secp256k1_pubkey_save(pubkey, &q);
+        return 1;
+    } else {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/tests_impl.h
new file mode 100644
index 000000000..765c7dd81
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/recovery/tests_impl.h
@@ -0,0 +1,393 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_TESTS_
+#define _SECP256K1_MODULE_RECOVERY_TESTS_
+
+static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    (void) msg32;
+    (void) key32;
+    (void) algo16;
+    (void) data;
+
+    /* On the first run, return 0 to force a second run */
+    if (counter == 0) {
+        memset(nonce32, 0, 32);
+        return 1;
+    }
+    /* On the second run, return an overflow to force a third run */
+    if (counter == 1) {
+        memset(nonce32, 0xff, 32);
+        return 1;
+    }
+    /* On the next run, return a valid nonce, but flip a coin as to whether or not to fail signing. */
+    memset(nonce32, 1, 32);
+    return secp256k1_rand_bits(1);
+}
+
+void test_ecdsa_recovery_api(void) {
+    /* Setup contexts that just count errors */
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey recpubkey;
+    secp256k1_ecdsa_signature normal_sig;
+    secp256k1_ecdsa_recoverable_signature recsig;
+    unsigned char privkey[32] = { 1 };
+    unsigned char message[32] = { 2 };
+    int32_t ecount = 0;
+    int recid = 0;
+    unsigned char sig[74];
+    unsigned char zero_privkey[32] = { 0 };
+    unsigned char over_privkey[32] = { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+                                       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+                                       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+                                       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff };
+
+    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Check bad contexts and NULLs for signing */
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_sign_recoverable(none, &recsig, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(sign, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(vrfy, &recsig, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, NULL, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, NULL, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, NULL, NULL, NULL) == 0);
+    CHECK(ecount == 5);
+    /* This will fail or succeed randomly, and in either case will not ARG_CHECK failure */
+    secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, recovery_test_nonce_function, NULL);
+    CHECK(ecount == 5);
+    /* These will all fail, but not in ARG_CHECK way */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, zero_privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, over_privkey, NULL, NULL) == 0);
+    /* This one will succeed. */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 5);
+
+    /* Check signing with a goofy nonce function */
+
+    /* Check bad contexts and NULLs for recovery */
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recover(none, &recpubkey, &recsig, message) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recover(sign, &recpubkey, &recsig, message) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(vrfy, &recpubkey, &recsig, message) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, message) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(both, NULL, &recsig, message) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, NULL, message) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, NULL) == 0);
+    CHECK(ecount == 5);
+
+    /* Check NULLs for conversion */
+    CHECK(secp256k1_ecdsa_sign(both, &normal_sig, message, privkey, NULL, NULL) == 1);
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, NULL, &recsig) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, &recsig) == 1);
+
+    /* Check NULLs for de/serialization */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, NULL, &recid, &recsig) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, NULL, &recsig) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, &recsig) == 1);
+
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, NULL, sig, recid) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, NULL, recid) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, -1) == 0);
+    CHECK(ecount == 6);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, 5) == 0);
+    CHECK(ecount == 7);
+    /* overflow in signature will fail but not affect ecount */
+    memcpy(sig, over_privkey, 32);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, recid) == 0);
+    CHECK(ecount == 7);
+
+    /* cleanup */
+    secp256k1_context_destroy(none);
+    secp256k1_context_destroy(sign);
+    secp256k1_context_destroy(vrfy);
+    secp256k1_context_destroy(both);
+}
+
+void test_ecdsa_recovery_end_to_end(void) {
+    unsigned char extra[32] = {0x00};
+    unsigned char privkey[32];
+    unsigned char message[32];
+    secp256k1_ecdsa_signature signature[5];
+    secp256k1_ecdsa_recoverable_signature rsignature[5];
+    unsigned char sig[74];
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey recpubkey;
+    int recid = 0;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar msg, key;
+        random_scalar_order_test(&msg);
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_scalar_get_b32(message, &msg);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Serialize/parse compact and verify/recover. */
+    extra[0] = 0;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[4], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[1], message, privkey, NULL, extra) == 1);
+    extra[31] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[2], message, privkey, NULL, extra) == 1);
+    extra[31] = 0;
+    extra[0] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(memcmp(&signature[4], &signature[0], 64) == 0);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    memset(&rsignature[4], 0, sizeof(rsignature[4]));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    /* Parse compact (with recovery id) and recover. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1);
+    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    /* Serialize/destroy/parse signature and verify again. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    sig[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0);
+    /* Recover again */
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 ||
+          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+}
+
+/* Tests several edge cases. */
+void test_ecdsa_recovery_edge_cases(void) {
+    const unsigned char msg32[32] = {
+        'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
+        'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
+        'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
+        's', 's', 'a', 'g', 'e', '.', '.', '.'
+    };
+    const unsigned char sig64[64] = {
+        /* Generated by signing the above message with nonce 'This is the nonce we will use...'
+         * and secret key 0 (which is not valid), resulting in recid 0. */
+        0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
+        0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
+        0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
+        0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
+        0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
+        0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
+        0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
+        0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
+    };
+    secp256k1_pubkey pubkey;
+    /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
+    const unsigned char sigb64[64] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+    };
+    secp256k1_pubkey pubkeyb;
+    secp256k1_ecdsa_recoverable_signature rsig;
+    secp256k1_ecdsa_signature sig;
+    int recid;
+
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 0));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 1));
+    CHECK(secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 2));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 3));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+
+    for (recid = 0; recid < 4; recid++) {
+        int i;
+        int recid2;
+        /* (4,4) encoded in DER. */
+        unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
+        unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
+        unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
+        unsigned char sigbderalt1[39] = {
+            0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt2[39] = {
+            0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        unsigned char sigbderalt3[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt4[40] = {
+            0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        /* (order + r,4) encoded in DER. */
+        unsigned char sigbderlong[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
+            0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
+            0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
+        };
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        for (recid2 = 0; recid2 < 4; recid2++) {
+            secp256k1_pubkey pubkey2b;
+            CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid2) == 1);
+            CHECK(secp256k1_ecdsa_recover(ctx, &pubkey2b, &rsig, msg32) == 1);
+            /* Verifying with (order + r,4) should always fail. */
+            CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderlong, sizeof(sigbderlong)) == 1);
+            CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        }
+        /* DER parsing tests. */
+        /* Zero length r/s. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0);
+        /* Leading zeros. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt1, sizeof(sigbderalt1)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt2, sizeof(sigbderalt2)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0);
+        sigbderalt3[4] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        sigbderalt4[7] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        /* Damage signature. */
+        sigbder[7]++;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        sigbder[7]--;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, 6) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder) - 1) == 0);
+        for(i = 0; i < 8; i++) {
+            int c;
+            unsigned char orig = sigbder[i];
+            /*Try every single-byte change.*/
+            for (c = 0; c < 256; c++) {
+                if (c == orig ) {
+                    continue;
+                }
+                sigbder[i] = c;
+                CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+            }
+            sigbder[i] = orig;
+        }
+    }
+
+    /* Test r/s equal to zero */
+    {
+        /* (1,1) encoded in DER. */
+        unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01};
+        unsigned char sigc64[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        secp256k1_pubkey pubkeyc;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyc, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 1);
+        sigcder[4] = 0;
+        sigc64[31] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+        sigcder[4] = 1;
+        sigcder[7] = 0;
+        sigc64[31] = 1;
+        sigc64[63] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+    }
+}
+
+void run_recovery_tests(void) {
+    int i;
+    for (i = 0; i < count; i++) {
+        test_ecdsa_recovery_api();
+    }
+    for (i = 0; i < 64*count; i++) {
+        test_ecdsa_recovery_end_to_end();
+    }
+    test_ecdsa_recovery_edge_cases();
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num.h
new file mode 100644
index 000000000..eff842200
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num.h
@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_NUM_
+#define _SECP256K1_NUM_
+
+#ifndef USE_NUM_NONE
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(USE_NUM_GMP)
+#include "num_gmp.h"
+#else
+#error "Please select num implementation"
+#endif
+
+/** Copy a number. */
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
+
+/** Convert a number's absolute value to a binary big-endian string.
+ *  There must be enough place. */
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a);
+
+/** Set a number to the value of a binary big-endian string. */
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen);
+
+/** Compute a modular inverse. The input must be less than the modulus. */
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
+
+/** Compute the jacobi symbol (a|b). b must be positive and odd. */
+static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Compare the absolute value of two numbers. */
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Test whether two number are equal (including sign). */
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
+
+/** Add two (signed) numbers. */
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Subtract two (signed) numbers. */
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Multiply two (signed) numbers. */
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
+
+/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
+    even if r was negative. */
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
+
+/** Right-shift the passed number by bits. */
+static void secp256k1_num_shift(secp256k1_num *r, int bits);
+
+/** Check whether a number is zero. */
+static int secp256k1_num_is_zero(const secp256k1_num *a);
+
+/** Check whether a number is one. */
+static int secp256k1_num_is_one(const secp256k1_num *a);
+
+/** Check whether a number is strictly negative. */
+static int secp256k1_num_is_neg(const secp256k1_num *a);
+
+/** Change a number's sign. */
+static void secp256k1_num_negate(secp256k1_num *r);
+
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp.h
new file mode 100644
index 000000000..7dd813088
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp.h
@@ -0,0 +1,20 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_NUM_REPR_
+#define _SECP256K1_NUM_REPR_
+
+#include <gmp.h>
+
+#define NUM_LIMBS ((256+GMP_NUMB_BITS-1)/GMP_NUMB_BITS)
+
+typedef struct {
+    mp_limb_t data[2*NUM_LIMBS];
+    int neg;
+    int limbs;
+} secp256k1_num;
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp_impl.h
new file mode 100644
index 000000000..3a46495ee
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_gmp_impl.h
@@ -0,0 +1,288 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_NUM_REPR_IMPL_H_
+#define _SECP256K1_NUM_REPR_IMPL_H_
+
+#include <string.h>
+#include <stdlib.h>
+#include <gmp.h>
+
+#include "util.h"
+#include "num.h"
+
+#ifdef VERIFY
+static void secp256k1_num_sanity(const secp256k1_num *a) {
+    VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
+}
+#else
+#define secp256k1_num_sanity(a) do { } while(0)
+#endif
+
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
+    *r = *a;
+}
+
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
+    unsigned char tmp[65];
+    int len = 0;
+    int shift = 0;
+    if (a->limbs>1 || a->data[0] != 0) {
+        len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
+    }
+    while (shift < len && tmp[shift] == 0) shift++;
+    VERIFY_CHECK(len-shift <= (int)rlen);
+    memset(r, 0, rlen - len + shift);
+    if (len > shift) {
+        memcpy(r + rlen - len + shift, tmp + shift, len - shift);
+    }
+    memset(tmp, 0, sizeof(tmp));
+}
+
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) {
+    int len;
+    VERIFY_CHECK(alen > 0);
+    VERIFY_CHECK(alen <= 64);
+    len = mpn_set_str(r->data, a, alen, 256);
+    if (len == 0) {
+        r->data[0] = 0;
+        len = 1;
+    }
+    VERIFY_CHECK(len <= NUM_LIMBS*2);
+    r->limbs = len;
+    r->neg = 0;
+    while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+        r->limbs--;
+    }
+}
+
+static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
+    r->limbs = a->limbs;
+    if (c != 0) {
+        VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
+        r->data[r->limbs++] = c;
+    }
+}
+
+static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
+    (void)c;
+    VERIFY_CHECK(c == 0);
+    r->limbs = a->limbs;
+    while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+        r->limbs--;
+    }
+}
+
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
+    secp256k1_num_sanity(r);
+    secp256k1_num_sanity(m);
+
+    if (r->limbs >= m->limbs) {
+        mp_limb_t t[2*NUM_LIMBS];
+        mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
+        memset(t, 0, sizeof(t));
+        r->limbs = m->limbs;
+        while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+            r->limbs--;
+        }
+    }
+
+    if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
+        secp256k1_num_sub_abs(r, m, r);
+        r->neg = 0;
+    }
+}
+
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
+    int i;
+    mp_limb_t g[NUM_LIMBS+1];
+    mp_limb_t u[NUM_LIMBS+1];
+    mp_limb_t v[NUM_LIMBS+1];
+    mp_size_t sn;
+    mp_size_t gn;
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(m);
+
+    /** mpn_gcdext computes: (G,S) = gcdext(U,V), where
+     *  * G = gcd(U,V)
+     *  * G = U*S + V*T
+     *  * U has equal or more limbs than V, and V has no padding
+     *  If we set U to be (a padded version of) a, and V = m:
+     *    G = a*S + m*T
+     *    G = a*S mod m
+     *  Assuming G=1:
+     *    S = 1/a mod m
+     */
+    VERIFY_CHECK(m->limbs <= NUM_LIMBS);
+    VERIFY_CHECK(m->data[m->limbs-1] != 0);
+    for (i = 0; i < m->limbs; i++) {
+        u[i] = (i < a->limbs) ? a->data[i] : 0;
+        v[i] = m->data[i];
+    }
+    sn = NUM_LIMBS+1;
+    gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
+    (void)gn;
+    VERIFY_CHECK(gn == 1);
+    VERIFY_CHECK(g[0] == 1);
+    r->neg = a->neg ^ m->neg;
+    if (sn < 0) {
+        mpn_sub(r->data, m->data, m->limbs, r->data, -sn);
+        r->limbs = m->limbs;
+        while (r->limbs > 1 && r->data[r->limbs-1]==0) {
+            r->limbs--;
+        }
+    } else {
+        r->limbs = sn;
+    }
+    memset(g, 0, sizeof(g));
+    memset(u, 0, sizeof(u));
+    memset(v, 0, sizeof(v));
+}
+
+static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) {
+    int ret;
+    mpz_t ga, gb;
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1));
+
+    mpz_inits(ga, gb, NULL);
+
+    mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data);
+    mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data);
+    if (a->neg) {
+        mpz_neg(ga, ga);
+    }
+
+    ret = mpz_jacobi(ga, gb);
+
+    mpz_clears(ga, gb, NULL);
+
+    return ret;
+}
+
+static int secp256k1_num_is_one(const secp256k1_num *a) {
+    return (a->limbs == 1 && a->data[0] == 1);
+}
+
+static int secp256k1_num_is_zero(const secp256k1_num *a) {
+    return (a->limbs == 1 && a->data[0] == 0);
+}
+
+static int secp256k1_num_is_neg(const secp256k1_num *a) {
+    return (a->limbs > 1 || a->data[0] != 0) && a->neg;
+}
+
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
+    if (a->limbs > b->limbs) {
+        return 1;
+    }
+    if (a->limbs < b->limbs) {
+        return -1;
+    }
+    return mpn_cmp(a->data, b->data, a->limbs);
+}
+
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
+    if (a->limbs > b->limbs) {
+        return 0;
+    }
+    if (a->limbs < b->limbs) {
+        return 0;
+    }
+    if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) {
+        return 0;
+    }
+    return mpn_cmp(a->data, b->data, a->limbs) == 0;
+}
+
+static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
+    if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
+        r->neg = a->neg;
+        if (a->limbs >= b->limbs) {
+            secp256k1_num_add_abs(r, a, b);
+        } else {
+            secp256k1_num_add_abs(r, b, a);
+        }
+    } else {
+        if (secp256k1_num_cmp(a, b) > 0) {
+            r->neg = a->neg;
+            secp256k1_num_sub_abs(r, a, b);
+        } else {
+            r->neg = b->neg ^ bneg;
+            secp256k1_num_sub_abs(r, b, a);
+        }
+    }
+}
+
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    secp256k1_num_subadd(r, a, b, 0);
+}
+
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    secp256k1_num_subadd(r, a, b, 1);
+}
+
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
+    mp_limb_t tmp[2*NUM_LIMBS+1];
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+
+    VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
+    if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
+        r->limbs = 1;
+        r->neg = 0;
+        r->data[0] = 0;
+        return;
+    }
+    if (a->limbs >= b->limbs) {
+        mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
+    } else {
+        mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
+    }
+    r->limbs = a->limbs + b->limbs;
+    if (r->limbs > 1 && tmp[r->limbs - 1]==0) {
+        r->limbs--;
+    }
+    VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
+    mpn_copyi(r->data, tmp, r->limbs);
+    r->neg = a->neg ^ b->neg;
+    memset(tmp, 0, sizeof(tmp));
+}
+
+static void secp256k1_num_shift(secp256k1_num *r, int bits) {
+    if (bits % GMP_NUMB_BITS) {
+        /* Shift within limbs. */
+        mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
+    }
+    if (bits >= GMP_NUMB_BITS) {
+        int i;
+        /* Shift full limbs. */
+        for (i = 0; i < r->limbs; i++) {
+            int index = i + (bits / GMP_NUMB_BITS);
+            if (index < r->limbs && index < 2*NUM_LIMBS) {
+                r->data[i] = r->data[index];
+            } else {
+                r->data[i] = 0;
+            }
+        }
+    }
+    while (r->limbs>1 && r->data[r->limbs-1]==0) {
+        r->limbs--;
+    }
+}
+
+static void secp256k1_num_negate(secp256k1_num *r) {
+    r->neg ^= 1;
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_impl.h
new file mode 100644
index 000000000..0b0e3a072
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/num_impl.h
@@ -0,0 +1,24 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_NUM_IMPL_H_
+#define _SECP256K1_NUM_IMPL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "num.h"
+
+#if defined(USE_NUM_GMP)
+#include "num_gmp_impl.h"
+#elif defined(USE_NUM_NONE)
+/* Nothing. */
+#else
+#error "Please select num implementation"
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar.h
new file mode 100644
index 000000000..27e9d8375
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar.h
@@ -0,0 +1,106 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_
+#define _SECP256K1_SCALAR_
+
+#include "num.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+/** Clear a scalar to prevent the leak of sensitive data. */
+static void secp256k1_scalar_clear(secp256k1_scalar *r);
+
+/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
+static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Access bits from a scalar. Not constant time. */
+static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Set a scalar from a big endian byte array. */
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
+
+/** Set a scalar to an unsigned integer. */
+static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
+
+/** Convert a scalar to a byte array. */
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
+
+/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
+
+/** Multiply two scalars (modulo the group order). */
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Shift a scalar right by some amount strictly between 0 and 16, returning
+ *  the low bits that were shifted off */
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
+
+/** Compute the square of a scalar (modulo the group order). */
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order). */
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the complement of a scalar (modulo the group order). */
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Check whether a scalar equals zero. */
+static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
+
+/** Check whether a scalar equals one. */
+static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
+
+/** Check whether a scalar, considered as an nonnegative integer, is even. */
+static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
+
+/** Check whether a scalar is higher than the group order divided by 2. */
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
+
+/** Conditionally negate a number, in constant time.
+ * Returns -1 if the number was negated, 1 otherwise */
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
+
+#ifndef USE_NUM_NONE
+/** Convert a scalar to a number. */
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
+
+/** Get the order of the group as a number. */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r);
+#endif
+
+/** Compare two scalars. */
+static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+#ifdef USE_ENDOMORPHISM
+/** Find r1 and r2 such that r1+r2*2^128 = a. */
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+#endif
+
+/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64.h
new file mode 100644
index 000000000..cff406038
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64.h
@@ -0,0 +1,19 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_
+#define _SECP256K1_SCALAR_REPR_
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef struct {
+    uint64_t d[4];
+} secp256k1_scalar;
+
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64_impl.h
new file mode 100644
index 000000000..56e7bd82a
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_4x64_impl.h
@@ -0,0 +1,949 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
+#define _SECP256K1_SCALAR_REPR_IMPL_H_
+
+/* Limbs of the secp256k1 order. */
+#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
+#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
+#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
+#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
+
+/* Limbs of 2^256 minus the secp256k1 order. */
+#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
+#define SECP256K1_N_C_1 (~SECP256K1_N_1)
+#define SECP256K1_N_C_2 (1)
+
+/* Limbs of half the secp256k1 order. */
+#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
+#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
+#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
+#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
+    r->d[0] = 0;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
+    r->d[0] = v;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
+    return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(offset + count <= 256);
+    if ((offset + count - 1) >> 6 == offset >> 6) {
+        return secp256k1_scalar_get_bits(a, offset, count);
+    } else {
+        VERIFY_CHECK((offset >> 6) + 1 < 4);
+        return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
+    no |= (a->d[2] < SECP256K1_N_2);
+    yes |= (a->d[2] > SECP256K1_N_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_1);
+    yes |= (a->d[1] > SECP256K1_N_1) & ~no;
+    yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
+    return yes;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
+    uint128_t t;
+    VERIFY_CHECK(overflow <= 1);
+    t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint64_t)r->d[3];
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+    return overflow;
+}
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    int overflow;
+    uint128_t t = (uint128_t)a->d[0] + b->d[0];
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[1] + b->d[1];
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[2] + b->d[2];
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)a->d[3] + b->d[3];
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    overflow = t + secp256k1_scalar_check_overflow(r);
+    VERIFY_CHECK(overflow == 0 || overflow == 1);
+    secp256k1_scalar_reduce(r, overflow);
+    return overflow;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    uint128_t t;
+    VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
+    t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
+    r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
+    r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
+    r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+    t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
+    r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+#ifdef VERIFY
+    VERIFY_CHECK((t >> 64) == 0);
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    int over;
+    r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
+    r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
+    r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56;
+    r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56;
+    over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
+    if (overflow) {
+        *overflow = over;
+    }
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
+    bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
+    bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
+    bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
+    uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
+    r->d[3] = t & nonzero;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[3] < SECP256K1_N_H_3);
+    yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
+    no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
+    yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
+    return yes;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint64_t mask = !flag - 1;
+    uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
+    uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
+
+/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd(a,b) { \
+    uint64_t tl, th; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c1 += th;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
+}
+
+/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
+#define muladd_fast(a,b) { \
+    uint64_t tl, th; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c1 += th;                 /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK(c1 >= th); \
+}
+
+/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd2(a,b) { \
+    uint64_t tl, th, th2, tl2; \
+    { \
+        uint128_t t = (uint128_t)a * b; \
+        th = t >> 64;               /* at most 0xFFFFFFFFFFFFFFFE */ \
+        tl = t; \
+    } \
+    th2 = th + th;                  /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
+    c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
+    tl2 = tl + tl;                  /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
+    th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFFFFFFFFFF */ \
+    c0 += tl2;                      /* overflow is handled on the next line */ \
+    th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
+    c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
+    c1 += th2;                      /* overflow is handled on the next line */ \
+    c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
+}
+
+/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define sumadd(a) { \
+    unsigned int over; \
+    c0 += (a);                  /* overflow is handled on the next line */ \
+    over = (c0 < (a)) ? 1 : 0; \
+    c1 += over;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
+}
+
+/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
+#define sumadd_fast(a) { \
+    c0 += (a);                 /* overflow is handled on the next line */ \
+    c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */
+#define extract(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = c2; \
+    c2 = 0; \
+}
+
+/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */
+#define extract_fast(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = 0; \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
+#ifdef USE_ASM_X86_64
+    /* Reduce 512 bits into 385. */
+    uint64_t m0, m1, m2, m3, m4, m5, m6;
+    uint64_t p0, p1, p2, p3, p4;
+    uint64_t c;
+
+    __asm__ __volatile__(
+    /* Preload. */
+    "movq 32(%%rsi), %%r11\n"
+    "movq 40(%%rsi), %%r12\n"
+    "movq 48(%%rsi), %%r13\n"
+    "movq 56(%%rsi), %%r14\n"
+    /* Initialize r8,r9,r10 */
+    "movq 0(%%rsi), %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9) += n0 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* extract m0 */
+    "movq %%r8, %q0\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10) += l1 */
+    "addq 8(%%rsi), %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r9,r10,r8) += n1 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += n0 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m1 */
+    "movq %%r9, %q1\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += l2 */
+    "addq 16(%%rsi), %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n2 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n1 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += n0 */
+    "addq %%r11, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract m2 */
+    "movq %%r10, %q2\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += l3 */
+    "addq 24(%%rsi), %%r8\n"
+    "adcq $0, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n3 * c0 */
+    "movq %8, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n2 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += n1 */
+    "addq %%r12, %%r8\n"
+    "adcq $0, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* extract m3 */
+    "movq %%r8, %q3\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += n3 * c1 */
+    "movq %9, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += n2 */
+    "addq %%r13, %%r9\n"
+    "adcq $0, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m4 */
+    "movq %%r9, %q4\n"
+    /* (r10,r8) += n3 */
+    "addq %%r14, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract m5 */
+    "movq %%r10, %q5\n"
+    /* extract m6 */
+    "movq %%r8, %q6\n"
+    : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
+    : "S"(l), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
+
+    /* Reduce 385 bits into 258. */
+    __asm__ __volatile__(
+    /* Preload */
+    "movq %q9, %%r11\n"
+    "movq %q10, %%r12\n"
+    "movq %q11, %%r13\n"
+    /* Initialize (r8,r9,r10) */
+    "movq %q5, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9) += m4 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* extract p0 */
+    "movq %%r8, %q0\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10) += m1 */
+    "addq %q6, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r9,r10,r8) += m5 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += m4 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* extract p1 */
+    "movq %%r9, %q1\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += m2 */
+    "addq %q7, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m6 * c0 */
+    "movq %12, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m5 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += m4 */
+    "addq %%r11, %%r10\n"
+    "adcq $0, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract p2 */
+    "movq %%r10, %q2\n"
+    /* (r8,r9) += m3 */
+    "addq %q8, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r8,r9) += m6 * c1 */
+    "movq %13, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* (r8,r9) += m5 */
+    "addq %%r12, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* extract p3 */
+    "movq %%r8, %q3\n"
+    /* (r9) += m6 */
+    "addq %%r13, %%r9\n"
+    /* extract p4 */
+    "movq %%r9, %q4\n"
+    : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
+    : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
+
+    /* Reduce 258 bits into 256. */
+    __asm__ __volatile__(
+    /* Preload */
+    "movq %q5, %%r10\n"
+    /* (rax,rdx) = p4 * c0 */
+    "movq %7, %%rax\n"
+    "mulq %%r10\n"
+    /* (rax,rdx) += p0 */
+    "addq %q1, %%rax\n"
+    "adcq $0, %%rdx\n"
+    /* extract r0 */
+    "movq %%rax, 0(%q6)\n"
+    /* Move to (r8,r9) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    /* (r8,r9) += p1 */
+    "addq %q2, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r8,r9) += p4 * c1 */
+    "movq %8, %%rax\n"
+    "mulq %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    /* Extract r1 */
+    "movq %%r8, 8(%q6)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r8) += p4 */
+    "addq %%r10, %%r9\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r8) += p2 */
+    "addq %q3, %%r9\n"
+    "adcq $0, %%r8\n"
+    /* Extract r2 */
+    "movq %%r9, 16(%q6)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r8,r9) += p3 */
+    "addq %q4, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract r3 */
+    "movq %%r8, 24(%q6)\n"
+    /* Extract c */
+    "movq %%r9, %q0\n"
+    : "=g"(c)
+    : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
+    : "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
+#else
+    uint128_t c;
+    uint64_t c0, c1, c2;
+    uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
+    uint64_t m0, m1, m2, m3, m4, m5;
+    uint32_t m6;
+    uint64_t p0, p1, p2, p3;
+    uint32_t p4;
+
+    /* Reduce 512 bits into 385. */
+    /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
+    c0 = l[0]; c1 = 0; c2 = 0;
+    muladd_fast(n0, SECP256K1_N_C_0);
+    extract_fast(m0);
+    sumadd_fast(l[1]);
+    muladd(n1, SECP256K1_N_C_0);
+    muladd(n0, SECP256K1_N_C_1);
+    extract(m1);
+    sumadd(l[2]);
+    muladd(n2, SECP256K1_N_C_0);
+    muladd(n1, SECP256K1_N_C_1);
+    sumadd(n0);
+    extract(m2);
+    sumadd(l[3]);
+    muladd(n3, SECP256K1_N_C_0);
+    muladd(n2, SECP256K1_N_C_1);
+    sumadd(n1);
+    extract(m3);
+    muladd(n3, SECP256K1_N_C_1);
+    sumadd(n2);
+    extract(m4);
+    sumadd_fast(n3);
+    extract_fast(m5);
+    VERIFY_CHECK(c0 <= 1);
+    m6 = c0;
+
+    /* Reduce 385 bits into 258. */
+    /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
+    c0 = m0; c1 = 0; c2 = 0;
+    muladd_fast(m4, SECP256K1_N_C_0);
+    extract_fast(p0);
+    sumadd_fast(m1);
+    muladd(m5, SECP256K1_N_C_0);
+    muladd(m4, SECP256K1_N_C_1);
+    extract(p1);
+    sumadd(m2);
+    muladd(m6, SECP256K1_N_C_0);
+    muladd(m5, SECP256K1_N_C_1);
+    sumadd(m4);
+    extract(p2);
+    sumadd_fast(m3);
+    muladd_fast(m6, SECP256K1_N_C_1);
+    sumadd_fast(m5);
+    extract_fast(p3);
+    p4 = c0 + m6;
+    VERIFY_CHECK(p4 <= 2);
+
+    /* Reduce 258 bits into 256. */
+    /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
+    c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
+    r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
+    r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p2 + (uint128_t)p4;
+    r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+    c += p3;
+    r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+#endif
+
+    /* Final reduction of r. */
+    secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
+}
+
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
+#ifdef USE_ASM_X86_64
+    const uint64_t *pb = b->d;
+    __asm__ __volatile__(
+    /* Preload */
+    "movq 0(%%rdi), %%r15\n"
+    "movq 8(%%rdi), %%rbx\n"
+    "movq 16(%%rdi), %%rcx\n"
+    "movq 0(%%rdx), %%r11\n"
+    "movq 8(%%rdx), %%r12\n"
+    "movq 16(%%rdx), %%r13\n"
+    "movq 24(%%rdx), %%r14\n"
+    /* (rax,rdx) = a0 * b0 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r11\n"
+    /* Extract l0 */
+    "movq %%rax, 0(%%rsi)\n"
+    /* (r8,r9,r10) = (rdx) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += a0 * b1 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a1 * b0 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l1 */
+    "movq %%r8, 8(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += a0 * b2 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a1 * b1 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a2 * b0 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l2 */
+    "movq %%r9, 16(%%rsi)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += a0 * b3 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Preload a3 */
+    "movq 24(%%rdi), %%r15\n"
+    /* (r10,r8,r9) += a1 * b2 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += a2 * b1 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += a3 * b0 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r11\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract l3 */
+    "movq %%r10, 24(%%rsi)\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += a1 * b3 */
+    "movq %%rbx, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a2 * b2 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a3 * b1 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l4 */
+    "movq %%r8, 32(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += a2 * b3 */
+    "movq %%rcx, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a3 * b2 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l5 */
+    "movq %%r9, 40(%%rsi)\n"
+    /* (r10,r8) += a3 * b3 */
+    "movq %%r15, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    /* Extract l6 */
+    "movq %%r10, 48(%%rsi)\n"
+    /* Extract l7 */
+    "movq %%r8, 56(%%rsi)\n"
+    : "+d"(pb)
+    : "S"(l), "D"(a->d)
+    : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
+#else
+    /* 160 bit accumulator. */
+    uint64_t c0 = 0, c1 = 0;
+    uint32_t c2 = 0;
+
+    /* l[0..7] = a[0..3] * b[0..3]. */
+    muladd_fast(a->d[0], b->d[0]);
+    extract_fast(l[0]);
+    muladd(a->d[0], b->d[1]);
+    muladd(a->d[1], b->d[0]);
+    extract(l[1]);
+    muladd(a->d[0], b->d[2]);
+    muladd(a->d[1], b->d[1]);
+    muladd(a->d[2], b->d[0]);
+    extract(l[2]);
+    muladd(a->d[0], b->d[3]);
+    muladd(a->d[1], b->d[2]);
+    muladd(a->d[2], b->d[1]);
+    muladd(a->d[3], b->d[0]);
+    extract(l[3]);
+    muladd(a->d[1], b->d[3]);
+    muladd(a->d[2], b->d[2]);
+    muladd(a->d[3], b->d[1]);
+    extract(l[4]);
+    muladd(a->d[2], b->d[3]);
+    muladd(a->d[3], b->d[2]);
+    extract(l[5]);
+    muladd_fast(a->d[3], b->d[3]);
+    extract_fast(l[6]);
+    VERIFY_CHECK(c1 == 0);
+    l[7] = c0;
+#endif
+}
+
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
+#ifdef USE_ASM_X86_64
+    __asm__ __volatile__(
+    /* Preload */
+    "movq 0(%%rdi), %%r11\n"
+    "movq 8(%%rdi), %%r12\n"
+    "movq 16(%%rdi), %%r13\n"
+    "movq 24(%%rdi), %%r14\n"
+    /* (rax,rdx) = a0 * a0 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r11\n"
+    /* Extract l0 */
+    "movq %%rax, 0(%%rsi)\n"
+    /* (r8,r9,r10) = (rdx,0) */
+    "movq %%rdx, %%r8\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += 2 * a0 * a1 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l1 */
+    "movq %%r8, 8(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += 2 * a0 * a2 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* (r9,r10,r8) += a1 * a1 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r12\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l2 */
+    "movq %%r9, 16(%%rsi)\n"
+    "xorq %%r9, %%r9\n"
+    /* (r10,r8,r9) += 2 * a0 * a3 */
+    "movq %%r11, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* (r10,r8,r9) += 2 * a1 * a2 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    "adcq $0, %%r9\n"
+    /* Extract l3 */
+    "movq %%r10, 24(%%rsi)\n"
+    "xorq %%r10, %%r10\n"
+    /* (r8,r9,r10) += 2 * a1 * a3 */
+    "movq %%r12, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* (r8,r9,r10) += a2 * a2 */
+    "movq %%r13, %%rax\n"
+    "mulq %%r13\n"
+    "addq %%rax, %%r8\n"
+    "adcq %%rdx, %%r9\n"
+    "adcq $0, %%r10\n"
+    /* Extract l4 */
+    "movq %%r8, 32(%%rsi)\n"
+    "xorq %%r8, %%r8\n"
+    /* (r9,r10,r8) += 2 * a2 * a3 */
+    "movq %%r13, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    "addq %%rax, %%r9\n"
+    "adcq %%rdx, %%r10\n"
+    "adcq $0, %%r8\n"
+    /* Extract l5 */
+    "movq %%r9, 40(%%rsi)\n"
+    /* (r10,r8) += a3 * a3 */
+    "movq %%r14, %%rax\n"
+    "mulq %%r14\n"
+    "addq %%rax, %%r10\n"
+    "adcq %%rdx, %%r8\n"
+    /* Extract l6 */
+    "movq %%r10, 48(%%rsi)\n"
+    /* Extract l7 */
+    "movq %%r8, 56(%%rsi)\n"
+    :
+    : "S"(l), "D"(a->d)
+    : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory");
+#else
+    /* 160 bit accumulator. */
+    uint64_t c0 = 0, c1 = 0;
+    uint32_t c2 = 0;
+
+    /* l[0..7] = a[0..3] * b[0..3]. */
+    muladd_fast(a->d[0], a->d[0]);
+    extract_fast(l[0]);
+    muladd2(a->d[0], a->d[1]);
+    extract(l[1]);
+    muladd2(a->d[0], a->d[2]);
+    muladd(a->d[1], a->d[1]);
+    extract(l[2]);
+    muladd2(a->d[0], a->d[3]);
+    muladd2(a->d[1], a->d[2]);
+    extract(l[3]);
+    muladd2(a->d[1], a->d[3]);
+    muladd(a->d[2], a->d[2]);
+    extract(l[4]);
+    muladd2(a->d[2], a->d[3]);
+    extract(l[5]);
+    muladd_fast(a->d[3], a->d[3]);
+    extract_fast(l[6]);
+    VERIFY_CHECK(c1 == 0);
+    l[7] = c0;
+#endif
+}
+
+#undef sumadd
+#undef sumadd_fast
+#undef muladd
+#undef muladd_fast
+#undef muladd2
+#undef extract
+#undef extract_fast
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    uint64_t l[8];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
+    r->d[3] = (r->d[3] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint64_t l[8];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    r1->d[0] = a->d[0];
+    r1->d[1] = a->d[1];
+    r1->d[2] = 0;
+    r1->d[3] = 0;
+    r2->d[0] = a->d[2];
+    r2->d[1] = a->d[3];
+    r2->d[2] = 0;
+    r2->d[3] = 0;
+}
+#endif
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
+    uint64_t l[8];
+    unsigned int shiftlimbs;
+    unsigned int shiftlow;
+    unsigned int shifthigh;
+    VERIFY_CHECK(shift >= 256);
+    secp256k1_scalar_mul_512(l, a, b);
+    shiftlimbs = shift >> 6;
+    shiftlow = shift & 0x3F;
+    shifthigh = 64 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32.h
new file mode 100644
index 000000000..1319664f6
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32.h
@@ -0,0 +1,19 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_
+#define _SECP256K1_SCALAR_REPR_
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef struct {
+    uint32_t d[8];
+} secp256k1_scalar;
+
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h
new file mode 100644
index 000000000..aae4f35c0
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_8x32_impl.h
@@ -0,0 +1,721 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
+#define _SECP256K1_SCALAR_REPR_IMPL_H_
+
+/* Limbs of the secp256k1 order. */
+#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
+#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
+#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
+#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
+#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
+#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
+
+/* Limbs of 2^256 minus the secp256k1 order. */
+#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
+#define SECP256K1_N_C_1 (~SECP256K1_N_1)
+#define SECP256K1_N_C_2 (~SECP256K1_N_2)
+#define SECP256K1_N_C_3 (~SECP256K1_N_3)
+#define SECP256K1_N_C_4 (1)
+
+/* Limbs of half the secp256k1 order. */
+#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
+#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
+#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
+#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
+#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
+    r->d[0] = 0;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+    r->d[4] = 0;
+    r->d[5] = 0;
+    r->d[6] = 0;
+    r->d[7] = 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
+    r->d[0] = v;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+    r->d[4] = 0;
+    r->d[5] = 0;
+    r->d[6] = 0;
+    r->d[7] = 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
+    return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(offset + count <= 256);
+    if ((offset + count - 1) >> 5 == offset >> 5) {
+        return secp256k1_scalar_get_bits(a, offset, count);
+    } else {
+        VERIFY_CHECK((offset >> 5) + 1 < 8);
+        return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
+    no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
+    no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
+    no |= (a->d[4] < SECP256K1_N_4);
+    yes |= (a->d[4] > SECP256K1_N_4) & ~no;
+    no |= (a->d[3] < SECP256K1_N_3) & ~yes;
+    yes |= (a->d[3] > SECP256K1_N_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_2) & ~yes;
+    yes |= (a->d[2] > SECP256K1_N_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_1) & ~no;
+    yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
+    return yes;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
+    uint64_t t;
+    VERIFY_CHECK(overflow <= 1);
+    t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
+    r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
+    r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
+    r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
+    r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
+    r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[5];
+    r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[6];
+    r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[7];
+    r->d[7] = t & 0xFFFFFFFFUL;
+    return overflow;
+}
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    int overflow;
+    uint64_t t = (uint64_t)a->d[0] + b->d[0];
+    r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[1] + b->d[1];
+    r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[2] + b->d[2];
+    r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[3] + b->d[3];
+    r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[4] + b->d[4];
+    r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[5] + b->d[5];
+    r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[6] + b->d[6];
+    r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[7] + b->d[7];
+    r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
+    overflow = t + secp256k1_scalar_check_overflow(r);
+    VERIFY_CHECK(overflow == 0 || overflow == 1);
+    secp256k1_scalar_reduce(r, overflow);
+    return overflow;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    uint64_t t;
+    VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
+    t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
+    r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
+    r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
+    r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
+    r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
+    r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
+    r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
+    r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
+    r->d[7] = t & 0xFFFFFFFFULL;
+#ifdef VERIFY
+    VERIFY_CHECK((t >> 32) == 0);
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    int over;
+    r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
+    r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
+    r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
+    r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
+    r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
+    r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
+    r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
+    r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
+    over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
+    if (overflow) {
+        *overflow = over;
+    }
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
+    bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
+    bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
+    bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
+    bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
+    bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
+    bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
+    bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
+    uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
+    r->d[7] = t & nonzero;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[7] < SECP256K1_N_H_7);
+    yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
+    no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
+    no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
+    no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
+    no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
+    yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
+    yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
+    yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
+    return yes;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint32_t mask = !flag - 1;
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
+    uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
+    r->d[7] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+
+/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
+
+/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd(a,b) { \
+    uint32_t tl, th; \
+    { \
+        uint64_t t = (uint64_t)a * b; \
+        th = t >> 32;         /* at most 0xFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFF */ \
+    c1 += th;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
+}
+
+/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
+#define muladd_fast(a,b) { \
+    uint32_t tl, th; \
+    { \
+        uint64_t t = (uint64_t)a * b; \
+        th = t >> 32;         /* at most 0xFFFFFFFE */ \
+        tl = t; \
+    } \
+    c0 += tl;                 /* overflow is handled on the next line */ \
+    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFF */ \
+    c1 += th;                 /* never overflows by contract (verified in the next line) */ \
+    VERIFY_CHECK(c1 >= th); \
+}
+
+/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd2(a,b) { \
+    uint32_t tl, th, th2, tl2; \
+    { \
+        uint64_t t = (uint64_t)a * b; \
+        th = t >> 32;               /* at most 0xFFFFFFFE */ \
+        tl = t; \
+    } \
+    th2 = th + th;                  /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
+    c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
+    tl2 = tl + tl;                  /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
+    th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFF */ \
+    c0 += tl2;                      /* overflow is handled on the next line */ \
+    th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
+    c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
+    c1 += th2;                      /* overflow is handled on the next line */ \
+    c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
+}
+
+/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define sumadd(a) { \
+    unsigned int over; \
+    c0 += (a);                  /* overflow is handled on the next line */ \
+    over = (c0 < (a)) ? 1 : 0; \
+    c1 += over;                 /* overflow is handled on the next line */ \
+    c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
+}
+
+/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
+#define sumadd_fast(a) { \
+    c0 += (a);                 /* overflow is handled on the next line */ \
+    c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
+    VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
+#define extract(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = c2; \
+    c2 = 0; \
+}
+
+/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
+#define extract_fast(n) { \
+    (n) = c0; \
+    c0 = c1; \
+    c1 = 0; \
+    VERIFY_CHECK(c2 == 0); \
+}
+
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
+    uint64_t c;
+    uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
+    uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
+    uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
+
+    /* 96 bit accumulator. */
+    uint32_t c0, c1, c2;
+
+    /* Reduce 512 bits into 385. */
+    /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
+    c0 = l[0]; c1 = 0; c2 = 0;
+    muladd_fast(n0, SECP256K1_N_C_0);
+    extract_fast(m0);
+    sumadd_fast(l[1]);
+    muladd(n1, SECP256K1_N_C_0);
+    muladd(n0, SECP256K1_N_C_1);
+    extract(m1);
+    sumadd(l[2]);
+    muladd(n2, SECP256K1_N_C_0);
+    muladd(n1, SECP256K1_N_C_1);
+    muladd(n0, SECP256K1_N_C_2);
+    extract(m2);
+    sumadd(l[3]);
+    muladd(n3, SECP256K1_N_C_0);
+    muladd(n2, SECP256K1_N_C_1);
+    muladd(n1, SECP256K1_N_C_2);
+    muladd(n0, SECP256K1_N_C_3);
+    extract(m3);
+    sumadd(l[4]);
+    muladd(n4, SECP256K1_N_C_0);
+    muladd(n3, SECP256K1_N_C_1);
+    muladd(n2, SECP256K1_N_C_2);
+    muladd(n1, SECP256K1_N_C_3);
+    sumadd(n0);
+    extract(m4);
+    sumadd(l[5]);
+    muladd(n5, SECP256K1_N_C_0);
+    muladd(n4, SECP256K1_N_C_1);
+    muladd(n3, SECP256K1_N_C_2);
+    muladd(n2, SECP256K1_N_C_3);
+    sumadd(n1);
+    extract(m5);
+    sumadd(l[6]);
+    muladd(n6, SECP256K1_N_C_0);
+    muladd(n5, SECP256K1_N_C_1);
+    muladd(n4, SECP256K1_N_C_2);
+    muladd(n3, SECP256K1_N_C_3);
+    sumadd(n2);
+    extract(m6);
+    sumadd(l[7]);
+    muladd(n7, SECP256K1_N_C_0);
+    muladd(n6, SECP256K1_N_C_1);
+    muladd(n5, SECP256K1_N_C_2);
+    muladd(n4, SECP256K1_N_C_3);
+    sumadd(n3);
+    extract(m7);
+    muladd(n7, SECP256K1_N_C_1);
+    muladd(n6, SECP256K1_N_C_2);
+    muladd(n5, SECP256K1_N_C_3);
+    sumadd(n4);
+    extract(m8);
+    muladd(n7, SECP256K1_N_C_2);
+    muladd(n6, SECP256K1_N_C_3);
+    sumadd(n5);
+    extract(m9);
+    muladd(n7, SECP256K1_N_C_3);
+    sumadd(n6);
+    extract(m10);
+    sumadd_fast(n7);
+    extract_fast(m11);
+    VERIFY_CHECK(c0 <= 1);
+    m12 = c0;
+
+    /* Reduce 385 bits into 258. */
+    /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
+    c0 = m0; c1 = 0; c2 = 0;
+    muladd_fast(m8, SECP256K1_N_C_0);
+    extract_fast(p0);
+    sumadd_fast(m1);
+    muladd(m9, SECP256K1_N_C_0);
+    muladd(m8, SECP256K1_N_C_1);
+    extract(p1);
+    sumadd(m2);
+    muladd(m10, SECP256K1_N_C_0);
+    muladd(m9, SECP256K1_N_C_1);
+    muladd(m8, SECP256K1_N_C_2);
+    extract(p2);
+    sumadd(m3);
+    muladd(m11, SECP256K1_N_C_0);
+    muladd(m10, SECP256K1_N_C_1);
+    muladd(m9, SECP256K1_N_C_2);
+    muladd(m8, SECP256K1_N_C_3);
+    extract(p3);
+    sumadd(m4);
+    muladd(m12, SECP256K1_N_C_0);
+    muladd(m11, SECP256K1_N_C_1);
+    muladd(m10, SECP256K1_N_C_2);
+    muladd(m9, SECP256K1_N_C_3);
+    sumadd(m8);
+    extract(p4);
+    sumadd(m5);
+    muladd(m12, SECP256K1_N_C_1);
+    muladd(m11, SECP256K1_N_C_2);
+    muladd(m10, SECP256K1_N_C_3);
+    sumadd(m9);
+    extract(p5);
+    sumadd(m6);
+    muladd(m12, SECP256K1_N_C_2);
+    muladd(m11, SECP256K1_N_C_3);
+    sumadd(m10);
+    extract(p6);
+    sumadd_fast(m7);
+    muladd_fast(m12, SECP256K1_N_C_3);
+    sumadd_fast(m11);
+    extract_fast(p7);
+    p8 = c0 + m12;
+    VERIFY_CHECK(p8 <= 2);
+
+    /* Reduce 258 bits into 256. */
+    /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
+    c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
+    r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
+    r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
+    r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
+    r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p4 + (uint64_t)p8;
+    r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p5;
+    r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p6;
+    r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p7;
+    r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
+
+    /* Final reduction of r. */
+    secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
+}
+
+static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    /* 96 bit accumulator. */
+    uint32_t c0 = 0, c1 = 0, c2 = 0;
+
+    /* l[0..15] = a[0..7] * b[0..7]. */
+    muladd_fast(a->d[0], b->d[0]);
+    extract_fast(l[0]);
+    muladd(a->d[0], b->d[1]);
+    muladd(a->d[1], b->d[0]);
+    extract(l[1]);
+    muladd(a->d[0], b->d[2]);
+    muladd(a->d[1], b->d[1]);
+    muladd(a->d[2], b->d[0]);
+    extract(l[2]);
+    muladd(a->d[0], b->d[3]);
+    muladd(a->d[1], b->d[2]);
+    muladd(a->d[2], b->d[1]);
+    muladd(a->d[3], b->d[0]);
+    extract(l[3]);
+    muladd(a->d[0], b->d[4]);
+    muladd(a->d[1], b->d[3]);
+    muladd(a->d[2], b->d[2]);
+    muladd(a->d[3], b->d[1]);
+    muladd(a->d[4], b->d[0]);
+    extract(l[4]);
+    muladd(a->d[0], b->d[5]);
+    muladd(a->d[1], b->d[4]);
+    muladd(a->d[2], b->d[3]);
+    muladd(a->d[3], b->d[2]);
+    muladd(a->d[4], b->d[1]);
+    muladd(a->d[5], b->d[0]);
+    extract(l[5]);
+    muladd(a->d[0], b->d[6]);
+    muladd(a->d[1], b->d[5]);
+    muladd(a->d[2], b->d[4]);
+    muladd(a->d[3], b->d[3]);
+    muladd(a->d[4], b->d[2]);
+    muladd(a->d[5], b->d[1]);
+    muladd(a->d[6], b->d[0]);
+    extract(l[6]);
+    muladd(a->d[0], b->d[7]);
+    muladd(a->d[1], b->d[6]);
+    muladd(a->d[2], b->d[5]);
+    muladd(a->d[3], b->d[4]);
+    muladd(a->d[4], b->d[3]);
+    muladd(a->d[5], b->d[2]);
+    muladd(a->d[6], b->d[1]);
+    muladd(a->d[7], b->d[0]);
+    extract(l[7]);
+    muladd(a->d[1], b->d[7]);
+    muladd(a->d[2], b->d[6]);
+    muladd(a->d[3], b->d[5]);
+    muladd(a->d[4], b->d[4]);
+    muladd(a->d[5], b->d[3]);
+    muladd(a->d[6], b->d[2]);
+    muladd(a->d[7], b->d[1]);
+    extract(l[8]);
+    muladd(a->d[2], b->d[7]);
+    muladd(a->d[3], b->d[6]);
+    muladd(a->d[4], b->d[5]);
+    muladd(a->d[5], b->d[4]);
+    muladd(a->d[6], b->d[3]);
+    muladd(a->d[7], b->d[2]);
+    extract(l[9]);
+    muladd(a->d[3], b->d[7]);
+    muladd(a->d[4], b->d[6]);
+    muladd(a->d[5], b->d[5]);
+    muladd(a->d[6], b->d[4]);
+    muladd(a->d[7], b->d[3]);
+    extract(l[10]);
+    muladd(a->d[4], b->d[7]);
+    muladd(a->d[5], b->d[6]);
+    muladd(a->d[6], b->d[5]);
+    muladd(a->d[7], b->d[4]);
+    extract(l[11]);
+    muladd(a->d[5], b->d[7]);
+    muladd(a->d[6], b->d[6]);
+    muladd(a->d[7], b->d[5]);
+    extract(l[12]);
+    muladd(a->d[6], b->d[7]);
+    muladd(a->d[7], b->d[6]);
+    extract(l[13]);
+    muladd_fast(a->d[7], b->d[7]);
+    extract_fast(l[14]);
+    VERIFY_CHECK(c1 == 0);
+    l[15] = c0;
+}
+
+static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
+    /* 96 bit accumulator. */
+    uint32_t c0 = 0, c1 = 0, c2 = 0;
+
+    /* l[0..15] = a[0..7]^2. */
+    muladd_fast(a->d[0], a->d[0]);
+    extract_fast(l[0]);
+    muladd2(a->d[0], a->d[1]);
+    extract(l[1]);
+    muladd2(a->d[0], a->d[2]);
+    muladd(a->d[1], a->d[1]);
+    extract(l[2]);
+    muladd2(a->d[0], a->d[3]);
+    muladd2(a->d[1], a->d[2]);
+    extract(l[3]);
+    muladd2(a->d[0], a->d[4]);
+    muladd2(a->d[1], a->d[3]);
+    muladd(a->d[2], a->d[2]);
+    extract(l[4]);
+    muladd2(a->d[0], a->d[5]);
+    muladd2(a->d[1], a->d[4]);
+    muladd2(a->d[2], a->d[3]);
+    extract(l[5]);
+    muladd2(a->d[0], a->d[6]);
+    muladd2(a->d[1], a->d[5]);
+    muladd2(a->d[2], a->d[4]);
+    muladd(a->d[3], a->d[3]);
+    extract(l[6]);
+    muladd2(a->d[0], a->d[7]);
+    muladd2(a->d[1], a->d[6]);
+    muladd2(a->d[2], a->d[5]);
+    muladd2(a->d[3], a->d[4]);
+    extract(l[7]);
+    muladd2(a->d[1], a->d[7]);
+    muladd2(a->d[2], a->d[6]);
+    muladd2(a->d[3], a->d[5]);
+    muladd(a->d[4], a->d[4]);
+    extract(l[8]);
+    muladd2(a->d[2], a->d[7]);
+    muladd2(a->d[3], a->d[6]);
+    muladd2(a->d[4], a->d[5]);
+    extract(l[9]);
+    muladd2(a->d[3], a->d[7]);
+    muladd2(a->d[4], a->d[6]);
+    muladd(a->d[5], a->d[5]);
+    extract(l[10]);
+    muladd2(a->d[4], a->d[7]);
+    muladd2(a->d[5], a->d[6]);
+    extract(l[11]);
+    muladd2(a->d[5], a->d[7]);
+    muladd(a->d[6], a->d[6]);
+    extract(l[12]);
+    muladd2(a->d[6], a->d[7]);
+    extract(l[13]);
+    muladd_fast(a->d[7], a->d[7]);
+    extract_fast(l[14]);
+    VERIFY_CHECK(c1 == 0);
+    l[15] = c0;
+}
+
+#undef sumadd
+#undef sumadd_fast
+#undef muladd
+#undef muladd_fast
+#undef muladd2
+#undef extract
+#undef extract_fast
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    uint32_t l[16];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
+    r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
+    r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
+    r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
+    r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
+    r->d[7] = (r->d[7] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint32_t l[16];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    r1->d[0] = a->d[0];
+    r1->d[1] = a->d[1];
+    r1->d[2] = a->d[2];
+    r1->d[3] = a->d[3];
+    r1->d[4] = 0;
+    r1->d[5] = 0;
+    r1->d[6] = 0;
+    r1->d[7] = 0;
+    r2->d[0] = a->d[4];
+    r2->d[1] = a->d[5];
+    r2->d[2] = a->d[6];
+    r2->d[3] = a->d[7];
+    r2->d[4] = 0;
+    r2->d[5] = 0;
+    r2->d[6] = 0;
+    r2->d[7] = 0;
+}
+#endif
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
+    uint32_t l[16];
+    unsigned int shiftlimbs;
+    unsigned int shiftlow;
+    unsigned int shifthigh;
+    VERIFY_CHECK(shift >= 256);
+    secp256k1_scalar_mul_512(l, a, b);
+    shiftlimbs = shift >> 5;
+    shiftlow = shift & 0x1F;
+    shifthigh = 32 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_impl.h
new file mode 100644
index 000000000..f5b237640
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_impl.h
@@ -0,0 +1,370 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_IMPL_H_
+#define _SECP256K1_SCALAR_IMPL_H_
+
+#include "group.h"
+#include "scalar.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low_impl.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64_impl.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32_impl.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+#ifndef USE_NUM_NONE
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
+    unsigned char c[32];
+    secp256k1_scalar_get_b32(c, a);
+    secp256k1_num_set_bin(r, c, 32);
+}
+
+/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    static const unsigned char order[32] = {
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
+    };
+#else
+    static const unsigned char order[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+    };
+#endif
+    secp256k1_num_set_bin(r, order, 32);
+}
+#endif
+
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    int i;
+    *r = 0;
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
+        if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
+            *r = i;
+    /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
+     * have a composite group order; fix it in exhaustive_tests.c). */
+    VERIFY_CHECK(*r != 0);
+}
+#else
+    secp256k1_scalar *t;
+    int i;
+    /* First compute x ^ (2^N - 1) for some values of N. */
+    secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
+
+    secp256k1_scalar_sqr(&x2,  x);
+    secp256k1_scalar_mul(&x2, &x2,  x);
+
+    secp256k1_scalar_sqr(&x3, &x2);
+    secp256k1_scalar_mul(&x3, &x3,  x);
+
+    secp256k1_scalar_sqr(&x4, &x3);
+    secp256k1_scalar_mul(&x4, &x4,  x);
+
+    secp256k1_scalar_sqr(&x6, &x4);
+    secp256k1_scalar_sqr(&x6, &x6);
+    secp256k1_scalar_mul(&x6, &x6, &x2);
+
+    secp256k1_scalar_sqr(&x7, &x6);
+    secp256k1_scalar_mul(&x7, &x7,  x);
+
+    secp256k1_scalar_sqr(&x8, &x7);
+    secp256k1_scalar_mul(&x8, &x8,  x);
+
+    secp256k1_scalar_sqr(&x15, &x8);
+    for (i = 0; i < 6; i++) {
+        secp256k1_scalar_sqr(&x15, &x15);
+    }
+    secp256k1_scalar_mul(&x15, &x15, &x7);
+
+    secp256k1_scalar_sqr(&x30, &x15);
+    for (i = 0; i < 14; i++) {
+        secp256k1_scalar_sqr(&x30, &x30);
+    }
+    secp256k1_scalar_mul(&x30, &x30, &x15);
+
+    secp256k1_scalar_sqr(&x60, &x30);
+    for (i = 0; i < 29; i++) {
+        secp256k1_scalar_sqr(&x60, &x60);
+    }
+    secp256k1_scalar_mul(&x60, &x60, &x30);
+
+    secp256k1_scalar_sqr(&x120, &x60);
+    for (i = 0; i < 59; i++) {
+        secp256k1_scalar_sqr(&x120, &x120);
+    }
+    secp256k1_scalar_mul(&x120, &x120, &x60);
+
+    secp256k1_scalar_sqr(&x127, &x120);
+    for (i = 0; i < 6; i++) {
+        secp256k1_scalar_sqr(&x127, &x127);
+    }
+    secp256k1_scalar_mul(&x127, &x127, &x7);
+
+    /* Then accumulate the final result (t starts at x127). */
+    t = &x127;
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 3; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 5; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 4; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 5; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x4); /* 1111 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 3; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 4; i++) { /* 000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 10; i++) { /* 0000000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 4; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
+    for (i = 0; i < 9; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 3; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 3; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 5; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x4); /* 1111 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 5; i++) { /* 000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 4; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 2; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 8; i++) { /* 000000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 3; i++) { /* 0 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    for (i = 0; i < 3; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 6; i++) { /* 00000 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, x); /* 1 */
+    for (i = 0; i < 8; i++) { /* 00 */
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(r, t, &x6); /* 111111 */
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(a->d[0] & 1);
+}
+#endif
+
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(USE_SCALAR_INV_BUILTIN)
+    secp256k1_scalar_inverse(r, x);
+#elif defined(USE_SCALAR_INV_NUM)
+    unsigned char b[32];
+    secp256k1_num n, m;
+    secp256k1_scalar t = *x;
+    secp256k1_scalar_get_b32(b, &t);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_scalar_order_get_num(&m);
+    secp256k1_num_mod_inverse(&n, &n, &m);
+    secp256k1_num_get_bin(b, 32, &n);
+    secp256k1_scalar_set_b32(r, b, NULL);
+    /* Verify that the inverse was computed correctly, without GMP code. */
+    secp256k1_scalar_mul(&t, &t, r);
+    CHECK(secp256k1_scalar_is_one(&t));
+#else
+#error "Please select scalar inverse implementation"
+#endif
+}
+
+#ifdef USE_ENDOMORPHISM
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/**
+ * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the
+ * full case we don't bother making k1 and k2 be small, we just want them to be
+ * nontrivial to get full test coverage for the exhaustive tests. We therefore
+ * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda.
+ */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER;
+}
+#else
+/**
+ * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
+ * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
+ *            0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
+ *
+ * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
+ * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
+ * and k2 have a small size.
+ * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
+ *
+ * - a1 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ * - b1 =     -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
+ * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
+ * - b2 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ *
+ * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
+ * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
+ * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
+ *
+ * g1, g2 are precomputed constants used to replace division with a rounded multiplication
+ * when decomposing the scalar for an endomorphism-based point multiplication.
+ *
+ * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
+ * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
+ *
+ * The derivation is described in the paper "Efficient Software Implementation of Public-Key
+ * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
+ * Section 4.3 (here we use a somewhat higher-precision estimate):
+ * d = a1*b2 - b1*a2
+ * g1 = round((2^272)*b2/d)
+ * g2 = round((2^272)*b1/d)
+ *
+ * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
+ * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
+ *
+ * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
+ */
+
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    secp256k1_scalar c1, c2;
+    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
+        0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
+        0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
+    );
+    static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
+        0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
+    );
+    static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+        0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
+    );
+    static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
+        0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
+    );
+    static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
+        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
+        0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
+    );
+    VERIFY_CHECK(r1 != a);
+    VERIFY_CHECK(r2 != a);
+    /* these _var calls are constant time since the shift amount is constant */
+    secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
+    secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
+    secp256k1_scalar_mul(&c1, &c1, &minus_b1);
+    secp256k1_scalar_mul(&c2, &c2, &minus_b2);
+    secp256k1_scalar_add(r2, &c1, &c2);
+    secp256k1_scalar_mul(r1, r2, &minus_lambda);
+    secp256k1_scalar_add(r1, r1, a);
+}
+#endif
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low.h
new file mode 100644
index 000000000..5574c44c7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low.h
@@ -0,0 +1,15 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_
+#define _SECP256K1_SCALAR_REPR_
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef uint32_t secp256k1_scalar;
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low_impl.h
new file mode 100644
index 000000000..4f94441f4
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/scalar_low_impl.h
@@ -0,0 +1,114 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
+#define _SECP256K1_SCALAR_REPR_IMPL_H_
+
+#include "scalar.h"
+
+#include <string.h>
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(*a & 1);
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; }
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; }
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    if (offset < 32)
+        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
+    else
+        return 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    return secp256k1_scalar_get_bits(a, offset, count);
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; }
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER;
+    return *r < *b;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    if (flag && bit < 32)
+        *r += (1 << bit);
+#ifdef VERIFY
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
+    int i;
+    *r = 0;
+    for (i = 0; i < 32; i++) {
+       *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+    }
+    /* just deny overflow, it basically always happens */
+    if (overflow) *overflow = 0;
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    memset(bin, 0, 32);
+    bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return *a == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    if (*a == 0) {
+        *r = 0;
+    } else {
+        *r = EXHAUSTIVE_TEST_ORDER - *a;
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return *a == 1;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    return *a > EXHAUSTIVE_TEST_ORDER / 2;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    if (flag) secp256k1_scalar_negate(r, r);
+    return flag ? -1 : 1;
+}
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = *r & ((1 << n) - 1);
+    *r >>= n;
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r1 = *a;
+    *r2 = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return *a == *b;
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/secp256k1.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/secp256k1.c
new file mode 100755
index 000000000..7d637bfad
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/secp256k1.c
@@ -0,0 +1,559 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include "include/secp256k1.h"
+
+#include "util.h"
+#include "num_impl.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_impl.h"
+#include "ecmult_const_impl.h"
+#include "ecmult_gen_impl.h"
+#include "ecdsa_impl.h"
+#include "eckey_impl.h"
+#include "hash_impl.h"
+
+#define ARG_CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        secp256k1_callback_call(&ctx->illegal_callback, #cond); \
+        return 0; \
+    } \
+} while(0)
+
+static void default_illegal_callback_fn(const char* str, void* data) {
+    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_illegal_callback = {
+    default_illegal_callback_fn,
+    NULL
+};
+
+static void default_error_callback_fn(const char* str, void* data) {
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+
+struct secp256k1_context_struct {
+    secp256k1_ecmult_context ecmult_ctx;
+    secp256k1_ecmult_gen_context ecmult_gen_ctx;
+    secp256k1_callback illegal_callback;
+    secp256k1_callback error_callback;
+};
+
+secp256k1_context* secp256k1_context_create(unsigned int flags) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = default_illegal_callback;
+    ret->error_callback = default_error_callback;
+
+    if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) {
+            secp256k1_callback_call(&ret->illegal_callback,
+                                    "Invalid flags");
+            free(ret);
+            return NULL;
+    }
+
+    secp256k1_ecmult_context_init(&ret->ecmult_ctx);
+    secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
+
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) {
+        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback);
+    }
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) {
+        secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback);
+    }
+
+    return ret;
+}
+
+secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = ctx->illegal_callback;
+    ret->error_callback = ctx->error_callback;
+    secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback);
+    secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback);
+    return ret;
+}
+
+void secp256k1_context_destroy(secp256k1_context* ctx) {
+    if (ctx != NULL) {
+        secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
+        secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
+
+        free(ctx);
+    }
+}
+
+void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_illegal_callback_fn;
+    }
+    ctx->illegal_callback.fn = fun;
+    ctx->illegal_callback.data = data;
+}
+
+void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_error_callback_fn;
+    }
+    ctx->error_callback.fn = fun;
+    ctx->error_callback.data = data;
+}
+
+static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        /* When the secp256k1_ge_storage type is exactly 64 byte, use its
+         * representation inside secp256k1_pubkey, as conversion is very fast.
+         * Note that secp256k1_pubkey_save must use the same representation. */
+        secp256k1_ge_storage s;
+        memcpy(&s, &pubkey->data[0], 64);
+        secp256k1_ge_from_storage(ge, &s);
+    } else {
+        /* Otherwise, fall back to 32-byte big endian for X and Y. */
+        secp256k1_fe x, y;
+        secp256k1_fe_set_b32(&x, pubkey->data);
+        secp256k1_fe_set_b32(&y, pubkey->data + 32);
+        secp256k1_ge_set_xy(ge, &x, &y);
+    }
+    ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
+    return 1;
+}
+
+static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        secp256k1_ge_storage s;
+        secp256k1_ge_to_storage(&s, ge);
+        memcpy(&pubkey->data[0], &s, 64);
+    } else {
+        VERIFY_CHECK(!secp256k1_ge_is_infinity(ge));
+        secp256k1_fe_normalize_var(&ge->x);
+        secp256k1_fe_normalize_var(&ge->y);
+        secp256k1_fe_get_b32(pubkey->data, &ge->x);
+        secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
+    }
+}
+
+int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) {
+    secp256k1_ge Q;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(input != NULL);
+    if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
+        return 0;
+    }
+    secp256k1_pubkey_save(pubkey, &Q);
+    secp256k1_ge_clear(&Q);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) {
+    secp256k1_ge Q;
+    size_t len;
+    int ret = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33 : 65));
+    len = *outputlen;
+    *outputlen = 0;
+    ARG_CHECK(output != NULL);
+    memset(output, 0, len);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION);
+    if (secp256k1_pubkey_load(ctx, &Q, pubkey)) {
+        ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION);
+        if (ret) {
+            *outputlen = len;
+        }
+    }
+    return ret;
+}
+
+static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+}
+
+static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input != NULL);
+
+    if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+        return 1;
+    } else {
+        memset(sig, 0, sizeof(*sig));
+        return 0;
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) {
+    secp256k1_scalar r, s;
+    int ret = 1;
+    int overflow = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+    } else {
+        memset(sig, 0, sizeof(*sig));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s);
+}
+
+int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) {
+    secp256k1_scalar r, s;
+    int ret = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin);
+    ret = secp256k1_scalar_is_high(&s);
+    if (sigout != NULL) {
+        if (ret) {
+            secp256k1_scalar_negate(&s, &s);
+        }
+        secp256k1_ecdsa_signature_save(sigout, &r, &s);
+    }
+
+    return ret;
+}
+
+int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return (!secp256k1_scalar_is_high(&s) &&
+            secp256k1_pubkey_load(ctx, &q, pubkey) &&
+            secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
+}
+
+static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   unsigned char keydata[112];
+   int keylen = 64;
+   secp256k1_rfc6979_hmac_sha256_t rng;
+   unsigned int i;
+   /* We feed a byte array to the PRNG as input, consisting of:
+    * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
+    * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
+    * - optionally 16 extra bytes with the algorithm name.
+    * Because the arguments have distinct fixed lengths it is not possible for
+    *  different argument mixtures to emulate each other and result in the same
+    *  nonces.
+    */
+   memcpy(keydata, key32, 32);
+   memcpy(keydata + 32, msg32, 32);
+   if (data != NULL) {
+       memcpy(keydata + 64, data, 32);
+       keylen = 96;
+   }
+   if (algo16 != NULL) {
+       memcpy(keydata + keylen, algo16, 16);
+       keylen += 16;
+   }
+   secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, keylen);
+   memset(keydata, 0, sizeof(keydata));
+   for (i = 0; i <= counter; i++) {
+       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+   }
+   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+   return 1;
+}
+
+const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
+const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
+
+int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            if (!overflow && !secp256k1_scalar_is_zero(&non)) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        memset(nonce32, 0, 32);
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_signature_save(signature, &r, &s);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) {
+    secp256k1_scalar sec;
+    int ret;
+    int overflow;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = !overflow && !secp256k1_scalar_is_zero(&sec);
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) {
+    secp256k1_gej pj;
+    secp256k1_ge p;
+    secp256k1_scalar sec;
+    int overflow;
+    int ret = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec));
+    if (ret) {
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec);
+        secp256k1_ge_set_gej(&p, &pj);
+        secp256k1_pubkey_save(pubkey, &p);
+    }
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar term;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+
+    ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term);
+    memset(seckey, 0, 32);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&term);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar term;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&term, tweak, &overflow);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar factor;
+    secp256k1_scalar sec;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor);
+    memset(seckey, 0, 32);
+    if (ret) {
+        secp256k1_scalar_get_b32(seckey, &sec);
+    }
+
+    secp256k1_scalar_clear(&sec);
+    secp256k1_scalar_clear(&factor);
+    return ret;
+}
+
+int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar factor;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
+
+    secp256k1_scalar_set_b32(&factor, tweak, &overflow);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
+        }
+    }
+
+    return ret;
+}
+
+int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) {
+    size_t i;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+
+    ARG_CHECK(pubnonce != NULL);
+    memset(pubnonce, 0, sizeof(*pubnonce));
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(pubnonces != NULL);
+
+    secp256k1_gej_set_infinity(&Qj);
+
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
+        secp256k1_gej_add_ge(&Qj, &Qj, &Q);
+    }
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(&Q, &Qj);
+    secp256k1_pubkey_save(pubnonce, &Q);
+    return 1;
+}
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+# include "modules/schnorr/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/main_impl.h"
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand.h
new file mode 100644
index 000000000..f8efa93c7
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand.h
@@ -0,0 +1,38 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_TESTRAND_H_
+#define _SECP256K1_TESTRAND_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+/* A non-cryptographic RNG used only for test infrastructure. */
+
+/** Seed the pseudorandom number generator for testing. */
+SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
+
+/** Generate a pseudorandom number in the range [0..2**32-1]. */
+static uint32_t secp256k1_rand32(void);
+
+/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or
+ *  more. */
+static uint32_t secp256k1_rand_bits(int bits);
+
+/** Generate a pseudorandom number in the range [0..range-1]. */
+static uint32_t secp256k1_rand_int(uint32_t range);
+
+/** Generate a pseudorandom 32-byte array. */
+static void secp256k1_rand256(unsigned char *b32);
+
+/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
+static void secp256k1_rand256_test(unsigned char *b32);
+
+/** Generate pseudorandom bytes with long sequences of zero and one bits. */
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len);
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand_impl.h
new file mode 100644
index 000000000..15c7b9f12
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/testrand_impl.h
@@ -0,0 +1,110 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_TESTRAND_IMPL_H_
+#define _SECP256K1_TESTRAND_IMPL_H_
+
+#include <stdint.h>
+#include <string.h>
+
+#include "testrand.h"
+#include "hash.h"
+
+static secp256k1_rfc6979_hmac_sha256_t secp256k1_test_rng;
+static uint32_t secp256k1_test_rng_precomputed[8];
+static int secp256k1_test_rng_precomputed_used = 8;
+static uint64_t secp256k1_test_rng_integer;
+static int secp256k1_test_rng_integer_bits_left = 0;
+
+SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
+    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
+}
+
+SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
+    if (secp256k1_test_rng_precomputed_used == 8) {
+        secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
+        secp256k1_test_rng_precomputed_used = 0;
+    }
+    return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
+}
+
+static uint32_t secp256k1_rand_bits(int bits) {
+    uint32_t ret;
+    if (secp256k1_test_rng_integer_bits_left < bits) {
+        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left);
+        secp256k1_test_rng_integer_bits_left += 32;
+    }
+    ret = secp256k1_test_rng_integer;
+    secp256k1_test_rng_integer >>= bits;
+    secp256k1_test_rng_integer_bits_left -= bits;
+    ret &= ((~((uint32_t)0)) >> (32 - bits));
+    return ret;
+}
+
+static uint32_t secp256k1_rand_int(uint32_t range) {
+    /* We want a uniform integer between 0 and range-1, inclusive.
+     * B is the smallest number such that range <= 2**B.
+     * two mechanisms implemented here:
+     * - generate B bits numbers until one below range is found, and return it
+     * - find the largest multiple M of range that is <= 2**(B+A), generate B+A
+     *   bits numbers until one below M is found, and return it modulo range
+     * The second mechanism consumes A more bits of entropy in every iteration,
+     * but may need fewer iterations due to M being closer to 2**(B+A) then
+     * range is to 2**B. The array below (indexed by B) contains a 0 when the
+     * first mechanism is to be used, and the number A otherwise.
+     */
+    static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0};
+    uint32_t trange, mult;
+    int bits = 0;
+    if (range <= 1) {
+        return 0;
+    }
+    trange = range - 1;
+    while (trange > 0) {
+        trange >>= 1;
+        bits++;
+    }
+    if (addbits[bits]) {
+        bits = bits + addbits[bits];
+        mult = ((~((uint32_t)0)) >> (32 - bits)) / range;
+        trange = range * mult;
+    } else {
+        trange = range;
+        mult = 1;
+    }
+    while(1) {
+        uint32_t x = secp256k1_rand_bits(bits);
+        if (x < trange) {
+            return (mult == 1) ? x : (x % range);
+        }
+    }
+}
+
+static void secp256k1_rand256(unsigned char *b32) {
+    secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
+}
+
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) {
+    size_t bits = 0;
+    memset(bytes, 0, len);
+    while (bits < len * 8) {
+        int now;
+        uint32_t val;
+        now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31;
+        val = secp256k1_rand_bits(1);
+        while (now > 0 && bits < len * 8) {
+            bytes[bits / 8] |= val << (bits % 8);
+            now--;
+            bits++;
+        }
+    }
+}
+
+static void secp256k1_rand256_test(unsigned char *b32) {
+    secp256k1_rand_bytes_test(b32, 32);
+}
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests.c
new file mode 100644
index 000000000..9ae7d3028
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests.c
@@ -0,0 +1,4525 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <time.h>
+
+#include "secp256k1.c"
+#include "include/secp256k1.h"
+#include "testrand_impl.h"
+
+#ifdef ENABLE_OPENSSL_TESTS
+#include "openssl/bn.h"
+#include "openssl/ec.h"
+#include "openssl/ecdsa.h"
+#include "openssl/obj_mac.h"
+#endif
+
+#include "contrib/lax_der_parsing.c"
+#include "contrib/lax_der_privatekey_parsing.c"
+
+#if !defined(VG_CHECK)
+# if defined(VALGRIND)
+#  include <valgrind/memcheck.h>
+#  define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
+#  define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
+# else
+#  define VG_UNDEF(x,y)
+#  define VG_CHECK(x,y)
+# endif
+#endif
+
+static int count = 64;
+static secp256k1_context *ctx = NULL;
+
+static void counting_illegal_callback_fn(const char* str, void* data) {
+    /* Dummy callback function that just counts. */
+    int32_t *p;
+    (void)str;
+    p = data;
+    (*p)++;
+}
+
+static void uncounting_illegal_callback_fn(const char* str, void* data) {
+    /* Dummy callback function that just counts (backwards). */
+    int32_t *p;
+    (void)str;
+    p = data;
+    (*p)--;
+}
+
+void random_field_element_test(secp256k1_fe *fe) {
+    do {
+        unsigned char b32[32];
+        secp256k1_rand256_test(b32);
+        if (secp256k1_fe_set_b32(fe, b32)) {
+            break;
+        }
+    } while(1);
+}
+
+void random_field_element_magnitude(secp256k1_fe *fe) {
+    secp256k1_fe zero;
+    int n = secp256k1_rand_int(9);
+    secp256k1_fe_normalize(fe);
+    if (n == 0) {
+        return;
+    }
+    secp256k1_fe_clear(&zero);
+    secp256k1_fe_negate(&zero, &zero, 0);
+    secp256k1_fe_mul_int(&zero, n - 1);
+    secp256k1_fe_add(fe, &zero);
+    VERIFY_CHECK(fe->magnitude == n);
+}
+
+void random_group_element_test(secp256k1_ge *ge) {
+    secp256k1_fe fe;
+    do {
+        random_field_element_test(&fe);
+        if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
+            secp256k1_fe_normalize(&ge->y);
+            break;
+        }
+    } while(1);
+}
+
+void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
+    secp256k1_fe z2, z3;
+    do {
+        random_field_element_test(&gej->z);
+        if (!secp256k1_fe_is_zero(&gej->z)) {
+            break;
+        }
+    } while(1);
+    secp256k1_fe_sqr(&z2, &gej->z);
+    secp256k1_fe_mul(&z3, &z2, &gej->z);
+    secp256k1_fe_mul(&gej->x, &ge->x, &z2);
+    secp256k1_fe_mul(&gej->y, &ge->y, &z3);
+    gej->infinity = ge->infinity;
+}
+
+void random_scalar_order_test(secp256k1_scalar *num) {
+    do {
+        unsigned char b32[32];
+        int overflow = 0;
+        secp256k1_rand256_test(b32);
+        secp256k1_scalar_set_b32(num, b32, &overflow);
+        if (overflow || secp256k1_scalar_is_zero(num)) {
+            continue;
+        }
+        break;
+    } while(1);
+}
+
+void random_scalar_order(secp256k1_scalar *num) {
+    do {
+        unsigned char b32[32];
+        int overflow = 0;
+        secp256k1_rand256(b32);
+        secp256k1_scalar_set_b32(num, b32, &overflow);
+        if (overflow || secp256k1_scalar_is_zero(num)) {
+            continue;
+        }
+        break;
+    } while(1);
+}
+
+void run_context_tests(void) {
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    unsigned char ctmp[32];
+    int32_t ecount;
+    int32_t ecount2;
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    secp256k1_gej pubj;
+    secp256k1_ge pub;
+    secp256k1_scalar msg, key, nonce;
+    secp256k1_scalar sigr, sigs;
+
+    ecount = 0;
+    ecount2 = 10;
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
+    CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
+
+    /*** clone and destroy all of them to make sure cloning was complete ***/
+    {
+        secp256k1_context *ctx_tmp;
+
+        ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
+        ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
+        ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_destroy(ctx_tmp);
+        ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
+    }
+
+    /* Verify that the error callback makes it across the clone. */
+    CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
+    /* And that it resets back to default. */
+    secp256k1_context_set_error_callback(sign, NULL, NULL);
+    CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
+
+    /*** attempt to use them ***/
+    random_scalar_order_test(&msg);
+    random_scalar_order_test(&key);
+    secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
+    secp256k1_ge_set_gej(&pub, &pubj);
+
+    /* Verify context-type checking illegal-argument errors. */
+    memset(ctmp, 1, 32);
+    CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
+    CHECK(ecount == 1);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
+    CHECK(ecount == 2);
+    VG_UNDEF(&sig, sizeof(sig));
+    CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
+    VG_CHECK(&sig, sizeof(sig));
+    CHECK(ecount2 == 10);
+    CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
+    CHECK(ecount2 == 11);
+    CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
+    CHECK(ecount2 == 12);
+    CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
+    CHECK(ecount2 == 13);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_context_randomize(vrfy, ctmp) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_context_randomize(sign, NULL) == 1);
+    CHECK(ecount2 == 13);
+    secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
+    secp256k1_context_set_illegal_callback(sign, NULL, NULL);
+
+    /* This shouldn't leak memory, due to already-set tests. */
+    secp256k1_ecmult_gen_context_build(&sign->ecmult_gen_ctx, NULL);
+    secp256k1_ecmult_context_build(&vrfy->ecmult_ctx, NULL);
+
+    /* obtain a working nonce */
+    do {
+        random_scalar_order_test(&nonce);
+    } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+
+    /* try signing */
+    CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+    CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+
+    /* try verifying */
+    CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+
+    /* cleanup */
+    secp256k1_context_destroy(none);
+    secp256k1_context_destroy(sign);
+    secp256k1_context_destroy(vrfy);
+    secp256k1_context_destroy(both);
+    /* Defined as no-op. */
+    secp256k1_context_destroy(NULL);
+}
+
+/***** HASH TESTS *****/
+
+void run_sha256_tests(void) {
+    static const char *inputs[8] = {
+        "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
+        "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
+        "For this sample, this 63-byte string will be used as input data",
+        "This is exactly 64 bytes long, not counting the terminating byte"
+    };
+    static const unsigned char outputs[8][32] = {
+        {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
+        {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
+        {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
+        {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d},
+        {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
+        {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
+        {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
+        {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
+    };
+    int i;
+    for (i = 0; i < 8; i++) {
+        unsigned char out[32];
+        secp256k1_sha256_t hasher;
+        secp256k1_sha256_initialize(&hasher);
+        secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+        secp256k1_sha256_finalize(&hasher, out);
+        CHECK(memcmp(out, outputs[i], 32) == 0);
+        if (strlen(inputs[i]) > 0) {
+            int split = secp256k1_rand_int(strlen(inputs[i]));
+            secp256k1_sha256_initialize(&hasher);
+            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+            secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+            secp256k1_sha256_finalize(&hasher, out);
+            CHECK(memcmp(out, outputs[i], 32) == 0);
+        }
+    }
+}
+
+void run_hmac_sha256_tests(void) {
+    static const char *keys[6] = {
+        "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
+        "\x4a\x65\x66\x65",
+        "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
+        "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
+        "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
+        "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
+    };
+    static const char *inputs[6] = {
+        "\x48\x69\x20\x54\x68\x65\x72\x65",
+        "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
+        "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
+        "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
+        "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
+        "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
+    };
+    static const unsigned char outputs[6][32] = {
+        {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
+        {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
+        {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
+        {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
+        {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
+        {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
+    };
+    int i;
+    for (i = 0; i < 6; i++) {
+        secp256k1_hmac_sha256_t hasher;
+        unsigned char out[32];
+        secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+        secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+        secp256k1_hmac_sha256_finalize(&hasher, out);
+        CHECK(memcmp(out, outputs[i], 32) == 0);
+        if (strlen(inputs[i]) > 0) {
+            int split = secp256k1_rand_int(strlen(inputs[i]));
+            secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+            secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+            secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+            secp256k1_hmac_sha256_finalize(&hasher, out);
+            CHECK(memcmp(out, outputs[i], 32) == 0);
+        }
+    }
+}
+
+void run_rfc6979_hmac_sha256_tests(void) {
+    static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
+    static const unsigned char out1[3][32] = {
+        {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
+        {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
+        {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
+    };
+
+    static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
+    static const unsigned char out2[3][32] = {
+        {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
+        {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
+        {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
+    };
+
+    secp256k1_rfc6979_hmac_sha256_t rng;
+    unsigned char out[32];
+    int i;
+
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
+    for (i = 0; i < 3; i++) {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        CHECK(memcmp(out, out1[i], 32) == 0);
+    }
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
+    for (i = 0; i < 3; i++) {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        CHECK(memcmp(out, out1[i], 32) != 0);
+    }
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
+    for (i = 0; i < 3; i++) {
+        secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+        CHECK(memcmp(out, out2[i], 32) == 0);
+    }
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+}
+
+/***** RANDOM TESTS *****/
+
+void test_rand_bits(int rand32, int bits) {
+    /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
+     * get a false negative chance below once in a billion */
+    static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
+    /* We try multiplying the results with various odd numbers, which shouldn't
+     * influence the uniform distribution modulo a power of 2. */
+    static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
+    /* We only select up to 6 bits from the output to analyse */
+    unsigned int usebits = bits > 6 ? 6 : bits;
+    unsigned int maxshift = bits - usebits;
+    /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
+       number, track all observed outcomes, one per bit in a uint64_t. */
+    uint64_t x[6][27] = {{0}};
+    unsigned int i, shift, m;
+    /* Multiply the output of all rand calls with the odd number m, which
+       should not change the uniformity of its distribution. */
+    for (i = 0; i < rounds[usebits]; i++) {
+        uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
+        CHECK((((uint64_t)r) >> bits) == 0);
+        for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+            uint32_t rm = r * mults[m];
+            for (shift = 0; shift <= maxshift; shift++) {
+                x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
+            }
+        }
+    }
+    for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+        for (shift = 0; shift <= maxshift; shift++) {
+            /* Test that the lower usebits bits of x[shift] are 1 */
+            CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
+        }
+    }
+}
+
+/* Subrange must be a whole divisor of range, and at most 64 */
+void test_rand_int(uint32_t range, uint32_t subrange) {
+    /* (1-1/subrange)^rounds < 1/10^9 */
+    int rounds = (subrange * 2073) / 100;
+    int i;
+    uint64_t x = 0;
+    CHECK((range % subrange) == 0);
+    for (i = 0; i < rounds; i++) {
+        uint32_t r = secp256k1_rand_int(range);
+        CHECK(r < range);
+        r = r % subrange;
+        x |= (((uint64_t)1) << r);
+    }
+    /* Test that the lower subrange bits of x are 1. */
+    CHECK(((~x) << (64 - subrange)) == 0);
+}
+
+void run_rand_bits(void) {
+    size_t b;
+    test_rand_bits(1, 32);
+    for (b = 1; b <= 32; b++) {
+        test_rand_bits(0, b);
+    }
+}
+
+void run_rand_int(void) {
+    static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
+    static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
+    unsigned int m, s;
+    for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
+        for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
+            test_rand_int(ms[m] * ss[s], ss[s]);
+        }
+    }
+}
+
+/***** NUM TESTS *****/
+
+#ifndef USE_NUM_NONE
+void random_num_negate(secp256k1_num *num) {
+    if (secp256k1_rand_bits(1)) {
+        secp256k1_num_negate(num);
+    }
+}
+
+void random_num_order_test(secp256k1_num *num) {
+    secp256k1_scalar sc;
+    random_scalar_order_test(&sc);
+    secp256k1_scalar_get_num(num, &sc);
+}
+
+void random_num_order(secp256k1_num *num) {
+    secp256k1_scalar sc;
+    random_scalar_order(&sc);
+    secp256k1_scalar_get_num(num, &sc);
+}
+
+void test_num_negate(void) {
+    secp256k1_num n1;
+    secp256k1_num n2;
+    random_num_order_test(&n1); /* n1 = R */
+    random_num_negate(&n1);
+    secp256k1_num_copy(&n2, &n1); /* n2 = R */
+    secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */
+    CHECK(secp256k1_num_is_zero(&n1));
+    secp256k1_num_copy(&n1, &n2); /* n1 = R */
+    secp256k1_num_negate(&n1); /* n1 = -R */
+    CHECK(!secp256k1_num_is_zero(&n1));
+    secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */
+    CHECK(secp256k1_num_is_zero(&n1));
+    secp256k1_num_copy(&n1, &n2); /* n1 = R */
+    secp256k1_num_negate(&n1); /* n1 = -R */
+    CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
+    secp256k1_num_negate(&n1); /* n1 = R */
+    CHECK(secp256k1_num_eq(&n1, &n2));
+}
+
+void test_num_add_sub(void) {
+    int i;
+    secp256k1_scalar s;
+    secp256k1_num n1;
+    secp256k1_num n2;
+    secp256k1_num n1p2, n2p1, n1m2, n2m1;
+    random_num_order_test(&n1); /* n1 = R1 */
+    if (secp256k1_rand_bits(1)) {
+        random_num_negate(&n1);
+    }
+    random_num_order_test(&n2); /* n2 = R2 */
+    if (secp256k1_rand_bits(1)) {
+        random_num_negate(&n2);
+    }
+    secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
+    secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
+    secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
+    secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */
+    CHECK(secp256k1_num_eq(&n1p2, &n2p1));
+    CHECK(!secp256k1_num_eq(&n1p2, &n1m2));
+    secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */
+    CHECK(secp256k1_num_eq(&n2m1, &n1m2));
+    CHECK(!secp256k1_num_eq(&n2m1, &n1));
+    secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */
+    CHECK(secp256k1_num_eq(&n2m1, &n1));
+    CHECK(!secp256k1_num_eq(&n2p1, &n1));
+    secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
+    CHECK(secp256k1_num_eq(&n2p1, &n1));
+
+    /* check is_one */
+    secp256k1_scalar_set_int(&s, 1);
+    secp256k1_scalar_get_num(&n1, &s);
+    CHECK(secp256k1_num_is_one(&n1));
+    /* check that 2^n + 1 is never 1 */
+    secp256k1_scalar_get_num(&n2, &s);
+    for (i = 0; i < 250; ++i) {
+        secp256k1_num_add(&n1, &n1, &n1);    /* n1 *= 2 */
+        secp256k1_num_add(&n1p2, &n1, &n2);  /* n1p2 = n1 + 1 */
+        CHECK(!secp256k1_num_is_one(&n1p2));
+    }
+}
+
+void test_num_mod(void) {
+    int i;
+    secp256k1_scalar s;
+    secp256k1_num order, n;
+
+    /* check that 0 mod anything is 0 */
+    random_scalar_order_test(&s);
+    secp256k1_scalar_get_num(&order, &s);
+    secp256k1_scalar_set_int(&s, 0);
+    secp256k1_scalar_get_num(&n, &s);
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+
+    /* check that anything mod 1 is 0 */
+    secp256k1_scalar_set_int(&s, 1);
+    secp256k1_scalar_get_num(&order, &s);
+    secp256k1_scalar_get_num(&n, &s);
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+
+    /* check that increasing the number past 2^256 does not break this */
+    random_scalar_order_test(&s);
+    secp256k1_scalar_get_num(&n, &s);
+    /* multiply by 2^8, which'll test this case with high probability */
+    for (i = 0; i < 8; ++i) {
+        secp256k1_num_add(&n, &n, &n);
+    }
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+}
+
+void test_num_jacobi(void) {
+    secp256k1_scalar sqr;
+    secp256k1_scalar small;
+    secp256k1_scalar five;  /* five is not a quadratic residue */
+    secp256k1_num order, n;
+    int i;
+    /* squares mod 5 are 1, 4 */
+    const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
+
+    /* check some small values with 5 as the order */
+    secp256k1_scalar_set_int(&five, 5);
+    secp256k1_scalar_get_num(&order, &five);
+    for (i = 0; i < 10; ++i) {
+        secp256k1_scalar_set_int(&small, i);
+        secp256k1_scalar_get_num(&n, &small);
+        CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
+    }
+
+    /** test large values with 5 as group order */
+    secp256k1_scalar_get_num(&order, &five);
+    /* we first need a scalar which is not a multiple of 5 */
+    do {
+        secp256k1_num fiven;
+        random_scalar_order_test(&sqr);
+        secp256k1_scalar_get_num(&fiven, &five);
+        secp256k1_scalar_get_num(&n, &sqr);
+        secp256k1_num_mod(&n, &fiven);
+    } while (secp256k1_num_is_zero(&n));
+    /* next force it to be a residue. 2 is a nonresidue mod 5 so we can
+     * just multiply by two, i.e. add the number to itself */
+    if (secp256k1_num_jacobi(&n, &order) == -1) {
+        secp256k1_num_add(&n, &n, &n);
+    }
+
+    /* test residue */
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+    /* test nonresidue */
+    secp256k1_num_add(&n, &n, &n);
+    CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+
+    /** test with secp group order as order */
+    secp256k1_scalar_order_get_num(&order);
+    random_scalar_order_test(&sqr);
+    secp256k1_scalar_sqr(&sqr, &sqr);
+    /* test residue */
+    secp256k1_scalar_get_num(&n, &sqr);
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+    /* test nonresidue */
+    secp256k1_scalar_mul(&sqr, &sqr, &five);
+    secp256k1_scalar_get_num(&n, &sqr);
+    CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+    /* test multiple of the order*/
+    CHECK(secp256k1_num_jacobi(&order, &order) == 0);
+
+    /* check one less than the order */
+    secp256k1_scalar_set_int(&small, 1);
+    secp256k1_scalar_get_num(&n, &small);
+    secp256k1_num_sub(&n, &order, &n);
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);  /* sage confirms this is 1 */
+}
+
+void run_num_smalltests(void) {
+    int i;
+    for (i = 0; i < 100*count; i++) {
+        test_num_negate();
+        test_num_add_sub();
+        test_num_mod();
+        test_num_jacobi();
+    }
+}
+#endif
+
+/***** SCALAR TESTS *****/
+
+void scalar_test(void) {
+    secp256k1_scalar s;
+    secp256k1_scalar s1;
+    secp256k1_scalar s2;
+#ifndef USE_NUM_NONE
+    secp256k1_num snum, s1num, s2num;
+    secp256k1_num order, half_order;
+#endif
+    unsigned char c[32];
+
+    /* Set 's' to a random scalar, with value 'snum'. */
+    random_scalar_order_test(&s);
+
+    /* Set 's1' to a random scalar, with value 's1num'. */
+    random_scalar_order_test(&s1);
+
+    /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
+    random_scalar_order_test(&s2);
+    secp256k1_scalar_get_b32(c, &s2);
+
+#ifndef USE_NUM_NONE
+    secp256k1_scalar_get_num(&snum, &s);
+    secp256k1_scalar_get_num(&s1num, &s1);
+    secp256k1_scalar_get_num(&s2num, &s2);
+
+    secp256k1_scalar_order_get_num(&order);
+    half_order = order;
+    secp256k1_num_shift(&half_order, 1);
+#endif
+
+    {
+        int i;
+        /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
+        secp256k1_scalar n;
+        secp256k1_scalar_set_int(&n, 0);
+        for (i = 0; i < 256; i += 4) {
+            secp256k1_scalar t;
+            int j;
+            secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
+            for (j = 0; j < 4; j++) {
+                secp256k1_scalar_add(&n, &n, &n);
+            }
+            secp256k1_scalar_add(&n, &n, &t);
+        }
+        CHECK(secp256k1_scalar_eq(&n, &s));
+    }
+
+    {
+        /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
+        secp256k1_scalar n;
+        int i = 0;
+        secp256k1_scalar_set_int(&n, 0);
+        while (i < 256) {
+            secp256k1_scalar t;
+            int j;
+            int now = secp256k1_rand_int(15) + 1;
+            if (now + i > 256) {
+                now = 256 - i;
+            }
+            secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
+            for (j = 0; j < now; j++) {
+                secp256k1_scalar_add(&n, &n, &n);
+            }
+            secp256k1_scalar_add(&n, &n, &t);
+            i += now;
+        }
+        CHECK(secp256k1_scalar_eq(&n, &s));
+    }
+
+#ifndef USE_NUM_NONE
+    {
+        /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
+        secp256k1_num rnum;
+        secp256k1_num r2num;
+        secp256k1_scalar r;
+        secp256k1_num_add(&rnum, &snum, &s2num);
+        secp256k1_num_mod(&rnum, &order);
+        secp256k1_scalar_add(&r, &s, &s2);
+        secp256k1_scalar_get_num(&r2num, &r);
+        CHECK(secp256k1_num_eq(&rnum, &r2num));
+    }
+
+    {
+        /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
+        secp256k1_scalar r;
+        secp256k1_num r2num;
+        secp256k1_num rnum;
+        secp256k1_num_mul(&rnum, &snum, &s2num);
+        secp256k1_num_mod(&rnum, &order);
+        secp256k1_scalar_mul(&r, &s, &s2);
+        secp256k1_scalar_get_num(&r2num, &r);
+        CHECK(secp256k1_num_eq(&rnum, &r2num));
+        /* The result can only be zero if at least one of the factors was zero. */
+        CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
+        /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
+        CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
+        CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
+    }
+
+    {
+        secp256k1_scalar neg;
+        secp256k1_num negnum;
+        secp256k1_num negnum2;
+        /* Check that comparison with zero matches comparison with zero on the number. */
+        CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
+        /* Check that comparison with the half order is equal to testing for high scalar. */
+        CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
+        secp256k1_scalar_negate(&neg, &s);
+        secp256k1_num_sub(&negnum, &order, &snum);
+        secp256k1_num_mod(&negnum, &order);
+        /* Check that comparison with the half order is equal to testing for high scalar after negation. */
+        CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
+        /* Negating should change the high property, unless the value was already zero. */
+        CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
+        secp256k1_scalar_get_num(&negnum2, &neg);
+        /* Negating a scalar should be equal to (order - n) mod order on the number. */
+        CHECK(secp256k1_num_eq(&negnum, &negnum2));
+        secp256k1_scalar_add(&neg, &neg, &s);
+        /* Adding a number to its negation should result in zero. */
+        CHECK(secp256k1_scalar_is_zero(&neg));
+        secp256k1_scalar_negate(&neg, &neg);
+        /* Negating zero should still result in zero. */
+        CHECK(secp256k1_scalar_is_zero(&neg));
+    }
+
+    {
+        /* Test secp256k1_scalar_mul_shift_var. */
+        secp256k1_scalar r;
+        secp256k1_num one;
+        secp256k1_num rnum;
+        secp256k1_num rnum2;
+        unsigned char cone[1] = {0x01};
+        unsigned int shift = 256 + secp256k1_rand_int(257);
+        secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
+        secp256k1_num_mul(&rnum, &s1num, &s2num);
+        secp256k1_num_shift(&rnum, shift - 1);
+        secp256k1_num_set_bin(&one, cone, 1);
+        secp256k1_num_add(&rnum, &rnum, &one);
+        secp256k1_num_shift(&rnum, 1);
+        secp256k1_scalar_get_num(&rnum2, &r);
+        CHECK(secp256k1_num_eq(&rnum, &rnum2));
+    }
+
+    {
+        /* test secp256k1_scalar_shr_int */
+        secp256k1_scalar r;
+        int i;
+        random_scalar_order_test(&r);
+        for (i = 0; i < 100; ++i) {
+            int low;
+            int shift = 1 + secp256k1_rand_int(15);
+            int expected = r.d[0] % (1 << shift);
+            low = secp256k1_scalar_shr_int(&r, shift);
+            CHECK(expected == low);
+        }
+    }
+#endif
+
+    {
+        /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
+        if (!secp256k1_scalar_is_zero(&s)) {
+            secp256k1_scalar inv;
+#ifndef USE_NUM_NONE
+            secp256k1_num invnum;
+            secp256k1_num invnum2;
+#endif
+            secp256k1_scalar_inverse(&inv, &s);
+#ifndef USE_NUM_NONE
+            secp256k1_num_mod_inverse(&invnum, &snum, &order);
+            secp256k1_scalar_get_num(&invnum2, &inv);
+            CHECK(secp256k1_num_eq(&invnum, &invnum2));
+#endif
+            secp256k1_scalar_mul(&inv, &inv, &s);
+            /* Multiplying a scalar with its inverse must result in one. */
+            CHECK(secp256k1_scalar_is_one(&inv));
+            secp256k1_scalar_inverse(&inv, &inv);
+            /* Inverting one must result in one. */
+            CHECK(secp256k1_scalar_is_one(&inv));
+#ifndef USE_NUM_NONE
+            secp256k1_scalar_get_num(&invnum, &inv);
+            CHECK(secp256k1_num_is_one(&invnum));
+#endif
+        }
+    }
+
+    {
+        /* Test commutativity of add. */
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar_add(&r1, &s1, &s2);
+        secp256k1_scalar_add(&r2, &s2, &s1);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar b;
+        int i;
+        /* Test add_bit. */
+        int bit = secp256k1_rand_bits(8);
+        secp256k1_scalar_set_int(&b, 1);
+        CHECK(secp256k1_scalar_is_one(&b));
+        for (i = 0; i < bit; i++) {
+            secp256k1_scalar_add(&b, &b, &b);
+        }
+        r1 = s1;
+        r2 = s1;
+        if (!secp256k1_scalar_add(&r1, &r1, &b)) {
+            /* No overflow happened. */
+            secp256k1_scalar_cadd_bit(&r2, bit, 1);
+            CHECK(secp256k1_scalar_eq(&r1, &r2));
+            /* cadd is a noop when flag is zero */
+            secp256k1_scalar_cadd_bit(&r2, bit, 0);
+            CHECK(secp256k1_scalar_eq(&r1, &r2));
+        }
+    }
+
+    {
+        /* Test commutativity of mul. */
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar_mul(&r1, &s1, &s2);
+        secp256k1_scalar_mul(&r2, &s2, &s1);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        /* Test associativity of add. */
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar_add(&r1, &s1, &s2);
+        secp256k1_scalar_add(&r1, &r1, &s);
+        secp256k1_scalar_add(&r2, &s2, &s);
+        secp256k1_scalar_add(&r2, &s1, &r2);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        /* Test associativity of mul. */
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar_mul(&r1, &s1, &s2);
+        secp256k1_scalar_mul(&r1, &r1, &s);
+        secp256k1_scalar_mul(&r2, &s2, &s);
+        secp256k1_scalar_mul(&r2, &s1, &r2);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        /* Test distributitivity of mul over add. */
+        secp256k1_scalar r1, r2, t;
+        secp256k1_scalar_add(&r1, &s1, &s2);
+        secp256k1_scalar_mul(&r1, &r1, &s);
+        secp256k1_scalar_mul(&r2, &s1, &s);
+        secp256k1_scalar_mul(&t, &s2, &s);
+        secp256k1_scalar_add(&r2, &r2, &t);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        /* Test square. */
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar_sqr(&r1, &s1);
+        secp256k1_scalar_mul(&r2, &s1, &s1);
+        CHECK(secp256k1_scalar_eq(&r1, &r2));
+    }
+
+    {
+        /* Test multiplicative identity. */
+        secp256k1_scalar r1, v1;
+        secp256k1_scalar_set_int(&v1,1);
+        secp256k1_scalar_mul(&r1, &s1, &v1);
+        CHECK(secp256k1_scalar_eq(&r1, &s1));
+    }
+
+    {
+        /* Test additive identity. */
+        secp256k1_scalar r1, v0;
+        secp256k1_scalar_set_int(&v0,0);
+        secp256k1_scalar_add(&r1, &s1, &v0);
+        CHECK(secp256k1_scalar_eq(&r1, &s1));
+    }
+
+    {
+        /* Test zero product property. */
+        secp256k1_scalar r1, v0;
+        secp256k1_scalar_set_int(&v0,0);
+        secp256k1_scalar_mul(&r1, &s1, &v0);
+        CHECK(secp256k1_scalar_eq(&r1, &v0));
+    }
+
+}
+
+void run_scalar_tests(void) {
+    int i;
+    for (i = 0; i < 128 * count; i++) {
+        scalar_test();
+    }
+
+    {
+        /* (-1)+1 should be zero. */
+        secp256k1_scalar s, o;
+        secp256k1_scalar_set_int(&s, 1);
+        CHECK(secp256k1_scalar_is_one(&s));
+        secp256k1_scalar_negate(&o, &s);
+        secp256k1_scalar_add(&o, &o, &s);
+        CHECK(secp256k1_scalar_is_zero(&o));
+        secp256k1_scalar_negate(&o, &o);
+        CHECK(secp256k1_scalar_is_zero(&o));
+    }
+
+#ifndef USE_NUM_NONE
+    {
+        /* A scalar with value of the curve order should be 0. */
+        secp256k1_num order;
+        secp256k1_scalar zero;
+        unsigned char bin[32];
+        int overflow = 0;
+        secp256k1_scalar_order_get_num(&order);
+        secp256k1_num_get_bin(bin, 32, &order);
+        secp256k1_scalar_set_b32(&zero, bin, &overflow);
+        CHECK(overflow == 1);
+        CHECK(secp256k1_scalar_is_zero(&zero));
+    }
+#endif
+
+    {
+        /* Does check_overflow check catch all ones? */
+        static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
+            0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+            0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
+        );
+        CHECK(secp256k1_scalar_check_overflow(&overflowed));
+    }
+
+    {
+        /* Static test vectors.
+         * These were reduced from ~10^12 random vectors based on comparison-decision
+         *  and edge-case coverage on 32-bit and 64-bit implementations.
+         * The responses were generated with Sage 5.9.
+         */
+        secp256k1_scalar x;
+        secp256k1_scalar y;
+        secp256k1_scalar z;
+        secp256k1_scalar zz;
+        secp256k1_scalar one;
+        secp256k1_scalar r1;
+        secp256k1_scalar r2;
+#if defined(USE_SCALAR_INV_NUM)
+        secp256k1_scalar zzv;
+#endif
+        int overflow;
+        unsigned char chal[33][2][32] = {
+            {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
+            {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
+              0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
+             {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
+              0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
+              0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
+              0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
+              0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
+              0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
+              0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
+              0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
+             {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
+              0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
+             {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+              0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
+              0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
+              0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
+             {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
+              0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
+              0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
+              0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
+            {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
+             {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
+            {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
+              0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
+            {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
+             {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
+              0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
+              0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
+            {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
+            {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
+              0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
+             {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+              0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
+              0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
+            {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
+              0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
+              0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
+              0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
+            {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
+              0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
+             {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
+              0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
+            {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+              0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
+             {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+              0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
+        };
+        unsigned char res[33][2][32] = {
+            {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
+              0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
+              0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
+              0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
+             {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
+              0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
+              0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
+              0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
+            {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
+              0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
+              0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
+              0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
+             {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
+              0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
+              0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
+              0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
+            {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
+              0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
+              0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
+              0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
+             {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
+              0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
+              0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
+              0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
+            {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
+              0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
+              0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
+              0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
+             {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
+              0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
+              0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
+              0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
+            {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
+              0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
+              0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
+              0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
+             {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
+              0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
+              0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
+              0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
+            {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
+              0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
+              0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
+              0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
+             {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
+              0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
+              0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
+              0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
+            {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
+              0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
+              0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
+              0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
+             {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
+              0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
+              0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
+              0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
+            {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
+              0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
+              0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
+              0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
+             {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
+              0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
+              0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
+              0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
+            {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
+              0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
+              0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
+              0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
+             {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
+              0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
+              0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
+              0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
+            {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
+              0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
+              0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
+              0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
+             {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
+              0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
+              0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
+              0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
+            {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
+              0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
+              0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
+              0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
+             {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
+              0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
+              0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
+              0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
+            {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
+              0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
+              0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
+              0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
+             {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
+              0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
+              0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
+              0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
+            {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
+              0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
+              0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
+              0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
+             {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
+              0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
+              0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
+              0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
+            {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
+              0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
+              0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
+              0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
+             {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
+              0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
+              0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
+              0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
+            {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
+              0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
+              0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
+              0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
+             {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
+              0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
+              0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
+              0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
+            {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
+              0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
+              0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
+              0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
+             {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
+              0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
+              0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
+              0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
+            {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
+              0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
+              0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
+              0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
+             {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
+              0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
+              0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
+              0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
+            {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
+              0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
+              0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
+              0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
+             {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
+              0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
+              0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
+              0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
+            {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
+              0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
+              0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
+              0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
+             {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
+              0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
+              0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
+              0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
+            {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
+              0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
+              0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
+              0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
+             {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
+              0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
+              0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
+              0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
+             {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+            {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
+              0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
+              0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
+              0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
+             {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
+              0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
+              0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
+              0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+              0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+              0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
+             {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
+              0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
+              0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
+              0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
+             {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
+              0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
+              0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
+              0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
+            {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
+              0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
+              0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
+              0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
+             {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
+              0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
+              0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
+              0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
+            {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
+              0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
+              0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
+              0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
+             {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
+              0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
+              0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
+              0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
+            {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
+              0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
+              0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
+              0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
+             {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
+              0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
+              0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
+              0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
+            {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
+              0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
+              0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
+              0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
+             {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
+              0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
+              0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
+              0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
+            {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
+              0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
+              0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
+              0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
+             {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
+              0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
+              0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
+              0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
+            {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+              0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+              0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+              0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
+             {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+              0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+              0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+              0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
+        };
+        secp256k1_scalar_set_int(&one, 1);
+        for (i = 0; i < 33; i++) {
+            secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_mul(&z, &x, &y);
+            CHECK(!secp256k1_scalar_check_overflow(&z));
+            CHECK(secp256k1_scalar_eq(&r1, &z));
+            if (!secp256k1_scalar_is_zero(&y)) {
+                secp256k1_scalar_inverse(&zz, &y);
+                CHECK(!secp256k1_scalar_check_overflow(&zz));
+#if defined(USE_SCALAR_INV_NUM)
+                secp256k1_scalar_inverse_var(&zzv, &y);
+                CHECK(secp256k1_scalar_eq(&zzv, &zz));
+#endif
+                secp256k1_scalar_mul(&z, &z, &zz);
+                CHECK(!secp256k1_scalar_check_overflow(&z));
+                CHECK(secp256k1_scalar_eq(&x, &z));
+                secp256k1_scalar_mul(&zz, &zz, &y);
+                CHECK(!secp256k1_scalar_check_overflow(&zz));
+                CHECK(secp256k1_scalar_eq(&one, &zz));
+            }
+            secp256k1_scalar_mul(&z, &x, &x);
+            CHECK(!secp256k1_scalar_check_overflow(&z));
+            secp256k1_scalar_sqr(&zz, &x);
+            CHECK(!secp256k1_scalar_check_overflow(&zz));
+            CHECK(secp256k1_scalar_eq(&zz, &z));
+            CHECK(secp256k1_scalar_eq(&r2, &zz));
+        }
+    }
+}
+
+/***** FIELD TESTS *****/
+
+void random_fe(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+
+void random_fe_test(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256_test(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+
+void random_fe_non_zero(secp256k1_fe *nz) {
+    int tries = 10;
+    while (--tries >= 0) {
+        random_fe(nz);
+        secp256k1_fe_normalize(nz);
+        if (!secp256k1_fe_is_zero(nz)) {
+            break;
+        }
+    }
+    /* Infinitesimal probability of spurious failure here */
+    CHECK(tries >= 0);
+}
+
+void random_fe_non_square(secp256k1_fe *ns) {
+    secp256k1_fe r;
+    random_fe_non_zero(ns);
+    if (secp256k1_fe_sqrt(&r, ns)) {
+        secp256k1_fe_negate(ns, ns, 1);
+    }
+}
+
+int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe an = *a;
+    secp256k1_fe bn = *b;
+    secp256k1_fe_normalize_weak(&an);
+    secp256k1_fe_normalize_var(&bn);
+    return secp256k1_fe_equal_var(&an, &bn);
+}
+
+int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
+    secp256k1_fe x;
+    secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_fe_mul(&x, a, ai);
+    return check_fe_equal(&x, &one);
+}
+
+void run_field_convert(void) {
+    static const unsigned char b32[32] = {
+        0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
+        0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
+        0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
+        0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
+    };
+    static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
+        0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
+        0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
+    );
+    static const secp256k1_fe fe = SECP256K1_FE_CONST(
+        0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
+        0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
+    );
+    secp256k1_fe fe2;
+    unsigned char b322[32];
+    secp256k1_fe_storage fes2;
+    /* Check conversions to fe. */
+    CHECK(secp256k1_fe_set_b32(&fe2, b32));
+    CHECK(secp256k1_fe_equal_var(&fe, &fe2));
+    secp256k1_fe_from_storage(&fe2, &fes);
+    CHECK(secp256k1_fe_equal_var(&fe, &fe2));
+    /* Check conversion from fe. */
+    secp256k1_fe_get_b32(b322, &fe);
+    CHECK(memcmp(b322, b32, 32) == 0);
+    secp256k1_fe_to_storage(&fes2, &fe);
+    CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
+}
+
+int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe t = *b;
+#ifdef VERIFY
+    t.magnitude = a->magnitude;
+    t.normalized = a->normalized;
+#endif
+    return memcmp(a, &t, sizeof(secp256k1_fe));
+}
+
+void run_field_misc(void) {
+    secp256k1_fe x;
+    secp256k1_fe y;
+    secp256k1_fe z;
+    secp256k1_fe q;
+    secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
+    int i, j;
+    for (i = 0; i < 5*count; i++) {
+        secp256k1_fe_storage xs, ys, zs;
+        random_fe(&x);
+        random_fe_non_zero(&y);
+        /* Test the fe equality and comparison operations. */
+        CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
+        CHECK(secp256k1_fe_equal_var(&x, &x));
+        z = x;
+        secp256k1_fe_add(&z,&y);
+        /* Test fe conditional move; z is not normalized here. */
+        q = x;
+        secp256k1_fe_cmov(&x, &z, 0);
+        VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
+        secp256k1_fe_cmov(&x, &x, 1);
+        CHECK(fe_memcmp(&x, &z) != 0);
+        CHECK(fe_memcmp(&x, &q) == 0);
+        secp256k1_fe_cmov(&q, &z, 1);
+        VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
+        CHECK(fe_memcmp(&q, &z) == 0);
+        secp256k1_fe_normalize_var(&x);
+        secp256k1_fe_normalize_var(&z);
+        CHECK(!secp256k1_fe_equal_var(&x, &z));
+        secp256k1_fe_normalize_var(&q);
+        secp256k1_fe_cmov(&q, &z, (i&1));
+        VERIFY_CHECK(q.normalized && q.magnitude == 1);
+        for (j = 0; j < 6; j++) {
+            secp256k1_fe_negate(&z, &z, j+1);
+            secp256k1_fe_normalize_var(&q);
+            secp256k1_fe_cmov(&q, &z, (j&1));
+            VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
+        }
+        secp256k1_fe_normalize_var(&z);
+        /* Test storage conversion and conditional moves. */
+        secp256k1_fe_to_storage(&xs, &x);
+        secp256k1_fe_to_storage(&ys, &y);
+        secp256k1_fe_to_storage(&zs, &z);
+        secp256k1_fe_storage_cmov(&zs, &xs, 0);
+        secp256k1_fe_storage_cmov(&zs, &zs, 1);
+        CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
+        secp256k1_fe_storage_cmov(&ys, &xs, 1);
+        CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
+        secp256k1_fe_from_storage(&x, &xs);
+        secp256k1_fe_from_storage(&y, &ys);
+        secp256k1_fe_from_storage(&z, &zs);
+        /* Test that mul_int, mul, and add agree. */
+        secp256k1_fe_add(&y, &x);
+        secp256k1_fe_add(&y, &x);
+        z = x;
+        secp256k1_fe_mul_int(&z, 3);
+        CHECK(check_fe_equal(&y, &z));
+        secp256k1_fe_add(&y, &x);
+        secp256k1_fe_add(&z, &x);
+        CHECK(check_fe_equal(&z, &y));
+        z = x;
+        secp256k1_fe_mul_int(&z, 5);
+        secp256k1_fe_mul(&q, &x, &fe5);
+        CHECK(check_fe_equal(&z, &q));
+        secp256k1_fe_negate(&x, &x, 1);
+        secp256k1_fe_add(&z, &x);
+        secp256k1_fe_add(&q, &x);
+        CHECK(check_fe_equal(&y, &z));
+        CHECK(check_fe_equal(&q, &y));
+    }
+}
+
+void run_field_inv(void) {
+    secp256k1_fe x, xi, xii;
+    int i;
+    for (i = 0; i < 10*count; i++) {
+        random_fe_non_zero(&x);
+        secp256k1_fe_inv(&xi, &x);
+        CHECK(check_fe_inverse(&x, &xi));
+        secp256k1_fe_inv(&xii, &xi);
+        CHECK(check_fe_equal(&x, &xii));
+    }
+}
+
+void run_field_inv_var(void) {
+    secp256k1_fe x, xi, xii;
+    int i;
+    for (i = 0; i < 10*count; i++) {
+        random_fe_non_zero(&x);
+        secp256k1_fe_inv_var(&xi, &x);
+        CHECK(check_fe_inverse(&x, &xi));
+        secp256k1_fe_inv_var(&xii, &xi);
+        CHECK(check_fe_equal(&x, &xii));
+    }
+}
+
+void run_field_inv_all_var(void) {
+    secp256k1_fe x[16], xi[16], xii[16];
+    int i;
+    /* Check it's safe to call for 0 elements */
+    secp256k1_fe_inv_all_var(xi, x, 0);
+    for (i = 0; i < count; i++) {
+        size_t j;
+        size_t len = secp256k1_rand_int(15) + 1;
+        for (j = 0; j < len; j++) {
+            random_fe_non_zero(&x[j]);
+        }
+        secp256k1_fe_inv_all_var(xi, x, len);
+        for (j = 0; j < len; j++) {
+            CHECK(check_fe_inverse(&x[j], &xi[j]));
+        }
+        secp256k1_fe_inv_all_var(xii, xi, len);
+        for (j = 0; j < len; j++) {
+            CHECK(check_fe_equal(&x[j], &xii[j]));
+        }
+    }
+}
+
+void run_sqr(void) {
+    secp256k1_fe x, s;
+
+    {
+        int i;
+        secp256k1_fe_set_int(&x, 1);
+        secp256k1_fe_negate(&x, &x, 1);
+
+        for (i = 1; i <= 512; ++i) {
+            secp256k1_fe_mul_int(&x, 2);
+            secp256k1_fe_normalize(&x);
+            secp256k1_fe_sqr(&s, &x);
+        }
+    }
+}
+
+void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
+    secp256k1_fe r1, r2;
+    int v = secp256k1_fe_sqrt(&r1, a);
+    CHECK((v == 0) == (k == NULL));
+
+    if (k != NULL) {
+        /* Check that the returned root is +/- the given known answer */
+        secp256k1_fe_negate(&r2, &r1, 1);
+        secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k);
+        secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2);
+        CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2));
+    }
+}
+
+void run_sqrt(void) {
+    secp256k1_fe ns, x, s, t;
+    int i;
+
+    /* Check sqrt(0) is 0 */
+    secp256k1_fe_set_int(&x, 0);
+    secp256k1_fe_sqr(&s, &x);
+    test_sqrt(&s, &x);
+
+    /* Check sqrt of small squares (and their negatives) */
+    for (i = 1; i <= 100; i++) {
+        secp256k1_fe_set_int(&x, i);
+        secp256k1_fe_sqr(&s, &x);
+        test_sqrt(&s, &x);
+        secp256k1_fe_negate(&t, &s, 1);
+        test_sqrt(&t, NULL);
+    }
+
+    /* Consistency checks for large random values */
+    for (i = 0; i < 10; i++) {
+        int j;
+        random_fe_non_square(&ns);
+        for (j = 0; j < count; j++) {
+            random_fe(&x);
+            secp256k1_fe_sqr(&s, &x);
+            test_sqrt(&s, &x);
+            secp256k1_fe_negate(&t, &s, 1);
+            test_sqrt(&t, NULL);
+            secp256k1_fe_mul(&t, &s, &ns);
+            test_sqrt(&t, NULL);
+        }
+    }
+}
+
+/***** GROUP TESTS *****/
+
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
+    CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
+}
+
+/* This compares jacobian points including their Z, not just their geometric meaning. */
+int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
+    secp256k1_gej a2;
+    secp256k1_gej b2;
+    int ret = 1;
+    ret &= a->infinity == b->infinity;
+    if (ret && !a->infinity) {
+        a2 = *a;
+        b2 = *b;
+        secp256k1_fe_normalize(&a2.x);
+        secp256k1_fe_normalize(&a2.y);
+        secp256k1_fe_normalize(&a2.z);
+        secp256k1_fe_normalize(&b2.x);
+        secp256k1_fe_normalize(&b2.y);
+        secp256k1_fe_normalize(&b2.z);
+        ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
+        ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
+        ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
+    }
+    return ret;
+}
+
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+    secp256k1_fe z2s;
+    secp256k1_fe u1, u2, s1, s2;
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+    secp256k1_fe_sqr(&z2s, &b->z);
+    secp256k1_fe_mul(&u1, &a->x, &z2s);
+    u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+    secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+    s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+    CHECK(secp256k1_fe_equal_var(&u1, &u2));
+    CHECK(secp256k1_fe_equal_var(&s1, &s2));
+}
+
+void test_ge(void) {
+    int i, i1;
+#ifdef USE_ENDOMORPHISM
+    int runs = 6;
+#else
+    int runs = 4;
+#endif
+    /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
+     * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
+     * All magnitudes are randomized.
+     * All 17*17 combinations of points are added to each other, using all applicable methods.
+     *
+     * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
+     */
+    secp256k1_ge *ge = (secp256k1_ge *)malloc(sizeof(secp256k1_ge) * (1 + 4 * runs));
+    secp256k1_gej *gej = (secp256k1_gej *)malloc(sizeof(secp256k1_gej) * (1 + 4 * runs));
+    secp256k1_fe *zinv = (secp256k1_fe *)malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+    secp256k1_fe zf;
+    secp256k1_fe zfi2, zfi3;
+
+    secp256k1_gej_set_infinity(&gej[0]);
+    secp256k1_ge_clear(&ge[0]);
+    secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
+    for (i = 0; i < runs; i++) {
+        int j;
+        secp256k1_ge g;
+        random_group_element_test(&g);
+#ifdef USE_ENDOMORPHISM
+        if (i >= runs - 2) {
+            secp256k1_ge_mul_lambda(&g, &ge[1]);
+        }
+        if (i >= runs - 1) {
+            secp256k1_ge_mul_lambda(&g, &g);
+        }
+#endif
+        ge[1 + 4 * i] = g;
+        ge[2 + 4 * i] = g;
+        secp256k1_ge_neg(&ge[3 + 4 * i], &g);
+        secp256k1_ge_neg(&ge[4 + 4 * i], &g);
+        secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
+        random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
+        secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
+        random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
+        for (j = 0; j < 4; j++) {
+            random_field_element_magnitude(&ge[1 + j + 4 * i].x);
+            random_field_element_magnitude(&ge[1 + j + 4 * i].y);
+            random_field_element_magnitude(&gej[1 + j + 4 * i].x);
+            random_field_element_magnitude(&gej[1 + j + 4 * i].y);
+            random_field_element_magnitude(&gej[1 + j + 4 * i].z);
+        }
+    }
+
+    /* Compute z inverses. */
+    {
+        secp256k1_fe *zs = malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+        for (i = 0; i < 4 * runs + 1; i++) {
+            if (i == 0) {
+                /* The point at infinity does not have a meaningful z inverse. Any should do. */
+                do {
+                    random_field_element_test(&zs[i]);
+                } while(secp256k1_fe_is_zero(&zs[i]));
+            } else {
+                zs[i] = gej[i].z;
+            }
+        }
+        secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
+        free(zs);
+    }
+
+    /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
+    do {
+        random_field_element_test(&zf);
+    } while(secp256k1_fe_is_zero(&zf));
+    random_field_element_magnitude(&zf);
+    secp256k1_fe_inv_var(&zfi3, &zf);
+    secp256k1_fe_sqr(&zfi2, &zfi3);
+    secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
+
+    for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
+        int i2;
+        for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
+            /* Compute reference result using gej + gej (var). */
+            secp256k1_gej refj, resj;
+            secp256k1_ge ref;
+            secp256k1_fe zr;
+            secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
+            /* Check Z ratio. */
+            if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
+                secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
+            }
+            secp256k1_ge_set_gej_var(&ref, &refj);
+
+            /* Test gej + ge with Z ratio result (var). */
+            secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
+            ge_equals_gej(&ref, &resj);
+            if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
+                secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
+            }
+
+            /* Test gej + ge (var, with additional Z factor). */
+            {
+                secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
+                secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
+                secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
+                random_field_element_magnitude(&ge2_zfi.x);
+                random_field_element_magnitude(&ge2_zfi.y);
+                secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
+                ge_equals_gej(&ref, &resj);
+            }
+
+            /* Test gej + ge (const). */
+            if (i2 != 0) {
+                /* secp256k1_gej_add_ge does not support its second argument being infinity. */
+                secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]);
+                ge_equals_gej(&ref, &resj);
+            }
+
+            /* Test doubling (var). */
+            if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
+                secp256k1_fe zr2;
+                /* Normal doubling with Z ratio result. */
+                secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
+                ge_equals_gej(&ref, &resj);
+                /* Check Z ratio. */
+                secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
+                /* Normal doubling. */
+                secp256k1_gej_double_var(&resj, &gej[i2], NULL);
+                ge_equals_gej(&ref, &resj);
+            }
+
+            /* Test adding opposites. */
+            if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) {
+                CHECK(secp256k1_ge_is_infinity(&ref));
+            }
+
+            /* Test adding infinity. */
+            if (i1 == 0) {
+                CHECK(secp256k1_ge_is_infinity(&ge[i1]));
+                CHECK(secp256k1_gej_is_infinity(&gej[i1]));
+                ge_equals_gej(&ref, &gej[i2]);
+            }
+            if (i2 == 0) {
+                CHECK(secp256k1_ge_is_infinity(&ge[i2]));
+                CHECK(secp256k1_gej_is_infinity(&gej[i2]));
+                ge_equals_gej(&ref, &gej[i1]);
+            }
+        }
+    }
+
+    /* Test adding all points together in random order equals infinity. */
+    {
+        secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
+        secp256k1_gej *gej_shuffled = (secp256k1_gej *)malloc((4 * runs + 1) * sizeof(secp256k1_gej));
+        for (i = 0; i < 4 * runs + 1; i++) {
+            gej_shuffled[i] = gej[i];
+        }
+        for (i = 0; i < 4 * runs + 1; i++) {
+            int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
+            if (swap != i) {
+                secp256k1_gej t = gej_shuffled[i];
+                gej_shuffled[i] = gej_shuffled[swap];
+                gej_shuffled[swap] = t;
+            }
+        }
+        for (i = 0; i < 4 * runs + 1; i++) {
+            secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
+        }
+        CHECK(secp256k1_gej_is_infinity(&sum));
+        free(gej_shuffled);
+    }
+
+    /* Test batch gej -> ge conversion with and without known z ratios. */
+    {
+        secp256k1_fe *zr = (secp256k1_fe *)malloc((4 * runs + 1) * sizeof(secp256k1_fe));
+        secp256k1_ge *ge_set_table = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
+        secp256k1_ge *ge_set_all = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
+        for (i = 0; i < 4 * runs + 1; i++) {
+            /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
+            if (i < 4 * runs) {
+                secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
+            }
+        }
+        secp256k1_ge_set_table_gej_var(ge_set_table, gej, zr, 4 * runs + 1);
+        secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1, &ctx->error_callback);
+        for (i = 0; i < 4 * runs + 1; i++) {
+            secp256k1_fe s;
+            random_fe_non_zero(&s);
+            secp256k1_gej_rescale(&gej[i], &s);
+            ge_equals_gej(&ge_set_table[i], &gej[i]);
+            ge_equals_gej(&ge_set_all[i], &gej[i]);
+        }
+        free(ge_set_table);
+        free(ge_set_all);
+        free(zr);
+    }
+
+    free(ge);
+    free(gej);
+    free(zinv);
+}
+
+void test_add_neg_y_diff_x(void) {
+    /* The point of this test is to check that we can add two points
+     * whose y-coordinates are negatives of each other but whose x
+     * coordinates differ. If the x-coordinates were the same, these
+     * points would be negatives of each other and their sum is
+     * infinity. This is cool because it "covers up" any degeneracy
+     * in the addition algorithm that would cause the xy coordinates
+     * of the sum to be wrong (since infinity has no xy coordinates).
+     * HOWEVER, if the x-coordinates are different, infinity is the
+     * wrong answer, and such degeneracies are exposed. This is the
+     * root of https://github.com/bitcoin-core/secp256k1/issues/257
+     * which this test is a regression test for.
+     *
+     * These points were generated in sage as
+     * # secp256k1 params
+     * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+     * C = EllipticCurve ([F (0), F (7)])
+     * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+     * N = FiniteField(G.order())
+     *
+     * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
+     * x = polygen(N)
+     * lam  = (1 - x^3).roots()[1][0]
+     *
+     * # random "bad pair"
+     * P = C.random_element()
+     * Q = -int(lam) * P
+     * print "    P: %x %x" % P.xy()
+     * print "    Q: %x %x" % Q.xy()
+     * print "P + Q: %x %x" % (P + Q).xy()
+     */
+    secp256k1_gej aj = SECP256K1_GEJ_CONST(
+        0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
+        0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
+        0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
+        0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
+    );
+    secp256k1_gej bj = SECP256K1_GEJ_CONST(
+        0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
+        0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
+        0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
+        0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
+    );
+    secp256k1_gej sumj = SECP256K1_GEJ_CONST(
+        0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
+        0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
+        0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
+        0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
+    );
+    secp256k1_ge b;
+    secp256k1_gej resj;
+    secp256k1_ge res;
+    secp256k1_ge_set_gej(&b, &bj);
+
+    secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
+
+    secp256k1_gej_add_ge(&resj, &aj, &b);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
+
+    secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
+}
+
+void run_ge(void) {
+    int i;
+    for (i = 0; i < count * 32; i++) {
+        test_ge();
+    }
+    test_add_neg_y_diff_x();
+}
+
+void test_ec_combine(void) {
+    secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_pubkey data[6];
+    const secp256k1_pubkey* d[6];
+    secp256k1_pubkey sd;
+    secp256k1_pubkey sd2;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+    int i;
+    for (i = 1; i <= 6; i++) {
+        secp256k1_scalar s;
+        random_scalar_order_test(&s);
+        secp256k1_scalar_add(&sum, &sum, &s);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
+        secp256k1_ge_set_gej(&Q, &Qj);
+        secp256k1_pubkey_save(&data[i - 1], &Q);
+        d[i - 1] = &data[i - 1];
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
+        secp256k1_ge_set_gej(&Q, &Qj);
+        secp256k1_pubkey_save(&sd, &Q);
+        CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
+        CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
+    }
+}
+
+void run_ec_combine(void) {
+    int i;
+    for (i = 0; i < count * 8; i++) {
+         test_ec_combine();
+    }
+}
+
+void test_group_decompress(const secp256k1_fe* x) {
+    /* The input itself, normalized. */
+    secp256k1_fe fex = *x;
+    secp256k1_fe fez;
+    /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
+    secp256k1_ge ge_quad, ge_even, ge_odd;
+    secp256k1_gej gej_quad;
+    /* Return values of the above calls. */
+    int res_quad, res_even, res_odd;
+
+    secp256k1_fe_normalize_var(&fex);
+
+    res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
+    res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
+    res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
+
+    CHECK(res_quad == res_even);
+    CHECK(res_quad == res_odd);
+
+    if (res_quad) {
+        secp256k1_fe_normalize_var(&ge_quad.x);
+        secp256k1_fe_normalize_var(&ge_odd.x);
+        secp256k1_fe_normalize_var(&ge_even.x);
+        secp256k1_fe_normalize_var(&ge_quad.y);
+        secp256k1_fe_normalize_var(&ge_odd.y);
+        secp256k1_fe_normalize_var(&ge_even.y);
+
+        /* No infinity allowed. */
+        CHECK(!ge_quad.infinity);
+        CHECK(!ge_even.infinity);
+        CHECK(!ge_odd.infinity);
+
+        /* Check that the x coordinates check out. */
+        CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
+        CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
+        CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
+
+        /* Check that the Y coordinate result in ge_quad is a square. */
+        CHECK(secp256k1_fe_is_quad_var(&ge_quad.y));
+
+        /* Check odd/even Y in ge_odd, ge_even. */
+        CHECK(secp256k1_fe_is_odd(&ge_odd.y));
+        CHECK(!secp256k1_fe_is_odd(&ge_even.y));
+
+        /* Check secp256k1_gej_has_quad_y_var. */
+        secp256k1_gej_set_ge(&gej_quad, &ge_quad);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+        do {
+            random_fe_test(&fez);
+        } while (secp256k1_fe_is_zero(&fez));
+        secp256k1_gej_rescale(&gej_quad, &fez);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+        secp256k1_gej_neg(&gej_quad, &gej_quad);
+        CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+        do {
+            random_fe_test(&fez);
+        } while (secp256k1_fe_is_zero(&fez));
+        secp256k1_gej_rescale(&gej_quad, &fez);
+        CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+        secp256k1_gej_neg(&gej_quad, &gej_quad);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+    }
+}
+
+void run_group_decompress(void) {
+    int i;
+    for (i = 0; i < count * 4; i++) {
+        secp256k1_fe fe;
+        random_fe_test(&fe);
+        test_group_decompress(&fe);
+    }
+}
+
+/***** ECMULT TESTS *****/
+
+void run_ecmult_chain(void) {
+    /* random starting point A (on the curve) */
+    secp256k1_gej a = SECP256K1_GEJ_CONST(
+        0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
+        0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
+        0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
+        0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
+    );
+    /* two random initial factors xn and gn */
+    secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
+        0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
+        0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
+    );
+    secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
+        0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
+        0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
+    );
+    /* two small multipliers to be applied to xn and gn in every iteration: */
+    static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
+    static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
+    /* accumulators with the resulting coefficients to A and G */
+    secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    /* actual points */
+    secp256k1_gej x;
+    secp256k1_gej x2;
+    int i;
+
+    /* the point being computed */
+    x = a;
+    for (i = 0; i < 200*count; i++) {
+        /* in each iteration, compute X = xn*X + gn*G; */
+        secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn);
+        /* also compute ae and ge: the actual accumulated factors for A and G */
+        /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
+        secp256k1_scalar_mul(&ae, &ae, &xn);
+        secp256k1_scalar_mul(&ge, &ge, &xn);
+        secp256k1_scalar_add(&ge, &ge, &gn);
+        /* modify xn and gn */
+        secp256k1_scalar_mul(&xn, &xn, &xf);
+        secp256k1_scalar_mul(&gn, &gn, &gf);
+
+        /* verify */
+        if (i == 19999) {
+            /* expected result after 19999 iterations */
+            secp256k1_gej rp = SECP256K1_GEJ_CONST(
+                0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
+                0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
+                0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
+                0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
+            );
+
+            secp256k1_gej_neg(&rp, &rp);
+            secp256k1_gej_add_var(&rp, &rp, &x, NULL);
+            CHECK(secp256k1_gej_is_infinity(&rp));
+        }
+    }
+    /* redo the computation, but directly with the resulting ae and ge coefficients: */
+    secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
+    secp256k1_gej_neg(&x2, &x2);
+    secp256k1_gej_add_var(&x2, &x2, &x, NULL);
+    CHECK(secp256k1_gej_is_infinity(&x2));
+}
+
+void test_point_times_order(const secp256k1_gej *point) {
+    /* X * (point + G) + (order-X) * (pointer + G) = 0 */
+    secp256k1_scalar x;
+    secp256k1_scalar nx;
+    secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_gej res1, res2;
+    secp256k1_ge res3;
+    unsigned char pub[65];
+    size_t psize = 65;
+    random_scalar_order_test(&x);
+    secp256k1_scalar_negate(&nx, &x);
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
+    secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
+    CHECK(secp256k1_gej_is_infinity(&res1));
+    CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
+    secp256k1_ge_set_gej(&res3, &res1);
+    CHECK(secp256k1_ge_is_infinity(&res3));
+    CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
+    CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
+    psize = 65;
+    CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
+    /* check zero/one edge cases */
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
+    secp256k1_ge_set_gej(&res3, &res1);
+    CHECK(secp256k1_ge_is_infinity(&res3));
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
+    secp256k1_ge_set_gej(&res3, &res1);
+    ge_equals_gej(&res3, point);
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
+    secp256k1_ge_set_gej(&res3, &res1);
+    ge_equals_ge(&res3, &secp256k1_ge_const_g);
+}
+
+void run_point_times_order(void) {
+    int i;
+    secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
+    static const secp256k1_fe xr = SECP256K1_FE_CONST(
+        0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
+        0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
+    );
+    for (i = 0; i < 500; i++) {
+        secp256k1_ge p;
+        if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
+            secp256k1_gej j;
+            CHECK(secp256k1_ge_is_valid_var(&p));
+            secp256k1_gej_set_ge(&j, &p);
+            CHECK(secp256k1_gej_is_valid_var(&j));
+            test_point_times_order(&j);
+        }
+        secp256k1_fe_sqr(&x, &x);
+    }
+    secp256k1_fe_normalize_var(&x);
+    CHECK(secp256k1_fe_equal_var(&x, &xr));
+}
+
+void ecmult_const_random_mult(void) {
+    /* random starting point A (on the curve) */
+    secp256k1_ge a = SECP256K1_GE_CONST(
+        0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
+        0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
+        0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
+        0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
+    );
+    /* random initial factor xn */
+    secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
+        0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
+        0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
+    );
+    /* expected xn * A (from sage) */
+    secp256k1_ge expected_b = SECP256K1_GE_CONST(
+        0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
+        0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
+        0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
+        0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
+    );
+    secp256k1_gej b;
+    secp256k1_ecmult_const(&b, &a, &xn);
+
+    CHECK(secp256k1_ge_is_valid_var(&a));
+    ge_equals_gej(&expected_b, &b);
+}
+
+void ecmult_const_commutativity(void) {
+    secp256k1_scalar a;
+    secp256k1_scalar b;
+    secp256k1_gej res1;
+    secp256k1_gej res2;
+    secp256k1_ge mid1;
+    secp256k1_ge mid2;
+    random_scalar_order_test(&a);
+    random_scalar_order_test(&b);
+
+    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
+    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
+    secp256k1_ge_set_gej(&mid1, &res1);
+    secp256k1_ge_set_gej(&mid2, &res2);
+    secp256k1_ecmult_const(&res1, &mid1, &b);
+    secp256k1_ecmult_const(&res2, &mid2, &a);
+    secp256k1_ge_set_gej(&mid1, &res1);
+    secp256k1_ge_set_gej(&mid2, &res2);
+    ge_equals_ge(&mid1, &mid2);
+}
+
+void ecmult_const_mult_zero_one(void) {
+    secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_scalar negone;
+    secp256k1_gej res1;
+    secp256k1_ge res2;
+    secp256k1_ge point;
+    secp256k1_scalar_negate(&negone, &one);
+
+    random_group_element_test(&point);
+    secp256k1_ecmult_const(&res1, &point, &zero);
+    secp256k1_ge_set_gej(&res2, &res1);
+    CHECK(secp256k1_ge_is_infinity(&res2));
+    secp256k1_ecmult_const(&res1, &point, &one);
+    secp256k1_ge_set_gej(&res2, &res1);
+    ge_equals_ge(&res2, &point);
+    secp256k1_ecmult_const(&res1, &point, &negone);
+    secp256k1_gej_neg(&res1, &res1);
+    secp256k1_ge_set_gej(&res2, &res1);
+    ge_equals_ge(&res2, &point);
+}
+
+void ecmult_const_chain_multiply(void) {
+    /* Check known result (randomly generated test problem from sage) */
+    const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
+        0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
+        0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
+    );
+    const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
+        0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
+        0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
+        0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
+        0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
+    );
+    secp256k1_gej point;
+    secp256k1_ge res;
+    int i;
+
+    secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
+    for (i = 0; i < 100; ++i) {
+        secp256k1_ge tmp;
+        secp256k1_ge_set_gej(&tmp, &point);
+        secp256k1_ecmult_const(&point, &tmp, &scalar);
+    }
+    secp256k1_ge_set_gej(&res, &point);
+    ge_equals_gej(&res, &expected_point);
+}
+
+void run_ecmult_const_tests(void) {
+    ecmult_const_mult_zero_one();
+    ecmult_const_random_mult();
+    ecmult_const_commutativity();
+    ecmult_const_chain_multiply();
+}
+
+void test_wnaf(const secp256k1_scalar *number, int w) {
+    secp256k1_scalar x, two, t;
+    int wnaf[256];
+    int zeroes = -1;
+    int i;
+    int bits;
+    secp256k1_scalar_set_int(&x, 0);
+    secp256k1_scalar_set_int(&two, 2);
+    bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
+    CHECK(bits <= 256);
+    for (i = bits-1; i >= 0; i--) {
+        int v = wnaf[i];
+        secp256k1_scalar_mul(&x, &x, &two);
+        if (v) {
+            CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
+            zeroes=0;
+            CHECK((v & 1) == 1); /* check non-zero elements are odd */
+            CHECK(v <= (1 << (w-1)) - 1); /* check range below */
+            CHECK(v >= -(1 << (w-1)) - 1); /* check range above */
+        } else {
+            CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */
+            zeroes++;
+        }
+        if (v >= 0) {
+            secp256k1_scalar_set_int(&t, v);
+        } else {
+            secp256k1_scalar_set_int(&t, -v);
+            secp256k1_scalar_negate(&t, &t);
+        }
+        secp256k1_scalar_add(&x, &x, &t);
+    }
+    CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
+}
+
+void test_constant_wnaf_negate(const secp256k1_scalar *number) {
+    secp256k1_scalar neg1 = *number;
+    secp256k1_scalar neg2 = *number;
+    int sign1 = 1;
+    int sign2 = 1;
+
+    if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
+        secp256k1_scalar_negate(&neg1, &neg1);
+        sign1 = -1;
+    }
+    sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
+    CHECK(sign1 == sign2);
+    CHECK(secp256k1_scalar_eq(&neg1, &neg2));
+}
+
+void test_constant_wnaf(const secp256k1_scalar *number, int w) {
+    secp256k1_scalar x, shift;
+    int wnaf[256] = {0};
+    int i;
+    int skew;
+    secp256k1_scalar num = *number;
+
+    secp256k1_scalar_set_int(&x, 0);
+    secp256k1_scalar_set_int(&shift, 1 << w);
+    /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < 16; ++i) {
+        secp256k1_scalar_shr_int(&num, 8);
+    }
+#endif
+    skew = secp256k1_wnaf_const(wnaf, num, w);
+
+    for (i = WNAF_SIZE(w); i >= 0; --i) {
+        secp256k1_scalar t;
+        int v = wnaf[i];
+        CHECK(v != 0); /* check nonzero */
+        CHECK(v & 1);  /* check parity */
+        CHECK(v > -(1 << w)); /* check range above */
+        CHECK(v < (1 << w));  /* check range below */
+
+        secp256k1_scalar_mul(&x, &x, &shift);
+        if (v >= 0) {
+            secp256k1_scalar_set_int(&t, v);
+        } else {
+            secp256k1_scalar_set_int(&t, -v);
+            secp256k1_scalar_negate(&t, &t);
+        }
+        secp256k1_scalar_add(&x, &x, &t);
+    }
+    /* Skew num because when encoding numbers as odd we use an offset */
+    secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
+    CHECK(secp256k1_scalar_eq(&x, &num));
+}
+
+void run_wnaf(void) {
+    int i;
+    secp256k1_scalar n = {{0}};
+
+    /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
+     *               have easier-to-diagnose failure modes  */
+    n.d[0] = 1;
+    test_constant_wnaf(&n, 4);
+    n.d[0] = 2;
+    test_constant_wnaf(&n, 4);
+    /* Random tests */
+    for (i = 0; i < count; i++) {
+        random_scalar_order(&n);
+        test_wnaf(&n, 4+(i%10));
+        test_constant_wnaf_negate(&n);
+        test_constant_wnaf(&n, 4 + (i % 10));
+    }
+    secp256k1_scalar_set_int(&n, 0);
+    CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
+    CHECK(secp256k1_scalar_is_zero(&n));
+    CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
+    CHECK(secp256k1_scalar_is_zero(&n));
+}
+
+void test_ecmult_constants(void) {
+    /* Test ecmult_gen() for [0..36) and [order-36..0). */
+    secp256k1_scalar x;
+    secp256k1_gej r;
+    secp256k1_ge ng;
+    int i;
+    int j;
+    secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
+    for (i = 0; i < 36; i++ ) {
+        secp256k1_scalar_set_int(&x, i);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
+        for (j = 0; j < i; j++) {
+            if (j == i - 1) {
+                ge_equals_gej(&secp256k1_ge_const_g, &r);
+            }
+            secp256k1_gej_add_ge(&r, &r, &ng);
+        }
+        CHECK(secp256k1_gej_is_infinity(&r));
+    }
+    for (i = 1; i <= 36; i++ ) {
+        secp256k1_scalar_set_int(&x, i);
+        secp256k1_scalar_negate(&x, &x);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
+        for (j = 0; j < i; j++) {
+            if (j == i - 1) {
+                ge_equals_gej(&ng, &r);
+            }
+            secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
+        }
+        CHECK(secp256k1_gej_is_infinity(&r));
+    }
+}
+
+void run_ecmult_constants(void) {
+    test_ecmult_constants();
+}
+
+void test_ecmult_gen_blind(void) {
+    /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
+    secp256k1_scalar key;
+    secp256k1_scalar b;
+    unsigned char seed32[32];
+    secp256k1_gej pgej;
+    secp256k1_gej pgej2;
+    secp256k1_gej i;
+    secp256k1_ge pge;
+    random_scalar_order_test(&key);
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
+    secp256k1_rand256(seed32);
+    b = ctx->ecmult_gen_ctx.blind;
+    i = ctx->ecmult_gen_ctx.initial;
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
+    CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
+    CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
+    secp256k1_ge_set_gej(&pge, &pgej);
+    ge_equals_gej(&pge, &pgej2);
+}
+
+void test_ecmult_gen_blind_reset(void) {
+    /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
+    secp256k1_scalar b;
+    secp256k1_gej initial;
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
+    b = ctx->ecmult_gen_ctx.blind;
+    initial = ctx->ecmult_gen_ctx.initial;
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
+    CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
+    CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
+}
+
+void run_ecmult_gen_blind(void) {
+    int i;
+    test_ecmult_gen_blind_reset();
+    for (i = 0; i < 10; i++) {
+        test_ecmult_gen_blind();
+    }
+}
+
+#ifdef USE_ENDOMORPHISM
+/***** ENDOMORPHISH TESTS *****/
+void test_scalar_split(void) {
+    secp256k1_scalar full;
+    secp256k1_scalar s1, slam;
+    const unsigned char zero[32] = {0};
+    unsigned char tmp[32];
+
+    random_scalar_order_test(&full);
+    secp256k1_scalar_split_lambda(&s1, &slam, &full);
+
+    /* check that both are <= 128 bits in size */
+    if (secp256k1_scalar_is_high(&s1)) {
+        secp256k1_scalar_negate(&s1, &s1);
+    }
+    if (secp256k1_scalar_is_high(&slam)) {
+        secp256k1_scalar_negate(&slam, &slam);
+    }
+
+    secp256k1_scalar_get_b32(tmp, &s1);
+    CHECK(memcmp(zero, tmp, 16) == 0);
+    secp256k1_scalar_get_b32(tmp, &slam);
+    CHECK(memcmp(zero, tmp, 16) == 0);
+}
+
+void run_endomorphism_tests(void) {
+    test_scalar_split();
+}
+#endif
+
+void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
+    unsigned char pubkeyc[65];
+    secp256k1_pubkey pubkey;
+    secp256k1_ge ge;
+    size_t pubkeyclen;
+    int32_t ecount;
+    ecount = 0;
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
+        /* Smaller sizes are tested exhaustively elsewhere. */
+        int32_t i;
+        memcpy(&pubkeyc[1], input, 64);
+        VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
+        for (i = 0; i < 256; i++) {
+            /* Try all type bytes. */
+            int xpass;
+            int ypass;
+            int ysign;
+            pubkeyc[0] = i;
+            /* What sign does this point have? */
+            ysign = (input[63] & 1) + 2;
+            /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
+            xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
+            /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
+            ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
+                ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
+            if (xpass || ypass) {
+                /* These cases must parse. */
+                unsigned char pubkeyo[65];
+                size_t outl;
+                memset(&pubkey, 0, sizeof(pubkey));
+                VG_UNDEF(&pubkey, sizeof(pubkey));
+                ecount = 0;
+                CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
+                VG_CHECK(&pubkey, sizeof(pubkey));
+                outl = 65;
+                VG_UNDEF(pubkeyo, 65);
+                CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+                VG_CHECK(pubkeyo, outl);
+                CHECK(outl == 33);
+                CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
+                CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
+                if (ypass) {
+                    /* This test isn't always done because we decode with alternative signs, so the y won't match. */
+                    CHECK(pubkeyo[0] == ysign);
+                    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+                    memset(&pubkey, 0, sizeof(pubkey));
+                    VG_UNDEF(&pubkey, sizeof(pubkey));
+                    secp256k1_pubkey_save(&pubkey, &ge);
+                    VG_CHECK(&pubkey, sizeof(pubkey));
+                    outl = 65;
+                    VG_UNDEF(pubkeyo, 65);
+                    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+                    VG_CHECK(pubkeyo, outl);
+                    CHECK(outl == 65);
+                    CHECK(pubkeyo[0] == 4);
+                    CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
+                }
+                CHECK(ecount == 0);
+            } else {
+                /* These cases must fail to parse. */
+                memset(&pubkey, 0xfe, sizeof(pubkey));
+                ecount = 0;
+                VG_UNDEF(&pubkey, sizeof(pubkey));
+                CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
+                VG_CHECK(&pubkey, sizeof(pubkey));
+                CHECK(ecount == 0);
+                CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+                CHECK(ecount == 1);
+            }
+        }
+    }
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+}
+
+void run_ec_pubkey_parse_test(void) {
+#define SECP256K1_EC_PARSE_TEST_NVALID (12)
+    const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
+        {
+            /* Point with leading and trailing zeros in x and y serialization. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
+            0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
+        },
+        {
+            /* Point with x equal to a 3rd root of unity.*/
+            0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
+            0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Point with largest x. (1/2) */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+            0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
+            0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
+        },
+        {
+            /* Point with largest x. (2/2) */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+            0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
+            0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
+        },
+        {
+            /* Point with smallest x. (1/2) */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Point with smallest x. (2/2) */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+            0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+        },
+        {
+            /* Point with largest y. (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with largest y. (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with largest y. (3/3) */
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with smallest y. (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Point with smallest y. (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Point with smallest y. (3/3) */
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
+        }
+    };
+#define SECP256K1_EC_PARSE_TEST_NXVALID (4)
+    const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* x on curve, y is from y^2 = x^3 + 8. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
+        }
+    };
+#define SECP256K1_EC_PARSE_TEST_NINVALID (7)
+    const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
+        {
+            /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
+            0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
+            0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Valid if x overflow ignored (x = 1 mod p). */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Valid if x overflow ignored (x = 1 mod p). */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+            0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+            0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+        },
+        {
+            /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+            0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
+            0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
+        },
+        {
+            /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+            0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
+            0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
+        },
+        {
+            /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
+            0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
+        },
+        {
+            /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
+            0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
+        }
+    };
+    const unsigned char pubkeyc[66] = {
+        /* Serialization of G. */
+        0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
+        0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
+        0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
+        0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
+        0xB8, 0x00
+    };
+    unsigned char sout[65];
+    unsigned char shortkey[2];
+    secp256k1_ge ge;
+    secp256k1_pubkey pubkey;
+    size_t len;
+    int32_t i;
+    int32_t ecount;
+    int32_t ecount2;
+    ecount = 0;
+    /* Nothing should be reading this far into pubkeyc. */
+    VG_UNDEF(&pubkeyc[65], 1);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    /* Zero length claimed, fail, zeroize, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(shortkey, 2);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* Length one claimed, fail, zeroize, no illegal arg error. */
+    for (i = 0; i < 256 ; i++) {
+        memset(&pubkey, 0xfe, sizeof(pubkey));
+        ecount = 0;
+        shortkey[0] = i;
+        VG_UNDEF(&shortkey[1], 1);
+        VG_UNDEF(&pubkey, sizeof(pubkey));
+        CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
+        VG_CHECK(&pubkey, sizeof(pubkey));
+        CHECK(ecount == 0);
+        CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+        CHECK(ecount == 1);
+    }
+    /* Length two claimed, fail, zeroize, no illegal arg error. */
+    for (i = 0; i < 65536 ; i++) {
+        memset(&pubkey, 0xfe, sizeof(pubkey));
+        ecount = 0;
+        shortkey[0] = i & 255;
+        shortkey[1] = i >> 8;
+        VG_UNDEF(&pubkey, sizeof(pubkey));
+        CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
+        VG_CHECK(&pubkey, sizeof(pubkey));
+        CHECK(ecount == 0);
+        CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+        CHECK(ecount == 1);
+    }
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
+    CHECK(ecount == 2);
+    /* NULL input string. Illegal arg and zeroize output. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 1);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 2);
+    /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* Valid parse. */
+    memset(&pubkey, 0, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    VG_UNDEF(&ge, sizeof(ge));
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+    VG_CHECK(&ge.x, sizeof(ge.x));
+    VG_CHECK(&ge.y, sizeof(ge.y));
+    VG_CHECK(&ge.infinity, sizeof(ge.infinity));
+    ge_equals_ge(&secp256k1_ge_const_g, &ge);
+    CHECK(ecount == 0);
+    /* secp256k1_ec_pubkey_serialize illegal args. */
+    ecount = 0;
+    len = 65;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+    CHECK(ecount == 1);
+    CHECK(len == 0);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+    CHECK(ecount == 2);
+    len = 65;
+    VG_UNDEF(sout, 65);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
+    VG_CHECK(sout, 65);
+    CHECK(ecount == 3);
+    CHECK(len == 0);
+    len = 65;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
+    CHECK(ecount == 4);
+    CHECK(len == 0);
+    len = 65;
+    VG_UNDEF(sout, 65);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+    VG_CHECK(sout, 65);
+    CHECK(ecount == 4);
+    CHECK(len == 65);
+    /* Multiple illegal args. Should still set arg error only once. */
+    ecount = 0;
+    ecount2 = 11;
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+    CHECK(ecount == 1);
+    /* Does the illegal arg callback actually change the behavior? */
+    secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+    CHECK(ecount == 1);
+    CHECK(ecount2 == 10);
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+    /* Try a bunch of prefabbed points with all possible encodings. */
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
+        ec_pubkey_parse_pointtest(valid[i], 1, 1);
+    }
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
+        ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
+    }
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
+        ec_pubkey_parse_pointtest(invalid[i], 0, 0);
+    }
+}
+
+void run_eckey_edge_case_test(void) {
+    const unsigned char orderc[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+    };
+    const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
+    unsigned char ctmp[33];
+    unsigned char ctmp2[33];
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey pubkey2;
+    secp256k1_pubkey pubkey_one;
+    secp256k1_pubkey pubkey_negone;
+    const secp256k1_pubkey *pubkeys[3];
+    size_t len;
+    int32_t ecount;
+    /* Group order is too large, reject. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* Maximum value is too large, reject. */
+    memset(ctmp, 255, 32);
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* Zero is too small, reject. */
+    memset(ctmp, 0, 32);
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* One must be accepted. */
+    ctmp[31] = 0x01;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    memset(&pubkey, 0, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    pubkey_one = pubkey;
+    /* Group order + 1 is too large, reject. */
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x42;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* -1 must be accepted. */
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    memset(&pubkey, 0, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    pubkey_negone = pubkey;
+    /* Tweak of zero leaves the value changed. */
+    memset(ctmp2, 0, 32);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
+    CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
+    memcpy(&pubkey2, &pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Multiply tweak of zero zeroizes the output. */
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Overflowing key tweak zeroizes. */
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Private key tweaks results in a key of zero. */
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
+    CHECK(memcmp(zeros, ctmp2, 32) == 0);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Tweak computation wraps and results in a key of 1. */
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
+    CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Tweak mul * 2 = 1+1. */
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Test argument errors. */
+    ecount = 0;
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    CHECK(ecount == 0);
+    /* Zeroize pubkey on parse error. */
+    memset(&pubkey, 0, 32);
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    memset(&pubkey2, 0, 32);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
+    CHECK(ecount == 2);
+    CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
+    /* Plain argument errors. */
+    ecount = 0;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
+    CHECK(ecount == 1);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 4;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 4;
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
+    CHECK(ecount == 1);
+    memset(&pubkey, 1, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* secp256k1_ec_pubkey_combine tests. */
+    ecount = 0;
+    pubkeys[0] = &pubkey_one;
+    VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
+    VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
+    VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 2);
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 3);
+    pubkeys[0] = &pubkey_negone;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    len = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    /* Result is infinity. */
+    pubkeys[0] = &pubkey_one;
+    pubkeys[1] = &pubkey_negone;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 3);
+    /* Passes through infinity but comes out one. */
+    pubkeys[2] = &pubkey_one;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    len = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    /* Adds to two. */
+    pubkeys[1] = &pubkey_one;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+}
+
+void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
+    secp256k1_scalar nonce;
+    do {
+        random_scalar_order_test(&nonce);
+    } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
+}
+
+void test_ecdsa_sign_verify(void) {
+    secp256k1_gej pubj;
+    secp256k1_ge pub;
+    secp256k1_scalar one;
+    secp256k1_scalar msg, key;
+    secp256k1_scalar sigr, sigs;
+    int recid;
+    int getrec;
+    random_scalar_order_test(&msg);
+    random_scalar_order_test(&key);
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
+    secp256k1_ge_set_gej(&pub, &pubj);
+    getrec = secp256k1_rand_bits(1);
+    random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
+    if (getrec) {
+        CHECK(recid >= 0 && recid < 4);
+    }
+    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    secp256k1_scalar_set_int(&one, 1);
+    secp256k1_scalar_add(&msg, &msg, &one);
+    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+}
+
+void run_ecdsa_sign_verify(void) {
+    int i;
+    for (i = 0; i < 10*count; i++) {
+        test_ecdsa_sign_verify();
+    }
+}
+
+/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
+static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    (void)msg32;
+    (void)key32;
+    (void)algo16;
+    memcpy(nonce32, data, 32);
+    return (counter == 0);
+}
+
+static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   /* Dummy nonce generator that has a fatal error on the first counter value. */
+   if (counter == 0) {
+       return 0;
+   }
+   return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
+}
+
+static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
+   if (counter < 3) {
+       memset(nonce32, counter==0 ? 0 : 255, 32);
+       if (counter == 2) {
+           nonce32[31]--;
+       }
+       return 1;
+   }
+   if (counter < 5) {
+       static const unsigned char order[] = {
+           0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+           0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+           0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+           0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+       };
+       memcpy(nonce32, order, 32);
+       if (counter == 4) {
+           nonce32[31]++;
+       }
+       return 1;
+   }
+   /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
+   /* If someone does fine a case where it retries for secp256k1, we'd like to know. */
+   if (counter > 5) {
+       return 0;
+   }
+   return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
+}
+
+int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
+    static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
+    return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
+}
+
+void test_ecdsa_end_to_end(void) {
+    unsigned char extra[32] = {0x00};
+    unsigned char privkey[32];
+    unsigned char message[32];
+    unsigned char privkey2[32];
+    secp256k1_ecdsa_signature signature[6];
+    secp256k1_scalar r, s;
+    unsigned char sig[74];
+    size_t siglen = 74;
+    unsigned char pubkeyc[65];
+    size_t pubkeyclen = 65;
+    secp256k1_pubkey pubkey;
+    unsigned char seckey[300];
+    size_t seckeylen = 300;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar msg, key;
+        random_scalar_order_test(&msg);
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_scalar_get_b32(message, &msg);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Verify exporting and importing public key. */
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
+    memset(&pubkey, 0, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
+
+    /* Verify private key import and export. */
+    CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
+    CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
+    CHECK(memcmp(privkey, privkey2, 32) == 0);
+
+    /* Optionally tweak the keys using addition. */
+    if (secp256k1_rand_int(3) == 0) {
+        int ret1;
+        int ret2;
+        unsigned char rnd[32];
+        secp256k1_pubkey pubkey2;
+        secp256k1_rand256_test(rnd);
+        ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
+        ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
+        CHECK(ret1 == ret2);
+        if (ret1 == 0) {
+            return;
+        }
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    }
+
+    /* Optionally tweak the keys using multiplication. */
+    if (secp256k1_rand_int(3) == 0) {
+        int ret1;
+        int ret2;
+        unsigned char rnd[32];
+        secp256k1_pubkey pubkey2;
+        secp256k1_rand256_test(rnd);
+        ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
+        ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
+        CHECK(ret1 == ret2);
+        if (ret1 == 0) {
+            return;
+        }
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    }
+
+    /* Sign. */
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
+    extra[31] = 1;
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
+    extra[31] = 0;
+    extra[0] = 1;
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
+    CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
+    CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
+    /* Verify. */
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
+    /* Test lower-S form, malleate, verify and fail, test again, malleate again */
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
+    CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+    CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
+
+    /* Serialize/parse DER and verify again */
+    CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+    memset(&signature[0], 0, sizeof(signature[0]));
+    CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+    /* Serialize/destroy/parse DER and verify again. */
+    siglen = 74;
+    CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+    sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
+    CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
+          secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
+}
+
+void test_random_pubkeys(void) {
+    secp256k1_ge elem;
+    secp256k1_ge elem2;
+    unsigned char in[65];
+    /* Generate some randomly sized pubkeys. */
+    size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
+    if (secp256k1_rand_bits(2) == 0) {
+        len = secp256k1_rand_bits(6);
+    }
+    if (len == 65) {
+      in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
+    } else {
+      in[0] = secp256k1_rand_bits(1) ? 2 : 3;
+    }
+    if (secp256k1_rand_bits(3) == 0) {
+        in[0] = secp256k1_rand_bits(8);
+    }
+    if (len > 1) {
+        secp256k1_rand256(&in[1]);
+    }
+    if (len > 33) {
+        secp256k1_rand256(&in[33]);
+    }
+    if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
+        unsigned char out[65];
+        unsigned char firstb;
+        int res;
+        size_t size = len;
+        firstb = in[0];
+        /* If the pubkey can be parsed, it should round-trip... */
+        CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
+        CHECK(size == len);
+        CHECK(memcmp(&in[1], &out[1], len-1) == 0);
+        /* ... except for the type of hybrid inputs. */
+        if ((in[0] != 6) && (in[0] != 7)) {
+            CHECK(in[0] == out[0]);
+        }
+        size = 65;
+        CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
+        CHECK(size == 65);
+        CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
+        ge_equals_ge(&elem,&elem2);
+        /* Check that the X9.62 hybrid type is checked. */
+        in[0] = secp256k1_rand_bits(1) ? 6 : 7;
+        res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
+        if (firstb == 2 || firstb == 3) {
+            if (in[0] == firstb + 4) {
+              CHECK(res);
+            } else {
+              CHECK(!res);
+            }
+        }
+        if (res) {
+            ge_equals_ge(&elem,&elem2);
+            CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
+            CHECK(memcmp(&in[1], &out[1], 64) == 0);
+        }
+    }
+}
+
+void run_random_pubkeys(void) {
+    int i;
+    for (i = 0; i < 10*count; i++) {
+        test_random_pubkeys();
+    }
+}
+
+void run_ecdsa_end_to_end(void) {
+    int i;
+    for (i = 0; i < 64*count; i++) {
+        test_ecdsa_end_to_end();
+    }
+}
+
+int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
+    static const unsigned char zeroes[32] = {0};
+#ifdef ENABLE_OPENSSL_TESTS
+    static const unsigned char max_scalar[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
+    };
+#endif
+
+    int ret = 0;
+
+    secp256k1_ecdsa_signature sig_der;
+    unsigned char roundtrip_der[2048];
+    unsigned char compact_der[64];
+    size_t len_der = 2048;
+    int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
+
+    secp256k1_ecdsa_signature sig_der_lax;
+    unsigned char roundtrip_der_lax[2048];
+    unsigned char compact_der_lax[64];
+    size_t len_der_lax = 2048;
+    int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
+
+#ifdef ENABLE_OPENSSL_TESTS
+    ECDSA_SIG *sig_openssl;
+    const unsigned char *sigptr;
+    unsigned char roundtrip_openssl[2048];
+    int len_openssl = 2048;
+    int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
+#endif
+
+    parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
+    if (parsed_der) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
+        valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
+    }
+    if (valid_der) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
+        roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
+    }
+
+    parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
+    if (parsed_der_lax) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
+        valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
+    }
+    if (valid_der_lax) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
+        roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
+    }
+
+    if (certainly_der) {
+        ret |= (!parsed_der) << 2;
+    }
+    if (certainly_not_der) {
+        ret |= (parsed_der) << 17;
+    }
+    if (valid_der) {
+        ret |= (!roundtrips_der) << 3;
+    }
+
+    if (valid_der) {
+        ret |= (!roundtrips_der_lax) << 12;
+        ret |= (len_der != len_der_lax) << 13;
+        ret |= (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0) << 14;
+    }
+    ret |= (roundtrips_der != roundtrips_der_lax) << 15;
+    if (parsed_der) {
+        ret |= (!parsed_der_lax) << 16;
+    }
+
+#ifdef ENABLE_OPENSSL_TESTS
+    sig_openssl = ECDSA_SIG_new();
+    sigptr = sig;
+    parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
+    if (parsed_openssl) {
+        valid_openssl = !BN_is_negative(sig_openssl->r) && !BN_is_negative(sig_openssl->s) && BN_num_bits(sig_openssl->r) > 0 && BN_num_bits(sig_openssl->r) <= 256 && BN_num_bits(sig_openssl->s) > 0 && BN_num_bits(sig_openssl->s) <= 256;
+        if (valid_openssl) {
+            unsigned char tmp[32] = {0};
+            BN_bn2bin(sig_openssl->r, tmp + 32 - BN_num_bytes(sig_openssl->r));
+            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+        }
+        if (valid_openssl) {
+            unsigned char tmp[32] = {0};
+            BN_bn2bin(sig_openssl->s, tmp + 32 - BN_num_bytes(sig_openssl->s));
+            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+        }
+    }
+    len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
+    if (len_openssl <= 2048) {
+        unsigned char *ptr = roundtrip_openssl;
+        CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
+        roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
+    } else {
+        len_openssl = 0;
+    }
+    ECDSA_SIG_free(sig_openssl);
+
+    ret |= (parsed_der && !parsed_openssl) << 4;
+    ret |= (valid_der && !valid_openssl) << 5;
+    ret |= (roundtrips_openssl && !parsed_der) << 6;
+    ret |= (roundtrips_der != roundtrips_openssl) << 7;
+    if (roundtrips_openssl) {
+        ret |= (len_der != (size_t)len_openssl) << 8;
+        ret |= (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0) << 9;
+    }
+#endif
+    return ret;
+}
+
+static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
+    size_t i;
+    for (i = 0; i < ptrlen; i++) {
+        int shift = ptrlen - 1 - i;
+        if (shift >= 4) {
+            ptr[i] = 0;
+        } else {
+            ptr[i] = (val >> shift) & 0xFF;
+        }
+    }
+}
+
+static void damage_array(unsigned char *sig, size_t *len) {
+    int pos;
+    int action = secp256k1_rand_bits(3);
+    if (action < 1 && *len > 3) {
+        /* Delete a byte. */
+        pos = secp256k1_rand_int(*len);
+        memmove(sig + pos, sig + pos + 1, *len - pos - 1);
+        (*len)--;
+        return;
+    } else if (action < 2 && *len < 2048) {
+        /* Insert a byte. */
+        pos = secp256k1_rand_int(1 + *len);
+        memmove(sig + pos + 1, sig + pos, *len - pos);
+        sig[pos] = secp256k1_rand_bits(8);
+        (*len)++;
+        return;
+    } else if (action < 4) {
+        /* Modify a byte. */
+        sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
+        return;
+    } else { /* action < 8 */
+        /* Modify a bit. */
+        sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
+        return;
+    }
+}
+
+static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
+    int der;
+    int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
+    size_t tlen, elen, glen;
+    int indet;
+    int n;
+
+    *len = 0;
+    der = secp256k1_rand_bits(2) == 0;
+    *certainly_der = der;
+    *certainly_not_der = 0;
+    indet = der ? 0 : secp256k1_rand_int(10) == 0;
+
+    for (n = 0; n < 2; n++) {
+        /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
+        nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
+        /* The length of the number in bytes (the first byte of which will always be nonzero) */
+        nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
+        CHECK(nlen[n] <= 232);
+        /* The top bit of the number. */
+        nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
+        /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
+        nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
+        /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
+        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
+        if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
+            *certainly_not_der = 1;
+        }
+        CHECK(nlen[n] + nzlen[n] <= 300);
+        /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
+        nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
+        if (!der) {
+            /* nlenlen[n] max 127 bytes */
+            int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            nlenlen[n] += add;
+            if (add != 0) {
+                *certainly_not_der = 1;
+            }
+        }
+        CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
+    }
+
+    /* The total length of the data to go, so far */
+    tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
+    CHECK(tlen <= 856);
+
+    /* The length of the garbage inside the tuple. */
+    elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
+    if (elen != 0) {
+        *certainly_not_der = 1;
+    }
+    tlen += elen;
+    CHECK(tlen <= 980);
+
+    /* The length of the garbage after the end of the tuple. */
+    glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
+    if (glen != 0) {
+        *certainly_not_der = 1;
+    }
+    CHECK(tlen + glen <= 990);
+
+    /* Write the tuple header. */
+    sig[(*len)++] = 0x30;
+    if (indet) {
+        /* Indeterminate length */
+        sig[(*len)++] = 0x80;
+        *certainly_not_der = 1;
+    } else {
+        int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
+        if (!der) {
+            int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            tlenlen += add;
+            if (add != 0) {
+                *certainly_not_der = 1;
+            }
+        }
+        if (tlenlen == 0) {
+            /* Short length notation */
+            sig[(*len)++] = tlen;
+        } else {
+            /* Long length notation */
+            sig[(*len)++] = 128 + tlenlen;
+            assign_big_endian(sig + *len, tlenlen, tlen);
+            *len += tlenlen;
+        }
+        tlen += tlenlen;
+    }
+    tlen += 2;
+    CHECK(tlen + glen <= 1119);
+
+    for (n = 0; n < 2; n++) {
+        /* Write the integer header. */
+        sig[(*len)++] = 0x02;
+        if (nlenlen[n] == 0) {
+            /* Short length notation */
+            sig[(*len)++] = nlen[n] + nzlen[n];
+        } else {
+            /* Long length notation. */
+            sig[(*len)++] = 128 + nlenlen[n];
+            assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
+            *len += nlenlen[n];
+        }
+        /* Write zero padding */
+        while (nzlen[n] > 0) {
+            sig[(*len)++] = 0x00;
+            nzlen[n]--;
+        }
+        if (nlen[n] == 32 && !nlow[n]) {
+            /* Special extra 16 0xFF bytes in "high" 32-byte numbers */
+            int i;
+            for (i = 0; i < 16; i++) {
+                sig[(*len)++] = 0xFF;
+            }
+            nlen[n] -= 16;
+        }
+        /* Write first byte of number */
+        if (nlen[n] > 0) {
+            sig[(*len)++] = nhbyte[n];
+            nlen[n]--;
+        }
+        /* Generate remaining random bytes of number */
+        secp256k1_rand_bytes_test(sig + *len, nlen[n]);
+        *len += nlen[n];
+        nlen[n] = 0;
+    }
+
+    /* Generate random garbage inside tuple. */
+    secp256k1_rand_bytes_test(sig + *len, elen);
+    *len += elen;
+
+    /* Generate end-of-contents bytes. */
+    if (indet) {
+        sig[(*len)++] = 0;
+        sig[(*len)++] = 0;
+        tlen += 2;
+    }
+    CHECK(tlen + glen <= 1121);
+
+    /* Generate random garbage outside tuple. */
+    secp256k1_rand_bytes_test(sig + *len, glen);
+    *len += glen;
+    tlen += glen;
+    CHECK(tlen <= 1121);
+    CHECK(tlen == *len);
+}
+
+void run_ecdsa_der_parse(void) {
+    int i,j;
+    for (i = 0; i < 200 * count; i++) {
+        unsigned char buffer[2048];
+        size_t buflen = 0;
+        int certainly_der = 0;
+        int certainly_not_der = 0;
+        random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
+        CHECK(buflen <= 2048);
+        for (j = 0; j < 16; j++) {
+            int ret = 0;
+            if (j > 0) {
+                damage_array(buffer, &buflen);
+                /* We don't know anything anymore about the DERness of the result */
+                certainly_der = 0;
+                certainly_not_der = 0;
+            }
+            ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der);
+            if (ret != 0) {
+                size_t k;
+                fprintf(stderr, "Failure %x on ", ret);
+                for (k = 0; k < buflen; k++) {
+                    fprintf(stderr, "%02x ", buffer[k]);
+                }
+                fprintf(stderr, "\n");
+            }
+            CHECK(ret == 0);
+        }
+    }
+}
+
+/* Tests several edge cases. */
+void test_ecdsa_edge_cases(void) {
+    int t;
+    secp256k1_ecdsa_signature sig;
+
+    /* Test the case where ECDSA recomputes a point that is infinity. */
+    {
+        secp256k1_gej keyj;
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        secp256k1_scalar_inverse(&ss, &ss);
+        secp256k1_scalar_set_int(&sr, 1);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
+        secp256k1_ge_set_gej(&key, &keyj);
+        msg = ss;
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Verify signature with r of zero fails. */
+    {
+        const unsigned char pubkey_mods_zero[33] = {
+            0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+            0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+            0x41
+        };
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 0);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Verify signature with s of zero fails. */
+    {
+        const unsigned char pubkey[33] = {
+            0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x01
+        };
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 0);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 1);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Verify signature with message 0 passes. */
+    {
+        const unsigned char pubkey[33] = {
+            0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x02
+        };
+        const unsigned char pubkey2[33] = {
+            0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+            0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+            0x43
+        };
+        secp256k1_ge key;
+        secp256k1_ge key2;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 2);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 2);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+    }
+
+    /* Verify signature with message 1 passes. */
+    {
+        const unsigned char pubkey[33] = {
+            0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
+            0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
+            0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
+            0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
+            0x25
+        };
+        const unsigned char pubkey2[33] = {
+            0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
+            0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
+            0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
+            0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
+            0x62
+        };
+        const unsigned char csr[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+            0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
+        };
+        secp256k1_ge key;
+        secp256k1_ge key2;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 1);
+        secp256k1_scalar_set_b32(&sr, csr, NULL);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 2);
+        secp256k1_scalar_inverse_var(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+    }
+
+    /* Verify signature with message -1 passes. */
+    {
+        const unsigned char pubkey[33] = {
+            0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
+            0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
+            0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
+            0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
+            0xf1
+        };
+        const unsigned char csr[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+            0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
+        };
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 1);
+        secp256k1_scalar_negate(&msg, &msg);
+        secp256k1_scalar_set_b32(&sr, csr, NULL);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 3);
+        secp256k1_scalar_inverse_var(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Signature where s would be zero. */
+    {
+        secp256k1_pubkey pubkey;
+        size_t siglen;
+        int32_t ecount;
+        unsigned char signature[72];
+        static const unsigned char nonce[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        static const unsigned char nonce2[32] = {
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+            0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+            0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
+        };
+        const unsigned char key[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        unsigned char msg[32] = {
+            0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
+            0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
+            0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
+            0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
+        };
+        ecount = 0;
+        secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
+        msg[31] = 0xaa;
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
+        CHECK(ecount == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
+        CHECK(ecount == 4);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
+        CHECK(ecount == 6);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
+        CHECK(ecount == 6);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+        CHECK(ecount == 7);
+        /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
+        CHECK(ecount == 8);
+        siglen = 72;
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
+        CHECK(ecount == 9);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
+        CHECK(ecount == 10);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
+        CHECK(ecount == 11);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
+        CHECK(ecount == 11);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
+        CHECK(ecount == 12);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
+        CHECK(ecount == 13);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
+        CHECK(ecount == 13);
+        siglen = 10;
+        /* Too little room for a signature does not fail via ARGCHECK. */
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
+        CHECK(ecount == 13);
+        ecount = 0;
+        CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
+        CHECK(ecount == 4);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
+        CHECK(ecount == 5);
+        memset(signature, 255, 64);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
+        CHECK(ecount == 5);
+        secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+    }
+
+    /* Nonce function corner cases. */
+    for (t = 0; t < 2; t++) {
+        static const unsigned char zero[32] = {0x00};
+        int i;
+        unsigned char key[32];
+        unsigned char msg[32];
+        secp256k1_ecdsa_signature sig2;
+        secp256k1_scalar sr[512], ss;
+        const unsigned char *extra;
+        extra = t == 0 ? NULL : zero;
+        memset(msg, 0, 32);
+        msg[31] = 1;
+        /* High key results in signature failure. */
+        memset(key, 0xFF, 32);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+        CHECK(is_empty_signature(&sig));
+        /* Zero key results in signature failure. */
+        memset(key, 0, 32);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+        CHECK(is_empty_signature(&sig));
+        /* Nonce function failure results in signature failure. */
+        key[31] = 1;
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
+        CHECK(is_empty_signature(&sig));
+        /* The retry loop successfully makes its way to the first good value. */
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
+        CHECK(!is_empty_signature(&sig));
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
+        CHECK(!is_empty_signature(&sig2));
+        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+        /* The default nonce function is deterministic. */
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+        CHECK(!is_empty_signature(&sig2));
+        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+        /* The default nonce function changes output with different messages. */
+        for(i = 0; i < 256; i++) {
+            int j;
+            msg[0] = i;
+            CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+            CHECK(!is_empty_signature(&sig2));
+            secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
+            for (j = 0; j < i; j++) {
+                CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
+            }
+        }
+        msg[0] = 0;
+        msg[31] = 2;
+        /* The default nonce function changes output with different keys. */
+        for(i = 256; i < 512; i++) {
+            int j;
+            key[0] = i - 256;
+            CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+            CHECK(!is_empty_signature(&sig2));
+            secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
+            for (j = 0; j < i; j++) {
+                CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
+            }
+        }
+        key[0] = 0;
+    }
+
+    {
+        /* Check that optional nonce arguments do not have equivalent effect. */
+        const unsigned char zeros[32] = {0};
+        unsigned char nonce[32];
+        unsigned char nonce2[32];
+        unsigned char nonce3[32];
+        unsigned char nonce4[32];
+        VG_UNDEF(nonce,32);
+        VG_UNDEF(nonce2,32);
+        VG_UNDEF(nonce3,32);
+        VG_UNDEF(nonce4,32);
+        CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
+        VG_CHECK(nonce,32);
+        CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
+        VG_CHECK(nonce2,32);
+        CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
+        VG_CHECK(nonce3,32);
+        CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
+        VG_CHECK(nonce4,32);
+        CHECK(memcmp(nonce, nonce2, 32) != 0);
+        CHECK(memcmp(nonce, nonce3, 32) != 0);
+        CHECK(memcmp(nonce, nonce4, 32) != 0);
+        CHECK(memcmp(nonce2, nonce3, 32) != 0);
+        CHECK(memcmp(nonce2, nonce4, 32) != 0);
+        CHECK(memcmp(nonce3, nonce4, 32) != 0);
+    }
+
+
+    /* Privkey export where pubkey is the point at infinity. */
+    {
+        unsigned char privkey[300];
+        unsigned char seckey[32] = {
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+            0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+            0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41,
+        };
+        size_t outlen = 300;
+        CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0));
+        outlen = 300;
+        CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1));
+    }
+}
+
+void run_ecdsa_edge_cases(void) {
+    test_ecdsa_edge_cases();
+}
+
+#ifdef ENABLE_OPENSSL_TESTS
+EC_KEY *get_openssl_key(const unsigned char *key32) {
+    unsigned char privkey[300];
+    size_t privkeylen;
+    const unsigned char* pbegin = privkey;
+    int compr = secp256k1_rand_bits(1);
+    EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
+    CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
+    CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
+    CHECK(EC_KEY_check_key(ec_key));
+    return ec_key;
+}
+
+void test_ecdsa_openssl(void) {
+    secp256k1_gej qj;
+    secp256k1_ge q;
+    secp256k1_scalar sigr, sigs;
+    secp256k1_scalar one;
+    secp256k1_scalar msg2;
+    secp256k1_scalar key, msg;
+    EC_KEY *ec_key;
+    unsigned int sigsize = 80;
+    size_t secp_sigsize = 80;
+    unsigned char message[32];
+    unsigned char signature[80];
+    unsigned char key32[32];
+    secp256k1_rand256_test(message);
+    secp256k1_scalar_set_b32(&msg, message, NULL);
+    random_scalar_order_test(&key);
+    secp256k1_scalar_get_b32(key32, &key);
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
+    secp256k1_ge_set_gej(&q, &qj);
+    ec_key = get_openssl_key(key32);
+    CHECK(ec_key != NULL);
+    CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
+    CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
+    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
+    secp256k1_scalar_set_int(&one, 1);
+    secp256k1_scalar_add(&msg2, &msg, &one);
+    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
+
+    random_sign(&sigr, &sigs, &key, &msg, NULL);
+    CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
+    CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
+
+    EC_KEY_free(ec_key);
+}
+
+void run_ecdsa_openssl(void) {
+    int i;
+    for (i = 0; i < 10*count; i++) {
+        test_ecdsa_openssl();
+    }
+}
+#endif
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/tests_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+# include "modules/schnorr/tests_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/tests_impl.h"
+#endif
+
+int main(int argc, char **argv) {
+    unsigned char seed16[16] = {0};
+    unsigned char run32[32] = {0};
+    /* find iteration count */
+    if (argc > 1) {
+        count = strtol(argv[1], NULL, 0);
+    }
+
+    /* find random seed */
+    if (argc > 2) {
+        int pos = 0;
+        const char* ch = argv[2];
+        while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
+            unsigned short sh;
+            if (sscanf(ch, "%2hx", &sh)) {
+                seed16[pos] = sh;
+            } else {
+                break;
+            }
+            ch += 2;
+            pos++;
+        }
+    } else {
+        FILE *frand = fopen("/dev/urandom", "r");
+        if ((frand == NULL) || !fread(&seed16, sizeof(seed16), 1, frand)) {
+            uint64_t t = time(NULL) * (uint64_t)1337;
+            seed16[0] ^= t;
+            seed16[1] ^= t >> 8;
+            seed16[2] ^= t >> 16;
+            seed16[3] ^= t >> 24;
+            seed16[4] ^= t >> 32;
+            seed16[5] ^= t >> 40;
+            seed16[6] ^= t >> 48;
+            seed16[7] ^= t >> 56;
+        }
+        fclose(frand);
+    }
+    secp256k1_rand_seed(seed16);
+
+    printf("test count = %i\n", count);
+    printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
+
+    /* initialize */
+    run_context_tests();
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    if (secp256k1_rand_bits(1)) {
+        secp256k1_rand256(run32);
+        CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
+    }
+
+    run_rand_bits();
+    run_rand_int();
+
+    run_sha256_tests();
+    run_hmac_sha256_tests();
+    run_rfc6979_hmac_sha256_tests();
+
+#ifndef USE_NUM_NONE
+    /* num tests */
+    run_num_smalltests();
+#endif
+
+    /* scalar tests */
+    run_scalar_tests();
+
+    /* field tests */
+    run_field_inv();
+    run_field_inv_var();
+    run_field_inv_all_var();
+    run_field_misc();
+    run_field_convert();
+    run_sqr();
+    run_sqrt();
+
+    /* group tests */
+    run_ge();
+    run_group_decompress();
+
+    /* ecmult tests */
+    run_wnaf();
+    run_point_times_order();
+    run_ecmult_chain();
+    run_ecmult_constants();
+    run_ecmult_gen_blind();
+    run_ecmult_const_tests();
+    run_ec_combine();
+
+    /* endomorphism tests */
+#ifdef USE_ENDOMORPHISM
+    run_endomorphism_tests();
+#endif
+
+    /* EC point parser test */
+    run_ec_pubkey_parse_test();
+
+    /* EC key edge cases */
+    run_eckey_edge_case_test();
+
+#ifdef ENABLE_MODULE_ECDH
+    /* ecdh tests */
+    run_ecdh_tests();
+#endif
+
+    /* ecdsa tests */
+    run_random_pubkeys();
+    run_ecdsa_der_parse();
+    run_ecdsa_sign_verify();
+    run_ecdsa_end_to_end();
+    run_ecdsa_edge_cases();
+#ifdef ENABLE_OPENSSL_TESTS
+    run_ecdsa_openssl();
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+    /* Schnorr tests */
+    run_schnorr_tests();
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+    /* ECDSA pubkey recovery tests */
+    run_recovery_tests();
+#endif
+
+    secp256k1_rand256(run32);
+    printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
+
+    /* shutdown */
+    secp256k1_context_destroy(ctx);
+
+    printf("no problems found\n");
+    return 0;
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests_exhaustive.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests_exhaustive.c
new file mode 100644
index 000000000..b040bb073
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/tests_exhaustive.c
@@ -0,0 +1,470 @@
+/***********************************************************************
+ * Copyright (c) 2016 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <time.h>
+
+#undef USE_ECMULT_STATIC_PRECOMPUTATION
+
+#ifndef EXHAUSTIVE_TEST_ORDER
+/* see group_impl.h for allowable values */
+#define EXHAUSTIVE_TEST_ORDER 13
+#define EXHAUSTIVE_TEST_LAMBDA 9   /* cube root of 1 mod 13 */
+#endif
+
+#include "include/secp256k1.h"
+#include "group.h"
+#include "secp256k1.c"
+#include "testrand_impl.h"
+
+#ifdef ENABLE_MODULE_RECOVERY
+#include "src/modules/recovery/main_impl.h"
+#include "include/secp256k1_recovery.h"
+#endif
+
+/** stolen from tests.c */
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
+    CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
+}
+
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+    secp256k1_fe z2s;
+    secp256k1_fe u1, u2, s1, s2;
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+    secp256k1_fe_sqr(&z2s, &b->z);
+    secp256k1_fe_mul(&u1, &a->x, &z2s);
+    u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+    secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+    s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+    CHECK(secp256k1_fe_equal_var(&u1, &u2));
+    CHECK(secp256k1_fe_equal_var(&s1, &s2));
+}
+
+void random_fe(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+/** END stolen from tests.c */
+
+int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+                                      const unsigned char *key32, const unsigned char *algo16,
+                                      void *data, unsigned int attempt) {
+    secp256k1_scalar s;
+    int *idata = data;
+    (void)msg32;
+    (void)key32;
+    (void)algo16;
+    /* Some nonces cannot be used because they'd cause s and/or r to be zero.
+     * The signing function has retry logic here that just re-calls the nonce
+     * function with an increased `attempt`. So if attempt > 0 this means we
+     * need to change the nonce to avoid an infinite loop. */
+    if (attempt > 0) {
+        *idata = (*idata + 1) % EXHAUSTIVE_TEST_ORDER;
+    }
+    secp256k1_scalar_set_int(&s, *idata);
+    secp256k1_scalar_get_b32(nonce32, &s);
+    return 1;
+}
+
+#ifdef USE_ENDOMORPHISM
+void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
+    int i;
+    for (i = 0; i < order; i++) {
+        secp256k1_ge res;
+        secp256k1_ge_mul_lambda(&res, &group[i]);
+        ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
+    }
+}
+#endif
+
+void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+    int i, j;
+
+    /* Sanity-check (and check infinity functions) */
+    CHECK(secp256k1_ge_is_infinity(&group[0]));
+    CHECK(secp256k1_gej_is_infinity(&groupj[0]));
+    for (i = 1; i < order; i++) {
+        CHECK(!secp256k1_ge_is_infinity(&group[i]));
+        CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
+    }
+
+    /* Check all addition formulae */
+    for (j = 0; j < order; j++) {
+        secp256k1_fe fe_inv;
+        secp256k1_fe_inv(&fe_inv, &groupj[j].z);
+        for (i = 0; i < order; i++) {
+            secp256k1_ge zless_gej;
+            secp256k1_gej tmp;
+            /* add_var */
+            secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+            /* add_ge */
+            if (j > 0) {
+                secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
+                ge_equals_gej(&group[(i + j) % order], &tmp);
+            }
+            /* add_ge_var */
+            secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+            /* add_zinv_var */
+            zless_gej.infinity = groupj[j].infinity;
+            zless_gej.x = groupj[j].x;
+            zless_gej.y = groupj[j].y;
+            secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+        }
+    }
+
+    /* Check doubling */
+    for (i = 0; i < order; i++) {
+        secp256k1_gej tmp;
+        if (i > 0) {
+            secp256k1_gej_double_nonzero(&tmp, &groupj[i], NULL);
+            ge_equals_gej(&group[(2 * i) % order], &tmp);
+        }
+        secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
+        ge_equals_gej(&group[(2 * i) % order], &tmp);
+    }
+
+    /* Check negation */
+    for (i = 1; i < order; i++) {
+        secp256k1_ge tmp;
+        secp256k1_gej tmpj;
+        secp256k1_ge_neg(&tmp, &group[i]);
+        ge_equals_ge(&group[order - i], &tmp);
+        secp256k1_gej_neg(&tmpj, &groupj[i]);
+        ge_equals_gej(&group[order - i], &tmpj);
+    }
+}
+
+void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+    int i, j, r_log;
+    for (r_log = 1; r_log < order; r_log++) {
+        for (j = 0; j < order; j++) {
+            for (i = 0; i < order; i++) {
+                secp256k1_gej tmp;
+                secp256k1_scalar na, ng;
+                secp256k1_scalar_set_int(&na, i);
+                secp256k1_scalar_set_int(&ng, j);
+
+                secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
+                ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
+
+                if (i > 0) {
+                    secp256k1_ecmult_const(&tmp, &group[i], &ng);
+                    ge_equals_gej(&group[(i * j) % order], &tmp);
+                }
+            }
+        }
+    }
+}
+
+void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
+    secp256k1_fe x;
+    unsigned char x_bin[32];
+    k %= EXHAUSTIVE_TEST_ORDER;
+    x = group[k].x;
+    secp256k1_fe_normalize(&x);
+    secp256k1_fe_get_b32(x_bin, &x);
+    secp256k1_scalar_set_b32(r, x_bin, NULL);
+}
+
+void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int s, r, msg, key;
+    for (s = 1; s < order; s++) {
+        for (r = 1; r < order; r++) {
+            for (msg = 1; msg < order; msg++) {
+                for (key = 1; key < order; key++) {
+                    secp256k1_ge nonconst_ge;
+                    secp256k1_ecdsa_signature sig;
+                    secp256k1_pubkey pk;
+                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
+                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
+                    int k, should_verify;
+                    unsigned char msg32[32];
+
+                    secp256k1_scalar_set_int(&s_s, s);
+                    secp256k1_scalar_set_int(&r_s, r);
+                    secp256k1_scalar_set_int(&msg_s, msg);
+                    secp256k1_scalar_set_int(&sk_s, key);
+
+                    /* Verify by hand */
+                    /* Run through every k value that gives us this r and check that *one* works.
+                     * Note there could be none, there could be multiple, ECDSA is weird. */
+                    should_verify = 0;
+                    for (k = 0; k < order; k++) {
+                        secp256k1_scalar check_x_s;
+                        r_from_k(&check_x_s, group, k);
+                        if (r_s == check_x_s) {
+                            secp256k1_scalar_set_int(&s_times_k_s, k);
+                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
+                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
+                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
+                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
+                        }
+                    }
+                    /* nb we have a "high s" rule */
+                    should_verify &= !secp256k1_scalar_is_high(&s_s);
+
+                    /* Verify by calling verify */
+                    secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
+                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+                    secp256k1_pubkey_save(&pk, &nonconst_ge);
+                    secp256k1_scalar_get_b32(msg32, &msg_s);
+                    CHECK(should_verify ==
+                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+                }
+            }
+        }
+    }
+}
+
+void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int i, j, k;
+
+    /* Loop */
+    for (i = 1; i < order; i++) {  /* message */
+        for (j = 1; j < order; j++) {  /* key */
+            for (k = 1; k < order; k++) {  /* nonce */
+                const int starting_k = k;
+                secp256k1_ecdsa_signature sig;
+                secp256k1_scalar sk, msg, r, s, expected_r;
+                unsigned char sk32[32], msg32[32];
+                secp256k1_scalar_set_int(&msg, i);
+                secp256k1_scalar_set_int(&sk, j);
+                secp256k1_scalar_get_b32(sk32, &sk);
+                secp256k1_scalar_get_b32(msg32, &msg);
+
+                secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+                secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
+                /* Note that we compute expected_r *after* signing -- this is important
+                 * because our nonce-computing function function might change k during
+                 * signing. */
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+
+                /* Overflow means we've tried every possible nonce */
+                if (k < starting_k) {
+                    break;
+                }
+            }
+        }
+    }
+
+    /* We would like to verify zero-knowledge here by counting how often every
+     * possible (s, r) tuple appears, but because the group order is larger
+     * than the field order, when coercing the x-values to scalar values, some
+     * appear more often than others, so we are actually not zero-knowledge.
+     * (This effect also appears in the real code, but the difference is on the
+     * order of 1/2^128th the field order, so the deviation is not useful to a
+     * computationally bounded attacker.)
+     */
+}
+
+#ifdef ENABLE_MODULE_RECOVERY
+void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int i, j, k;
+
+    /* Loop */
+    for (i = 1; i < order; i++) {  /* message */
+        for (j = 1; j < order; j++) {  /* key */
+            for (k = 1; k < order; k++) {  /* nonce */
+                const int starting_k = k;
+                secp256k1_fe r_dot_y_normalized;
+                secp256k1_ecdsa_recoverable_signature rsig;
+                secp256k1_ecdsa_signature sig;
+                secp256k1_scalar sk, msg, r, s, expected_r;
+                unsigned char sk32[32], msg32[32];
+                int expected_recid;
+                int recid;
+                secp256k1_scalar_set_int(&msg, i);
+                secp256k1_scalar_set_int(&sk, j);
+                secp256k1_scalar_get_b32(sk32, &sk);
+                secp256k1_scalar_get_b32(msg32, &msg);
+
+                secp256k1_ecdsa_sign_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+                /* Check directly */
+                secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig);
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+                /* In computing the recid, there is an overflow condition that is disabled in
+                 * scalar_low_impl.h `secp256k1_scalar_set_b32` because almost every r.y value
+                 * will exceed the group order, and our signing code always holds out for r
+                 * values that don't overflow, so with a proper overflow check the tests would
+                 * loop indefinitely. */
+                r_dot_y_normalized = group[k].y;
+                secp256k1_fe_normalize(&r_dot_y_normalized);
+                /* Also the recovery id is flipped depending if we hit the low-s branch */
+                if ((k * s) % order == (i + r * j) % order) {
+                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 1 : 0;
+                } else {
+                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 0 : 1;
+                }
+                CHECK(recid == expected_recid);
+
+                /* Convert to a standard sig then check */
+                secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
+                /* Note that we compute expected_r *after* signing -- this is important
+                 * because our nonce-computing function function might change k during
+                 * signing. */
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+
+                /* Overflow means we've tried every possible nonce */
+                if (k < starting_k) {
+                    break;
+                }
+            }
+        }
+    }
+}
+
+void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    /* This is essentially a copy of test_exhaustive_verify, with recovery added */
+    int s, r, msg, key;
+    for (s = 1; s < order; s++) {
+        for (r = 1; r < order; r++) {
+            for (msg = 1; msg < order; msg++) {
+                for (key = 1; key < order; key++) {
+                    secp256k1_ge nonconst_ge;
+                    secp256k1_ecdsa_recoverable_signature rsig;
+                    secp256k1_ecdsa_signature sig;
+                    secp256k1_pubkey pk;
+                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
+                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
+                    int recid = 0;
+                    int k, should_verify;
+                    unsigned char msg32[32];
+
+                    secp256k1_scalar_set_int(&s_s, s);
+                    secp256k1_scalar_set_int(&r_s, r);
+                    secp256k1_scalar_set_int(&msg_s, msg);
+                    secp256k1_scalar_set_int(&sk_s, key);
+                    secp256k1_scalar_get_b32(msg32, &msg_s);
+
+                    /* Verify by hand */
+                    /* Run through every k value that gives us this r and check that *one* works.
+                     * Note there could be none, there could be multiple, ECDSA is weird. */
+                    should_verify = 0;
+                    for (k = 0; k < order; k++) {
+                        secp256k1_scalar check_x_s;
+                        r_from_k(&check_x_s, group, k);
+                        if (r_s == check_x_s) {
+                            secp256k1_scalar_set_int(&s_times_k_s, k);
+                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
+                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
+                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
+                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
+                        }
+                    }
+                    /* nb we have a "high s" rule */
+                    should_verify &= !secp256k1_scalar_is_high(&s_s);
+
+                    /* We would like to try recovering the pubkey and checking that it matches,
+                     * but pubkey recovery is impossible in the exhaustive tests (the reason
+                     * being that there are 12 nonzero r values, 12 nonzero points, and no
+                     * overlap between the sets, so there are no valid signatures). */
+
+                    /* Verify by converting to a standard signature and calling verify */
+                    secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
+                    secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+                    secp256k1_pubkey_save(&pk, &nonconst_ge);
+                    CHECK(should_verify ==
+                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+                }
+            }
+        }
+    }
+}
+#endif
+
+int main(void) {
+    int i;
+    secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
+    secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
+
+    /* Build context */
+    secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    /* TODO set z = 1, then do num_tests runs with random z values */
+
+    /* Generate the entire group */
+    secp256k1_gej_set_infinity(&groupj[0]);
+    secp256k1_ge_set_gej(&group[0], &groupj[0]);
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        /* Set a different random z-value for each Jacobian point */
+        secp256k1_fe z;
+        random_fe(&z);
+
+        secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
+        secp256k1_ge_set_gej(&group[i], &groupj[i]);
+        secp256k1_gej_rescale(&groupj[i], &z);
+
+        /* Verify against ecmult_gen */
+        {
+            secp256k1_scalar scalar_i;
+            secp256k1_gej generatedj;
+            secp256k1_ge generated;
+
+            secp256k1_scalar_set_int(&scalar_i, i);
+            secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i);
+            secp256k1_ge_set_gej(&generated, &generatedj);
+
+            CHECK(group[i].infinity == 0);
+            CHECK(generated.infinity == 0);
+            CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x));
+            CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y));
+        }
+    }
+
+    /* Run the tests */
+#ifdef USE_ENDOMORPHISM
+    test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER);
+#endif
+    test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+
+#ifdef ENABLE_MODULE_RECOVERY
+    test_exhaustive_recovery_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_recovery_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+#endif
+
+    secp256k1_context_destroy(ctx);
+    return 0;
+}
+
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/util.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/util.h
new file mode 100644
index 000000000..4092a86c9
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/util.h
@@ -0,0 +1,113 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_UTIL_H_
+#define _SECP256K1_UTIL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <stdio.h>
+
+typedef struct {
+    void (*fn)(const char *text, void* data);
+    const void* data;
+} secp256k1_callback;
+
+static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
+    cb->fn(text, (void*)cb->data);
+}
+
+#ifdef DETERMINISTIC
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s\n", msg); \
+    abort(); \
+} while(0);
+#else
+#define TEST_FAILURE(msg) do { \
+    fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \
+    abort(); \
+} while(0)
+#endif
+
+#ifdef HAVE_BUILTIN_EXPECT
+#define EXPECT(x,c) __builtin_expect((x),(c))
+#else
+#define EXPECT(x,c) (x)
+#endif
+
+#ifdef DETERMINISTIC
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed"); \
+    } \
+} while(0)
+#else
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        TEST_FAILURE("test condition failed: " #cond); \
+    } \
+} while(0)
+#endif
+
+/* Like assert(), but when VERIFY is defined, and side-effect safe. */
+#if defined(COVERAGE)
+#define VERIFY_CHECK(check)
+#define VERIFY_SETUP(stmt)
+#elif defined(VERIFY)
+#define VERIFY_CHECK CHECK
+#define VERIFY_SETUP(stmt) do { stmt; } while(0)
+#else
+#define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
+#define VERIFY_SETUP(stmt)
+#endif
+
+static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
+    void *ret = malloc(size);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
+    return ret;
+}
+
+/* Macro for restrict, when available and not in a VERIFY build. */
+#if defined(SECP256K1_BUILD) && defined(VERIFY)
+# define SECP256K1_RESTRICT
+#else
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(3,0)
+#   define SECP256K1_RESTRICT __restrict__
+#  elif (defined(_MSC_VER) && _MSC_VER >= 1400)
+#   define SECP256K1_RESTRICT __restrict
+#  else
+#   define SECP256K1_RESTRICT
+#  endif
+# else
+#  define SECP256K1_RESTRICT restrict
+# endif
+#endif
+
+#if defined(_WIN32)
+# define I64FORMAT "I64d"
+# define I64uFORMAT "I64u"
+#else
+# define I64FORMAT "lld"
+# define I64uFORMAT "llu"
+#endif
+
+#if defined(HAVE___INT128)
+# if defined(__GNUC__)
+#  define SECP256K1_GNUC_EXT __extension__
+# else
+#  define SECP256K1_GNUC_EXT
+# endif
+SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+#endif
+
+#endif
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/panic_cb.go b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/panic_cb.go
new file mode 100644
index 000000000..6d59a1d24
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/panic_cb.go
@@ -0,0 +1,21 @@
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be found in
+// the LICENSE file.
+
+package secp256k1
+
+import "C"
+import "unsafe"
+
+// Callbacks for converting libsecp256k1 internal faults into
+// recoverable Go panics.
+
+//export secp256k1GoPanicIllegal
+func secp256k1GoPanicIllegal(msg *C.char, data unsafe.Pointer) {
+	panic("illegal argument: " + C.GoString(msg))
+}
+
+//export secp256k1GoPanicError
+func secp256k1GoPanicError(msg *C.char, data unsafe.Pointer) {
+	panic("internal error: " + C.GoString(msg))
+}
diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/secp256.go b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/secp256.go
new file mode 100644
index 000000000..35d0eef34
--- /dev/null
+++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/secp256.go
@@ -0,0 +1,167 @@
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be found in
+// the LICENSE file.
+
+// Package secp256k1 wraps the bitcoin secp256k1 C library.
+package secp256k1
+
+/*
+#cgo CFLAGS: -I./libsecp256k1
+#cgo CFLAGS: -I./libsecp256k1/src/
+#define USE_NUM_NONE
+#define USE_FIELD_10X26
+#define USE_FIELD_INV_BUILTIN
+#define USE_SCALAR_8X32
+#define USE_SCALAR_INV_BUILTIN
+#define NDEBUG
+#include "./libsecp256k1/src/secp256k1.c"
+#include "./libsecp256k1/src/modules/recovery/main_impl.h"
+#include "ext.h"
+
+typedef void (*callbackFunc) (const char* msg, void* data);
+extern void secp256k1GoPanicIllegal(const char* msg, void* data);
+extern void secp256k1GoPanicError(const char* msg, void* data);
+*/
+import "C"
+
+import (
+	"errors"
+	"math/big"
+	"unsafe"
+)
+
+var context *C.secp256k1_context
+
+func init() {
+	// around 20 ms on a modern CPU.
+	context = C.secp256k1_context_create_sign_verify()
+	C.secp256k1_context_set_illegal_callback(context, C.callbackFunc(C.secp256k1GoPanicIllegal), nil)
+	C.secp256k1_context_set_error_callback(context, C.callbackFunc(C.secp256k1GoPanicError), nil)
+}
+
+var (
+	ErrInvalidMsgLen       = errors.New("invalid message length, need 32 bytes")
+	ErrInvalidSignatureLen = errors.New("invalid signature length")
+	ErrInvalidRecoveryID   = errors.New("invalid signature recovery id")
+	ErrInvalidKey          = errors.New("invalid private key")
+	ErrInvalidPubkey       = errors.New("invalid public key")
+	ErrSignFailed          = errors.New("signing failed")
+	ErrRecoverFailed       = errors.New("recovery failed")
+)
+
+// Sign creates a recoverable ECDSA signature.
+// The produced signature is in the 65-byte [R || S || V] format where V is 0 or 1.
+//
+// The caller is responsible for ensuring that msg cannot be chosen
+// directly by an attacker. It is usually preferable to use a cryptographic
+// hash function on any input before handing it to this function.
+func Sign(msg []byte, seckey []byte) ([]byte, error) {
+	if len(msg) != 32 {
+		return nil, ErrInvalidMsgLen
+	}
+	if len(seckey) != 32 {
+		return nil, ErrInvalidKey
+	}
+	seckeydata := (*C.uchar)(unsafe.Pointer(&seckey[0]))
+	if C.secp256k1_ec_seckey_verify(context, seckeydata) != 1 {
+		return nil, ErrInvalidKey
+	}
+
+	var (
+		msgdata   = (*C.uchar)(unsafe.Pointer(&msg[0]))
+		noncefunc = C.secp256k1_nonce_function_rfc6979
+		sigstruct C.secp256k1_ecdsa_recoverable_signature
+	)
+	if C.secp256k1_ecdsa_sign_recoverable(context, &sigstruct, msgdata, seckeydata, noncefunc, nil) == 0 {
+		return nil, ErrSignFailed
+	}
+
+	var (
+		sig     = make([]byte, 65)
+		sigdata = (*C.uchar)(unsafe.Pointer(&sig[0]))
+		recid   C.int
+	)
+	C.secp256k1_ecdsa_recoverable_signature_serialize_compact(context, sigdata, &recid, &sigstruct)
+	sig[64] = byte(recid) // add back recid to get 65 bytes sig
+	return sig, nil
+}
+
+// RecoverPubkey returns the public key of the signer.
+// msg must be the 32-byte hash of the message to be signed.
+// sig must be a 65-byte compact ECDSA signature containing the
+// recovery id as the last element.
+func RecoverPubkey(msg []byte, sig []byte) ([]byte, error) {
+	if len(msg) != 32 {
+		return nil, ErrInvalidMsgLen
+	}
+	if err := checkSignature(sig); err != nil {
+		return nil, err
+	}
+
+	var (
+		pubkey  = make([]byte, 65)
+		sigdata = (*C.uchar)(unsafe.Pointer(&sig[0]))
+		msgdata = (*C.uchar)(unsafe.Pointer(&msg[0]))
+	)
+	if C.secp256k1_ext_ecdsa_recover(context, (*C.uchar)(unsafe.Pointer(&pubkey[0])), sigdata, msgdata) == 0 {
+		return nil, ErrRecoverFailed
+	}
+	return pubkey, nil
+}
+
+// VerifySignature checks that the given pubkey created signature over message.
+// The signature should be in [R || S] format.
+func VerifySignature(pubkey, msg, signature []byte) bool {
+	if len(msg) != 32 || len(signature) != 64 || len(pubkey) == 0 {
+		return false
+	}
+	sigdata := (*C.uchar)(unsafe.Pointer(&signature[0]))
+	msgdata := (*C.uchar)(unsafe.Pointer(&msg[0]))
+	keydata := (*C.uchar)(unsafe.Pointer(&pubkey[0]))
+	return C.secp256k1_ext_ecdsa_verify(context, sigdata, msgdata, keydata, C.size_t(len(pubkey))) != 0
+}
+
+// DecompressPubkey parses a public key in the 33-byte compressed format.
+// It returns non-nil coordinates if the public key is valid.
+func DecompressPubkey(pubkey []byte) (x, y *big.Int) {
+	if len(pubkey) != 33 {
+		return nil, nil
+	}
+	var (
+		pubkeydata = (*C.uchar)(unsafe.Pointer(&pubkey[0]))
+		pubkeylen  = C.size_t(len(pubkey))
+		out        = make([]byte, 65)
+		outdata    = (*C.uchar)(unsafe.Pointer(&out[0]))
+		outlen     = C.size_t(len(out))
+	)
+	if C.secp256k1_ext_reencode_pubkey(context, outdata, outlen, pubkeydata, pubkeylen) == 0 {
+		return nil, nil
+	}
+	return new(big.Int).SetBytes(out[1:33]), new(big.Int).SetBytes(out[33:])
+}
+
+// CompressPubkey encodes a public key to 33-byte compressed format.
+func CompressPubkey(x, y *big.Int) []byte {
+	var (
+		pubkey     = S256().Marshal(x, y)
+		pubkeydata = (*C.uchar)(unsafe.Pointer(&pubkey[0]))
+		pubkeylen  = C.size_t(len(pubkey))
+		out        = make([]byte, 33)
+		outdata    = (*C.uchar)(unsafe.Pointer(&out[0]))
+		outlen     = C.size_t(len(out))
+	)
+	if C.secp256k1_ext_reencode_pubkey(context, outdata, outlen, pubkeydata, pubkeylen) == 0 {
+		panic("libsecp256k1 error")
+	}
+	return out
+}
+
+func checkSignature(sig []byte) error {
+	if len(sig) != 65 {
+		return ErrInvalidSignatureLen
+	}
+	if sig[64] >= 4 {
+		return ErrInvalidRecoveryID
+	}
+	return nil
+}
diff --git a/vendor/vendor.json b/vendor/vendor.json
index 3f5d3792e..5d97bb491 100644
--- a/vendor/vendor.json
+++ b/vendor/vendor.json
@@ -263,6 +263,12 @@
 			"revisionTime": "2018-01-22T22:25:45Z"
 		},
 		{
+			"checksumSHA1": "09V3eE1EhOkdfksyjsH+03c5fQg=",
+			"path": "github.com/ethereum/go-ethereum/crypto/secp256k1",
+			"revision": "78ec90717aaa34c6ac981e791ca7fb04077cca33",
+			"revisionTime": "2019-04-17T12:50:41Z"
+		},
+		{
 			"checksumSHA1": "7oFpbmDfGobwKsFLIf6wMUvVoKw=",
 			"path": "github.com/fatih/color",
 			"revision": "5ec5d9d3c2cf82e9688b34e9bc27a94d616a7193",