crypto, crypto/ecies, crypto/secp256k1: libsecp256k1 scalar mult

thanks to Felix Lange (fjl) for help with design & impl

1 files changed, 0 insertions, 397 deletions

diff --git a/crypto/curve.go b/crypto/curve.go
deleted file mode 100644
index 48f3f5e9c..000000000
--- a/crypto/curve.go
+++ /dev/null
@@ -1,397 +0,0 @@
-// Copyright 2010 The Go Authors. All rights reserved.
-// Copyright 2011 ThePiachu. 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 crypto
-
-import (
-	"crypto/elliptic"
-	"io"
-	"math/big"
-	"sync"
-)
-
-// 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,
-	}
-}
-
-// IsOnBitCurve 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
-}
-
-//TODO: double check if it is okay
-// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
-func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
-	// We have a slight problem in that the identity of the group (the
-	// point at infinity) cannot be represented in (x, y) form on a finite
-	// machine. Thus the standard add/double algorithm has to be tweaked
-	// slightly: our initial state is not the identity, but x, and we
-	// ignore the first true bit in |k|.  If we don't find any true bits in
-	// |k|, then we return nil, nil, because we cannot return the identity
-	// element.
-
-	Bz := new(big.Int).SetInt64(1)
-	x := Bx
-	y := By
-	z := Bz
-
-	seenFirstTrue := false
-	for _, byte := range k {
-		for bitNum := 0; bitNum < 8; bitNum++ {
-			if seenFirstTrue {
-				x, y, z = BitCurve.doubleJacobian(x, y, z)
-			}
-			if byte&0x80 == 0x80 {
-				if !seenFirstTrue {
-					seenFirstTrue = true
-				} else {
-					x, y, z = BitCurve.addJacobian(Bx, By, Bz, x, y, z)
-				}
-			}
-			byte <<= 1
-		}
-	}
-
-	if !seenFirstTrue {
-		return nil, nil
-	}
-
-	return BitCurve.affineFromJacobian(x, y, z)
-}
-
-// 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)
-}
-
-var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
-
-//TODO: double check if it is okay
-// GenerateKey returns a public/private key pair. The private key is generated
-// using the given reader, which must return random data.
-func (BitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
-	byteLen := (BitCurve.BitSize + 7) >> 3
-	priv = make([]byte, byteLen)
-
-	for x == nil {
-		_, err = io.ReadFull(rand, priv)
-		if err != nil {
-			return
-		}
-		// We have to mask off any excess bits in the case that the size of the
-		// underlying field is not a whole number of bytes.
-		priv[0] &= mask[BitCurve.BitSize%8]
-		// This is because, in tests, rand will return all zeros and we don't
-		// want to get the point at infinity and loop forever.
-		priv[1] ^= 0x42
-		x, y = BitCurve.ScalarBaseMult(priv)
-	}
-	return
-}
-
-// 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
-
-	xBytes := x.Bytes()
-	copy(ret[1+byteLen-len(xBytes):], xBytes)
-	yBytes := y.Bytes()
-	copy(ret[1+2*byteLen-len(yBytes):], yBytes)
-	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
-}
-
-//curve parameters taken from:
-//http://www.secg.org/collateral/sec2_final.pdf
-
-var initonce sync.Once
-var ecp160k1 *BitCurve
-var ecp192k1 *BitCurve
-var ecp224k1 *BitCurve
-var ecp256k1 *BitCurve
-
-func initAll() {
-	initS160()
-	initS192()
-	initS224()
-	initS256()
-}
-
-func initS160() {
-	// See SEC 2 section 2.4.1
-	ecp160k1 = new(BitCurve)
-	ecp160k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", 16)
-	ecp160k1.N, _ = new(big.Int).SetString("0100000000000000000001B8FA16DFAB9ACA16B6B3", 16)
-	ecp160k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000007", 16)
-	ecp160k1.Gx, _ = new(big.Int).SetString("3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", 16)
-	ecp160k1.Gy, _ = new(big.Int).SetString("938CF935318FDCED6BC28286531733C3F03C4FEE", 16)
-	ecp160k1.BitSize = 160
-}
-
-func initS192() {
-	// See SEC 2 section 2.5.1
-	ecp192k1 = new(BitCurve)
-	ecp192k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", 16)
-	ecp192k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D", 16)
-	ecp192k1.B, _ = new(big.Int).SetString("000000000000000000000000000000000000000000000003", 16)
-	ecp192k1.Gx, _ = new(big.Int).SetString("DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", 16)
-	ecp192k1.Gy, _ = new(big.Int).SetString("9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D", 16)
-	ecp192k1.BitSize = 192
-}
-
-func initS224() {
-	// See SEC 2 section 2.6.1
-	ecp224k1 = new(BitCurve)
-	ecp224k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", 16)
-	ecp224k1.N, _ = new(big.Int).SetString("010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7", 16)
-	ecp224k1.B, _ = new(big.Int).SetString("00000000000000000000000000000000000000000000000000000005", 16)
-	ecp224k1.Gx, _ = new(big.Int).SetString("A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", 16)
-	ecp224k1.Gy, _ = new(big.Int).SetString("7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5", 16)
-	ecp224k1.BitSize = 224
-}
-
-func initS256() {
-	// See SEC 2 section 2.7.1
-	ecp256k1 = new(BitCurve)
-	ecp256k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
-	ecp256k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
-	ecp256k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
-	ecp256k1.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
-	ecp256k1.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
-	ecp256k1.BitSize = 256
-}
-
-// S160 returns a BitCurve which implements secp160k1 (see SEC 2 section 2.4.1)
-func S160() *BitCurve {
-	initonce.Do(initAll)
-	return ecp160k1
-}
-
-// S192 returns a BitCurve which implements secp192k1 (see SEC 2 section 2.5.1)
-func S192() *BitCurve {
-	initonce.Do(initAll)
-	return ecp192k1
-}
-
-// S224 returns a BitCurve which implements secp224k1 (see SEC 2 section 2.6.1)
-func S224() *BitCurve {
-	initonce.Do(initAll)
-	return ecp224k1
-}
-
-// S256 returns a BitCurve which implements secp256k1 (see SEC 2 section 2.7.1)
-func S256() *BitCurve {
-	initonce.Do(initAll)
-	return ecp256k1
-}