1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
|
[](https://travis-ci.org/herumi/bls)
# BLS threshold signature
An implementation of BLS threshold signature
# Installation Requirements
Create a working directory (e.g., work) and clone the following repositories.
```
mkdir work
cd work
git clone git://github.com/herumi/xbyak.git
git clone git://github.com/herumi/cybozulib.git
git clone git://github.com/herumi/mcl.git
git clone git://github.com/herumi/bls.git
git clone git://github.com/herumi/cybozulib_ext ; for only Windows
```
# Build and test for Linux
Specifiy UNIT=4 or 6 always to make. Default UNIT is 6.
To make lib/libbls.a and test, run
```
cd bls
make test UNIT=4
```
To make sample programs, run
```
make sample_test
```
# Build and test for Windows
```
cd mcl
mklib
cd ..\bls
mklib
mk test\bls_test.cpp
bls_test.exe
```
# API
## Basic API
BLS signature
```
e : G2 x G1 -> Fp12 ; optimal ate pairing over BN curve
Q in G2 ; fixed global parameter
H : {str} -> G1
s in Fr: secret key
sQ in G2; public key
s H(m) in G1; signature of m
verify ; e(sQ, H(m)) = e(Q, s H(m))
```
```
void bls::init();
```
Initialize this library. Call this once to use the other api.
```
void SecretKey::init();
```
Initialize the instance of SecretKey. `s` is a random number.
```
void SecretKey::getPublicKey(PublicKey& pub) const;
```
Get public key `sQ` for the secret key `s`.
```
void SecretKey::sign(Sign& sign, const std::string& m) const;
```
Make sign `s H(m)` from message m.
```
bool Sign::verify(const PublicKey& pub, const std::string& m) const;
```
Verify sign with pub and m and return true if it is valid.
```
e(sQ, H(m)) == e(Q, s H(m))
```
### Secret Sharing API
```
void SecretKey::getMasterSecretKey(SecretKeyVec& msk, size_t k) const;
```
Prepare k-out-of-n secret sharing for the secret key.
`msk[0]` is the original secret key `s` and `msk[i]` for i > 0 are random secret key.
```
void SecretKey::set(const SecretKeyVec& msk, const Id& id);
```
Make secret key f(id) from msk and id where f(x) = msk[0] + msk[1] x + ... + msk[k-1] x^{k-1}.
You can make a public key `f(id)Q` from each secret key f(id) for id != 0 and sign a message.
```
void Sign::recover(const SignVec& signVec, const IdVec& idVec);
```
Collect k pair of sign `f(id) H(m)` and `id` for a message m and recover the original signature `s H(m)` for the secret key `s`.
### PoP (Proof of Possesion)
```
void SecretKey::getPop(Sign& pop) const;
```
Sign pub and make a pop `s H(sQ)`
```
bool Sign::verify(const PublicKey& pub) const;
```
Verify a public key by pop.
# Go
```
make test_go
```
# License
modified new BSD License
http://opensource.org/licenses/BSD-3-Clause
# Author
MITSUNARI Shigeo(herumi@nifty.com)
|
