-
Notifications
You must be signed in to change notification settings - Fork 54
/
multiplication_commitment.go
221 lines (190 loc) · 6.68 KB
/
multiplication_commitment.go
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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
/*
* Copyright 2017 XLAB d.o.o.
*
* 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 df
import (
"math/big"
"github.com/xlab-si/emmy/crypto/common"
)
// MultiplicationProver proves for given commitments
// c1 = g^x1 * h^r1, c2 = g^x2 * h^r2, c3 = g^x3 * h^r3 that x3 = x1 * x2.
// Proof consists of three parallel proofs:
// (1) proof that we can open c1
// (2) proof that we can open c2
// (3) proof that we can open c3, where c3 is seen as
// c3 = G^x3 * H^r3 = G^(x1*x2) * H^r1*x2 * H^(r3 - r1*x2) = c1^x2 * H^(r3 - r1*x2),
// thus a new "G" is c1, "x" is x2, and "r3" is r3 - r1*x2.
type MultiplicationProver struct {
committer1 *Committer
committer2 *Committer
committer3 *Committer
challengeSpaceSize int
y1 *big.Int
s1 *big.Int
y *big.Int
s2 *big.Int
s3 *big.Int
}
func NewMultiplicationProver(committer1, committer2,
committer3 *Committer,
challengeSpaceSize int) *MultiplicationProver {
return &MultiplicationProver{
committer1: committer1,
committer2: committer2,
committer3: committer3,
challengeSpaceSize: challengeSpaceSize,
}
}
func (p *MultiplicationProver) GetProofRandomData() (*big.Int, *big.Int, *big.Int) {
nLen := p.committer1.QRSpecialRSA.N.BitLen()
b1 := new(big.Int).Exp(big.NewInt(2), big.NewInt(int64(nLen+p.challengeSpaceSize)), nil)
b1.Mul(b1, p.committer1.T)
b2 := new(big.Int).Exp(big.NewInt(2), big.NewInt(int64(
p.committer1.B+2*nLen+p.challengeSpaceSize)), nil)
// y1 and y from [0, T * 2^(NLength + ChallengeSpaceSize))
// s1, s2, s3 from [0, 2^(B + 2*NLength + ChallengeSpaceSize))
y1 := common.GetRandomInt(b1)
y := common.GetRandomInt(b1)
p.y1 = y1
p.y = y
s1 := common.GetRandomInt(b2)
s2 := common.GetRandomInt(b2)
s3 := common.GetRandomInt(b2)
p.s1 = s1
p.s2 = s2
p.s3 = s3
// d1 = G^y1 * H^s1
// d2 = G^y * H^s2
// d3 = c1^y * H^s3
d1 := p.committer1.ComputeCommit(y1, s1) // ComputeCommit can be called on any of the committers
d2 := p.committer1.ComputeCommit(y, s2)
a1, r1 := p.committer1.GetDecommitMsg()
c1 := p.committer1.ComputeCommit(a1, r1)
l := p.committer1.QRSpecialRSA.Exp(c1, y)
r := p.committer1.QRSpecialRSA.Exp(p.committer1.H, s3)
d3 := p.committer1.QRSpecialRSA.Mul(l, r)
return d1, d2, d3
}
func (p *MultiplicationProver) GetProofData(challenge *big.Int) (*big.Int, *big.Int,
*big.Int, *big.Int, *big.Int) {
// u1 = y1 + challenge*a1 (in Z, not modulo)
// u = y + challenge*a2 (in Z, not modulo)
// v1 = s1 + challenge*r1 (in Z, not modulo)
// v2 = s2 + challenge*r2 (in Z, not modulo)
// v3 = s3 + challenge*(r3 - a2 * r1) (in Z, not modulo)
a1, r1 := p.committer1.GetDecommitMsg()
a2, r2 := p.committer2.GetDecommitMsg()
_, r3 := p.committer3.GetDecommitMsg()
u1 := new(big.Int).Mul(challenge, a1)
u1.Add(u1, p.y1)
u := new(big.Int).Mul(challenge, a2)
u.Add(u, p.y)
v1 := new(big.Int).Mul(challenge, r1)
v1.Add(v1, p.s1)
v2 := new(big.Int).Mul(challenge, r2)
v2.Add(v2, p.s2)
r := new(big.Int).Mul(a2, r1)
r.Sub(r3, r)
v3 := new(big.Int).Mul(challenge, r)
v3.Add(v3, p.s3)
return u1, u, v1, v2, v3
}
// MultiplicationProof presents all three messages in sigma protocol - useful when challenge
// is generated by prover via Fiat-Shamir.
type MultiplicationProof struct {
ProofRandomData1 *big.Int
ProofRandomData2 *big.Int
Challenge *big.Int
ProofDataU1 *big.Int
ProofDataU *big.Int
ProofDataV1 *big.Int
ProofDataV2 *big.Int
ProofDataV3 *big.Int
}
func NewMultiplicationProof(proofRandomData1, proofRandomData2, challenge, proofDataU1, proofDataU,
proofDataV1, proofDataV2, proofDataV3 *big.Int) *MultiplicationProof {
return &MultiplicationProof{
ProofRandomData1: proofRandomData1,
ProofRandomData2: proofRandomData2,
Challenge: challenge,
ProofDataU1: proofDataU1,
ProofDataU: proofDataU,
ProofDataV1: proofDataV1,
ProofDataV2: proofDataV2,
ProofDataV3: proofDataV3,
}
}
type MultiplicationVerifier struct {
receiver1 *Receiver
receiver2 *Receiver
receiver3 *Receiver
challengeSpaceSize int
challenge *big.Int
d1 *big.Int
d2 *big.Int
d3 *big.Int
}
func NewMultiplicationVerifier(receiver1, receiver2,
receiver3 *Receiver,
challengeSpaceSize int) *MultiplicationVerifier {
return &MultiplicationVerifier{
receiver1: receiver1,
receiver2: receiver2,
receiver3: receiver3,
challengeSpaceSize: challengeSpaceSize,
}
}
func (v *MultiplicationVerifier) SetProofRandomData(d1, d2, d3 *big.Int) {
v.d1 = d1
v.d2 = d2
v.d3 = d3
}
func (v *MultiplicationVerifier) GetChallenge() *big.Int {
b := new(big.Int).Exp(big.NewInt(2), big.NewInt(int64(v.challengeSpaceSize)), nil)
challenge := common.GetRandomInt(b)
v.challenge = challenge
return challenge
}
// SetChallenge is used when Fiat-Shamir is used - when challenge is generated using hash by the prover.
func (v *MultiplicationVerifier) SetChallenge(challenge *big.Int) {
v.challenge = challenge
}
func (v *MultiplicationVerifier) Verify(u1, u, v1, v2, v3 *big.Int) bool {
// verify:
// G^u1 * H^v1 = d1 * c1^challenge
// G^u * H^v2 = d2 * c2^challenge
// c1^u * H^v3 = d3 * c3^challenge
left1 := v.receiver1.ComputeCommit(u1, v1)
right1 := v.receiver1.QRSpecialRSA.Exp(v.receiver1.Commitment, v.challenge)
right1 = v.receiver1.QRSpecialRSA.Mul(v.d1, right1)
left2 := v.receiver1.ComputeCommit(u, v2)
right2 := v.receiver1.QRSpecialRSA.Exp(v.receiver2.Commitment, v.challenge)
right2 = v.receiver1.QRSpecialRSA.Mul(v.d2, right2)
tmp1 := v.receiver3.QRSpecialRSA.Exp(v.receiver1.Commitment, u) // c1^u
// TODO
v3Abs := new(big.Int).Abs(v3)
var tmp2 *big.Int // H^v3
if v3Abs.Cmp(v3) == 0 {
tmp2 = v.receiver3.QRSpecialRSA.Exp(v.receiver3.H, v3)
} else {
tmp2 = v.receiver3.QRSpecialRSA.Exp(v.receiver3.H, v3Abs)
tmp2 = v.receiver3.QRSpecialRSA.Inv(tmp2)
}
left3 := v.receiver3.QRSpecialRSA.Mul(tmp1, tmp2)
right3 := v.receiver1.QRSpecialRSA.Exp(v.receiver3.Commitment, v.challenge)
right3 = v.receiver1.QRSpecialRSA.Mul(v.d3, right3)
return left1.Cmp(right1) == 0 && left2.Cmp(right2) == 0 && left3.Cmp(right3) == 0
}