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
|
package seal
import (
. "kesim.org/seal/common"
"kesim.org/seal/schnorr"
)
type Bit struct {
id Bytes
set bool
α *Scalar
β *Scalar
*Commitment
Proof *Proof
*Stage
}
type Commitment struct {
A *Point // g^α
B *Point // g^β
C *Point // g^(ab)g^(set)
}
// This is a construction of a proof of a statement of the form
//
// [(C = g^(αβ)) && (A = g^α) && (Β = g^β)]
// || [(C = g^(αβ+1)) && (A = g^α) && (Β = g^β)]
//
// for given C, A and B
type Proof struct {
A *schnorr.Proof // Proof for knowledge of α in A = G^α
B *schnorr.Proof // Proof for knowledge of β in B = G^β
C struct { // Proof for knowledge of statement above
Ch [2]*Scalar
R [2]*Scalar
}
}
func NewBit(id Bytes, set bool) *Bit {
α, β := Curve.RandomScalar(), Curve.RandomScalar()
return NewBitFromScalars(id, set, α, β)
}
func NewBitFromScalars(id Bytes, set bool, α, β *Scalar) *Bit {
b := &Bit{
id: id,
set: set,
α: α,
β: β,
}
b.commit()
b.proof()
return b
}
func Int2Bits(id Bytes, val int, bitlength int) []*Bit {
if bitlength < 0 || bitlength > 32 {
return nil
}
bits := make([]*Bit, bitlength)
for i := range bitlength {
bits[i] = NewBit(id, (val>>(bitlength-i-1))&1 != 0)
}
return bits
}
func (b *Bit) IsSet() bool {
return b.set
}
func (b *Bit) commit() {
if b.Commitment != nil {
return
}
var C *Point
c := b.α.Mul(b.β)
if b.set {
C = G.Exp(c.Add(One))
} else {
C = G.Exp(c)
}
b.Commitment = &Commitment{
C: C,
A: G.Exp(b.α),
B: G.Exp(b.β),
}
}
func (s *Bit) proof() {
if s.Proof != nil {
return
}
var e [2][2]*Point
var r1, r2, w *Scalar
r1 = Curve.RandomScalar()
r2 = Curve.RandomScalar()
w = Curve.RandomScalar()
s.commit()
c := s.Commitment
if s.set {
e[0][0] = G.Exp(r1)
e[0][1] = c.B.Exp(r1).Mul(G.Exp(w))
e[1][0] = G.Exp(r2)
e[1][1] = c.B.Exp(r2)
} else {
e[0][0] = G.Exp(r1)
e[0][1] = c.B.Exp(r1)
e[1][0] = G.Exp(r2).Mul(c.A.Exp(w))
e[1][1] = c.B.Exp(r2).Mul(c.C.Div(G).Exp(w))
}
ch := Challenge(G, c.C, c.A, c.B, e[0][0], e[0][1], e[1][0], e[1][1], s.id)
pr := &Proof{}
if s.set {
pr.C.Ch[0] = w
pr.C.Ch[1] = ch.Sub(w)
pr.C.R[0] = r1.Sub(s.α.Mul(pr.C.Ch[0]))
pr.C.R[1] = r2.Sub(s.α.Mul(pr.C.Ch[1]))
} else {
pr.C.Ch[0] = ch.Sub(w)
pr.C.Ch[1] = w
pr.C.R[0] = r1.Sub(s.α.Mul(pr.C.Ch[0]))
pr.C.R[1] = r2
}
pr.A = (*schnorr.Statement)(s.α).Proof(s.id)
pr.B = (*schnorr.Statement)(s.β).Proof(s.id)
s.Proof = pr
}
func (c *Commitment) Verify(id Bytes, p *Proof) bool {
var e [2][2]*Point
e[0][0] = G.Exp(p.C.R[0]).Mul(c.A.Exp(p.C.Ch[0]))
e[0][1] = c.B.Exp(p.C.R[0]).Mul(c.C.Exp(p.C.Ch[0]))
e[1][0] = G.Exp(p.C.R[1]).Mul(c.A.Exp(p.C.Ch[1]))
e[1][1] = c.B.Exp(p.C.R[1]).Mul(c.C.Div(G).Exp(p.C.Ch[1]))
ch := Challenge(G, c.C, c.A, c.B, e[0][0], e[0][1], e[1][0], e[1][1], id)
return p.C.Ch[0].Add(p.C.Ch[1]).Equal(ch) &&
(*schnorr.Commitment)(c.A).Verify(p.A, id) &&
(*schnorr.Commitment)(c.B).Verify(p.B, id)
}
|
