forked from cypherstack/spark
-
Notifications
You must be signed in to change notification settings - Fork 1
/
chaum.py
167 lines (142 loc) · 4.8 KB
/
chaum.py
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
# Aggregated modified Chaum proving system
from dumb25519 import Z, Point, PointVector, Scalar, ScalarVector, hash_to_scalar, random_scalar
import transcript
class ChaumParameters:
def __init__(self,F,G,H,U):
if not isinstance(F,Point):
raise TypeError('Bad type for parameter F!')
if not isinstance(G,Point):
raise TypeError('Bad type for parameter G!')
if not isinstance(H,Point):
raise TypeError('Bad type for parameter H!')
if not isinstance(U,Point):
raise TypeError('Bad type for parameter U!')
self.F = F
self.G = G
self.H = H
self.U = U
class ChaumStatement:
def __init__(self,params,context,S,T):
if not isinstance(params,ChaumParameters):
raise TypeError('Bad type for parameters!')
if not isinstance(S,PointVector):
raise TypeError('Bad type for Chaum statement input S!')
if not isinstance(T,PointVector):
raise TypeError('Bad type for Chaum statement input T!')
if not len(S) == len(T):
raise ValueError('Size mismatch for Chaum statement!')
self.F = params.F
self.G = params.G
self.H = params.H
self.U = params.U
self.context = context
self.S = S
self.T = T
class ChaumWitness:
def __init__(self,x,y,z):
if not isinstance(x,ScalarVector):
raise TypeError('Bad type for Chaum witness x!')
if not isinstance(y,ScalarVector):
raise TypeError('Bad type for Chaum witness y!')
if not isinstance(z,ScalarVector):
raise TypeError('Bad type for Chaum witness z!')
if not len(x) == len(y) and len(y) == len(z):
raise ValueError('Size mismatch for Chaum witness!')
self.x = x
self.y = y
self.z = z
class ChaumProof:
def __repr__(self):
return repr(hash_to_scalar(
self.A1,
self.A2,
self.t1,
self.t2,
self.t3
))
def __init__(self,A1,A2,t1,t2,t3):
if not isinstance(A1,Point):
raise TypeError('Bad type for Chaum proof element A1!')
if not isinstance(A2,PointVector):
raise TypeError('Bad type for Chaum proof element A2!')
if not isinstance(t1,ScalarVector):
raise TypeError('Bad type for Chaum proof element t1!')
if not isinstance(t2,Scalar):
raise TypeError('Bad type for Chaum proof element t2!')
if not isinstance(t3,Scalar):
raise TypeError('Bad type for Chaum proof element t3!')
if not len(A2) == len(t1):
raise ValueError('Size mismatch in Chaum proof!')
self.A1 = A1
self.A2 = A2
self.t1 = t1
self.t2 = t2
self.t3 = t3
def challenge(statement,A1,A2):
if not isinstance(statement,ChaumStatement):
raise TypeError('Bad type for Chaum statement!')
if not isinstance(A1,Point):
raise TypeError('Bad type for challenge input A1!')
if not isinstance(A2,PointVector):
raise TypeError('Bad type for challenge input A2!')
tr = transcript.Transcript('Modified Chaum')
tr.update(statement.F)
tr.update(statement.G)
tr.update(statement.H)
tr.update(statement.U)
tr.update(statement.context)
tr.update(statement.S)
tr.update(statement.T)
tr.update(A1)
tr.update(A2)
return tr.challenge()
def prove(statement,witness):
if not isinstance(statement,ChaumStatement):
raise TypeError('Bad type for Chaum statement!')
if not isinstance(witness,ChaumWitness):
raise TypeError('Bad type for Chaum witness!')
n = len(statement.S)
# Check the statement validity
for i in range(n):
if not statement.S[i] == witness.x[i]*statement.F + witness.y[i]*statement.G + witness.z[i]*statement.H:
raise ArithmeticError('Invalid Chaum statement!')
if not statement.U == witness.x[i]*statement.T[i] + witness.y[i]*statement.G:
raise ArithmeticError('Invalid Chaum statement!')
r = ScalarVector([random_scalar() for _ in range(n)])
s = ScalarVector([random_scalar() for _ in range(n)])
t = random_scalar()
A1 = t*statement.H
for i in range(n):
A1 += r[i]*statement.F + s[i]*statement.G
A2 = PointVector([r[i]*statement.T[i] + s[i]*statement.G for i in range(n)])
c = challenge(statement,A1,A2)
t1 = ScalarVector([r[i] + c**(i+1)*witness.x[i] for i in range(n)])
t2 = Scalar(0)
t3 = t
for i in range(n):
t2 += s[i] + c**(i+1)*witness.y[i]
t3 += c**(i+1)*witness.z[i]
return ChaumProof(A1,A2,t1,t2,t3)
def verify(statement,proof):
if not isinstance(statement,ChaumStatement):
raise TypeError('Bad type for Chaum statement!')
if not isinstance(proof,ChaumProof):
raise TypeError('Bad type for Chaum proof!')
if not len(proof.A2) == len(statement.S):
raise ValueError('Size mismatch in Chaum verification!')
n = len(statement.S)
c = challenge(statement,proof.A1,proof.A2)
L = proof.A1
R = proof.t2*statement.G + proof.t3*statement.H
for i in range(n):
L += c**(i+1)*statement.S[i]
R += proof.t1[i]*statement.F
if not L == R:
raise ArithmeticError('Failed Chaum verification!')
L = Z
R = proof.t2*statement.G
for i in range(n):
L += proof.A2[i] + c**(i+1)*statement.U
R += proof.t1[i]*statement.T[i]
if not L == R:
raise ArithmeticError('Failed Chaum verification!')