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
|
from typing import (
Tuple,
)
from _hashlib import (
HASH,
)
from py_ecc.fields import (
optimized_bls12_381_FQ as FQ,
optimized_bls12_381_FQ2 as FQ2,
)
from py_ecc.optimized_bls12_381 import (
add,
field_modulus,
iso_map_G1,
iso_map_G2,
multiply_clear_cofactor_G1,
multiply_clear_cofactor_G2,
optimized_swu_G1,
optimized_swu_G2,
)
from .constants import (
HASH_TO_FIELD_L,
)
from .hash import (
expand_message_xmd,
os2ip,
)
from .typing import (
G1Uncompressed,
G2Uncompressed,
)
# Hash to G2
def hash_to_G2(message: bytes, DST: bytes, hash_function: HASH) -> G2Uncompressed:
"""
Convert a message to a point on G2 as defined here:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-6.6.3
The idea is to first hash into FQ2 and then use SSWU to map the result into G2.
Contents and inputs follow the ciphersuite ``BLS12381G2_XMD:SHA-256_SSWU_RO_``
defined here:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-8.8.2
"""
u0, u1 = hash_to_field_FQ2(message, 2, DST, hash_function)
q0 = map_to_curve_G2(u0)
q1 = map_to_curve_G2(u1)
r = add(q0, q1)
p = clear_cofactor_G2(r)
return p
def hash_to_field_FQ2(
message: bytes, count: int, DST: bytes, hash_function: HASH
) -> Tuple[FQ2, ...]:
"""
Hash To Base Field for FQ2
Convert a message to a point in the finite field as defined here:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-5.3
"""
M = 2 # m is the extension degree of FQ2
len_in_bytes = count * M * HASH_TO_FIELD_L
pseudo_random_bytes = expand_message_xmd(message, DST, len_in_bytes, hash_function)
u = []
for i in range(0, count):
e = []
for j in range(0, M):
elem_offset = HASH_TO_FIELD_L * (j + i * M)
tv = pseudo_random_bytes[elem_offset : elem_offset + HASH_TO_FIELD_L]
e.append(os2ip(tv) % field_modulus)
u.append(FQ2(e))
return tuple(u)
def map_to_curve_G2(u: FQ2) -> G2Uncompressed:
"""
Map To Curve for G2
First, convert FQ2 point to a point on the 3-Isogeny curve.
SWU Map: https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-6.6.3
Second, map 3-Isogeny curve to BLS12-381-G2 curve.
3-Isogeny Map:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#appendix-C.3
"""
(x, y, z) = optimized_swu_G2(u)
return iso_map_G2(x, y, z)
def clear_cofactor_G2(p: G2Uncompressed) -> G2Uncompressed:
"""
Clear Cofactor via Multiplication
Ensure a point falls in the correct sub group of the curve.
"""
return multiply_clear_cofactor_G2(p)
# --- G1 ---
def hash_to_G1(message: bytes, DST: bytes, hash_function: HASH) -> G1Uncompressed:
"""
Convert a message to a point on G1 as defined here:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-6.6.3
The idea is to first hash into FQ and then use SSWU to map the result into G1.
Contents and inputs follow the ciphersuite ``BLS12381G1_XMD:SHA-256_SSWU_RO_``
defined here:
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-09#section-8.8.1
"""
u0, u1 = hash_to_field_FQ(message, 2, DST, hash_function)
q0 = map_to_curve_G1(u0)
q1 = map_to_curve_G1(u1)
r = add(q0, q1)
p = clear_cofactor_G1(r)
return p
def hash_to_field_FQ(
message: bytes, count: int, DST: bytes, hash_function: HASH
) -> Tuple[FQ, ...]:
"""
Hash To Base Field for FQ
Convert a message to a point in the finite field as defined here:
https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-5.3
"""
M = 1 # m is the extension degree of FQ
len_in_bytes = count * M * HASH_TO_FIELD_L
pseudo_random_bytes = expand_message_xmd(message, DST, len_in_bytes, hash_function)
u = []
for i in range(0, count):
elem_offset = HASH_TO_FIELD_L * (i * M)
tv = pseudo_random_bytes[elem_offset : elem_offset + HASH_TO_FIELD_L]
u.append(FQ(os2ip(tv) % field_modulus))
return tuple(u)
def map_to_curve_G1(u: FQ) -> G1Uncompressed:
"""
Map To Curve for G1
First, convert FQ point to a point on the 11-Isogeny curve.
SWU Map: https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-09#section-6.6.3
Second, map 11-Isogeny curve to BLS12-381-G1 curve.
11-Isogeny Map:
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-09#name-11-isogeny-map-for-bls12-38
"""
(x, y, z) = optimized_swu_G1(u)
return iso_map_G1(x, y, z)
def clear_cofactor_G1(p: G1Uncompressed) -> G1Uncompressed:
"""
Clear Cofactor via Multiplication
Ensure a point falls in the correct subgroup of the curve.
"""
return multiply_clear_cofactor_G1(p)
|
