-
Notifications
You must be signed in to change notification settings - Fork 2
/
swu.go
142 lines (138 loc) · 4.04 KB
/
swu.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
package bls12381
// swuMapG1 is implementation of Simplified Shallue-van de Woestijne-Ulas Method
// follows the implmentation at draft-irtf-cfrg-hash-to-curve-06.
func swuMapG1(u *fe) (*fe, *fe) {
var params = swuParamsForG1
var tv [4]*fe
for i := 0; i < 4; i++ {
tv[i] = new(fe)
}
square(tv[0], u)
mul(tv[0], tv[0], params.z)
square(tv[1], tv[0])
x1 := new(fe)
add(x1, tv[0], tv[1])
inverse(x1, x1)
e1 := x1.isZero()
one := new(fe).one()
add(x1, x1, one)
if e1 {
x1.set(params.zInv)
}
mul(x1, x1, params.minusBOverA)
gx1 := new(fe)
square(gx1, x1)
add(gx1, gx1, params.a)
mul(gx1, gx1, x1)
add(gx1, gx1, params.b)
x2 := new(fe)
mul(x2, tv[0], x1)
mul(tv[1], tv[0], tv[1])
gx2 := new(fe)
mul(gx2, gx1, tv[1])
e2 := !isQuadraticNonResidue(gx1)
x, y2 := new(fe), new(fe)
if e2 {
x.set(x1)
y2.set(gx1)
} else {
x.set(x2)
y2.set(gx2)
}
y := new(fe)
sqrt(y, y2)
if y.sign() != u.sign() {
neg(y, y)
}
return x, y
}
// swuMapG2 is implementation of Simplified Shallue-van de Woestijne-Ulas Method
// defined at draft-irtf-cfrg-hash-to-curve-06.
func swuMapG2(e *fp2, u *fe2) (*fe2, *fe2) {
if e == nil {
e = newFp2()
}
params := swuParamsForG2
var tv [4]*fe2
for i := 0; i < 4; i++ {
tv[i] = e.new()
}
e.square(tv[0], u)
e.mul(tv[0], tv[0], params.z)
e.square(tv[1], tv[0])
x1 := e.new()
fp2Add(x1, tv[0], tv[1])
e.inverse(x1, x1)
e1 := x1.isZero()
fp2Add(x1, x1, e.one())
if e1 {
x1.set(params.zInv)
}
e.mul(x1, x1, params.minusBOverA)
gx1 := e.new()
e.square(gx1, x1)
fp2Add(gx1, gx1, params.a)
e.mul(gx1, gx1, x1)
fp2Add(gx1, gx1, params.b)
x2 := e.new()
e.mul(x2, tv[0], x1)
e.mul(tv[1], tv[0], tv[1])
gx2 := e.new()
e.mul(gx2, gx1, tv[1])
e2 := !e.isQuadraticNonResidue(gx1)
x, y2 := e.new(), e.new()
if e2 {
x.set(x1)
y2.set(gx1)
} else {
x.set(x2)
y2.set(gx2)
}
y := e.new()
e.sqrtBLST(y, y2)
if y.sign() != u.sign() {
fp2Neg(y, y)
}
return x, y
}
var swuParamsForG1 = struct {
z *fe
zInv *fe
a *fe
b *fe
minusBOverA *fe
}{
a: &fe{0x2f65aa0e9af5aa51, 0x86464c2d1e8416c3, 0xb85ce591b7bd31e2, 0x27e11c91b5f24e7c, 0x28376eda6bfc1835, 0x155455c3e5071d85},
b: &fe{0xfb996971fe22a1e0, 0x9aa93eb35b742d6f, 0x8c476013de99c5c4, 0x873e27c3a221e571, 0xca72b5e45a52d888, 0x06824061418a386b},
z: &fe{0x886c00000023ffdc, 0x0f70008d3090001d, 0x77672417ed5828c3, 0x9dac23e943dc1740, 0x50553f1b9c131521, 0x078c712fbe0ab6e8},
zInv: &fe{0x0e8a2e8ba2e83e10, 0x5b28ba2ca4d745d1, 0x678cd5473847377a, 0x4c506dd8a8076116, 0x9bcb227d79284139, 0x0e8d3154b0ba099a},
minusBOverA: &fe{0x052583c93555a7fe, 0x3b40d72430f93c82, 0x1b75faa0105ec983, 0x2527e7dc63851767, 0x99fffd1f34fc181d, 0x097cab54770ca0d3},
}
var swuParamsForG2 = struct {
z *fe2
zInv *fe2
a *fe2
b *fe2
minusBOverA *fe2
}{
a: &fe2{
fe{0, 0, 0, 0, 0, 0},
fe{0xe53a000003135242, 0x01080c0fdef80285, 0xe7889edbe340f6bd, 0x0b51375126310601, 0x02d6985717c744ab, 0x1220b4e979ea5467},
},
b: &fe2{
fe{0x22ea00000cf89db2, 0x6ec832df71380aa4, 0x6e1b94403db5a66e, 0x75bf3c53a79473ba, 0x3dd3a569412c0a34, 0x125cdb5e74dc4fd1},
fe{0x22ea00000cf89db2, 0x6ec832df71380aa4, 0x6e1b94403db5a66e, 0x75bf3c53a79473ba, 0x3dd3a569412c0a34, 0x125cdb5e74dc4fd1},
},
z: &fe2{
fe{0x87ebfffffff9555c, 0x656fffe5da8ffffa, 0x0fd0749345d33ad2, 0xd951e663066576f4, 0xde291a3d41e980d3, 0x0815664c7dfe040d},
fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
},
zInv: &fe2{
fe{0xacd0000000011110, 0x9dd9999dc88ccccd, 0xb5ca2ac9b76352bf, 0xf1b574bcf4bc90ce, 0x42dab41f28a77081, 0x132fc6ac14cd1e12},
fe{0xe396ffffffff2223, 0x4fbf332fcd0d9998, 0x0c4bbd3c1aff4cc4, 0x6b9c91267926ca58, 0x29ae4da6aef7f496, 0x10692e942f195791},
},
minusBOverA: &fe2{
fe{0x903c555555474fb3, 0x5f98cc95ce451105, 0x9f8e582eefe0fade, 0xc68946b6aebbd062, 0x467a4ad10ee6de53, 0x0e7146f483e23a05},
fe{0x29c2aaaaaab85af8, 0xbf133368e30eeefa, 0xc7a27a7206cffb45, 0x9dee04ce44c9425c, 0x04a15ce53464ce83, 0x0b8fcaf5b59dac95},
},
}