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
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
|
package p751
//go:generate go run ../templates/gen.go P751
import (
"github.com/cloudflare/circl/dh/sidh/internal/common"
"golang.org/x/sys/cpu"
)
const (
// Number of uint64 limbs used to store field element
FpWords = 12
)
var (
// HasBMI2 signals support for MULX which is in BMI2
HasBMI2 = cpu.X86.HasBMI2
// HasADXandBMI2 signals support for ADX and BMI2
HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX
// P751 is a prime used by field Fp751
P751 = common.Fp{
0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff,
0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff,
0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c,
}
// P751x2 = 2*p751 - 1
P751x2 = common.Fp{
0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,
0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED,
0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38,
}
// P751p1 = p751 + 1
P751p1 = common.Fp{
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000,
0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c,
}
// P751R2 = (2^768)^2 mod p
P751R2 = common.Fp{
0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E,
0xF40BFE2082A2E706, 0x4932CCA8904F8751, 0x1F735F1F1EE7FC81,
0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90,
0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35,
}
// P751p1Zeros number of 0 digits in the least significant part of P751+1
P751p1Zeros = 5
// 1*R mod p
one = common.Fp2{
A: common.Fp{
0x00000000000249ad, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x8310000000000000,
0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e,
0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2,
},
}
// 1/2 * R mod p
half = common.Fp2{
A: common.Fp{
0x00000000000124D6, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000,
0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52,
0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F,
},
}
// 6*R mod p
six = common.Fp2{
A: common.Fp{
0x00000000000DBA10, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x3500000000000000,
0x3714FE4EB8399915, 0xC3A2584753EB43F4, 0xA3151D605C520428,
0xC116CF5232C7C978, 0x49A84D4B8EFAF6AA, 0x0000305731E97514,
},
}
params = common.SidhParams{
ID: common.Fp751,
// SIDH public key byte size.
PublicKeySize: 564,
// SIDH shared secret byte size.
SharedSecretSize: 188,
A: common.DomainParams{
// The x-coordinate of PA
AffineP: common.Fp2{
A: common.Fp{
0x884F46B74000BAA8, 0xBA52630F939DEC20, 0xC16FB97BA714A04D,
0x082536745B1AB3DB, 0x1117157F446F9E82, 0xD2F27D621A018490,
0x6B24AB523D544BCD, 0x9307D6AA2EA85C94, 0xE1A096729528F20F,
0x896446F868F3255C, 0x2401D996B1BFF8A5, 0x00000EF8786A5C0A,
},
B: common.Fp{
0xAEB78B3B96F59394, 0xAB26681E29C90B74, 0xE520AC30FDC4ACF1,
0x870AAAE3A4B8111B, 0xF875BDB738D64EFF, 0x50109A7ECD7ED6BC,
0x4CC64848FF0C56FB, 0xE617CB6C519102C9, 0x9C74B3835921E609,
0xC91DDAE4A35A7146, 0x7FC82A155C1B9129, 0x0000214FA6B980B3,
},
},
// The x-coordinate of QA
AffineQ: common.Fp2{
A: common.Fp{
0x0F93CC38680A8CA9, 0x762E733822E7FED7, 0xE549F005AC0ADB67,
0x94A71FDD2C43A4ED, 0xD48645C2B04721C5, 0x432DA1FE4D4CA4DC,
0xBC99655FAA7A80E8, 0xB2C6D502BCFD4823, 0xEE92F40CA2EC8BDB,
0x7B074132EFB6D16C, 0x3340B46FA38A7633, 0x0000215749657F6C,
},
B: common.Fp{
0xECFF375BF3079F4C, 0xFBFE74B043E80EF3, 0x17376CBE3C5C7AD1,
0xC06327A7E29CDBF2, 0x2111649C438BF3D4, 0xC1F9298261BA2E97,
0x1F9FECE869CFD1C2, 0x01A39B4FC9346D62, 0x147CD1D3E82A3C9F,
0xDE84E9D249E533EE, 0x1C48A5ADFB7C578D, 0x000061ACA0B82E1D,
},
},
// The x-coordinate of RA = PA-QA
AffineR: common.Fp2{
A: common.Fp{
0x1600C525D41059F1, 0xA596899A0A1D83F7, 0x6BFDEED6D2B23F35,
0x5C7E707270C23910, 0x276CA1A4E8369411, 0xB193651A602925A0,
0x243D239F1CA1F04A, 0x543DC6DA457860AD, 0xCDA590F325181DE9,
0xD3AB7ACFDA80B395, 0x6C97468580FDDF7B, 0x0000352A3E5C4C77,
},
B: common.Fp{
0x9B794F9FD1CC3EE8, 0xDB32E40A9B2FD23E, 0x26192A2542E42B67,
0xA18E94FCA045BCE7, 0x96DC1BC38E7CDA2D, 0x9A1D91B752487DE2,
0xCC63763987436DA3, 0x1316717AACCC551D, 0xC4C368A4632AFE72,
0x4B6EA85C9CCD5710, 0x7A12CAD582C7BC9A, 0x00001C7E240149BF,
},
},
// Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1
SecretBitLen: 372,
// SecretBitLen in bytes.
SecretByteLen: 47,
// 2-torsion group computation strategy
IsogenyStrategy: []uint32{
0x50, 0x30, 0x1B, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,
0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07,
0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,
0x01, 0x01, 0x01, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02,
0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03,
0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15,
0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03,
0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01,
0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02,
0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02,
0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x14, 0x0C, 0x07,
0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,
0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
0x02, 0x01, 0x01, 0x01, 0x08, 0x05, 0x03, 0x02, 0x01, 0x01,
0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01,
0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
0x01, 0x01, 0x02, 0x01, 0x01,
},
},
B: common.DomainParams{
// The x-coordinate of PB
AffineP: common.Fp2{
A: common.Fp{
0x85691AAF4015F88C, 0x7478C5B8C36E9631, 0x7EF2A185DE4DD6E2,
0x943BBEE46BEB9DC7, 0x1A3EC62798792D22, 0x791BC4B084B31D69,
0x03DBE6522CEA17C4, 0x04749AA65D665D83, 0x3D52B5C45EF450F3,
0x0B4219848E36947D, 0xA4CF7070466BDE27, 0x0000334B1FA6D193,
},
B: common.Fp{
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
},
},
// The x-coordinate of QB
AffineQ: common.Fp2{
A: common.Fp{
0x8E7CB3FA53211340, 0xD67CE54F7A05EEE0, 0xFDDC2C8BCE46FC38,
0x08587FAE3110DF1E, 0xD6B8246FA22B058B, 0x4DAC3ACC905A5DBD,
0x51D0BF2FADCED3E8, 0xE5A2406DF6484425, 0x907F177584F671B8,
0x4738A2FFCCED051C, 0x2B0067B4177E4853, 0x00002806AC948D3D,
},
B: common.Fp{
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
},
},
// The x-coordinate of RB = PB - QB
AffineR: common.Fp2{
A: common.Fp{
0xB56457016D1D6D1C, 0x03DECCB38F39C491, 0xDFB910AC8A559452,
0xA9D0F17D1FF24883, 0x8562BBAF515C248C, 0x249B2A6DDB1CB67D,
0x3131AF96FB46835C, 0xE10258398480C3E1, 0xEAB5E2B872D4FAB1,
0xB71E63875FAEB1DF, 0xF8384D4F13757CF6, 0x0000361EC9B09912,
},
B: common.Fp{
0x58C967899ED16EF4, 0x81998376DC622A4B, 0x3D1C1DCFE0B12681,
0x9347DEBB953E1730, 0x9ABB344D3A82C2D7, 0xE4881BD2820552B2,
0x0037247923D90266, 0x2E3156EDB157E5A5, 0xF86A46A7506823F7,
0x8FE5523A7B7F1CFC, 0xFA3CFFA38372F67B, 0x0000692DCE85FFBD,
},
},
// Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1.
SecretBitLen: 378,
// SecretBitLen in bytes.
SecretByteLen: 48,
// 3-torsion group computation strategy
IsogenyStrategy: []uint32{
0x70, 0x3F, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,
0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08,
0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01,
0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
0x01, 0x01, 0x02, 0x01, 0x01, 0x1F, 0x10, 0x08, 0x04, 0x02,
0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02,
0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04,
0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x31, 0x1F, 0x10,
0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01,
0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01,
0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
0x15, 0x0C, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x03, 0x02,
0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05,
0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,
0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01,
},
},
OneFp2: one,
HalfFp2: half,
MsgLen: 32,
// SIKEp751 provides 128 bit of classical security ([SIKE], 5.1)
KemSize: 32,
// ceil(751+7/8)
Bytelen: 94,
CiphertextSize: 32 + 564,
InitCurve: common.ProjectiveCurveParameters{
A: six,
C: one,
},
}
)
func init() {
common.Register(common.Fp751, ¶ms)
}
|
