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
#[cfg(feature = "test-utils")]
#[cfg(test)]
mod tests {
// Random prime with no nice properties for Montgomery friendliness
mod fp_ugly_tests {
// Field modulus
const MODULUS: [u64; 2] = [0x5A0E852097C48043, 0x7EA2A3A646684E9D];
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
fp2::define_fp_core!(typename = FpUgly, modulus = MODULUS,);
fp2::define_fp_tests!(FpUgly);
// FpUglyExt: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
fp2::define_fp2_from_modulus!(typename = FpUglyExt, base_typename = Fp, modulus = MODULUS,);
fp2::define_fp2_tests!(FpUglyExt, MODULUS, 1);
#[test]
fn check_sum_of_products_flag() {
assert!(!FpUgly::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
mod fp127_tests {
// Field modulus
const MODULUS: [u64; 2] = [0xFFFFFFFFFFFFFFFF, 0x7FFFFFFFFFFFFFFF];
// Fp139: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
// p = 2^127 - 1
fp2::define_fp_core!(typename = Fp127, modulus = MODULUS,);
fp2::define_fp_tests!(Fp127);
// Fp127Ext: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
fp2::define_fp2_from_modulus!(typename = Fp127Ext, base_typename = Fp, modulus = MODULUS,);
fp2::define_fp2_tests!(Fp127Ext, MODULUS, 2);
#[test]
fn check_sum_of_products_flag() {
assert!(!Fp127::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
mod fp251_tests {
// Field modulus
const MODULUS: [u64; 4] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0x04FFFFFFFFFFFFFF,
];
// Fp251: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
// p = 5*2^248 - 1
fp2::define_fp_core!(typename = Fp251, modulus = MODULUS,);
// Fp251Ext: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
fp2::define_fp2_from_type!(typename = Fp251Ext, base_field = Fp251,);
fp2::define_fp_tests!(Fp251);
fp2::define_fp2_tests!(Fp251Ext, MODULUS, 5);
#[test]
fn check_sum_of_products_flag() {
assert!(!Fp251::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
mod fp383_tests {
// Field modulus
const MODULUS: [u64; 6] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0x40FFFFFFFFFFFFFF,
];
// Fp383: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
// p = 65 * 2**376 - 1
fp2::define_fp_core!(typename = Fp383, modulus = MODULUS,);
// Fp383Ext: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
// Macro input generated with scripts/gen_fp.sage
fp2::define_fp2_from_type!(typename = Fp383Ext, base_field = Fp383,);
// For define_fp2_tests we must include a u64 nqr_re such that
// nqr_re + i is a non-quadratic residue in Fp2
fp2::define_fp_tests!(Fp383);
fp2::define_fp2_tests!(Fp383Ext, MODULUS, 6);
#[test]
fn check_sum_of_products_flag() {
assert!(!Fp383::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
mod fp434_tests {
// NIST lvl 1 SIKE prime: p = 2^216 * 3^137 - 1
// Fp434Ext: a finite field element GF(p^2) with modulus x^2 + 1.
const MODULUS: [u64; 7] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFDC1767AE2FFFFFF,
0x7BC65C783158AEA3,
0x6CFC5FD681C52056,
0x0002341F27177344,
];
fp2::define_fp2_from_modulus!(
typename = Fp434Ext,
base_typename = Fp434,
modulus = MODULUS,
);
// For define_fp2_tests we must include a u64 nqr_re such that
// nqr_re + i is a non-quadratic residue in Fp2
fp2::define_fp_tests!(Fp434);
fp2::define_fp2_tests!(Fp434Ext, MODULUS, 2);
#[test]
fn check_sum_of_products_flag() {
assert!(!Fp434::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
// This modulus is very close to the value R = 2^(64 * 14) and so
// needs an extra conditional subtraction in the sum of products
// method.
mod fp896_tests {
const MODULUS: [u64; 14] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xA7FFFFFFFFFFFFFF,
];
// Fp896: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
fp2::define_fp_core!(typename = Fp896, modulus = MODULUS,);
// Fp896Ext: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
fp2::define_fp2_from_type!(typename = Fp896Ext, base_field = Fp896,);
fp2::define_fp_tests!(Fp896);
fp2::define_fp2_tests!(Fp896Ext, MODULUS, 2);
#[test]
fn check_sum_of_products_flag() {
assert!(Fp896::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
// When the word length is larger than 20, we slightly modify set_mul
mod fp1554_tests {
static MODULUS: [u64; 25] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0x0000000000047FFF,
];
// Fp896: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
fp2::define_fp_core!(typename = Fp1554, modulus = MODULUS,);
fp2::define_fp_tests!(Fp1554);
#[test]
fn check_sum_of_products_flag() {
assert!(!Fp1554::SUM_OF_PRODUCTS_ADDITIONAL_SUB);
}
}
mod fp648_tests {
static MODULUS: [u64; 11] = [
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xFFFFFFFFFFFFFFFF,
0xAB4C1EC4E9A4421A,
0xA1A751E0FF03064A,
0x5C5381A82432B77B,
0x74F54CC513A36773,
0x152EF0C01F75CCD4,
0xA53054622A07450C,
0xF81DCB46FD3F8B4D,
0x00000000000000DA,
];
// Fp648: a finite field element GF(p) with p = 3 mod 4.
// Contents are opaque, all functions are constant-time.
fp2::define_fp_core!(typename = Fp648, modulus = MODULUS,);
// Fp648Ext: a finite field element GF(p^2) with modulus x^2 + 1.
// Contents are opaque, all functions are constant-time.
fp2::define_fp2_from_type!(typename = Fp648Ext, base_field = Fp648,);
fp2::define_fp_tests!(Fp648);
fp2::define_fp2_tests!(Fp648Ext, MODULUS, 6);
}
}