1 /* Copyright (c) 2020, Google Inc.
2  *
3  * Permission to use, copy, modify, and/or distribute this software for any
4  * purpose with or without fee is hereby granted, provided that the above
5  * copyright notice and this permission notice appear in all copies.
6  *
7  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
10  * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
12  * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
13  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
14 
15 // This file is generated by make_tables.go.
16 
17 // Base point pre computation
18 // --------------------------
19 //
20 // Two different sorts of precomputed tables are used in the following code.
21 // Each contain various points on the curve, where each point is three field
22 // elements (x, y, z).
23 //
24 // For the base point table, z is usually 1 (0 for the point at infinity).
25 // This table has 2 * 16 elements, starting with the following:
26 // index | bits    | point
27 // ------+---------+------------------------------
28 //     0 | 0 0 0 0 | 0G
29 //     1 | 0 0 0 1 | 1G
30 //     2 | 0 0 1 0 | 2^64G
31 //     3 | 0 0 1 1 | (2^64 + 1)G
32 //     4 | 0 1 0 0 | 2^128G
33 //     5 | 0 1 0 1 | (2^128 + 1)G
34 //     6 | 0 1 1 0 | (2^128 + 2^64)G
35 //     7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
36 //     8 | 1 0 0 0 | 2^192G
37 //     9 | 1 0 0 1 | (2^192 + 1)G
38 //    10 | 1 0 1 0 | (2^192 + 2^64)G
39 //    11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
40 //    12 | 1 1 0 0 | (2^192 + 2^128)G
41 //    13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
42 //    14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
43 //    15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
44 // followed by a copy of this with each element multiplied by 2^32.
45 //
46 // The reason for this is so that we can clock bits into four different
47 // locations when doing simple scalar multiplies against the base point,
48 // and then another four locations using the second 16 elements.
49 //
50 // Tables for other points have table[i] = iG for i in 0 .. 16.
51 
52 // fiat_p256_g_pre_comp is the table of precomputed base points
53 #if defined(BORINGSSL_NISTP256_64BIT)
54 static const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = {
55     {{{0x79e730d418a9143c, 0x75ba95fc5fedb601, 0x79fb732b77622510,
56        0x18905f76a53755c6},
57       {0xddf25357ce95560a, 0x8b4ab8e4ba19e45c, 0xd2e88688dd21f325,
58        0x8571ff1825885d85}},
59      {{0x4f922fc516a0d2bb, 0x0d5cc16c1a623499, 0x9241cf3a57c62c8b,
60        0x2f5e6961fd1b667f},
61       {0x5c15c70bf5a01797, 0x3d20b44d60956192, 0x04911b37071fdb52,
62        0xf648f9168d6f0f7b}},
63      {{0x9e566847e137bbbc, 0xe434469e8a6a0bec, 0xb1c4276179d73463,
64        0x5abe0285133d0015},
65       {0x92aa837cc04c7dab, 0x573d9f4c43260c07, 0x0c93156278e6cc37,
66        0x94bb725b6b6f7383}},
67      {{0x62a8c244bfe20925, 0x91c19ac38fdce867, 0x5a96a5d5dd387063,
68        0x61d587d421d324f6},
69       {0xe87673a2a37173ea, 0x2384800853778b65, 0x10f8441e05bab43e,
70        0xfa11fe124621efbe}},
71      {{0x1c891f2b2cb19ffd, 0x01ba8d5bb1923c23, 0xb6d03d678ac5ca8e,
72        0x586eb04c1f13bedc},
73       {0x0c35c6e527e8ed09, 0x1e81a33c1819ede2, 0x278fd6c056c652fa,
74        0x19d5ac0870864f11}},
75      {{0x62577734d2b533d5, 0x673b8af6a1bdddc0, 0x577e7c9aa79ec293,
76        0xbb6de651c3b266b1},
77       {0xe7e9303ab65259b3, 0xd6a0afd3d03a7480, 0xc5ac83d19b3cfc27,
78        0x60b4619a5d18b99b}},
79      {{0xbd6a38e11ae5aa1c, 0xb8b7652b49e73658, 0x0b130014ee5f87ed,
80        0x9d0f27b2aeebffcd},
81       {0xca9246317a730a55, 0x9c955b2fddbbc83a, 0x07c1dfe0ac019a71,
82        0x244a566d356ec48d}},
83      {{0x56f8410ef4f8b16a, 0x97241afec47b266a, 0x0a406b8e6d9c87c1,
84        0x803f3e02cd42ab1b},
85       {0x7f0309a804dbec69, 0xa83b85f73bbad05f, 0xc6097273ad8e197f,
86        0xc097440e5067adc1}},
87      {{0x846a56f2c379ab34, 0xa8ee068b841df8d1, 0x20314459176c68ef,
88        0xf1af32d5915f1f30},
89       {0x99c375315d75bd50, 0x837cffbaf72f67bc, 0x0613a41848d7723f,
90        0x23d0f130e2d41c8b}},
91      {{0xed93e225d5be5a2b, 0x6fe799835934f3c6, 0x4314092622626ffc,
92        0x50bbb4d97990216a},
93       {0x378191c6e57ec63e, 0x65422c40181dcdb2, 0x41a8099b0236e0f6,
94        0x2b10011801fe49c3}},
95      {{0xfc68b5c59b391593, 0xc385f5a2598270fc, 0x7144f3aad19adcbb,
96        0xdd55899983fbae0c},
97       {0x93b88b8e74b82ff4, 0xd2e03c4071e734c9, 0x9a7a9eaf43c0322a,
98        0xe6e4c551149d6041}},
99      {{0x5fe14bfe80ec21fe, 0xf6ce116ac255be82, 0x98bc5a072f4a5d67,
100        0xfad27148db7e63af},
101       {0x90c0b6ac29ab05b3, 0x37a9a83c4e251ae6, 0x0a7dc875c2aade7d,
102        0x77387de39f0e1a84}},
103      {{0x1e9ecc49a56c0dd7, 0xa5cffcd846086c74, 0x8f7a1408f505aece,
104        0xb37b85c0bef0c47e},
105       {0x3596b6e4cc0e6a8f, 0xfd6d4bbf6b388f23, 0xaba453fac39cef4e,
106        0x9c135ac8f9f628d5}},
107      {{0x0a1c729495c8f8be, 0x2961c4803bf362bf, 0x9e418403df63d4ac,
108        0xc109f9cb91ece900},
109       {0xc2d095d058945705, 0xb9083d96ddeb85c0, 0x84692b8d7a40449b,
110        0x9bc3344f2eee1ee1}},
111      {{0x0d5ae35642913074, 0x55491b2748a542b1, 0x469ca665b310732a,
112        0x29591d525f1a4cc1},
113       {0xe76f5b6bb84f983f, 0xbe7eef419f5f84e1, 0x1200d49680baa189,
114        0x6376551f18ef332c}}},
115     {{{0x202886024147519a, 0xd0981eac26b372f0, 0xa9d4a7caa785ebc8,
116        0xd953c50ddbdf58e9},
117       {0x9d6361ccfd590f8f, 0x72e9626b44e6c917, 0x7fd9611022eb64cf,
118        0x863ebb7e9eb288f3}},
119      {{0x4fe7ee31b0e63d34, 0xf4600572a9e54fab, 0xc0493334d5e7b5a4,
120        0x8589fb9206d54831},
121       {0xaa70f5cc6583553a, 0x0879094ae25649e5, 0xcc90450710044652,
122        0xebb0696d02541c4f}},
123      {{0xabbaa0c03b89da99, 0xa6f2d79eb8284022, 0x27847862b81c05e8,
124        0x337a4b5905e54d63},
125       {0x3c67500d21f7794a, 0x207005b77d6d7f61, 0x0a5a378104cfd6e8,
126        0x0d65e0d5f4c2fbd6}},
127      {{0xd433e50f6d3549cf, 0x6f33696ffacd665e, 0x695bfdacce11fcb4,
128        0x810ee252af7c9860},
129       {0x65450fe17159bb2c, 0xf7dfbebe758b357b, 0x2b057e74d69fea72,
130        0xd485717a92731745}},
131      {{0xce1f69bbe83f7669, 0x09f8ae8272877d6b, 0x9548ae543244278d,
132        0x207755dee3c2c19c},
133       {0x87bd61d96fef1945, 0x18813cefb12d28c3, 0x9fbcd1d672df64aa,
134        0x48dc5ee57154b00d}},
135      {{0xef0f469ef49a3154, 0x3e85a5956e2b2e9a, 0x45aaec1eaa924a9c,
136        0xaa12dfc8a09e4719},
137       {0x26f272274df69f1d, 0xe0e4c82ca2ff5e73, 0xb9d8ce73b7a9dd44,
138        0x6c036e73e48ca901}},
139      {{0xe1e421e1a47153f0, 0xb86c3b79920418c9, 0x93bdce87705d7672,
140        0xf25ae793cab79a77},
141       {0x1f3194a36d869d0c, 0x9d55c8824986c264, 0x49fb5ea3096e945e,
142        0x39b8e65313db0a3e}},
143      {{0xe3417bc035d0b34a, 0x440b386b8327c0a7, 0x8fb7262dac0362d1,
144        0x2c41114ce0cdf943},
145       {0x2ba5cef1ad95a0b1, 0xc09b37a867d54362, 0x26d6cdd201e486c9,
146        0x20477abf42ff9297}},
147      {{0x0f121b41bc0a67d2, 0x62d4760a444d248a, 0x0e044f1d659b4737,
148        0x08fde365250bb4a8},
149       {0xaceec3da848bf287, 0xc2a62182d3369d6e, 0x3582dfdc92449482,
150        0x2f7e2fd2565d6cd7}},
151      {{0x0a0122b5178a876b, 0x51ff96ff085104b4, 0x050b31ab14f29f76,
152        0x84abb28b5f87d4e6},
153       {0xd5ed439f8270790a, 0x2d6cb59d85e3f46b, 0x75f55c1b6c1e2212,
154        0xe5436f6717655640}},
155      {{0xc2965ecc9aeb596d, 0x01ea03e7023c92b4, 0x4704b4b62e013961,
156        0x0ca8fd3f905ea367},
157       {0x92523a42551b2b61, 0x1eb7a89c390fcd06, 0xe7f1d2be0392a63e,
158        0x96dca2644ddb0c33}},
159      {{0x231c210e15339848, 0xe87a28e870778c8d, 0x9d1de6616956e170,
160        0x4ac3c9382bb09c0b},
161       {0x19be05516998987d, 0x8b2376c4ae09f4d6, 0x1de0b7651a3f933d,
162        0x380d94c7e39705f4}},
163      {{0x3685954b8c31c31d, 0x68533d005bf21a0c, 0x0bd7626e75c79ec9,
164        0xca17754742c69d54},
165       {0xcc6edafff6d2dbb2, 0xfd0d8cbd174a9d18, 0x875e8793aa4578e8,
166        0xa976a7139cab2ce6}},
167      {{0xce37ab11b43ea1db, 0x0a7ff1a95259d292, 0x851b02218f84f186,
168        0xa7222beadefaad13},
169       {0xa2ac78ec2b0a9144, 0x5a024051f2fa59c5, 0x91d1eca56147ce38,
170        0xbe94d523bc2ac690}},
171      {{0x2d8daefd79ec1a0f, 0x3bbcd6fdceb39c97, 0xf5575ffc58f61a95,
172        0xdbd986c4adf7b420},
173       {0x81aa881415f39eb7, 0x6ee2fcf5b98d976c, 0x5465475dcf2f717d,
174        0x8e24d3c46860bbd0}}}};
175 #else
176 static const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = {
177     {{{0x18a9143c, 0x79e730d4, 0x5fedb601, 0x75ba95fc, 0x77622510, 0x79fb732b,
178        0xa53755c6, 0x18905f76},
179       {0xce95560a, 0xddf25357, 0xba19e45c, 0x8b4ab8e4, 0xdd21f325, 0xd2e88688,
180        0x25885d85, 0x8571ff18}},
181      {{0x16a0d2bb, 0x4f922fc5, 0x1a623499, 0x0d5cc16c, 0x57c62c8b, 0x9241cf3a,
182        0xfd1b667f, 0x2f5e6961},
183       {0xf5a01797, 0x5c15c70b, 0x60956192, 0x3d20b44d, 0x071fdb52, 0x04911b37,
184        0x8d6f0f7b, 0xf648f916}},
185      {{0xe137bbbc, 0x9e566847, 0x8a6a0bec, 0xe434469e, 0x79d73463, 0xb1c42761,
186        0x133d0015, 0x5abe0285},
187       {0xc04c7dab, 0x92aa837c, 0x43260c07, 0x573d9f4c, 0x78e6cc37, 0x0c931562,
188        0x6b6f7383, 0x94bb725b}},
189      {{0xbfe20925, 0x62a8c244, 0x8fdce867, 0x91c19ac3, 0xdd387063, 0x5a96a5d5,
190        0x21d324f6, 0x61d587d4},
191       {0xa37173ea, 0xe87673a2, 0x53778b65, 0x23848008, 0x05bab43e, 0x10f8441e,
192        0x4621efbe, 0xfa11fe12}},
193      {{0x2cb19ffd, 0x1c891f2b, 0xb1923c23, 0x01ba8d5b, 0x8ac5ca8e, 0xb6d03d67,
194        0x1f13bedc, 0x586eb04c},
195       {0x27e8ed09, 0x0c35c6e5, 0x1819ede2, 0x1e81a33c, 0x56c652fa, 0x278fd6c0,
196        0x70864f11, 0x19d5ac08}},
197      {{0xd2b533d5, 0x62577734, 0xa1bdddc0, 0x673b8af6, 0xa79ec293, 0x577e7c9a,
198        0xc3b266b1, 0xbb6de651},
199       {0xb65259b3, 0xe7e9303a, 0xd03a7480, 0xd6a0afd3, 0x9b3cfc27, 0xc5ac83d1,
200        0x5d18b99b, 0x60b4619a}},
201      {{0x1ae5aa1c, 0xbd6a38e1, 0x49e73658, 0xb8b7652b, 0xee5f87ed, 0x0b130014,
202        0xaeebffcd, 0x9d0f27b2},
203       {0x7a730a55, 0xca924631, 0xddbbc83a, 0x9c955b2f, 0xac019a71, 0x07c1dfe0,
204        0x356ec48d, 0x244a566d}},
205      {{0xf4f8b16a, 0x56f8410e, 0xc47b266a, 0x97241afe, 0x6d9c87c1, 0x0a406b8e,
206        0xcd42ab1b, 0x803f3e02},
207       {0x04dbec69, 0x7f0309a8, 0x3bbad05f, 0xa83b85f7, 0xad8e197f, 0xc6097273,
208        0x5067adc1, 0xc097440e}},
209      {{0xc379ab34, 0x846a56f2, 0x841df8d1, 0xa8ee068b, 0x176c68ef, 0x20314459,
210        0x915f1f30, 0xf1af32d5},
211       {0x5d75bd50, 0x99c37531, 0xf72f67bc, 0x837cffba, 0x48d7723f, 0x0613a418,
212        0xe2d41c8b, 0x23d0f130}},
213      {{0xd5be5a2b, 0xed93e225, 0x5934f3c6, 0x6fe79983, 0x22626ffc, 0x43140926,
214        0x7990216a, 0x50bbb4d9},
215       {0xe57ec63e, 0x378191c6, 0x181dcdb2, 0x65422c40, 0x0236e0f6, 0x41a8099b,
216        0x01fe49c3, 0x2b100118}},
217      {{0x9b391593, 0xfc68b5c5, 0x598270fc, 0xc385f5a2, 0xd19adcbb, 0x7144f3aa,
218        0x83fbae0c, 0xdd558999},
219       {0x74b82ff4, 0x93b88b8e, 0x71e734c9, 0xd2e03c40, 0x43c0322a, 0x9a7a9eaf,
220        0x149d6041, 0xe6e4c551}},
221      {{0x80ec21fe, 0x5fe14bfe, 0xc255be82, 0xf6ce116a, 0x2f4a5d67, 0x98bc5a07,
222        0xdb7e63af, 0xfad27148},
223       {0x29ab05b3, 0x90c0b6ac, 0x4e251ae6, 0x37a9a83c, 0xc2aade7d, 0x0a7dc875,
224        0x9f0e1a84, 0x77387de3}},
225      {{0xa56c0dd7, 0x1e9ecc49, 0x46086c74, 0xa5cffcd8, 0xf505aece, 0x8f7a1408,
226        0xbef0c47e, 0xb37b85c0},
227       {0xcc0e6a8f, 0x3596b6e4, 0x6b388f23, 0xfd6d4bbf, 0xc39cef4e, 0xaba453fa,
228        0xf9f628d5, 0x9c135ac8}},
229      {{0x95c8f8be, 0x0a1c7294, 0x3bf362bf, 0x2961c480, 0xdf63d4ac, 0x9e418403,
230        0x91ece900, 0xc109f9cb},
231       {0x58945705, 0xc2d095d0, 0xddeb85c0, 0xb9083d96, 0x7a40449b, 0x84692b8d,
232        0x2eee1ee1, 0x9bc3344f}},
233      {{0x42913074, 0x0d5ae356, 0x48a542b1, 0x55491b27, 0xb310732a, 0x469ca665,
234        0x5f1a4cc1, 0x29591d52},
235       {0xb84f983f, 0xe76f5b6b, 0x9f5f84e1, 0xbe7eef41, 0x80baa189, 0x1200d496,
236        0x18ef332c, 0x6376551f}}},
237     {{{0x4147519a, 0x20288602, 0x26b372f0, 0xd0981eac, 0xa785ebc8, 0xa9d4a7ca,
238        0xdbdf58e9, 0xd953c50d},
239       {0xfd590f8f, 0x9d6361cc, 0x44e6c917, 0x72e9626b, 0x22eb64cf, 0x7fd96110,
240        0x9eb288f3, 0x863ebb7e}},
241      {{0xb0e63d34, 0x4fe7ee31, 0xa9e54fab, 0xf4600572, 0xd5e7b5a4, 0xc0493334,
242        0x06d54831, 0x8589fb92},
243       {0x6583553a, 0xaa70f5cc, 0xe25649e5, 0x0879094a, 0x10044652, 0xcc904507,
244        0x02541c4f, 0xebb0696d}},
245      {{0x3b89da99, 0xabbaa0c0, 0xb8284022, 0xa6f2d79e, 0xb81c05e8, 0x27847862,
246        0x05e54d63, 0x337a4b59},
247       {0x21f7794a, 0x3c67500d, 0x7d6d7f61, 0x207005b7, 0x04cfd6e8, 0x0a5a3781,
248        0xf4c2fbd6, 0x0d65e0d5}},
249      {{0x6d3549cf, 0xd433e50f, 0xfacd665e, 0x6f33696f, 0xce11fcb4, 0x695bfdac,
250        0xaf7c9860, 0x810ee252},
251       {0x7159bb2c, 0x65450fe1, 0x758b357b, 0xf7dfbebe, 0xd69fea72, 0x2b057e74,
252        0x92731745, 0xd485717a}},
253      {{0xe83f7669, 0xce1f69bb, 0x72877d6b, 0x09f8ae82, 0x3244278d, 0x9548ae54,
254        0xe3c2c19c, 0x207755de},
255       {0x6fef1945, 0x87bd61d9, 0xb12d28c3, 0x18813cef, 0x72df64aa, 0x9fbcd1d6,
256        0x7154b00d, 0x48dc5ee5}},
257      {{0xf49a3154, 0xef0f469e, 0x6e2b2e9a, 0x3e85a595, 0xaa924a9c, 0x45aaec1e,
258        0xa09e4719, 0xaa12dfc8},
259       {0x4df69f1d, 0x26f27227, 0xa2ff5e73, 0xe0e4c82c, 0xb7a9dd44, 0xb9d8ce73,
260        0xe48ca901, 0x6c036e73}},
261      {{0xa47153f0, 0xe1e421e1, 0x920418c9, 0xb86c3b79, 0x705d7672, 0x93bdce87,
262        0xcab79a77, 0xf25ae793},
263       {0x6d869d0c, 0x1f3194a3, 0x4986c264, 0x9d55c882, 0x096e945e, 0x49fb5ea3,
264        0x13db0a3e, 0x39b8e653}},
265      {{0x35d0b34a, 0xe3417bc0, 0x8327c0a7, 0x440b386b, 0xac0362d1, 0x8fb7262d,
266        0xe0cdf943, 0x2c41114c},
267       {0xad95a0b1, 0x2ba5cef1, 0x67d54362, 0xc09b37a8, 0x01e486c9, 0x26d6cdd2,
268        0x42ff9297, 0x20477abf}},
269      {{0xbc0a67d2, 0x0f121b41, 0x444d248a, 0x62d4760a, 0x659b4737, 0x0e044f1d,
270        0x250bb4a8, 0x08fde365},
271       {0x848bf287, 0xaceec3da, 0xd3369d6e, 0xc2a62182, 0x92449482, 0x3582dfdc,
272        0x565d6cd7, 0x2f7e2fd2}},
273      {{0x178a876b, 0x0a0122b5, 0x085104b4, 0x51ff96ff, 0x14f29f76, 0x050b31ab,
274        0x5f87d4e6, 0x84abb28b},
275       {0x8270790a, 0xd5ed439f, 0x85e3f46b, 0x2d6cb59d, 0x6c1e2212, 0x75f55c1b,
276        0x17655640, 0xe5436f67}},
277      {{0x9aeb596d, 0xc2965ecc, 0x023c92b4, 0x01ea03e7, 0x2e013961, 0x4704b4b6,
278        0x905ea367, 0x0ca8fd3f},
279       {0x551b2b61, 0x92523a42, 0x390fcd06, 0x1eb7a89c, 0x0392a63e, 0xe7f1d2be,
280        0x4ddb0c33, 0x96dca264}},
281      {{0x15339848, 0x231c210e, 0x70778c8d, 0xe87a28e8, 0x6956e170, 0x9d1de661,
282        0x2bb09c0b, 0x4ac3c938},
283       {0x6998987d, 0x19be0551, 0xae09f4d6, 0x8b2376c4, 0x1a3f933d, 0x1de0b765,
284        0xe39705f4, 0x380d94c7}},
285      {{0x8c31c31d, 0x3685954b, 0x5bf21a0c, 0x68533d00, 0x75c79ec9, 0x0bd7626e,
286        0x42c69d54, 0xca177547},
287       {0xf6d2dbb2, 0xcc6edaff, 0x174a9d18, 0xfd0d8cbd, 0xaa4578e8, 0x875e8793,
288        0x9cab2ce6, 0xa976a713}},
289      {{0xb43ea1db, 0xce37ab11, 0x5259d292, 0x0a7ff1a9, 0x8f84f186, 0x851b0221,
290        0xdefaad13, 0xa7222bea},
291       {0x2b0a9144, 0xa2ac78ec, 0xf2fa59c5, 0x5a024051, 0x6147ce38, 0x91d1eca5,
292        0xbc2ac690, 0xbe94d523}},
293      {{0x79ec1a0f, 0x2d8daefd, 0xceb39c97, 0x3bbcd6fd, 0x58f61a95, 0xf5575ffc,
294        0xadf7b420, 0xdbd986c4},
295       {0x15f39eb7, 0x81aa8814, 0xb98d976c, 0x6ee2fcf5, 0xcf2f717d, 0x5465475d,
296        0x6860bbd0, 0x8e24d3c4}}}};
297 #endif
298