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04daec86 | 1 | /* |
edea42c6 | 2 | * Copyright 2010-2017 The OpenSSL Project Authors. All Rights Reserved. |
4f22f405 RS |
3 | * |
4 | * Licensed under the OpenSSL license (the "License"). You may not use | |
5 | * this file except in compliance with the License. You can obtain a copy | |
6 | * in the file LICENSE in the source distribution or at | |
7 | * https://www.openssl.org/source/license.html | |
04daec86 | 8 | */ |
4f22f405 | 9 | |
3e00b4c9 | 10 | /* Copyright 2011 Google Inc. |
04daec86 | 11 | * |
3e00b4c9 | 12 | * Licensed under the Apache License, Version 2.0 (the "License"); |
04daec86 | 13 | * |
3e00b4c9 BM |
14 | * you may not use this file except in compliance with the License. |
15 | * You may obtain a copy of the License at | |
04daec86 | 16 | * |
3e00b4c9 | 17 | * http://www.apache.org/licenses/LICENSE-2.0 |
04daec86 | 18 | * |
3e00b4c9 BM |
19 | * Unless required by applicable law or agreed to in writing, software |
20 | * distributed under the License is distributed on an "AS IS" BASIS, | |
21 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
22 | * See the License for the specific language governing permissions and | |
23 | * limitations under the License. | |
04daec86 BM |
24 | */ |
25 | ||
26 | /* | |
27 | * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication | |
28 | * | |
29 | * Inspired by Daniel J. Bernstein's public domain nistp224 implementation | |
30 | * and Adam Langley's public domain 64-bit C implementation of curve25519 | |
31 | */ | |
e0d6132b BM |
32 | |
33 | #include <openssl/opensslconf.h> | |
effaf4de RS |
34 | #ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 |
35 | NON_EMPTY_TRANSLATION_UNIT | |
36 | #else | |
e0d6132b | 37 | |
0f113f3e MC |
38 | # include <stdint.h> |
39 | # include <string.h> | |
40 | # include <openssl/err.h> | |
41 | # include "ec_lcl.h" | |
04daec86 | 42 | |
0f113f3e | 43 | # if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) |
396cb565 | 44 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
0f113f3e MC |
45 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
46 | * platforms */ | |
47 | # else | |
48 | # error "Need GCC 3.1 or later to define type uint128_t" | |
49 | # endif | |
04daec86 BM |
50 | |
51 | typedef uint8_t u8; | |
3e00b4c9 | 52 | typedef uint64_t u64; |
04daec86 | 53 | |
04daec86 | 54 | /******************************************************************************/ |
1d97c843 TH |
55 | /*- |
56 | * INTERNAL REPRESENTATION OF FIELD ELEMENTS | |
04daec86 BM |
57 | * |
58 | * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 | |
3e00b4c9 BM |
59 | * using 64-bit coefficients called 'limbs', |
60 | * and sometimes (for multiplication results) as | |
04daec86 | 61 | * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 |
3e00b4c9 BM |
62 | * using 128-bit coefficients called 'widelimbs'. |
63 | * A 4-limb representation is an 'felem'; | |
64 | * a 7-widelimb representation is a 'widefelem'. | |
65 | * Even within felems, bits of adjacent limbs overlap, and we don't always | |
66 | * reduce the representations: we ensure that inputs to each felem | |
04daec86 BM |
67 | * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, |
68 | * and fit into a 128-bit word without overflow. The coefficients are then | |
3e00b4c9 BM |
69 | * again partially reduced to obtain an felem satisfying a_i < 2^57. |
70 | * We only reduce to the unique minimal representation at the end of the | |
71 | * computation. | |
04daec86 BM |
72 | */ |
73 | ||
3e00b4c9 BM |
74 | typedef uint64_t limb; |
75 | typedef uint128_t widelimb; | |
76 | ||
77 | typedef limb felem[4]; | |
78 | typedef widelimb widefelem[7]; | |
04daec86 | 79 | |
0f113f3e | 80 | /* |
46f4e1be | 81 | * Field element represented as a byte array. 28*8 = 224 bits is also the |
0f113f3e MC |
82 | * group order size for the elliptic curve, and we also use this type for |
83 | * scalars for point multiplication. | |
84 | */ | |
396cb565 BM |
85 | typedef u8 felem_bytearray[28]; |
86 | ||
87 | static const felem_bytearray nistp224_curve_params[5] = { | |
0f113f3e MC |
88 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ |
89 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, | |
90 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, | |
91 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ | |
92 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, | |
93 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, | |
94 | {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ | |
95 | 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, | |
96 | 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, | |
97 | {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ | |
98 | 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, | |
99 | 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, | |
100 | {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ | |
101 | 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, | |
102 | 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} | |
396cb565 | 103 | }; |
04daec86 | 104 | |
1d97c843 TH |
105 | /*- |
106 | * Precomputed multiples of the standard generator | |
3e00b4c9 BM |
107 | * Points are given in coordinates (X, Y, Z) where Z normally is 1 |
108 | * (0 for the point at infinity). | |
109 | * For each field element, slice a_0 is word 0, etc. | |
110 | * | |
111 | * The table has 2 * 16 elements, starting with the following: | |
112 | * index | bits | point | |
113 | * ------+---------+------------------------------ | |
114 | * 0 | 0 0 0 0 | 0G | |
115 | * 1 | 0 0 0 1 | 1G | |
116 | * 2 | 0 0 1 0 | 2^56G | |
117 | * 3 | 0 0 1 1 | (2^56 + 1)G | |
118 | * 4 | 0 1 0 0 | 2^112G | |
119 | * 5 | 0 1 0 1 | (2^112 + 1)G | |
120 | * 6 | 0 1 1 0 | (2^112 + 2^56)G | |
121 | * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G | |
122 | * 8 | 1 0 0 0 | 2^168G | |
123 | * 9 | 1 0 0 1 | (2^168 + 1)G | |
124 | * 10 | 1 0 1 0 | (2^168 + 2^56)G | |
125 | * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G | |
126 | * 12 | 1 1 0 0 | (2^168 + 2^112)G | |
127 | * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G | |
128 | * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G | |
129 | * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G | |
130 | * followed by a copy of this with each element multiplied by 2^28. | |
131 | * | |
132 | * The reason for this is so that we can clock bits into four different | |
133 | * locations when doing simple scalar multiplies against the base point, | |
134 | * and then another four locations using the second 16 elements. | |
135 | */ | |
4eb504ae AP |
136 | static const felem gmul[2][16][3] = { |
137 | {{{0, 0, 0, 0}, | |
138 | {0, 0, 0, 0}, | |
139 | {0, 0, 0, 0}}, | |
140 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, | |
141 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, | |
142 | {1, 0, 0, 0}}, | |
143 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, | |
144 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, | |
145 | {1, 0, 0, 0}}, | |
146 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, | |
147 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, | |
148 | {1, 0, 0, 0}}, | |
149 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, | |
150 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, | |
151 | {1, 0, 0, 0}}, | |
152 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, | |
153 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, | |
154 | {1, 0, 0, 0}}, | |
155 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, | |
156 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, | |
157 | {1, 0, 0, 0}}, | |
158 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, | |
159 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, | |
160 | {1, 0, 0, 0}}, | |
161 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, | |
162 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, | |
163 | {1, 0, 0, 0}}, | |
164 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, | |
165 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, | |
166 | {1, 0, 0, 0}}, | |
167 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, | |
168 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, | |
169 | {1, 0, 0, 0}}, | |
170 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, | |
171 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, | |
172 | {1, 0, 0, 0}}, | |
173 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, | |
174 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, | |
175 | {1, 0, 0, 0}}, | |
176 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, | |
177 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, | |
178 | {1, 0, 0, 0}}, | |
179 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, | |
180 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, | |
181 | {1, 0, 0, 0}}, | |
182 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, | |
183 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, | |
184 | {1, 0, 0, 0}}}, | |
0f113f3e MC |
185 | {{{0, 0, 0, 0}, |
186 | {0, 0, 0, 0}, | |
187 | {0, 0, 0, 0}}, | |
188 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, | |
189 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, | |
190 | {1, 0, 0, 0}}, | |
191 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, | |
192 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, | |
193 | {1, 0, 0, 0}}, | |
194 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, | |
195 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, | |
196 | {1, 0, 0, 0}}, | |
197 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, | |
198 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, | |
199 | {1, 0, 0, 0}}, | |
200 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, | |
201 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, | |
202 | {1, 0, 0, 0}}, | |
203 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, | |
204 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, | |
205 | {1, 0, 0, 0}}, | |
206 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, | |
207 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, | |
208 | {1, 0, 0, 0}}, | |
209 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, | |
210 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, | |
211 | {1, 0, 0, 0}}, | |
212 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, | |
213 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, | |
214 | {1, 0, 0, 0}}, | |
215 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, | |
216 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, | |
217 | {1, 0, 0, 0}}, | |
218 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, | |
219 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, | |
220 | {1, 0, 0, 0}}, | |
221 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, | |
222 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, | |
223 | {1, 0, 0, 0}}, | |
224 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, | |
225 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, | |
226 | {1, 0, 0, 0}}, | |
227 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, | |
228 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, | |
229 | {1, 0, 0, 0}}, | |
230 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, | |
231 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, | |
232 | {1, 0, 0, 0}}} | |
233 | }; | |
04daec86 BM |
234 | |
235 | /* Precomputation for the group generator. */ | |
3aef36ff | 236 | struct nistp224_pre_comp_st { |
0f113f3e | 237 | felem g_pre_comp[2][16][3]; |
2f545ae4 | 238 | CRYPTO_REF_COUNT references; |
9b398ef2 | 239 | CRYPTO_RWLOCK *lock; |
3aef36ff | 240 | }; |
04daec86 BM |
241 | |
242 | const EC_METHOD *EC_GFp_nistp224_method(void) | |
0f113f3e MC |
243 | { |
244 | static const EC_METHOD ret = { | |
245 | EC_FLAGS_DEFAULT_OCT, | |
246 | NID_X9_62_prime_field, | |
247 | ec_GFp_nistp224_group_init, | |
248 | ec_GFp_simple_group_finish, | |
249 | ec_GFp_simple_group_clear_finish, | |
250 | ec_GFp_nist_group_copy, | |
251 | ec_GFp_nistp224_group_set_curve, | |
252 | ec_GFp_simple_group_get_curve, | |
253 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 254 | ec_group_simple_order_bits, |
0f113f3e MC |
255 | ec_GFp_simple_group_check_discriminant, |
256 | ec_GFp_simple_point_init, | |
257 | ec_GFp_simple_point_finish, | |
258 | ec_GFp_simple_point_clear_finish, | |
259 | ec_GFp_simple_point_copy, | |
260 | ec_GFp_simple_point_set_to_infinity, | |
261 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
262 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
263 | ec_GFp_simple_point_set_affine_coordinates, | |
264 | ec_GFp_nistp224_point_get_affine_coordinates, | |
265 | 0 /* point_set_compressed_coordinates */ , | |
266 | 0 /* point2oct */ , | |
267 | 0 /* oct2point */ , | |
268 | ec_GFp_simple_add, | |
269 | ec_GFp_simple_dbl, | |
270 | ec_GFp_simple_invert, | |
271 | ec_GFp_simple_is_at_infinity, | |
272 | ec_GFp_simple_is_on_curve, | |
273 | ec_GFp_simple_cmp, | |
274 | ec_GFp_simple_make_affine, | |
275 | ec_GFp_simple_points_make_affine, | |
276 | ec_GFp_nistp224_points_mul, | |
277 | ec_GFp_nistp224_precompute_mult, | |
278 | ec_GFp_nistp224_have_precompute_mult, | |
279 | ec_GFp_nist_field_mul, | |
280 | ec_GFp_nist_field_sqr, | |
281 | 0 /* field_div */ , | |
282 | 0 /* field_encode */ , | |
283 | 0 /* field_decode */ , | |
9ff9bccc DSH |
284 | 0, /* field_set_to_one */ |
285 | ec_key_simple_priv2oct, | |
286 | ec_key_simple_oct2priv, | |
287 | 0, /* set private */ | |
288 | ec_key_simple_generate_key, | |
289 | ec_key_simple_check_key, | |
290 | ec_key_simple_generate_public_key, | |
291 | 0, /* keycopy */ | |
292 | 0, /* keyfinish */ | |
293 | ecdh_simple_compute_key | |
0f113f3e MC |
294 | }; |
295 | ||
296 | return &ret; | |
297 | } | |
298 | ||
299 | /* | |
300 | * Helper functions to convert field elements to/from internal representation | |
301 | */ | |
3e00b4c9 | 302 | static void bin28_to_felem(felem out, const u8 in[28]) |
0f113f3e MC |
303 | { |
304 | out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; | |
305 | out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; | |
306 | out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; | |
9fbbdd73 | 307 | out[3] = (*((const uint64_t *)(in+20))) >> 8; |
0f113f3e | 308 | } |
04daec86 | 309 | |
3e00b4c9 | 310 | static void felem_to_bin28(u8 out[28], const felem in) |
0f113f3e MC |
311 | { |
312 | unsigned i; | |
313 | for (i = 0; i < 7; ++i) { | |
314 | out[i] = in[0] >> (8 * i); | |
315 | out[i + 7] = in[1] >> (8 * i); | |
316 | out[i + 14] = in[2] >> (8 * i); | |
317 | out[i + 21] = in[3] >> (8 * i); | |
318 | } | |
319 | } | |
04daec86 BM |
320 | |
321 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ | |
322 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | |
0f113f3e MC |
323 | { |
324 | unsigned i; | |
325 | for (i = 0; i < len; ++i) | |
326 | out[i] = in[len - 1 - i]; | |
327 | } | |
04daec86 BM |
328 | |
329 | /* From OpenSSL BIGNUM to internal representation */ | |
3e00b4c9 | 330 | static int BN_to_felem(felem out, const BIGNUM *bn) |
0f113f3e MC |
331 | { |
332 | felem_bytearray b_in; | |
333 | felem_bytearray b_out; | |
334 | unsigned num_bytes; | |
335 | ||
336 | /* BN_bn2bin eats leading zeroes */ | |
16f8d4eb | 337 | memset(b_out, 0, sizeof(b_out)); |
0f113f3e | 338 | num_bytes = BN_num_bytes(bn); |
cbe29648 | 339 | if (num_bytes > sizeof(b_out)) { |
0f113f3e MC |
340 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
341 | return 0; | |
342 | } | |
343 | if (BN_is_negative(bn)) { | |
344 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
345 | return 0; | |
346 | } | |
347 | num_bytes = BN_bn2bin(bn, b_in); | |
348 | flip_endian(b_out, b_in, num_bytes); | |
349 | bin28_to_felem(out, b_out); | |
350 | return 1; | |
351 | } | |
04daec86 BM |
352 | |
353 | /* From internal representation to OpenSSL BIGNUM */ | |
3e00b4c9 | 354 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) |
0f113f3e MC |
355 | { |
356 | felem_bytearray b_in, b_out; | |
357 | felem_to_bin28(b_in, in); | |
cbe29648 RS |
358 | flip_endian(b_out, b_in, sizeof(b_out)); |
359 | return BN_bin2bn(b_out, sizeof(b_out), out); | |
0f113f3e | 360 | } |
04daec86 BM |
361 | |
362 | /******************************************************************************/ | |
3a83462d | 363 | /*- |
0f113f3e | 364 | * FIELD OPERATIONS |
04daec86 BM |
365 | * |
366 | * Field operations, using the internal representation of field elements. | |
367 | * NB! These operations are specific to our point multiplication and cannot be | |
368 | * expected to be correct in general - e.g., multiplication with a large scalar | |
369 | * will cause an overflow. | |
370 | * | |
371 | */ | |
372 | ||
3e00b4c9 | 373 | static void felem_one(felem out) |
0f113f3e MC |
374 | { |
375 | out[0] = 1; | |
376 | out[1] = 0; | |
377 | out[2] = 0; | |
378 | out[3] = 0; | |
379 | } | |
3e00b4c9 BM |
380 | |
381 | static void felem_assign(felem out, const felem in) | |
0f113f3e MC |
382 | { |
383 | out[0] = in[0]; | |
384 | out[1] = in[1]; | |
385 | out[2] = in[2]; | |
386 | out[3] = in[3]; | |
387 | } | |
3e00b4c9 | 388 | |
04daec86 | 389 | /* Sum two field elements: out += in */ |
3e00b4c9 | 390 | static void felem_sum(felem out, const felem in) |
0f113f3e MC |
391 | { |
392 | out[0] += in[0]; | |
393 | out[1] += in[1]; | |
394 | out[2] += in[2]; | |
395 | out[3] += in[3]; | |
396 | } | |
04daec86 | 397 | |
3e00b4c9 BM |
398 | /* Get negative value: out = -in */ |
399 | /* Assumes in[i] < 2^57 */ | |
400 | static void felem_neg(felem out, const felem in) | |
0f113f3e MC |
401 | { |
402 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); | |
403 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
404 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
405 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
406 | ||
407 | /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ | |
408 | out[0] = two58p2 - in[0]; | |
409 | out[1] = two58m42m2 - in[1]; | |
410 | out[2] = two58m2 - in[2]; | |
411 | out[3] = two58m2 - in[3]; | |
412 | } | |
3e00b4c9 | 413 | |
04daec86 BM |
414 | /* Subtract field elements: out -= in */ |
415 | /* Assumes in[i] < 2^57 */ | |
3e00b4c9 | 416 | static void felem_diff(felem out, const felem in) |
0f113f3e MC |
417 | { |
418 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); | |
419 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
420 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
421 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
422 | ||
423 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
424 | out[0] += two58p2; | |
425 | out[1] += two58m42m2; | |
426 | out[2] += two58m2; | |
427 | out[3] += two58m2; | |
428 | ||
429 | out[0] -= in[0]; | |
430 | out[1] -= in[1]; | |
431 | out[2] -= in[2]; | |
432 | out[3] -= in[3]; | |
433 | } | |
04daec86 | 434 | |
3e00b4c9 | 435 | /* Subtract in unreduced 128-bit mode: out -= in */ |
04daec86 | 436 | /* Assumes in[i] < 2^119 */ |
3e00b4c9 | 437 | static void widefelem_diff(widefelem out, const widefelem in) |
0f113f3e MC |
438 | { |
439 | static const widelimb two120 = ((widelimb) 1) << 120; | |
440 | static const widelimb two120m64 = (((widelimb) 1) << 120) - | |
441 | (((widelimb) 1) << 64); | |
442 | static const widelimb two120m104m64 = (((widelimb) 1) << 120) - | |
443 | (((widelimb) 1) << 104) - (((widelimb) 1) << 64); | |
444 | ||
445 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
446 | out[0] += two120; | |
447 | out[1] += two120m64; | |
448 | out[2] += two120m64; | |
449 | out[3] += two120; | |
450 | out[4] += two120m104m64; | |
451 | out[5] += two120m64; | |
452 | out[6] += two120m64; | |
453 | ||
454 | out[0] -= in[0]; | |
455 | out[1] -= in[1]; | |
456 | out[2] -= in[2]; | |
457 | out[3] -= in[3]; | |
458 | out[4] -= in[4]; | |
459 | out[5] -= in[5]; | |
460 | out[6] -= in[6]; | |
461 | } | |
04daec86 BM |
462 | |
463 | /* Subtract in mixed mode: out128 -= in64 */ | |
464 | /* in[i] < 2^63 */ | |
3e00b4c9 | 465 | static void felem_diff_128_64(widefelem out, const felem in) |
0f113f3e MC |
466 | { |
467 | static const widelimb two64p8 = (((widelimb) 1) << 64) + | |
468 | (((widelimb) 1) << 8); | |
469 | static const widelimb two64m8 = (((widelimb) 1) << 64) - | |
470 | (((widelimb) 1) << 8); | |
471 | static const widelimb two64m48m8 = (((widelimb) 1) << 64) - | |
472 | (((widelimb) 1) << 48) - (((widelimb) 1) << 8); | |
473 | ||
474 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
475 | out[0] += two64p8; | |
476 | out[1] += two64m48m8; | |
477 | out[2] += two64m8; | |
478 | out[3] += two64m8; | |
479 | ||
480 | out[0] -= in[0]; | |
481 | out[1] -= in[1]; | |
482 | out[2] -= in[2]; | |
483 | out[3] -= in[3]; | |
484 | } | |
485 | ||
486 | /* | |
487 | * Multiply a field element by a scalar: out = out * scalar The scalars we | |
488 | * actually use are small, so results fit without overflow | |
489 | */ | |
3e00b4c9 | 490 | static void felem_scalar(felem out, const limb scalar) |
0f113f3e MC |
491 | { |
492 | out[0] *= scalar; | |
493 | out[1] *= scalar; | |
494 | out[2] *= scalar; | |
495 | out[3] *= scalar; | |
496 | } | |
497 | ||
498 | /* | |
499 | * Multiply an unreduced field element by a scalar: out = out * scalar The | |
500 | * scalars we actually use are small, so results fit without overflow | |
501 | */ | |
3e00b4c9 | 502 | static void widefelem_scalar(widefelem out, const widelimb scalar) |
0f113f3e MC |
503 | { |
504 | out[0] *= scalar; | |
505 | out[1] *= scalar; | |
506 | out[2] *= scalar; | |
507 | out[3] *= scalar; | |
508 | out[4] *= scalar; | |
509 | out[5] *= scalar; | |
510 | out[6] *= scalar; | |
511 | } | |
04daec86 BM |
512 | |
513 | /* Square a field element: out = in^2 */ | |
3e00b4c9 | 514 | static void felem_square(widefelem out, const felem in) |
0f113f3e MC |
515 | { |
516 | limb tmp0, tmp1, tmp2; | |
517 | tmp0 = 2 * in[0]; | |
518 | tmp1 = 2 * in[1]; | |
519 | tmp2 = 2 * in[2]; | |
520 | out[0] = ((widelimb) in[0]) * in[0]; | |
521 | out[1] = ((widelimb) in[0]) * tmp1; | |
522 | out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; | |
523 | out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; | |
524 | out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; | |
525 | out[5] = ((widelimb) in[3]) * tmp2; | |
526 | out[6] = ((widelimb) in[3]) * in[3]; | |
527 | } | |
04daec86 BM |
528 | |
529 | /* Multiply two field elements: out = in1 * in2 */ | |
3e00b4c9 | 530 | static void felem_mul(widefelem out, const felem in1, const felem in2) |
0f113f3e MC |
531 | { |
532 | out[0] = ((widelimb) in1[0]) * in2[0]; | |
533 | out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; | |
534 | out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + | |
4eb504ae | 535 | ((widelimb) in1[2]) * in2[0]; |
0f113f3e | 536 | out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + |
4eb504ae | 537 | ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; |
0f113f3e | 538 | out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + |
4eb504ae | 539 | ((widelimb) in1[3]) * in2[1]; |
0f113f3e MC |
540 | out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; |
541 | out[6] = ((widelimb) in1[3]) * in2[3]; | |
542 | } | |
04daec86 | 543 | |
3a83462d MC |
544 | /*- |
545 | * Reduce seven 128-bit coefficients to four 64-bit coefficients. | |
3e00b4c9 BM |
546 | * Requires in[i] < 2^126, |
547 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ | |
548 | static void felem_reduce(felem out, const widefelem in) | |
0f113f3e MC |
549 | { |
550 | static const widelimb two127p15 = (((widelimb) 1) << 127) + | |
551 | (((widelimb) 1) << 15); | |
552 | static const widelimb two127m71 = (((widelimb) 1) << 127) - | |
553 | (((widelimb) 1) << 71); | |
554 | static const widelimb two127m71m55 = (((widelimb) 1) << 127) - | |
555 | (((widelimb) 1) << 71) - (((widelimb) 1) << 55); | |
556 | widelimb output[5]; | |
557 | ||
558 | /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ | |
559 | output[0] = in[0] + two127p15; | |
560 | output[1] = in[1] + two127m71m55; | |
561 | output[2] = in[2] + two127m71; | |
562 | output[3] = in[3]; | |
563 | output[4] = in[4]; | |
564 | ||
565 | /* Eliminate in[4], in[5], in[6] */ | |
566 | output[4] += in[6] >> 16; | |
567 | output[3] += (in[6] & 0xffff) << 40; | |
568 | output[2] -= in[6]; | |
569 | ||
570 | output[3] += in[5] >> 16; | |
571 | output[2] += (in[5] & 0xffff) << 40; | |
572 | output[1] -= in[5]; | |
573 | ||
574 | output[2] += output[4] >> 16; | |
575 | output[1] += (output[4] & 0xffff) << 40; | |
576 | output[0] -= output[4]; | |
577 | ||
578 | /* Carry 2 -> 3 -> 4 */ | |
579 | output[3] += output[2] >> 56; | |
580 | output[2] &= 0x00ffffffffffffff; | |
581 | ||
582 | output[4] = output[3] >> 56; | |
583 | output[3] &= 0x00ffffffffffffff; | |
584 | ||
585 | /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ | |
586 | ||
587 | /* Eliminate output[4] */ | |
588 | output[2] += output[4] >> 16; | |
589 | /* output[2] < 2^56 + 2^56 = 2^57 */ | |
590 | output[1] += (output[4] & 0xffff) << 40; | |
591 | output[0] -= output[4]; | |
592 | ||
593 | /* Carry 0 -> 1 -> 2 -> 3 */ | |
594 | output[1] += output[0] >> 56; | |
595 | out[0] = output[0] & 0x00ffffffffffffff; | |
596 | ||
597 | output[2] += output[1] >> 56; | |
598 | /* output[2] < 2^57 + 2^72 */ | |
599 | out[1] = output[1] & 0x00ffffffffffffff; | |
600 | output[3] += output[2] >> 56; | |
601 | /* output[3] <= 2^56 + 2^16 */ | |
602 | out[2] = output[2] & 0x00ffffffffffffff; | |
603 | ||
50e735f9 MC |
604 | /*- |
605 | * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, | |
606 | * out[3] <= 2^56 + 2^16 (due to final carry), | |
607 | * so out < 2*p | |
608 | */ | |
0f113f3e MC |
609 | out[3] = output[3]; |
610 | } | |
04daec86 | 611 | |
3e00b4c9 | 612 | static void felem_square_reduce(felem out, const felem in) |
0f113f3e MC |
613 | { |
614 | widefelem tmp; | |
615 | felem_square(tmp, in); | |
616 | felem_reduce(out, tmp); | |
617 | } | |
04daec86 | 618 | |
3e00b4c9 | 619 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) |
0f113f3e MC |
620 | { |
621 | widefelem tmp; | |
622 | felem_mul(tmp, in1, in2); | |
623 | felem_reduce(out, tmp); | |
624 | } | |
625 | ||
626 | /* | |
627 | * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always | |
628 | * call felem_reduce first) | |
629 | */ | |
3e00b4c9 | 630 | static void felem_contract(felem out, const felem in) |
0f113f3e MC |
631 | { |
632 | static const int64_t two56 = ((limb) 1) << 56; | |
633 | /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ | |
634 | /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ | |
635 | int64_t tmp[4], a; | |
636 | tmp[0] = in[0]; | |
637 | tmp[1] = in[1]; | |
638 | tmp[2] = in[2]; | |
639 | tmp[3] = in[3]; | |
640 | /* Case 1: a = 1 iff in >= 2^224 */ | |
641 | a = (in[3] >> 56); | |
642 | tmp[0] -= a; | |
643 | tmp[1] += a << 40; | |
644 | tmp[3] &= 0x00ffffffffffffff; | |
645 | /* | |
646 | * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 | |
647 | * and the lower part is non-zero | |
648 | */ | |
649 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | | |
650 | (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); | |
651 | a &= 0x00ffffffffffffff; | |
652 | /* turn a into an all-one mask (if a = 0) or an all-zero mask */ | |
653 | a = (a - 1) >> 63; | |
654 | /* subtract 2^224 - 2^96 + 1 if a is all-one */ | |
655 | tmp[3] &= a ^ 0xffffffffffffffff; | |
656 | tmp[2] &= a ^ 0xffffffffffffffff; | |
657 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; | |
658 | tmp[0] -= 1 & a; | |
659 | ||
660 | /* | |
661 | * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be | |
662 | * non-zero, so we only need one step | |
663 | */ | |
664 | a = tmp[0] >> 63; | |
665 | tmp[0] += two56 & a; | |
666 | tmp[1] -= 1 & a; | |
667 | ||
668 | /* carry 1 -> 2 -> 3 */ | |
669 | tmp[2] += tmp[1] >> 56; | |
670 | tmp[1] &= 0x00ffffffffffffff; | |
671 | ||
672 | tmp[3] += tmp[2] >> 56; | |
673 | tmp[2] &= 0x00ffffffffffffff; | |
674 | ||
675 | /* Now 0 <= out < p */ | |
676 | out[0] = tmp[0]; | |
677 | out[1] = tmp[1]; | |
678 | out[2] = tmp[2]; | |
679 | out[3] = tmp[3]; | |
680 | } | |
681 | ||
682 | /* | |
683 | * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field | |
684 | * elements are reduced to in < 2^225, so we only need to check three cases: | |
685 | * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 | |
686 | */ | |
3e00b4c9 | 687 | static limb felem_is_zero(const felem in) |
0f113f3e MC |
688 | { |
689 | limb zero, two224m96p1, two225m97p2; | |
690 | ||
691 | zero = in[0] | in[1] | in[2] | in[3]; | |
692 | zero = (((int64_t) (zero) - 1) >> 63) & 1; | |
693 | two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) | |
694 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); | |
695 | two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; | |
696 | two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) | |
697 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); | |
698 | two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; | |
699 | return (zero | two224m96p1 | two225m97p2); | |
700 | } | |
04daec86 | 701 | |
c55b786a | 702 | static int felem_is_zero_int(const void *in) |
0f113f3e MC |
703 | { |
704 | return (int)(felem_is_zero(in) & ((limb) 1)); | |
705 | } | |
3e00b4c9 | 706 | |
04daec86 BM |
707 | /* Invert a field element */ |
708 | /* Computation chain copied from djb's code */ | |
3e00b4c9 | 709 | static void felem_inv(felem out, const felem in) |
0f113f3e MC |
710 | { |
711 | felem ftmp, ftmp2, ftmp3, ftmp4; | |
712 | widefelem tmp; | |
713 | unsigned i; | |
714 | ||
715 | felem_square(tmp, in); | |
716 | felem_reduce(ftmp, tmp); /* 2 */ | |
717 | felem_mul(tmp, in, ftmp); | |
718 | felem_reduce(ftmp, tmp); /* 2^2 - 1 */ | |
719 | felem_square(tmp, ftmp); | |
720 | felem_reduce(ftmp, tmp); /* 2^3 - 2 */ | |
721 | felem_mul(tmp, in, ftmp); | |
722 | felem_reduce(ftmp, tmp); /* 2^3 - 1 */ | |
723 | felem_square(tmp, ftmp); | |
724 | felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ | |
725 | felem_square(tmp, ftmp2); | |
726 | felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ | |
727 | felem_square(tmp, ftmp2); | |
728 | felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ | |
729 | felem_mul(tmp, ftmp2, ftmp); | |
730 | felem_reduce(ftmp, tmp); /* 2^6 - 1 */ | |
731 | felem_square(tmp, ftmp); | |
732 | felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ | |
733 | for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ | |
734 | felem_square(tmp, ftmp2); | |
735 | felem_reduce(ftmp2, tmp); | |
736 | } | |
737 | felem_mul(tmp, ftmp2, ftmp); | |
738 | felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ | |
739 | felem_square(tmp, ftmp2); | |
740 | felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ | |
741 | for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ | |
742 | felem_square(tmp, ftmp3); | |
743 | felem_reduce(ftmp3, tmp); | |
744 | } | |
745 | felem_mul(tmp, ftmp3, ftmp2); | |
746 | felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ | |
747 | felem_square(tmp, ftmp2); | |
748 | felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ | |
749 | for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ | |
750 | felem_square(tmp, ftmp3); | |
751 | felem_reduce(ftmp3, tmp); | |
752 | } | |
753 | felem_mul(tmp, ftmp3, ftmp2); | |
754 | felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ | |
755 | felem_square(tmp, ftmp3); | |
756 | felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ | |
757 | for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ | |
758 | felem_square(tmp, ftmp4); | |
759 | felem_reduce(ftmp4, tmp); | |
760 | } | |
761 | felem_mul(tmp, ftmp3, ftmp4); | |
762 | felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ | |
763 | felem_square(tmp, ftmp3); | |
764 | felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ | |
765 | for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ | |
766 | felem_square(tmp, ftmp4); | |
767 | felem_reduce(ftmp4, tmp); | |
768 | } | |
769 | felem_mul(tmp, ftmp2, ftmp4); | |
770 | felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ | |
771 | for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ | |
772 | felem_square(tmp, ftmp2); | |
773 | felem_reduce(ftmp2, tmp); | |
774 | } | |
775 | felem_mul(tmp, ftmp2, ftmp); | |
776 | felem_reduce(ftmp, tmp); /* 2^126 - 1 */ | |
777 | felem_square(tmp, ftmp); | |
778 | felem_reduce(ftmp, tmp); /* 2^127 - 2 */ | |
779 | felem_mul(tmp, ftmp, in); | |
780 | felem_reduce(ftmp, tmp); /* 2^127 - 1 */ | |
781 | for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ | |
782 | felem_square(tmp, ftmp); | |
783 | felem_reduce(ftmp, tmp); | |
784 | } | |
785 | felem_mul(tmp, ftmp, ftmp3); | |
786 | felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ | |
787 | } | |
788 | ||
789 | /* | |
790 | * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy | |
791 | * out to itself. | |
792 | */ | |
793 | static void copy_conditional(felem out, const felem in, limb icopy) | |
794 | { | |
795 | unsigned i; | |
796 | /* | |
797 | * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one | |
798 | */ | |
799 | const limb copy = -icopy; | |
800 | for (i = 0; i < 4; ++i) { | |
801 | const limb tmp = copy & (in[i] ^ out[i]); | |
802 | out[i] ^= tmp; | |
803 | } | |
804 | } | |
04daec86 | 805 | |
04daec86 | 806 | /******************************************************************************/ |
3a83462d | 807 | /*- |
0f113f3e | 808 | * ELLIPTIC CURVE POINT OPERATIONS |
04daec86 BM |
809 | * |
810 | * Points are represented in Jacobian projective coordinates: | |
811 | * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), | |
812 | * or to the point at infinity if Z == 0. | |
813 | * | |
814 | */ | |
815 | ||
1d97c843 TH |
816 | /*- |
817 | * Double an elliptic curve point: | |
04daec86 BM |
818 | * (X', Y', Z') = 2 * (X, Y, Z), where |
819 | * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 | |
820 | * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 | |
821 | * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z | |
822 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, | |
0f113f3e | 823 | * while x_out == y_in is not (maybe this works, but it's not tested). |
1d97c843 | 824 | */ |
04daec86 | 825 | static void |
3e00b4c9 BM |
826 | point_double(felem x_out, felem y_out, felem z_out, |
827 | const felem x_in, const felem y_in, const felem z_in) | |
0f113f3e MC |
828 | { |
829 | widefelem tmp, tmp2; | |
830 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
831 | ||
832 | felem_assign(ftmp, x_in); | |
833 | felem_assign(ftmp2, x_in); | |
834 | ||
835 | /* delta = z^2 */ | |
836 | felem_square(tmp, z_in); | |
837 | felem_reduce(delta, tmp); | |
838 | ||
839 | /* gamma = y^2 */ | |
840 | felem_square(tmp, y_in); | |
841 | felem_reduce(gamma, tmp); | |
842 | ||
843 | /* beta = x*gamma */ | |
844 | felem_mul(tmp, x_in, gamma); | |
845 | felem_reduce(beta, tmp); | |
846 | ||
847 | /* alpha = 3*(x-delta)*(x+delta) */ | |
848 | felem_diff(ftmp, delta); | |
849 | /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ | |
850 | felem_sum(ftmp2, delta); | |
851 | /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ | |
852 | felem_scalar(ftmp2, 3); | |
853 | /* ftmp2[i] < 3 * 2^58 < 2^60 */ | |
854 | felem_mul(tmp, ftmp, ftmp2); | |
855 | /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ | |
856 | felem_reduce(alpha, tmp); | |
857 | ||
858 | /* x' = alpha^2 - 8*beta */ | |
859 | felem_square(tmp, alpha); | |
860 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
861 | felem_assign(ftmp, beta); | |
862 | felem_scalar(ftmp, 8); | |
863 | /* ftmp[i] < 8 * 2^57 = 2^60 */ | |
864 | felem_diff_128_64(tmp, ftmp); | |
865 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
866 | felem_reduce(x_out, tmp); | |
867 | ||
868 | /* z' = (y + z)^2 - gamma - delta */ | |
869 | felem_sum(delta, gamma); | |
870 | /* delta[i] < 2^57 + 2^57 = 2^58 */ | |
871 | felem_assign(ftmp, y_in); | |
872 | felem_sum(ftmp, z_in); | |
873 | /* ftmp[i] < 2^57 + 2^57 = 2^58 */ | |
874 | felem_square(tmp, ftmp); | |
875 | /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ | |
876 | felem_diff_128_64(tmp, delta); | |
877 | /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ | |
878 | felem_reduce(z_out, tmp); | |
879 | ||
880 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
881 | felem_scalar(beta, 4); | |
882 | /* beta[i] < 4 * 2^57 = 2^59 */ | |
883 | felem_diff(beta, x_out); | |
884 | /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ | |
885 | felem_mul(tmp, alpha, beta); | |
886 | /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ | |
887 | felem_square(tmp2, gamma); | |
888 | /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
889 | widefelem_scalar(tmp2, 8); | |
890 | /* tmp2[i] < 8 * 2^116 = 2^119 */ | |
891 | widefelem_diff(tmp, tmp2); | |
892 | /* tmp[i] < 2^119 + 2^120 < 2^121 */ | |
893 | felem_reduce(y_out, tmp); | |
894 | } | |
04daec86 | 895 | |
1d97c843 TH |
896 | /*- |
897 | * Add two elliptic curve points: | |
04daec86 BM |
898 | * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where |
899 | * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - | |
900 | * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 | |
901 | * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - | |
902 | * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 | |
3e00b4c9 BM |
903 | * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
904 | * | |
905 | * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. | |
906 | */ | |
04daec86 | 907 | |
0f113f3e MC |
908 | /* |
909 | * This function is not entirely constant-time: it includes a branch for | |
910 | * checking whether the two input points are equal, (while not equal to the | |
911 | * point at infinity). This case never happens during single point | |
912 | * multiplication, so there is no timing leak for ECDH or ECDSA signing. | |
913 | */ | |
3e00b4c9 | 914 | static void point_add(felem x3, felem y3, felem z3, |
0f113f3e MC |
915 | const felem x1, const felem y1, const felem z1, |
916 | const int mixed, const felem x2, const felem y2, | |
917 | const felem z2) | |
918 | { | |
919 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; | |
920 | widefelem tmp, tmp2; | |
921 | limb z1_is_zero, z2_is_zero, x_equal, y_equal; | |
922 | ||
923 | if (!mixed) { | |
924 | /* ftmp2 = z2^2 */ | |
925 | felem_square(tmp, z2); | |
926 | felem_reduce(ftmp2, tmp); | |
927 | ||
928 | /* ftmp4 = z2^3 */ | |
929 | felem_mul(tmp, ftmp2, z2); | |
930 | felem_reduce(ftmp4, tmp); | |
931 | ||
932 | /* ftmp4 = z2^3*y1 */ | |
933 | felem_mul(tmp2, ftmp4, y1); | |
934 | felem_reduce(ftmp4, tmp2); | |
935 | ||
936 | /* ftmp2 = z2^2*x1 */ | |
937 | felem_mul(tmp2, ftmp2, x1); | |
938 | felem_reduce(ftmp2, tmp2); | |
939 | } else { | |
940 | /* | |
941 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) | |
942 | */ | |
943 | ||
944 | /* ftmp4 = z2^3*y1 */ | |
945 | felem_assign(ftmp4, y1); | |
946 | ||
947 | /* ftmp2 = z2^2*x1 */ | |
948 | felem_assign(ftmp2, x1); | |
949 | } | |
950 | ||
951 | /* ftmp = z1^2 */ | |
952 | felem_square(tmp, z1); | |
953 | felem_reduce(ftmp, tmp); | |
954 | ||
955 | /* ftmp3 = z1^3 */ | |
956 | felem_mul(tmp, ftmp, z1); | |
957 | felem_reduce(ftmp3, tmp); | |
958 | ||
959 | /* tmp = z1^3*y2 */ | |
960 | felem_mul(tmp, ftmp3, y2); | |
961 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
962 | ||
963 | /* ftmp3 = z1^3*y2 - z2^3*y1 */ | |
964 | felem_diff_128_64(tmp, ftmp4); | |
965 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
966 | felem_reduce(ftmp3, tmp); | |
967 | ||
968 | /* tmp = z1^2*x2 */ | |
969 | felem_mul(tmp, ftmp, x2); | |
970 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
971 | ||
972 | /* ftmp = z1^2*x2 - z2^2*x1 */ | |
973 | felem_diff_128_64(tmp, ftmp2); | |
974 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
975 | felem_reduce(ftmp, tmp); | |
976 | ||
977 | /* | |
978 | * the formulae are incorrect if the points are equal so we check for | |
979 | * this and do doubling if this happens | |
980 | */ | |
981 | x_equal = felem_is_zero(ftmp); | |
982 | y_equal = felem_is_zero(ftmp3); | |
983 | z1_is_zero = felem_is_zero(z1); | |
984 | z2_is_zero = felem_is_zero(z2); | |
985 | /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ | |
986 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { | |
987 | point_double(x3, y3, z3, x1, y1, z1); | |
988 | return; | |
989 | } | |
990 | ||
991 | /* ftmp5 = z1*z2 */ | |
992 | if (!mixed) { | |
993 | felem_mul(tmp, z1, z2); | |
994 | felem_reduce(ftmp5, tmp); | |
995 | } else { | |
996 | /* special case z2 = 0 is handled later */ | |
997 | felem_assign(ftmp5, z1); | |
998 | } | |
999 | ||
1000 | /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ | |
1001 | felem_mul(tmp, ftmp, ftmp5); | |
1002 | felem_reduce(z_out, tmp); | |
1003 | ||
1004 | /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ | |
1005 | felem_assign(ftmp5, ftmp); | |
1006 | felem_square(tmp, ftmp); | |
1007 | felem_reduce(ftmp, tmp); | |
1008 | ||
1009 | /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ | |
1010 | felem_mul(tmp, ftmp, ftmp5); | |
1011 | felem_reduce(ftmp5, tmp); | |
1012 | ||
1013 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
1014 | felem_mul(tmp, ftmp2, ftmp); | |
1015 | felem_reduce(ftmp2, tmp); | |
1016 | ||
1017 | /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ | |
1018 | felem_mul(tmp, ftmp4, ftmp5); | |
1019 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
1020 | ||
1021 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ | |
1022 | felem_square(tmp2, ftmp3); | |
1023 | /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ | |
1024 | ||
1025 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ | |
1026 | felem_diff_128_64(tmp2, ftmp5); | |
1027 | /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
1028 | ||
1029 | /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
1030 | felem_assign(ftmp5, ftmp2); | |
1031 | felem_scalar(ftmp5, 2); | |
1032 | /* ftmp5[i] < 2 * 2^57 = 2^58 */ | |
1033 | ||
50e735f9 MC |
1034 | /*- |
1035 | * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - | |
1036 | * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 | |
1037 | */ | |
0f113f3e MC |
1038 | felem_diff_128_64(tmp2, ftmp5); |
1039 | /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ | |
1040 | felem_reduce(x_out, tmp2); | |
1041 | ||
1042 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ | |
1043 | felem_diff(ftmp2, x_out); | |
1044 | /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ | |
1045 | ||
1046 | /* | |
1047 | * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) | |
1048 | */ | |
1049 | felem_mul(tmp2, ftmp3, ftmp2); | |
1050 | /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ | |
1051 | ||
50e735f9 MC |
1052 | /*- |
1053 | * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - | |
1054 | * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 | |
1055 | */ | |
0f113f3e MC |
1056 | widefelem_diff(tmp2, tmp); |
1057 | /* tmp2[i] < 2^118 + 2^120 < 2^121 */ | |
1058 | felem_reduce(y_out, tmp2); | |
1059 | ||
1060 | /* | |
1061 | * the result (x_out, y_out, z_out) is incorrect if one of the inputs is | |
1062 | * the point at infinity, so we need to check for this separately | |
1063 | */ | |
1064 | ||
1065 | /* | |
1066 | * if point 1 is at infinity, copy point 2 to output, and vice versa | |
1067 | */ | |
1068 | copy_conditional(x_out, x2, z1_is_zero); | |
1069 | copy_conditional(x_out, x1, z2_is_zero); | |
1070 | copy_conditional(y_out, y2, z1_is_zero); | |
1071 | copy_conditional(y_out, y1, z2_is_zero); | |
1072 | copy_conditional(z_out, z2, z1_is_zero); | |
1073 | copy_conditional(z_out, z1, z2_is_zero); | |
1074 | felem_assign(x3, x_out); | |
1075 | felem_assign(y3, y_out); | |
1076 | felem_assign(z3, z_out); | |
1077 | } | |
04daec86 | 1078 | |
dbd87ffc MC |
1079 | /* |
1080 | * select_point selects the |idx|th point from a precomputation table and | |
1081 | * copies it to out. | |
1082 | * The pre_comp array argument should be size of |size| argument | |
1083 | */ | |
0f113f3e MC |
1084 | static void select_point(const u64 idx, unsigned int size, |
1085 | const felem pre_comp[][3], felem out[3]) | |
1086 | { | |
1087 | unsigned i, j; | |
1088 | limb *outlimbs = &out[0][0]; | |
0f113f3e | 1089 | |
88f4c6f3 | 1090 | memset(out, 0, sizeof(*out) * 3); |
0f113f3e MC |
1091 | for (i = 0; i < size; i++) { |
1092 | const limb *inlimbs = &pre_comp[i][0][0]; | |
1093 | u64 mask = i ^ idx; | |
1094 | mask |= mask >> 4; | |
1095 | mask |= mask >> 2; | |
1096 | mask |= mask >> 1; | |
1097 | mask &= 1; | |
1098 | mask--; | |
1099 | for (j = 0; j < 4 * 3; j++) | |
1100 | outlimbs[j] |= inlimbs[j] & mask; | |
1101 | } | |
1102 | } | |
3e00b4c9 BM |
1103 | |
1104 | /* get_bit returns the |i|th bit in |in| */ | |
1105 | static char get_bit(const felem_bytearray in, unsigned i) | |
0f113f3e MC |
1106 | { |
1107 | if (i >= 224) | |
1108 | return 0; | |
1109 | return (in[i >> 3] >> (i & 7)) & 1; | |
1110 | } | |
1111 | ||
1112 | /* | |
1113 | * Interleaved point multiplication using precomputed point multiples: The | |
1114 | * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars | |
1115 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the | |
1116 | * generator, using certain (large) precomputed multiples in g_pre_comp. | |
1117 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out | |
1118 | */ | |
3e00b4c9 | 1119 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
0f113f3e MC |
1120 | const felem_bytearray scalars[], |
1121 | const unsigned num_points, const u8 *g_scalar, | |
1122 | const int mixed, const felem pre_comp[][17][3], | |
1123 | const felem g_pre_comp[2][16][3]) | |
1124 | { | |
1125 | int i, skip; | |
1126 | unsigned num; | |
1127 | unsigned gen_mul = (g_scalar != NULL); | |
1128 | felem nq[3], tmp[4]; | |
1129 | u64 bits; | |
1130 | u8 sign, digit; | |
1131 | ||
1132 | /* set nq to the point at infinity */ | |
16f8d4eb | 1133 | memset(nq, 0, sizeof(nq)); |
0f113f3e MC |
1134 | |
1135 | /* | |
1136 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples | |
1137 | * of the generator (two in each of the last 28 rounds) and additions of | |
1138 | * other points multiples (every 5th round). | |
1139 | */ | |
1140 | skip = 1; /* save two point operations in the first | |
1141 | * round */ | |
1142 | for (i = (num_points ? 220 : 27); i >= 0; --i) { | |
1143 | /* double */ | |
1144 | if (!skip) | |
1145 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1146 | ||
1147 | /* add multiples of the generator */ | |
1148 | if (gen_mul && (i <= 27)) { | |
1149 | /* first, look 28 bits upwards */ | |
1150 | bits = get_bit(g_scalar, i + 196) << 3; | |
1151 | bits |= get_bit(g_scalar, i + 140) << 2; | |
1152 | bits |= get_bit(g_scalar, i + 84) << 1; | |
1153 | bits |= get_bit(g_scalar, i + 28); | |
1154 | /* select the point to add, in constant time */ | |
1155 | select_point(bits, 16, g_pre_comp[1], tmp); | |
1156 | ||
1157 | if (!skip) { | |
1158 | /* value 1 below is argument for "mixed" */ | |
1159 | point_add(nq[0], nq[1], nq[2], | |
1160 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1161 | } else { | |
1162 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1163 | skip = 0; | |
1164 | } | |
1165 | ||
1166 | /* second, look at the current position */ | |
1167 | bits = get_bit(g_scalar, i + 168) << 3; | |
1168 | bits |= get_bit(g_scalar, i + 112) << 2; | |
1169 | bits |= get_bit(g_scalar, i + 56) << 1; | |
1170 | bits |= get_bit(g_scalar, i); | |
1171 | /* select the point to add, in constant time */ | |
1172 | select_point(bits, 16, g_pre_comp[0], tmp); | |
1173 | point_add(nq[0], nq[1], nq[2], | |
1174 | nq[0], nq[1], nq[2], | |
1175 | 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); | |
1176 | } | |
1177 | ||
1178 | /* do other additions every 5 doublings */ | |
1179 | if (num_points && (i % 5 == 0)) { | |
1180 | /* loop over all scalars */ | |
1181 | for (num = 0; num < num_points; ++num) { | |
1182 | bits = get_bit(scalars[num], i + 4) << 5; | |
1183 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1184 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1185 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1186 | bits |= get_bit(scalars[num], i) << 1; | |
1187 | bits |= get_bit(scalars[num], i - 1); | |
1188 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1189 | ||
1190 | /* select the point to add or subtract */ | |
1191 | select_point(digit, 17, pre_comp[num], tmp); | |
1192 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative | |
1193 | * point */ | |
1194 | copy_conditional(tmp[1], tmp[3], sign); | |
1195 | ||
1196 | if (!skip) { | |
1197 | point_add(nq[0], nq[1], nq[2], | |
1198 | nq[0], nq[1], nq[2], | |
1199 | mixed, tmp[0], tmp[1], tmp[2]); | |
1200 | } else { | |
1201 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1202 | skip = 0; | |
1203 | } | |
1204 | } | |
1205 | } | |
1206 | } | |
1207 | felem_assign(x_out, nq[0]); | |
1208 | felem_assign(y_out, nq[1]); | |
1209 | felem_assign(z_out, nq[2]); | |
1210 | } | |
04daec86 BM |
1211 | |
1212 | /******************************************************************************/ | |
0f113f3e MC |
1213 | /* |
1214 | * FUNCTIONS TO MANAGE PRECOMPUTATION | |
04daec86 BM |
1215 | */ |
1216 | ||
1217 | static NISTP224_PRE_COMP *nistp224_pre_comp_new() | |
0f113f3e | 1218 | { |
b51bce94 RS |
1219 | NISTP224_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
1220 | ||
0f113f3e MC |
1221 | if (!ret) { |
1222 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1223 | return ret; | |
1224 | } | |
9b398ef2 | 1225 | |
0f113f3e | 1226 | ret->references = 1; |
9b398ef2 AG |
1227 | |
1228 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1229 | if (ret->lock == NULL) { | |
1230 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1231 | OPENSSL_free(ret); | |
1232 | return NULL; | |
1233 | } | |
0f113f3e MC |
1234 | return ret; |
1235 | } | |
04daec86 | 1236 | |
3aef36ff | 1237 | NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *p) |
0f113f3e | 1238 | { |
9b398ef2 | 1239 | int i; |
3aef36ff | 1240 | if (p != NULL) |
2f545ae4 | 1241 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
3aef36ff | 1242 | return p; |
0f113f3e | 1243 | } |
04daec86 | 1244 | |
3aef36ff | 1245 | void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *p) |
0f113f3e | 1246 | { |
9b398ef2 AG |
1247 | int i; |
1248 | ||
1249 | if (p == NULL) | |
1250 | return; | |
1251 | ||
2f545ae4 | 1252 | CRYPTO_DOWN_REF(&p->references, &i, p->lock); |
9b398ef2 AG |
1253 | REF_PRINT_COUNT("EC_nistp224", x); |
1254 | if (i > 0) | |
0f113f3e | 1255 | return; |
9b398ef2 AG |
1256 | REF_ASSERT_ISNT(i < 0); |
1257 | ||
1258 | CRYPTO_THREAD_lock_free(p->lock); | |
3aef36ff | 1259 | OPENSSL_free(p); |
0f113f3e | 1260 | } |
04daec86 BM |
1261 | |
1262 | /******************************************************************************/ | |
0f113f3e MC |
1263 | /* |
1264 | * OPENSSL EC_METHOD FUNCTIONS | |
04daec86 BM |
1265 | */ |
1266 | ||
1267 | int ec_GFp_nistp224_group_init(EC_GROUP *group) | |
0f113f3e MC |
1268 | { |
1269 | int ret; | |
1270 | ret = ec_GFp_simple_group_init(group); | |
1271 | group->a_is_minus3 = 1; | |
1272 | return ret; | |
1273 | } | |
04daec86 BM |
1274 | |
1275 | int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
0f113f3e MC |
1276 | const BIGNUM *a, const BIGNUM *b, |
1277 | BN_CTX *ctx) | |
1278 | { | |
1279 | int ret = 0; | |
1280 | BN_CTX *new_ctx = NULL; | |
1281 | BIGNUM *curve_p, *curve_a, *curve_b; | |
1282 | ||
1283 | if (ctx == NULL) | |
1284 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1285 | return 0; | |
1286 | BN_CTX_start(ctx); | |
edea42c6 PY |
1287 | curve_p = BN_CTX_get(ctx); |
1288 | curve_a = BN_CTX_get(ctx); | |
1289 | curve_b = BN_CTX_get(ctx); | |
1290 | if (curve_b == NULL) | |
0f113f3e MC |
1291 | goto err; |
1292 | BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); | |
1293 | BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1294 | BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); | |
1295 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { | |
1296 | ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, | |
1297 | EC_R_WRONG_CURVE_PARAMETERS); | |
1298 | goto err; | |
1299 | } | |
1300 | group->field_mod_func = BN_nist_mod_224; | |
1301 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1302 | err: | |
1303 | BN_CTX_end(ctx); | |
23a1d5e9 | 1304 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1305 | return ret; |
1306 | } | |
1307 | ||
1308 | /* | |
1309 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = | |
1310 | * (X/Z^2, Y/Z^3) | |
1311 | */ | |
04daec86 | 1312 | int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, |
0f113f3e MC |
1313 | const EC_POINT *point, |
1314 | BIGNUM *x, BIGNUM *y, | |
1315 | BN_CTX *ctx) | |
1316 | { | |
1317 | felem z1, z2, x_in, y_in, x_out, y_out; | |
1318 | widefelem tmp; | |
1319 | ||
1320 | if (EC_POINT_is_at_infinity(group, point)) { | |
1321 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1322 | EC_R_POINT_AT_INFINITY); | |
1323 | return 0; | |
1324 | } | |
ace8f546 AP |
1325 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1326 | (!BN_to_felem(z1, point->Z))) | |
0f113f3e MC |
1327 | return 0; |
1328 | felem_inv(z2, z1); | |
1329 | felem_square(tmp, z2); | |
1330 | felem_reduce(z1, tmp); | |
1331 | felem_mul(tmp, x_in, z1); | |
1332 | felem_reduce(x_in, tmp); | |
1333 | felem_contract(x_out, x_in); | |
1334 | if (x != NULL) { | |
1335 | if (!felem_to_BN(x, x_out)) { | |
1336 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1337 | ERR_R_BN_LIB); | |
1338 | return 0; | |
1339 | } | |
1340 | } | |
1341 | felem_mul(tmp, z1, z2); | |
1342 | felem_reduce(z1, tmp); | |
1343 | felem_mul(tmp, y_in, z1); | |
1344 | felem_reduce(y_in, tmp); | |
1345 | felem_contract(y_out, y_in); | |
1346 | if (y != NULL) { | |
1347 | if (!felem_to_BN(y, y_out)) { | |
1348 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1349 | ERR_R_BN_LIB); | |
1350 | return 0; | |
1351 | } | |
1352 | } | |
1353 | return 1; | |
1354 | } | |
1355 | ||
1356 | static void make_points_affine(size_t num, felem points[ /* num */ ][3], | |
1357 | felem tmp_felems[ /* num+1 */ ]) | |
1358 | { | |
1359 | /* | |
1360 | * Runs in constant time, unless an input is the point at infinity (which | |
1361 | * normally shouldn't happen). | |
1362 | */ | |
1363 | ec_GFp_nistp_points_make_affine_internal(num, | |
1364 | points, | |
1365 | sizeof(felem), | |
1366 | tmp_felems, | |
1367 | (void (*)(void *))felem_one, | |
0f113f3e MC |
1368 | felem_is_zero_int, |
1369 | (void (*)(void *, const void *)) | |
1370 | felem_assign, | |
1371 | (void (*)(void *, const void *)) | |
1372 | felem_square_reduce, (void (*) | |
1373 | (void *, | |
1374 | const void | |
1375 | *, | |
1376 | const void | |
1377 | *)) | |
1378 | felem_mul_reduce, | |
1379 | (void (*)(void *, const void *)) | |
1380 | felem_inv, | |
1381 | (void (*)(void *, const void *)) | |
1382 | felem_contract); | |
1383 | } | |
1384 | ||
1385 | /* | |
1386 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL | |
1387 | * values Result is stored in r (r can equal one of the inputs). | |
1388 | */ | |
04daec86 | 1389 | int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, |
0f113f3e MC |
1390 | const BIGNUM *scalar, size_t num, |
1391 | const EC_POINT *points[], | |
1392 | const BIGNUM *scalars[], BN_CTX *ctx) | |
1393 | { | |
1394 | int ret = 0; | |
1395 | int j; | |
1396 | unsigned i; | |
1397 | int mixed = 0; | |
1398 | BN_CTX *new_ctx = NULL; | |
1399 | BIGNUM *x, *y, *z, *tmp_scalar; | |
1400 | felem_bytearray g_secret; | |
1401 | felem_bytearray *secrets = NULL; | |
16f8d4eb | 1402 | felem (*pre_comp)[17][3] = NULL; |
0f113f3e MC |
1403 | felem *tmp_felems = NULL; |
1404 | felem_bytearray tmp; | |
1405 | unsigned num_bytes; | |
1406 | int have_pre_comp = 0; | |
1407 | size_t num_points = num; | |
1408 | felem x_in, y_in, z_in, x_out, y_out, z_out; | |
1409 | NISTP224_PRE_COMP *pre = NULL; | |
1410 | const felem(*g_pre_comp)[16][3] = NULL; | |
1411 | EC_POINT *generator = NULL; | |
1412 | const EC_POINT *p = NULL; | |
1413 | const BIGNUM *p_scalar = NULL; | |
1414 | ||
1415 | if (ctx == NULL) | |
1416 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1417 | return 0; | |
1418 | BN_CTX_start(ctx); | |
edea42c6 PY |
1419 | x = BN_CTX_get(ctx); |
1420 | y = BN_CTX_get(ctx); | |
1421 | z = BN_CTX_get(ctx); | |
1422 | tmp_scalar = BN_CTX_get(ctx); | |
1423 | if (tmp_scalar == NULL) | |
0f113f3e MC |
1424 | goto err; |
1425 | ||
1426 | if (scalar != NULL) { | |
3aef36ff | 1427 | pre = group->pre_comp.nistp224; |
0f113f3e MC |
1428 | if (pre) |
1429 | /* we have precomputation, try to use it */ | |
1430 | g_pre_comp = (const felem(*)[16][3])pre->g_pre_comp; | |
1431 | else | |
1432 | /* try to use the standard precomputation */ | |
1433 | g_pre_comp = &gmul[0]; | |
1434 | generator = EC_POINT_new(group); | |
1435 | if (generator == NULL) | |
1436 | goto err; | |
1437 | /* get the generator from precomputation */ | |
1438 | if (!felem_to_BN(x, g_pre_comp[0][1][0]) || | |
1439 | !felem_to_BN(y, g_pre_comp[0][1][1]) || | |
1440 | !felem_to_BN(z, g_pre_comp[0][1][2])) { | |
1441 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1442 | goto err; | |
1443 | } | |
1444 | if (!EC_POINT_set_Jprojective_coordinates_GFp(group, | |
1445 | generator, x, y, z, | |
1446 | ctx)) | |
1447 | goto err; | |
1448 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
1449 | /* precomputation matches generator */ | |
1450 | have_pre_comp = 1; | |
1451 | else | |
1452 | /* | |
1453 | * we don't have valid precomputation: treat the generator as a | |
1454 | * random point | |
1455 | */ | |
1456 | num_points = num_points + 1; | |
1457 | } | |
1458 | ||
1459 | if (num_points > 0) { | |
1460 | if (num_points >= 3) { | |
1461 | /* | |
1462 | * unless we precompute multiples for just one or two points, | |
1463 | * converting those into affine form is time well spent | |
1464 | */ | |
1465 | mixed = 1; | |
1466 | } | |
b51bce94 RS |
1467 | secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); |
1468 | pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
1469 | if (mixed) |
1470 | tmp_felems = | |
16f8d4eb | 1471 | OPENSSL_malloc(sizeof(felem) * (num_points * 17 + 1)); |
0f113f3e MC |
1472 | if ((secrets == NULL) || (pre_comp == NULL) |
1473 | || (mixed && (tmp_felems == NULL))) { | |
1474 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
1475 | goto err; | |
1476 | } | |
1477 | ||
1478 | /* | |
1479 | * we treat NULL scalars as 0, and NULL points as points at infinity, | |
1480 | * i.e., they contribute nothing to the linear combination | |
1481 | */ | |
0f113f3e MC |
1482 | for (i = 0; i < num_points; ++i) { |
1483 | if (i == num) | |
1484 | /* the generator */ | |
1485 | { | |
1486 | p = EC_GROUP_get0_generator(group); | |
1487 | p_scalar = scalar; | |
1488 | } else | |
1489 | /* the i^th point */ | |
1490 | { | |
1491 | p = points[i]; | |
1492 | p_scalar = scalars[i]; | |
1493 | } | |
1494 | if ((p_scalar != NULL) && (p != NULL)) { | |
1495 | /* reduce scalar to 0 <= scalar < 2^224 */ | |
1496 | if ((BN_num_bits(p_scalar) > 224) | |
1497 | || (BN_is_negative(p_scalar))) { | |
1498 | /* | |
1499 | * this is an unusual input, and we don't guarantee | |
1500 | * constant-timeness | |
1501 | */ | |
ace8f546 | 1502 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
0f113f3e MC |
1503 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1504 | goto err; | |
1505 | } | |
1506 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1507 | } else | |
1508 | num_bytes = BN_bn2bin(p_scalar, tmp); | |
1509 | flip_endian(secrets[i], tmp, num_bytes); | |
1510 | /* precompute multiples */ | |
ace8f546 AP |
1511 | if ((!BN_to_felem(x_out, p->X)) || |
1512 | (!BN_to_felem(y_out, p->Y)) || | |
1513 | (!BN_to_felem(z_out, p->Z))) | |
0f113f3e MC |
1514 | goto err; |
1515 | felem_assign(pre_comp[i][1][0], x_out); | |
1516 | felem_assign(pre_comp[i][1][1], y_out); | |
1517 | felem_assign(pre_comp[i][1][2], z_out); | |
1518 | for (j = 2; j <= 16; ++j) { | |
1519 | if (j & 1) { | |
1520 | point_add(pre_comp[i][j][0], pre_comp[i][j][1], | |
1521 | pre_comp[i][j][2], pre_comp[i][1][0], | |
1522 | pre_comp[i][1][1], pre_comp[i][1][2], 0, | |
1523 | pre_comp[i][j - 1][0], | |
1524 | pre_comp[i][j - 1][1], | |
1525 | pre_comp[i][j - 1][2]); | |
1526 | } else { | |
1527 | point_double(pre_comp[i][j][0], pre_comp[i][j][1], | |
1528 | pre_comp[i][j][2], pre_comp[i][j / 2][0], | |
1529 | pre_comp[i][j / 2][1], | |
1530 | pre_comp[i][j / 2][2]); | |
1531 | } | |
1532 | } | |
1533 | } | |
1534 | } | |
1535 | if (mixed) | |
1536 | make_points_affine(num_points * 17, pre_comp[0], tmp_felems); | |
1537 | } | |
1538 | ||
1539 | /* the scalar for the generator */ | |
1540 | if ((scalar != NULL) && (have_pre_comp)) { | |
16f8d4eb | 1541 | memset(g_secret, 0, sizeof(g_secret)); |
0f113f3e MC |
1542 | /* reduce scalar to 0 <= scalar < 2^224 */ |
1543 | if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { | |
1544 | /* | |
1545 | * this is an unusual input, and we don't guarantee | |
1546 | * constant-timeness | |
1547 | */ | |
ace8f546 | 1548 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
0f113f3e MC |
1549 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1550 | goto err; | |
1551 | } | |
1552 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1553 | } else | |
1554 | num_bytes = BN_bn2bin(scalar, tmp); | |
1555 | flip_endian(g_secret, tmp, num_bytes); | |
1556 | /* do the multiplication with generator precomputation */ | |
1557 | batch_mul(x_out, y_out, z_out, | |
1558 | (const felem_bytearray(*))secrets, num_points, | |
1559 | g_secret, | |
1560 | mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); | |
1561 | } else | |
1562 | /* do the multiplication without generator precomputation */ | |
1563 | batch_mul(x_out, y_out, z_out, | |
1564 | (const felem_bytearray(*))secrets, num_points, | |
1565 | NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); | |
1566 | /* reduce the output to its unique minimal representation */ | |
1567 | felem_contract(x_in, x_out); | |
1568 | felem_contract(y_in, y_out); | |
1569 | felem_contract(z_in, z_out); | |
1570 | if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || | |
1571 | (!felem_to_BN(z, z_in))) { | |
1572 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1573 | goto err; | |
1574 | } | |
1575 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); | |
1576 | ||
1577 | err: | |
1578 | BN_CTX_end(ctx); | |
8fdc3734 | 1579 | EC_POINT_free(generator); |
23a1d5e9 | 1580 | BN_CTX_free(new_ctx); |
b548a1f1 RS |
1581 | OPENSSL_free(secrets); |
1582 | OPENSSL_free(pre_comp); | |
1583 | OPENSSL_free(tmp_felems); | |
0f113f3e MC |
1584 | return ret; |
1585 | } | |
04daec86 BM |
1586 | |
1587 | int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
0f113f3e MC |
1588 | { |
1589 | int ret = 0; | |
1590 | NISTP224_PRE_COMP *pre = NULL; | |
1591 | int i, j; | |
1592 | BN_CTX *new_ctx = NULL; | |
1593 | BIGNUM *x, *y; | |
1594 | EC_POINT *generator = NULL; | |
1595 | felem tmp_felems[32]; | |
1596 | ||
1597 | /* throw away old precomputation */ | |
2c52ac9b | 1598 | EC_pre_comp_free(group); |
0f113f3e MC |
1599 | if (ctx == NULL) |
1600 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1601 | return 0; | |
1602 | BN_CTX_start(ctx); | |
edea42c6 PY |
1603 | x = BN_CTX_get(ctx); |
1604 | y = BN_CTX_get(ctx); | |
1605 | if (y == NULL) | |
0f113f3e MC |
1606 | goto err; |
1607 | /* get the generator */ | |
1608 | if (group->generator == NULL) | |
1609 | goto err; | |
1610 | generator = EC_POINT_new(group); | |
1611 | if (generator == NULL) | |
1612 | goto err; | |
1613 | BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); | |
1614 | BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); | |
1615 | if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) | |
1616 | goto err; | |
1617 | if ((pre = nistp224_pre_comp_new()) == NULL) | |
1618 | goto err; | |
1619 | /* | |
1620 | * if the generator is the standard one, use built-in precomputation | |
1621 | */ | |
1622 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { | |
1623 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
615614c8 | 1624 | goto done; |
0f113f3e | 1625 | } |
ace8f546 AP |
1626 | if ((!BN_to_felem(pre->g_pre_comp[0][1][0], group->generator->X)) || |
1627 | (!BN_to_felem(pre->g_pre_comp[0][1][1], group->generator->Y)) || | |
1628 | (!BN_to_felem(pre->g_pre_comp[0][1][2], group->generator->Z))) | |
0f113f3e MC |
1629 | goto err; |
1630 | /* | |
1631 | * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, | |
1632 | * 2^140*G, 2^196*G for the second one | |
1633 | */ | |
1634 | for (i = 1; i <= 8; i <<= 1) { | |
1635 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
1636 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], | |
1637 | pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); | |
1638 | for (j = 0; j < 27; ++j) { | |
1639 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
1640 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], | |
1641 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1642 | } | |
1643 | if (i == 8) | |
1644 | break; | |
1645 | point_double(pre->g_pre_comp[0][2 * i][0], | |
1646 | pre->g_pre_comp[0][2 * i][1], | |
1647 | pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], | |
1648 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1649 | for (j = 0; j < 27; ++j) { | |
1650 | point_double(pre->g_pre_comp[0][2 * i][0], | |
1651 | pre->g_pre_comp[0][2 * i][1], | |
1652 | pre->g_pre_comp[0][2 * i][2], | |
1653 | pre->g_pre_comp[0][2 * i][0], | |
1654 | pre->g_pre_comp[0][2 * i][1], | |
1655 | pre->g_pre_comp[0][2 * i][2]); | |
1656 | } | |
1657 | } | |
1658 | for (i = 0; i < 2; i++) { | |
1659 | /* g_pre_comp[i][0] is the point at infinity */ | |
1660 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); | |
1661 | /* the remaining multiples */ | |
1662 | /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ | |
1663 | point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], | |
1664 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], | |
1665 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], | |
1666 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1667 | pre->g_pre_comp[i][2][2]); | |
1668 | /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ | |
1669 | point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], | |
1670 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], | |
1671 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1672 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1673 | pre->g_pre_comp[i][2][2]); | |
1674 | /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ | |
1675 | point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], | |
1676 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], | |
1677 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1678 | 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], | |
1679 | pre->g_pre_comp[i][4][2]); | |
1680 | /* | |
1681 | * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G | |
1682 | */ | |
1683 | point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], | |
1684 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], | |
1685 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], | |
1686 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1687 | pre->g_pre_comp[i][2][2]); | |
1688 | for (j = 1; j < 8; ++j) { | |
1689 | /* odd multiples: add G resp. 2^28*G */ | |
1690 | point_add(pre->g_pre_comp[i][2 * j + 1][0], | |
1691 | pre->g_pre_comp[i][2 * j + 1][1], | |
1692 | pre->g_pre_comp[i][2 * j + 1][2], | |
1693 | pre->g_pre_comp[i][2 * j][0], | |
1694 | pre->g_pre_comp[i][2 * j][1], | |
1695 | pre->g_pre_comp[i][2 * j][2], 0, | |
1696 | pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], | |
1697 | pre->g_pre_comp[i][1][2]); | |
1698 | } | |
1699 | } | |
1700 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); | |
1701 | ||
615614c8 | 1702 | done: |
3aef36ff | 1703 | SETPRECOMP(group, nistp224, pre); |
0f113f3e | 1704 | pre = NULL; |
3aef36ff | 1705 | ret = 1; |
04daec86 | 1706 | err: |
0f113f3e | 1707 | BN_CTX_end(ctx); |
8fdc3734 | 1708 | EC_POINT_free(generator); |
23a1d5e9 | 1709 | BN_CTX_free(new_ctx); |
3aef36ff | 1710 | EC_nistp224_pre_comp_free(pre); |
0f113f3e MC |
1711 | return ret; |
1712 | } | |
04daec86 BM |
1713 | |
1714 | int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) | |
0f113f3e | 1715 | { |
3aef36ff | 1716 | return HAVEPRECOMP(group, nistp224); |
0f113f3e | 1717 | } |
396cb565 | 1718 | |
04daec86 | 1719 | #endif |