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04daec86 BM |
1 | /* |
2 | * Written by Emilia Kasper (Google) for the OpenSSL project. | |
3 | */ | |
3e00b4c9 | 4 | /* Copyright 2011 Google Inc. |
04daec86 | 5 | * |
3e00b4c9 | 6 | * Licensed under the Apache License, Version 2.0 (the "License"); |
04daec86 | 7 | * |
3e00b4c9 BM |
8 | * you may not use this file except in compliance with the License. |
9 | * You may obtain a copy of the License at | |
04daec86 | 10 | * |
3e00b4c9 | 11 | * http://www.apache.org/licenses/LICENSE-2.0 |
04daec86 | 12 | * |
3e00b4c9 BM |
13 | * Unless required by applicable law or agreed to in writing, software |
14 | * distributed under the License is distributed on an "AS IS" BASIS, | |
15 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
16 | * See the License for the specific language governing permissions and | |
17 | * limitations under the License. | |
04daec86 BM |
18 | */ |
19 | ||
20 | /* | |
21 | * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication | |
22 | * | |
23 | * Inspired by Daniel J. Bernstein's public domain nistp224 implementation | |
24 | * and Adam Langley's public domain 64-bit C implementation of curve25519 | |
25 | */ | |
e0d6132b BM |
26 | |
27 | #include <openssl/opensslconf.h> | |
effaf4de RS |
28 | #ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 |
29 | NON_EMPTY_TRANSLATION_UNIT | |
30 | #else | |
e0d6132b | 31 | |
0f113f3e MC |
32 | # include <stdint.h> |
33 | # include <string.h> | |
34 | # include <openssl/err.h> | |
35 | # include "ec_lcl.h" | |
04daec86 | 36 | |
0f113f3e | 37 | # if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) |
396cb565 | 38 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
0f113f3e MC |
39 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
40 | * platforms */ | |
41 | # else | |
42 | # error "Need GCC 3.1 or later to define type uint128_t" | |
43 | # endif | |
04daec86 BM |
44 | |
45 | typedef uint8_t u8; | |
3e00b4c9 BM |
46 | typedef uint64_t u64; |
47 | typedef int64_t s64; | |
04daec86 | 48 | |
04daec86 | 49 | /******************************************************************************/ |
1d97c843 TH |
50 | /*- |
51 | * INTERNAL REPRESENTATION OF FIELD ELEMENTS | |
04daec86 BM |
52 | * |
53 | * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 | |
3e00b4c9 BM |
54 | * using 64-bit coefficients called 'limbs', |
55 | * and sometimes (for multiplication results) as | |
04daec86 | 56 | * 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 |
57 | * using 128-bit coefficients called 'widelimbs'. |
58 | * A 4-limb representation is an 'felem'; | |
59 | * a 7-widelimb representation is a 'widefelem'. | |
60 | * Even within felems, bits of adjacent limbs overlap, and we don't always | |
61 | * reduce the representations: we ensure that inputs to each felem | |
04daec86 BM |
62 | * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, |
63 | * and fit into a 128-bit word without overflow. The coefficients are then | |
3e00b4c9 BM |
64 | * again partially reduced to obtain an felem satisfying a_i < 2^57. |
65 | * We only reduce to the unique minimal representation at the end of the | |
66 | * computation. | |
04daec86 BM |
67 | */ |
68 | ||
3e00b4c9 BM |
69 | typedef uint64_t limb; |
70 | typedef uint128_t widelimb; | |
71 | ||
72 | typedef limb felem[4]; | |
73 | typedef widelimb widefelem[7]; | |
04daec86 | 74 | |
0f113f3e MC |
75 | /* |
76 | * Field element represented as a byte arrary. 28*8 = 224 bits is also the | |
77 | * group order size for the elliptic curve, and we also use this type for | |
78 | * scalars for point multiplication. | |
79 | */ | |
396cb565 BM |
80 | typedef u8 felem_bytearray[28]; |
81 | ||
82 | static const felem_bytearray nistp224_curve_params[5] = { | |
0f113f3e MC |
83 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ |
84 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, | |
85 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, | |
86 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ | |
87 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, | |
88 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, | |
89 | {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ | |
90 | 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, | |
91 | 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, | |
92 | {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ | |
93 | 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, | |
94 | 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, | |
95 | {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ | |
96 | 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, | |
97 | 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} | |
396cb565 | 98 | }; |
04daec86 | 99 | |
1d97c843 TH |
100 | /*- |
101 | * Precomputed multiples of the standard generator | |
3e00b4c9 BM |
102 | * Points are given in coordinates (X, Y, Z) where Z normally is 1 |
103 | * (0 for the point at infinity). | |
104 | * For each field element, slice a_0 is word 0, etc. | |
105 | * | |
106 | * The table has 2 * 16 elements, starting with the following: | |
107 | * index | bits | point | |
108 | * ------+---------+------------------------------ | |
109 | * 0 | 0 0 0 0 | 0G | |
110 | * 1 | 0 0 0 1 | 1G | |
111 | * 2 | 0 0 1 0 | 2^56G | |
112 | * 3 | 0 0 1 1 | (2^56 + 1)G | |
113 | * 4 | 0 1 0 0 | 2^112G | |
114 | * 5 | 0 1 0 1 | (2^112 + 1)G | |
115 | * 6 | 0 1 1 0 | (2^112 + 2^56)G | |
116 | * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G | |
117 | * 8 | 1 0 0 0 | 2^168G | |
118 | * 9 | 1 0 0 1 | (2^168 + 1)G | |
119 | * 10 | 1 0 1 0 | (2^168 + 2^56)G | |
120 | * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G | |
121 | * 12 | 1 1 0 0 | (2^168 + 2^112)G | |
122 | * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G | |
123 | * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G | |
124 | * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G | |
125 | * followed by a copy of this with each element multiplied by 2^28. | |
126 | * | |
127 | * The reason for this is so that we can clock bits into four different | |
128 | * locations when doing simple scalar multiplies against the base point, | |
129 | * and then another four locations using the second 16 elements. | |
130 | */ | |
4eb504ae AP |
131 | static const felem gmul[2][16][3] = { |
132 | {{{0, 0, 0, 0}, | |
133 | {0, 0, 0, 0}, | |
134 | {0, 0, 0, 0}}, | |
135 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, | |
136 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, | |
137 | {1, 0, 0, 0}}, | |
138 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, | |
139 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, | |
140 | {1, 0, 0, 0}}, | |
141 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, | |
142 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, | |
143 | {1, 0, 0, 0}}, | |
144 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, | |
145 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, | |
146 | {1, 0, 0, 0}}, | |
147 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, | |
148 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, | |
149 | {1, 0, 0, 0}}, | |
150 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, | |
151 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, | |
152 | {1, 0, 0, 0}}, | |
153 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, | |
154 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, | |
155 | {1, 0, 0, 0}}, | |
156 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, | |
157 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, | |
158 | {1, 0, 0, 0}}, | |
159 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, | |
160 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, | |
161 | {1, 0, 0, 0}}, | |
162 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, | |
163 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, | |
164 | {1, 0, 0, 0}}, | |
165 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, | |
166 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, | |
167 | {1, 0, 0, 0}}, | |
168 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, | |
169 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, | |
170 | {1, 0, 0, 0}}, | |
171 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, | |
172 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, | |
173 | {1, 0, 0, 0}}, | |
174 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, | |
175 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, | |
176 | {1, 0, 0, 0}}, | |
177 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, | |
178 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, | |
179 | {1, 0, 0, 0}}}, | |
0f113f3e MC |
180 | {{{0, 0, 0, 0}, |
181 | {0, 0, 0, 0}, | |
182 | {0, 0, 0, 0}}, | |
183 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, | |
184 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, | |
185 | {1, 0, 0, 0}}, | |
186 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, | |
187 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, | |
188 | {1, 0, 0, 0}}, | |
189 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, | |
190 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, | |
191 | {1, 0, 0, 0}}, | |
192 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, | |
193 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, | |
194 | {1, 0, 0, 0}}, | |
195 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, | |
196 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, | |
197 | {1, 0, 0, 0}}, | |
198 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, | |
199 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, | |
200 | {1, 0, 0, 0}}, | |
201 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, | |
202 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, | |
203 | {1, 0, 0, 0}}, | |
204 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, | |
205 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, | |
206 | {1, 0, 0, 0}}, | |
207 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, | |
208 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, | |
209 | {1, 0, 0, 0}}, | |
210 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, | |
211 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, | |
212 | {1, 0, 0, 0}}, | |
213 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, | |
214 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, | |
215 | {1, 0, 0, 0}}, | |
216 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, | |
217 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, | |
218 | {1, 0, 0, 0}}, | |
219 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, | |
220 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, | |
221 | {1, 0, 0, 0}}, | |
222 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, | |
223 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, | |
224 | {1, 0, 0, 0}}, | |
225 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, | |
226 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, | |
227 | {1, 0, 0, 0}}} | |
228 | }; | |
04daec86 BM |
229 | |
230 | /* Precomputation for the group generator. */ | |
3aef36ff | 231 | struct nistp224_pre_comp_st { |
0f113f3e MC |
232 | felem g_pre_comp[2][16][3]; |
233 | int references; | |
9b398ef2 | 234 | CRYPTO_RWLOCK *lock; |
3aef36ff | 235 | }; |
04daec86 BM |
236 | |
237 | const EC_METHOD *EC_GFp_nistp224_method(void) | |
0f113f3e MC |
238 | { |
239 | static const EC_METHOD ret = { | |
240 | EC_FLAGS_DEFAULT_OCT, | |
241 | NID_X9_62_prime_field, | |
242 | ec_GFp_nistp224_group_init, | |
243 | ec_GFp_simple_group_finish, | |
244 | ec_GFp_simple_group_clear_finish, | |
245 | ec_GFp_nist_group_copy, | |
246 | ec_GFp_nistp224_group_set_curve, | |
247 | ec_GFp_simple_group_get_curve, | |
248 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 249 | ec_group_simple_order_bits, |
0f113f3e MC |
250 | ec_GFp_simple_group_check_discriminant, |
251 | ec_GFp_simple_point_init, | |
252 | ec_GFp_simple_point_finish, | |
253 | ec_GFp_simple_point_clear_finish, | |
254 | ec_GFp_simple_point_copy, | |
255 | ec_GFp_simple_point_set_to_infinity, | |
256 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
257 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
258 | ec_GFp_simple_point_set_affine_coordinates, | |
259 | ec_GFp_nistp224_point_get_affine_coordinates, | |
260 | 0 /* point_set_compressed_coordinates */ , | |
261 | 0 /* point2oct */ , | |
262 | 0 /* oct2point */ , | |
263 | ec_GFp_simple_add, | |
264 | ec_GFp_simple_dbl, | |
265 | ec_GFp_simple_invert, | |
266 | ec_GFp_simple_is_at_infinity, | |
267 | ec_GFp_simple_is_on_curve, | |
268 | ec_GFp_simple_cmp, | |
269 | ec_GFp_simple_make_affine, | |
270 | ec_GFp_simple_points_make_affine, | |
271 | ec_GFp_nistp224_points_mul, | |
272 | ec_GFp_nistp224_precompute_mult, | |
273 | ec_GFp_nistp224_have_precompute_mult, | |
274 | ec_GFp_nist_field_mul, | |
275 | ec_GFp_nist_field_sqr, | |
276 | 0 /* field_div */ , | |
277 | 0 /* field_encode */ , | |
278 | 0 /* field_decode */ , | |
9ff9bccc DSH |
279 | 0, /* field_set_to_one */ |
280 | ec_key_simple_priv2oct, | |
281 | ec_key_simple_oct2priv, | |
282 | 0, /* set private */ | |
283 | ec_key_simple_generate_key, | |
284 | ec_key_simple_check_key, | |
285 | ec_key_simple_generate_public_key, | |
286 | 0, /* keycopy */ | |
287 | 0, /* keyfinish */ | |
288 | ecdh_simple_compute_key | |
0f113f3e MC |
289 | }; |
290 | ||
291 | return &ret; | |
292 | } | |
293 | ||
294 | /* | |
295 | * Helper functions to convert field elements to/from internal representation | |
296 | */ | |
3e00b4c9 | 297 | static void bin28_to_felem(felem out, const u8 in[28]) |
0f113f3e MC |
298 | { |
299 | out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; | |
300 | out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; | |
301 | out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; | |
9fbbdd73 | 302 | out[3] = (*((const uint64_t *)(in+20))) >> 8; |
0f113f3e | 303 | } |
04daec86 | 304 | |
3e00b4c9 | 305 | static void felem_to_bin28(u8 out[28], const felem in) |
0f113f3e MC |
306 | { |
307 | unsigned i; | |
308 | for (i = 0; i < 7; ++i) { | |
309 | out[i] = in[0] >> (8 * i); | |
310 | out[i + 7] = in[1] >> (8 * i); | |
311 | out[i + 14] = in[2] >> (8 * i); | |
312 | out[i + 21] = in[3] >> (8 * i); | |
313 | } | |
314 | } | |
04daec86 BM |
315 | |
316 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ | |
317 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | |
0f113f3e MC |
318 | { |
319 | unsigned i; | |
320 | for (i = 0; i < len; ++i) | |
321 | out[i] = in[len - 1 - i]; | |
322 | } | |
04daec86 BM |
323 | |
324 | /* From OpenSSL BIGNUM to internal representation */ | |
3e00b4c9 | 325 | static int BN_to_felem(felem out, const BIGNUM *bn) |
0f113f3e MC |
326 | { |
327 | felem_bytearray b_in; | |
328 | felem_bytearray b_out; | |
329 | unsigned num_bytes; | |
330 | ||
331 | /* BN_bn2bin eats leading zeroes */ | |
16f8d4eb | 332 | memset(b_out, 0, sizeof(b_out)); |
0f113f3e MC |
333 | num_bytes = BN_num_bytes(bn); |
334 | if (num_bytes > sizeof b_out) { | |
335 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
336 | return 0; | |
337 | } | |
338 | if (BN_is_negative(bn)) { | |
339 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
340 | return 0; | |
341 | } | |
342 | num_bytes = BN_bn2bin(bn, b_in); | |
343 | flip_endian(b_out, b_in, num_bytes); | |
344 | bin28_to_felem(out, b_out); | |
345 | return 1; | |
346 | } | |
04daec86 BM |
347 | |
348 | /* From internal representation to OpenSSL BIGNUM */ | |
3e00b4c9 | 349 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) |
0f113f3e MC |
350 | { |
351 | felem_bytearray b_in, b_out; | |
352 | felem_to_bin28(b_in, in); | |
353 | flip_endian(b_out, b_in, sizeof b_out); | |
354 | return BN_bin2bn(b_out, sizeof b_out, out); | |
355 | } | |
04daec86 BM |
356 | |
357 | /******************************************************************************/ | |
3a83462d | 358 | /*- |
0f113f3e | 359 | * FIELD OPERATIONS |
04daec86 BM |
360 | * |
361 | * Field operations, using the internal representation of field elements. | |
362 | * NB! These operations are specific to our point multiplication and cannot be | |
363 | * expected to be correct in general - e.g., multiplication with a large scalar | |
364 | * will cause an overflow. | |
365 | * | |
366 | */ | |
367 | ||
3e00b4c9 | 368 | static void felem_one(felem out) |
0f113f3e MC |
369 | { |
370 | out[0] = 1; | |
371 | out[1] = 0; | |
372 | out[2] = 0; | |
373 | out[3] = 0; | |
374 | } | |
3e00b4c9 BM |
375 | |
376 | static void felem_assign(felem out, const felem in) | |
0f113f3e MC |
377 | { |
378 | out[0] = in[0]; | |
379 | out[1] = in[1]; | |
380 | out[2] = in[2]; | |
381 | out[3] = in[3]; | |
382 | } | |
3e00b4c9 | 383 | |
04daec86 | 384 | /* Sum two field elements: out += in */ |
3e00b4c9 | 385 | static void felem_sum(felem out, const felem in) |
0f113f3e MC |
386 | { |
387 | out[0] += in[0]; | |
388 | out[1] += in[1]; | |
389 | out[2] += in[2]; | |
390 | out[3] += in[3]; | |
391 | } | |
04daec86 | 392 | |
3e00b4c9 BM |
393 | /* Get negative value: out = -in */ |
394 | /* Assumes in[i] < 2^57 */ | |
395 | static void felem_neg(felem out, const felem in) | |
0f113f3e MC |
396 | { |
397 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); | |
398 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
399 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
400 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
401 | ||
402 | /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ | |
403 | out[0] = two58p2 - in[0]; | |
404 | out[1] = two58m42m2 - in[1]; | |
405 | out[2] = two58m2 - in[2]; | |
406 | out[3] = two58m2 - in[3]; | |
407 | } | |
3e00b4c9 | 408 | |
04daec86 BM |
409 | /* Subtract field elements: out -= in */ |
410 | /* Assumes in[i] < 2^57 */ | |
3e00b4c9 | 411 | static void felem_diff(felem out, const felem in) |
0f113f3e MC |
412 | { |
413 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); | |
414 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
415 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
416 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
417 | ||
418 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
419 | out[0] += two58p2; | |
420 | out[1] += two58m42m2; | |
421 | out[2] += two58m2; | |
422 | out[3] += two58m2; | |
423 | ||
424 | out[0] -= in[0]; | |
425 | out[1] -= in[1]; | |
426 | out[2] -= in[2]; | |
427 | out[3] -= in[3]; | |
428 | } | |
04daec86 | 429 | |
3e00b4c9 | 430 | /* Subtract in unreduced 128-bit mode: out -= in */ |
04daec86 | 431 | /* Assumes in[i] < 2^119 */ |
3e00b4c9 | 432 | static void widefelem_diff(widefelem out, const widefelem in) |
0f113f3e MC |
433 | { |
434 | static const widelimb two120 = ((widelimb) 1) << 120; | |
435 | static const widelimb two120m64 = (((widelimb) 1) << 120) - | |
436 | (((widelimb) 1) << 64); | |
437 | static const widelimb two120m104m64 = (((widelimb) 1) << 120) - | |
438 | (((widelimb) 1) << 104) - (((widelimb) 1) << 64); | |
439 | ||
440 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
441 | out[0] += two120; | |
442 | out[1] += two120m64; | |
443 | out[2] += two120m64; | |
444 | out[3] += two120; | |
445 | out[4] += two120m104m64; | |
446 | out[5] += two120m64; | |
447 | out[6] += two120m64; | |
448 | ||
449 | out[0] -= in[0]; | |
450 | out[1] -= in[1]; | |
451 | out[2] -= in[2]; | |
452 | out[3] -= in[3]; | |
453 | out[4] -= in[4]; | |
454 | out[5] -= in[5]; | |
455 | out[6] -= in[6]; | |
456 | } | |
04daec86 BM |
457 | |
458 | /* Subtract in mixed mode: out128 -= in64 */ | |
459 | /* in[i] < 2^63 */ | |
3e00b4c9 | 460 | static void felem_diff_128_64(widefelem out, const felem in) |
0f113f3e MC |
461 | { |
462 | static const widelimb two64p8 = (((widelimb) 1) << 64) + | |
463 | (((widelimb) 1) << 8); | |
464 | static const widelimb two64m8 = (((widelimb) 1) << 64) - | |
465 | (((widelimb) 1) << 8); | |
466 | static const widelimb two64m48m8 = (((widelimb) 1) << 64) - | |
467 | (((widelimb) 1) << 48) - (((widelimb) 1) << 8); | |
468 | ||
469 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
470 | out[0] += two64p8; | |
471 | out[1] += two64m48m8; | |
472 | out[2] += two64m8; | |
473 | out[3] += two64m8; | |
474 | ||
475 | out[0] -= in[0]; | |
476 | out[1] -= in[1]; | |
477 | out[2] -= in[2]; | |
478 | out[3] -= in[3]; | |
479 | } | |
480 | ||
481 | /* | |
482 | * Multiply a field element by a scalar: out = out * scalar The scalars we | |
483 | * actually use are small, so results fit without overflow | |
484 | */ | |
3e00b4c9 | 485 | static void felem_scalar(felem out, const limb scalar) |
0f113f3e MC |
486 | { |
487 | out[0] *= scalar; | |
488 | out[1] *= scalar; | |
489 | out[2] *= scalar; | |
490 | out[3] *= scalar; | |
491 | } | |
492 | ||
493 | /* | |
494 | * Multiply an unreduced field element by a scalar: out = out * scalar The | |
495 | * scalars we actually use are small, so results fit without overflow | |
496 | */ | |
3e00b4c9 | 497 | static void widefelem_scalar(widefelem out, const widelimb scalar) |
0f113f3e MC |
498 | { |
499 | out[0] *= scalar; | |
500 | out[1] *= scalar; | |
501 | out[2] *= scalar; | |
502 | out[3] *= scalar; | |
503 | out[4] *= scalar; | |
504 | out[5] *= scalar; | |
505 | out[6] *= scalar; | |
506 | } | |
04daec86 BM |
507 | |
508 | /* Square a field element: out = in^2 */ | |
3e00b4c9 | 509 | static void felem_square(widefelem out, const felem in) |
0f113f3e MC |
510 | { |
511 | limb tmp0, tmp1, tmp2; | |
512 | tmp0 = 2 * in[0]; | |
513 | tmp1 = 2 * in[1]; | |
514 | tmp2 = 2 * in[2]; | |
515 | out[0] = ((widelimb) in[0]) * in[0]; | |
516 | out[1] = ((widelimb) in[0]) * tmp1; | |
517 | out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; | |
518 | out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; | |
519 | out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; | |
520 | out[5] = ((widelimb) in[3]) * tmp2; | |
521 | out[6] = ((widelimb) in[3]) * in[3]; | |
522 | } | |
04daec86 BM |
523 | |
524 | /* Multiply two field elements: out = in1 * in2 */ | |
3e00b4c9 | 525 | static void felem_mul(widefelem out, const felem in1, const felem in2) |
0f113f3e MC |
526 | { |
527 | out[0] = ((widelimb) in1[0]) * in2[0]; | |
528 | out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; | |
529 | out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + | |
4eb504ae | 530 | ((widelimb) in1[2]) * in2[0]; |
0f113f3e | 531 | out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + |
4eb504ae | 532 | ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; |
0f113f3e | 533 | out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + |
4eb504ae | 534 | ((widelimb) in1[3]) * in2[1]; |
0f113f3e MC |
535 | out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; |
536 | out[6] = ((widelimb) in1[3]) * in2[3]; | |
537 | } | |
04daec86 | 538 | |
3a83462d MC |
539 | /*- |
540 | * Reduce seven 128-bit coefficients to four 64-bit coefficients. | |
3e00b4c9 BM |
541 | * Requires in[i] < 2^126, |
542 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ | |
543 | static void felem_reduce(felem out, const widefelem in) | |
0f113f3e MC |
544 | { |
545 | static const widelimb two127p15 = (((widelimb) 1) << 127) + | |
546 | (((widelimb) 1) << 15); | |
547 | static const widelimb two127m71 = (((widelimb) 1) << 127) - | |
548 | (((widelimb) 1) << 71); | |
549 | static const widelimb two127m71m55 = (((widelimb) 1) << 127) - | |
550 | (((widelimb) 1) << 71) - (((widelimb) 1) << 55); | |
551 | widelimb output[5]; | |
552 | ||
553 | /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ | |
554 | output[0] = in[0] + two127p15; | |
555 | output[1] = in[1] + two127m71m55; | |
556 | output[2] = in[2] + two127m71; | |
557 | output[3] = in[3]; | |
558 | output[4] = in[4]; | |
559 | ||
560 | /* Eliminate in[4], in[5], in[6] */ | |
561 | output[4] += in[6] >> 16; | |
562 | output[3] += (in[6] & 0xffff) << 40; | |
563 | output[2] -= in[6]; | |
564 | ||
565 | output[3] += in[5] >> 16; | |
566 | output[2] += (in[5] & 0xffff) << 40; | |
567 | output[1] -= in[5]; | |
568 | ||
569 | output[2] += output[4] >> 16; | |
570 | output[1] += (output[4] & 0xffff) << 40; | |
571 | output[0] -= output[4]; | |
572 | ||
573 | /* Carry 2 -> 3 -> 4 */ | |
574 | output[3] += output[2] >> 56; | |
575 | output[2] &= 0x00ffffffffffffff; | |
576 | ||
577 | output[4] = output[3] >> 56; | |
578 | output[3] &= 0x00ffffffffffffff; | |
579 | ||
580 | /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ | |
581 | ||
582 | /* Eliminate output[4] */ | |
583 | output[2] += output[4] >> 16; | |
584 | /* output[2] < 2^56 + 2^56 = 2^57 */ | |
585 | output[1] += (output[4] & 0xffff) << 40; | |
586 | output[0] -= output[4]; | |
587 | ||
588 | /* Carry 0 -> 1 -> 2 -> 3 */ | |
589 | output[1] += output[0] >> 56; | |
590 | out[0] = output[0] & 0x00ffffffffffffff; | |
591 | ||
592 | output[2] += output[1] >> 56; | |
593 | /* output[2] < 2^57 + 2^72 */ | |
594 | out[1] = output[1] & 0x00ffffffffffffff; | |
595 | output[3] += output[2] >> 56; | |
596 | /* output[3] <= 2^56 + 2^16 */ | |
597 | out[2] = output[2] & 0x00ffffffffffffff; | |
598 | ||
50e735f9 MC |
599 | /*- |
600 | * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, | |
601 | * out[3] <= 2^56 + 2^16 (due to final carry), | |
602 | * so out < 2*p | |
603 | */ | |
0f113f3e MC |
604 | out[3] = output[3]; |
605 | } | |
04daec86 | 606 | |
3e00b4c9 | 607 | static void felem_square_reduce(felem out, const felem in) |
0f113f3e MC |
608 | { |
609 | widefelem tmp; | |
610 | felem_square(tmp, in); | |
611 | felem_reduce(out, tmp); | |
612 | } | |
04daec86 | 613 | |
3e00b4c9 | 614 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) |
0f113f3e MC |
615 | { |
616 | widefelem tmp; | |
617 | felem_mul(tmp, in1, in2); | |
618 | felem_reduce(out, tmp); | |
619 | } | |
620 | ||
621 | /* | |
622 | * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always | |
623 | * call felem_reduce first) | |
624 | */ | |
3e00b4c9 | 625 | static void felem_contract(felem out, const felem in) |
0f113f3e MC |
626 | { |
627 | static const int64_t two56 = ((limb) 1) << 56; | |
628 | /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ | |
629 | /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ | |
630 | int64_t tmp[4], a; | |
631 | tmp[0] = in[0]; | |
632 | tmp[1] = in[1]; | |
633 | tmp[2] = in[2]; | |
634 | tmp[3] = in[3]; | |
635 | /* Case 1: a = 1 iff in >= 2^224 */ | |
636 | a = (in[3] >> 56); | |
637 | tmp[0] -= a; | |
638 | tmp[1] += a << 40; | |
639 | tmp[3] &= 0x00ffffffffffffff; | |
640 | /* | |
641 | * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 | |
642 | * and the lower part is non-zero | |
643 | */ | |
644 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | | |
645 | (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); | |
646 | a &= 0x00ffffffffffffff; | |
647 | /* turn a into an all-one mask (if a = 0) or an all-zero mask */ | |
648 | a = (a - 1) >> 63; | |
649 | /* subtract 2^224 - 2^96 + 1 if a is all-one */ | |
650 | tmp[3] &= a ^ 0xffffffffffffffff; | |
651 | tmp[2] &= a ^ 0xffffffffffffffff; | |
652 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; | |
653 | tmp[0] -= 1 & a; | |
654 | ||
655 | /* | |
656 | * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be | |
657 | * non-zero, so we only need one step | |
658 | */ | |
659 | a = tmp[0] >> 63; | |
660 | tmp[0] += two56 & a; | |
661 | tmp[1] -= 1 & a; | |
662 | ||
663 | /* carry 1 -> 2 -> 3 */ | |
664 | tmp[2] += tmp[1] >> 56; | |
665 | tmp[1] &= 0x00ffffffffffffff; | |
666 | ||
667 | tmp[3] += tmp[2] >> 56; | |
668 | tmp[2] &= 0x00ffffffffffffff; | |
669 | ||
670 | /* Now 0 <= out < p */ | |
671 | out[0] = tmp[0]; | |
672 | out[1] = tmp[1]; | |
673 | out[2] = tmp[2]; | |
674 | out[3] = tmp[3]; | |
675 | } | |
676 | ||
677 | /* | |
678 | * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field | |
679 | * elements are reduced to in < 2^225, so we only need to check three cases: | |
680 | * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 | |
681 | */ | |
3e00b4c9 | 682 | static limb felem_is_zero(const felem in) |
0f113f3e MC |
683 | { |
684 | limb zero, two224m96p1, two225m97p2; | |
685 | ||
686 | zero = in[0] | in[1] | in[2] | in[3]; | |
687 | zero = (((int64_t) (zero) - 1) >> 63) & 1; | |
688 | two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) | |
689 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); | |
690 | two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; | |
691 | two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) | |
692 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); | |
693 | two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; | |
694 | return (zero | two224m96p1 | two225m97p2); | |
695 | } | |
04daec86 | 696 | |
3e00b4c9 | 697 | static limb felem_is_zero_int(const felem in) |
0f113f3e MC |
698 | { |
699 | return (int)(felem_is_zero(in) & ((limb) 1)); | |
700 | } | |
3e00b4c9 | 701 | |
04daec86 BM |
702 | /* Invert a field element */ |
703 | /* Computation chain copied from djb's code */ | |
3e00b4c9 | 704 | static void felem_inv(felem out, const felem in) |
0f113f3e MC |
705 | { |
706 | felem ftmp, ftmp2, ftmp3, ftmp4; | |
707 | widefelem tmp; | |
708 | unsigned i; | |
709 | ||
710 | felem_square(tmp, in); | |
711 | felem_reduce(ftmp, tmp); /* 2 */ | |
712 | felem_mul(tmp, in, ftmp); | |
713 | felem_reduce(ftmp, tmp); /* 2^2 - 1 */ | |
714 | felem_square(tmp, ftmp); | |
715 | felem_reduce(ftmp, tmp); /* 2^3 - 2 */ | |
716 | felem_mul(tmp, in, ftmp); | |
717 | felem_reduce(ftmp, tmp); /* 2^3 - 1 */ | |
718 | felem_square(tmp, ftmp); | |
719 | felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ | |
720 | felem_square(tmp, ftmp2); | |
721 | felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ | |
722 | felem_square(tmp, ftmp2); | |
723 | felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ | |
724 | felem_mul(tmp, ftmp2, ftmp); | |
725 | felem_reduce(ftmp, tmp); /* 2^6 - 1 */ | |
726 | felem_square(tmp, ftmp); | |
727 | felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ | |
728 | for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ | |
729 | felem_square(tmp, ftmp2); | |
730 | felem_reduce(ftmp2, tmp); | |
731 | } | |
732 | felem_mul(tmp, ftmp2, ftmp); | |
733 | felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ | |
734 | felem_square(tmp, ftmp2); | |
735 | felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ | |
736 | for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ | |
737 | felem_square(tmp, ftmp3); | |
738 | felem_reduce(ftmp3, tmp); | |
739 | } | |
740 | felem_mul(tmp, ftmp3, ftmp2); | |
741 | felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ | |
742 | felem_square(tmp, ftmp2); | |
743 | felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ | |
744 | for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ | |
745 | felem_square(tmp, ftmp3); | |
746 | felem_reduce(ftmp3, tmp); | |
747 | } | |
748 | felem_mul(tmp, ftmp3, ftmp2); | |
749 | felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ | |
750 | felem_square(tmp, ftmp3); | |
751 | felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ | |
752 | for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ | |
753 | felem_square(tmp, ftmp4); | |
754 | felem_reduce(ftmp4, tmp); | |
755 | } | |
756 | felem_mul(tmp, ftmp3, ftmp4); | |
757 | felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ | |
758 | felem_square(tmp, ftmp3); | |
759 | felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ | |
760 | for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ | |
761 | felem_square(tmp, ftmp4); | |
762 | felem_reduce(ftmp4, tmp); | |
763 | } | |
764 | felem_mul(tmp, ftmp2, ftmp4); | |
765 | felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ | |
766 | for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ | |
767 | felem_square(tmp, ftmp2); | |
768 | felem_reduce(ftmp2, tmp); | |
769 | } | |
770 | felem_mul(tmp, ftmp2, ftmp); | |
771 | felem_reduce(ftmp, tmp); /* 2^126 - 1 */ | |
772 | felem_square(tmp, ftmp); | |
773 | felem_reduce(ftmp, tmp); /* 2^127 - 2 */ | |
774 | felem_mul(tmp, ftmp, in); | |
775 | felem_reduce(ftmp, tmp); /* 2^127 - 1 */ | |
776 | for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ | |
777 | felem_square(tmp, ftmp); | |
778 | felem_reduce(ftmp, tmp); | |
779 | } | |
780 | felem_mul(tmp, ftmp, ftmp3); | |
781 | felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ | |
782 | } | |
783 | ||
784 | /* | |
785 | * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy | |
786 | * out to itself. | |
787 | */ | |
788 | static void copy_conditional(felem out, const felem in, limb icopy) | |
789 | { | |
790 | unsigned i; | |
791 | /* | |
792 | * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one | |
793 | */ | |
794 | const limb copy = -icopy; | |
795 | for (i = 0; i < 4; ++i) { | |
796 | const limb tmp = copy & (in[i] ^ out[i]); | |
797 | out[i] ^= tmp; | |
798 | } | |
799 | } | |
04daec86 | 800 | |
04daec86 | 801 | /******************************************************************************/ |
3a83462d | 802 | /*- |
0f113f3e | 803 | * ELLIPTIC CURVE POINT OPERATIONS |
04daec86 BM |
804 | * |
805 | * Points are represented in Jacobian projective coordinates: | |
806 | * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), | |
807 | * or to the point at infinity if Z == 0. | |
808 | * | |
809 | */ | |
810 | ||
1d97c843 TH |
811 | /*- |
812 | * Double an elliptic curve point: | |
04daec86 BM |
813 | * (X', Y', Z') = 2 * (X, Y, Z), where |
814 | * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 | |
815 | * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 | |
816 | * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z | |
817 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, | |
0f113f3e | 818 | * while x_out == y_in is not (maybe this works, but it's not tested). |
1d97c843 | 819 | */ |
04daec86 | 820 | static void |
3e00b4c9 BM |
821 | point_double(felem x_out, felem y_out, felem z_out, |
822 | const felem x_in, const felem y_in, const felem z_in) | |
0f113f3e MC |
823 | { |
824 | widefelem tmp, tmp2; | |
825 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
826 | ||
827 | felem_assign(ftmp, x_in); | |
828 | felem_assign(ftmp2, x_in); | |
829 | ||
830 | /* delta = z^2 */ | |
831 | felem_square(tmp, z_in); | |
832 | felem_reduce(delta, tmp); | |
833 | ||
834 | /* gamma = y^2 */ | |
835 | felem_square(tmp, y_in); | |
836 | felem_reduce(gamma, tmp); | |
837 | ||
838 | /* beta = x*gamma */ | |
839 | felem_mul(tmp, x_in, gamma); | |
840 | felem_reduce(beta, tmp); | |
841 | ||
842 | /* alpha = 3*(x-delta)*(x+delta) */ | |
843 | felem_diff(ftmp, delta); | |
844 | /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ | |
845 | felem_sum(ftmp2, delta); | |
846 | /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ | |
847 | felem_scalar(ftmp2, 3); | |
848 | /* ftmp2[i] < 3 * 2^58 < 2^60 */ | |
849 | felem_mul(tmp, ftmp, ftmp2); | |
850 | /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ | |
851 | felem_reduce(alpha, tmp); | |
852 | ||
853 | /* x' = alpha^2 - 8*beta */ | |
854 | felem_square(tmp, alpha); | |
855 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
856 | felem_assign(ftmp, beta); | |
857 | felem_scalar(ftmp, 8); | |
858 | /* ftmp[i] < 8 * 2^57 = 2^60 */ | |
859 | felem_diff_128_64(tmp, ftmp); | |
860 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
861 | felem_reduce(x_out, tmp); | |
862 | ||
863 | /* z' = (y + z)^2 - gamma - delta */ | |
864 | felem_sum(delta, gamma); | |
865 | /* delta[i] < 2^57 + 2^57 = 2^58 */ | |
866 | felem_assign(ftmp, y_in); | |
867 | felem_sum(ftmp, z_in); | |
868 | /* ftmp[i] < 2^57 + 2^57 = 2^58 */ | |
869 | felem_square(tmp, ftmp); | |
870 | /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ | |
871 | felem_diff_128_64(tmp, delta); | |
872 | /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ | |
873 | felem_reduce(z_out, tmp); | |
874 | ||
875 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
876 | felem_scalar(beta, 4); | |
877 | /* beta[i] < 4 * 2^57 = 2^59 */ | |
878 | felem_diff(beta, x_out); | |
879 | /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ | |
880 | felem_mul(tmp, alpha, beta); | |
881 | /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ | |
882 | felem_square(tmp2, gamma); | |
883 | /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
884 | widefelem_scalar(tmp2, 8); | |
885 | /* tmp2[i] < 8 * 2^116 = 2^119 */ | |
886 | widefelem_diff(tmp, tmp2); | |
887 | /* tmp[i] < 2^119 + 2^120 < 2^121 */ | |
888 | felem_reduce(y_out, tmp); | |
889 | } | |
04daec86 | 890 | |
1d97c843 TH |
891 | /*- |
892 | * Add two elliptic curve points: | |
04daec86 BM |
893 | * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where |
894 | * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - | |
895 | * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 | |
896 | * 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) - | |
897 | * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 | |
3e00b4c9 BM |
898 | * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
899 | * | |
900 | * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. | |
901 | */ | |
04daec86 | 902 | |
0f113f3e MC |
903 | /* |
904 | * This function is not entirely constant-time: it includes a branch for | |
905 | * checking whether the two input points are equal, (while not equal to the | |
906 | * point at infinity). This case never happens during single point | |
907 | * multiplication, so there is no timing leak for ECDH or ECDSA signing. | |
908 | */ | |
3e00b4c9 | 909 | static void point_add(felem x3, felem y3, felem z3, |
0f113f3e MC |
910 | const felem x1, const felem y1, const felem z1, |
911 | const int mixed, const felem x2, const felem y2, | |
912 | const felem z2) | |
913 | { | |
914 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; | |
915 | widefelem tmp, tmp2; | |
916 | limb z1_is_zero, z2_is_zero, x_equal, y_equal; | |
917 | ||
918 | if (!mixed) { | |
919 | /* ftmp2 = z2^2 */ | |
920 | felem_square(tmp, z2); | |
921 | felem_reduce(ftmp2, tmp); | |
922 | ||
923 | /* ftmp4 = z2^3 */ | |
924 | felem_mul(tmp, ftmp2, z2); | |
925 | felem_reduce(ftmp4, tmp); | |
926 | ||
927 | /* ftmp4 = z2^3*y1 */ | |
928 | felem_mul(tmp2, ftmp4, y1); | |
929 | felem_reduce(ftmp4, tmp2); | |
930 | ||
931 | /* ftmp2 = z2^2*x1 */ | |
932 | felem_mul(tmp2, ftmp2, x1); | |
933 | felem_reduce(ftmp2, tmp2); | |
934 | } else { | |
935 | /* | |
936 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) | |
937 | */ | |
938 | ||
939 | /* ftmp4 = z2^3*y1 */ | |
940 | felem_assign(ftmp4, y1); | |
941 | ||
942 | /* ftmp2 = z2^2*x1 */ | |
943 | felem_assign(ftmp2, x1); | |
944 | } | |
945 | ||
946 | /* ftmp = z1^2 */ | |
947 | felem_square(tmp, z1); | |
948 | felem_reduce(ftmp, tmp); | |
949 | ||
950 | /* ftmp3 = z1^3 */ | |
951 | felem_mul(tmp, ftmp, z1); | |
952 | felem_reduce(ftmp3, tmp); | |
953 | ||
954 | /* tmp = z1^3*y2 */ | |
955 | felem_mul(tmp, ftmp3, y2); | |
956 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
957 | ||
958 | /* ftmp3 = z1^3*y2 - z2^3*y1 */ | |
959 | felem_diff_128_64(tmp, ftmp4); | |
960 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
961 | felem_reduce(ftmp3, tmp); | |
962 | ||
963 | /* tmp = z1^2*x2 */ | |
964 | felem_mul(tmp, ftmp, x2); | |
965 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
966 | ||
967 | /* ftmp = z1^2*x2 - z2^2*x1 */ | |
968 | felem_diff_128_64(tmp, ftmp2); | |
969 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
970 | felem_reduce(ftmp, tmp); | |
971 | ||
972 | /* | |
973 | * the formulae are incorrect if the points are equal so we check for | |
974 | * this and do doubling if this happens | |
975 | */ | |
976 | x_equal = felem_is_zero(ftmp); | |
977 | y_equal = felem_is_zero(ftmp3); | |
978 | z1_is_zero = felem_is_zero(z1); | |
979 | z2_is_zero = felem_is_zero(z2); | |
980 | /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ | |
981 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { | |
982 | point_double(x3, y3, z3, x1, y1, z1); | |
983 | return; | |
984 | } | |
985 | ||
986 | /* ftmp5 = z1*z2 */ | |
987 | if (!mixed) { | |
988 | felem_mul(tmp, z1, z2); | |
989 | felem_reduce(ftmp5, tmp); | |
990 | } else { | |
991 | /* special case z2 = 0 is handled later */ | |
992 | felem_assign(ftmp5, z1); | |
993 | } | |
994 | ||
995 | /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ | |
996 | felem_mul(tmp, ftmp, ftmp5); | |
997 | felem_reduce(z_out, tmp); | |
998 | ||
999 | /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ | |
1000 | felem_assign(ftmp5, ftmp); | |
1001 | felem_square(tmp, ftmp); | |
1002 | felem_reduce(ftmp, tmp); | |
1003 | ||
1004 | /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ | |
1005 | felem_mul(tmp, ftmp, ftmp5); | |
1006 | felem_reduce(ftmp5, tmp); | |
1007 | ||
1008 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
1009 | felem_mul(tmp, ftmp2, ftmp); | |
1010 | felem_reduce(ftmp2, tmp); | |
1011 | ||
1012 | /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ | |
1013 | felem_mul(tmp, ftmp4, ftmp5); | |
1014 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
1015 | ||
1016 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ | |
1017 | felem_square(tmp2, ftmp3); | |
1018 | /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ | |
1019 | ||
1020 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ | |
1021 | felem_diff_128_64(tmp2, ftmp5); | |
1022 | /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
1023 | ||
1024 | /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
1025 | felem_assign(ftmp5, ftmp2); | |
1026 | felem_scalar(ftmp5, 2); | |
1027 | /* ftmp5[i] < 2 * 2^57 = 2^58 */ | |
1028 | ||
50e735f9 MC |
1029 | /*- |
1030 | * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - | |
1031 | * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 | |
1032 | */ | |
0f113f3e MC |
1033 | felem_diff_128_64(tmp2, ftmp5); |
1034 | /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ | |
1035 | felem_reduce(x_out, tmp2); | |
1036 | ||
1037 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ | |
1038 | felem_diff(ftmp2, x_out); | |
1039 | /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ | |
1040 | ||
1041 | /* | |
1042 | * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) | |
1043 | */ | |
1044 | felem_mul(tmp2, ftmp3, ftmp2); | |
1045 | /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ | |
1046 | ||
50e735f9 MC |
1047 | /*- |
1048 | * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - | |
1049 | * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 | |
1050 | */ | |
0f113f3e MC |
1051 | widefelem_diff(tmp2, tmp); |
1052 | /* tmp2[i] < 2^118 + 2^120 < 2^121 */ | |
1053 | felem_reduce(y_out, tmp2); | |
1054 | ||
1055 | /* | |
1056 | * the result (x_out, y_out, z_out) is incorrect if one of the inputs is | |
1057 | * the point at infinity, so we need to check for this separately | |
1058 | */ | |
1059 | ||
1060 | /* | |
1061 | * if point 1 is at infinity, copy point 2 to output, and vice versa | |
1062 | */ | |
1063 | copy_conditional(x_out, x2, z1_is_zero); | |
1064 | copy_conditional(x_out, x1, z2_is_zero); | |
1065 | copy_conditional(y_out, y2, z1_is_zero); | |
1066 | copy_conditional(y_out, y1, z2_is_zero); | |
1067 | copy_conditional(z_out, z2, z1_is_zero); | |
1068 | copy_conditional(z_out, z1, z2_is_zero); | |
1069 | felem_assign(x3, x_out); | |
1070 | felem_assign(y3, y_out); | |
1071 | felem_assign(z3, z_out); | |
1072 | } | |
04daec86 | 1073 | |
dbd87ffc MC |
1074 | /* |
1075 | * select_point selects the |idx|th point from a precomputation table and | |
1076 | * copies it to out. | |
1077 | * The pre_comp array argument should be size of |size| argument | |
1078 | */ | |
0f113f3e MC |
1079 | static void select_point(const u64 idx, unsigned int size, |
1080 | const felem pre_comp[][3], felem out[3]) | |
1081 | { | |
1082 | unsigned i, j; | |
1083 | limb *outlimbs = &out[0][0]; | |
0f113f3e | 1084 | |
88f4c6f3 | 1085 | memset(out, 0, sizeof(*out) * 3); |
0f113f3e MC |
1086 | for (i = 0; i < size; i++) { |
1087 | const limb *inlimbs = &pre_comp[i][0][0]; | |
1088 | u64 mask = i ^ idx; | |
1089 | mask |= mask >> 4; | |
1090 | mask |= mask >> 2; | |
1091 | mask |= mask >> 1; | |
1092 | mask &= 1; | |
1093 | mask--; | |
1094 | for (j = 0; j < 4 * 3; j++) | |
1095 | outlimbs[j] |= inlimbs[j] & mask; | |
1096 | } | |
1097 | } | |
3e00b4c9 BM |
1098 | |
1099 | /* get_bit returns the |i|th bit in |in| */ | |
1100 | static char get_bit(const felem_bytearray in, unsigned i) | |
0f113f3e MC |
1101 | { |
1102 | if (i >= 224) | |
1103 | return 0; | |
1104 | return (in[i >> 3] >> (i & 7)) & 1; | |
1105 | } | |
1106 | ||
1107 | /* | |
1108 | * Interleaved point multiplication using precomputed point multiples: The | |
1109 | * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars | |
1110 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the | |
1111 | * generator, using certain (large) precomputed multiples in g_pre_comp. | |
1112 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out | |
1113 | */ | |
3e00b4c9 | 1114 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
0f113f3e MC |
1115 | const felem_bytearray scalars[], |
1116 | const unsigned num_points, const u8 *g_scalar, | |
1117 | const int mixed, const felem pre_comp[][17][3], | |
1118 | const felem g_pre_comp[2][16][3]) | |
1119 | { | |
1120 | int i, skip; | |
1121 | unsigned num; | |
1122 | unsigned gen_mul = (g_scalar != NULL); | |
1123 | felem nq[3], tmp[4]; | |
1124 | u64 bits; | |
1125 | u8 sign, digit; | |
1126 | ||
1127 | /* set nq to the point at infinity */ | |
16f8d4eb | 1128 | memset(nq, 0, sizeof(nq)); |
0f113f3e MC |
1129 | |
1130 | /* | |
1131 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples | |
1132 | * of the generator (two in each of the last 28 rounds) and additions of | |
1133 | * other points multiples (every 5th round). | |
1134 | */ | |
1135 | skip = 1; /* save two point operations in the first | |
1136 | * round */ | |
1137 | for (i = (num_points ? 220 : 27); i >= 0; --i) { | |
1138 | /* double */ | |
1139 | if (!skip) | |
1140 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1141 | ||
1142 | /* add multiples of the generator */ | |
1143 | if (gen_mul && (i <= 27)) { | |
1144 | /* first, look 28 bits upwards */ | |
1145 | bits = get_bit(g_scalar, i + 196) << 3; | |
1146 | bits |= get_bit(g_scalar, i + 140) << 2; | |
1147 | bits |= get_bit(g_scalar, i + 84) << 1; | |
1148 | bits |= get_bit(g_scalar, i + 28); | |
1149 | /* select the point to add, in constant time */ | |
1150 | select_point(bits, 16, g_pre_comp[1], tmp); | |
1151 | ||
1152 | if (!skip) { | |
1153 | /* value 1 below is argument for "mixed" */ | |
1154 | point_add(nq[0], nq[1], nq[2], | |
1155 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1156 | } else { | |
1157 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1158 | skip = 0; | |
1159 | } | |
1160 | ||
1161 | /* second, look at the current position */ | |
1162 | bits = get_bit(g_scalar, i + 168) << 3; | |
1163 | bits |= get_bit(g_scalar, i + 112) << 2; | |
1164 | bits |= get_bit(g_scalar, i + 56) << 1; | |
1165 | bits |= get_bit(g_scalar, i); | |
1166 | /* select the point to add, in constant time */ | |
1167 | select_point(bits, 16, g_pre_comp[0], tmp); | |
1168 | point_add(nq[0], nq[1], nq[2], | |
1169 | nq[0], nq[1], nq[2], | |
1170 | 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); | |
1171 | } | |
1172 | ||
1173 | /* do other additions every 5 doublings */ | |
1174 | if (num_points && (i % 5 == 0)) { | |
1175 | /* loop over all scalars */ | |
1176 | for (num = 0; num < num_points; ++num) { | |
1177 | bits = get_bit(scalars[num], i + 4) << 5; | |
1178 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1179 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1180 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1181 | bits |= get_bit(scalars[num], i) << 1; | |
1182 | bits |= get_bit(scalars[num], i - 1); | |
1183 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1184 | ||
1185 | /* select the point to add or subtract */ | |
1186 | select_point(digit, 17, pre_comp[num], tmp); | |
1187 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative | |
1188 | * point */ | |
1189 | copy_conditional(tmp[1], tmp[3], sign); | |
1190 | ||
1191 | if (!skip) { | |
1192 | point_add(nq[0], nq[1], nq[2], | |
1193 | nq[0], nq[1], nq[2], | |
1194 | mixed, tmp[0], tmp[1], tmp[2]); | |
1195 | } else { | |
1196 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1197 | skip = 0; | |
1198 | } | |
1199 | } | |
1200 | } | |
1201 | } | |
1202 | felem_assign(x_out, nq[0]); | |
1203 | felem_assign(y_out, nq[1]); | |
1204 | felem_assign(z_out, nq[2]); | |
1205 | } | |
04daec86 BM |
1206 | |
1207 | /******************************************************************************/ | |
0f113f3e MC |
1208 | /* |
1209 | * FUNCTIONS TO MANAGE PRECOMPUTATION | |
04daec86 BM |
1210 | */ |
1211 | ||
1212 | static NISTP224_PRE_COMP *nistp224_pre_comp_new() | |
0f113f3e | 1213 | { |
b51bce94 RS |
1214 | NISTP224_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
1215 | ||
0f113f3e MC |
1216 | if (!ret) { |
1217 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1218 | return ret; | |
1219 | } | |
9b398ef2 | 1220 | |
0f113f3e | 1221 | ret->references = 1; |
9b398ef2 AG |
1222 | |
1223 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1224 | if (ret->lock == NULL) { | |
1225 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1226 | OPENSSL_free(ret); | |
1227 | return NULL; | |
1228 | } | |
0f113f3e MC |
1229 | return ret; |
1230 | } | |
04daec86 | 1231 | |
3aef36ff | 1232 | NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *p) |
0f113f3e | 1233 | { |
9b398ef2 | 1234 | int i; |
3aef36ff | 1235 | if (p != NULL) |
9b398ef2 | 1236 | CRYPTO_atomic_add(&p->references, 1, &i, p->lock); |
3aef36ff | 1237 | return p; |
0f113f3e | 1238 | } |
04daec86 | 1239 | |
3aef36ff | 1240 | void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *p) |
0f113f3e | 1241 | { |
9b398ef2 AG |
1242 | int i; |
1243 | ||
1244 | if (p == NULL) | |
1245 | return; | |
1246 | ||
1247 | CRYPTO_atomic_add(&p->references, -1, &i, p->lock); | |
1248 | REF_PRINT_COUNT("EC_nistp224", x); | |
1249 | if (i > 0) | |
0f113f3e | 1250 | return; |
9b398ef2 AG |
1251 | REF_ASSERT_ISNT(i < 0); |
1252 | ||
1253 | CRYPTO_THREAD_lock_free(p->lock); | |
3aef36ff | 1254 | OPENSSL_free(p); |
0f113f3e | 1255 | } |
04daec86 BM |
1256 | |
1257 | /******************************************************************************/ | |
0f113f3e MC |
1258 | /* |
1259 | * OPENSSL EC_METHOD FUNCTIONS | |
04daec86 BM |
1260 | */ |
1261 | ||
1262 | int ec_GFp_nistp224_group_init(EC_GROUP *group) | |
0f113f3e MC |
1263 | { |
1264 | int ret; | |
1265 | ret = ec_GFp_simple_group_init(group); | |
1266 | group->a_is_minus3 = 1; | |
1267 | return ret; | |
1268 | } | |
04daec86 BM |
1269 | |
1270 | int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
0f113f3e MC |
1271 | const BIGNUM *a, const BIGNUM *b, |
1272 | BN_CTX *ctx) | |
1273 | { | |
1274 | int ret = 0; | |
1275 | BN_CTX *new_ctx = NULL; | |
1276 | BIGNUM *curve_p, *curve_a, *curve_b; | |
1277 | ||
1278 | if (ctx == NULL) | |
1279 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1280 | return 0; | |
1281 | BN_CTX_start(ctx); | |
1282 | if (((curve_p = BN_CTX_get(ctx)) == NULL) || | |
1283 | ((curve_a = BN_CTX_get(ctx)) == NULL) || | |
1284 | ((curve_b = BN_CTX_get(ctx)) == NULL)) | |
1285 | goto err; | |
1286 | BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); | |
1287 | BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1288 | BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); | |
1289 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { | |
1290 | ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, | |
1291 | EC_R_WRONG_CURVE_PARAMETERS); | |
1292 | goto err; | |
1293 | } | |
1294 | group->field_mod_func = BN_nist_mod_224; | |
1295 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1296 | err: | |
1297 | BN_CTX_end(ctx); | |
23a1d5e9 | 1298 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1299 | return ret; |
1300 | } | |
1301 | ||
1302 | /* | |
1303 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = | |
1304 | * (X/Z^2, Y/Z^3) | |
1305 | */ | |
04daec86 | 1306 | int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, |
0f113f3e MC |
1307 | const EC_POINT *point, |
1308 | BIGNUM *x, BIGNUM *y, | |
1309 | BN_CTX *ctx) | |
1310 | { | |
1311 | felem z1, z2, x_in, y_in, x_out, y_out; | |
1312 | widefelem tmp; | |
1313 | ||
1314 | if (EC_POINT_is_at_infinity(group, point)) { | |
1315 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1316 | EC_R_POINT_AT_INFINITY); | |
1317 | return 0; | |
1318 | } | |
ace8f546 AP |
1319 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1320 | (!BN_to_felem(z1, point->Z))) | |
0f113f3e MC |
1321 | return 0; |
1322 | felem_inv(z2, z1); | |
1323 | felem_square(tmp, z2); | |
1324 | felem_reduce(z1, tmp); | |
1325 | felem_mul(tmp, x_in, z1); | |
1326 | felem_reduce(x_in, tmp); | |
1327 | felem_contract(x_out, x_in); | |
1328 | if (x != NULL) { | |
1329 | if (!felem_to_BN(x, x_out)) { | |
1330 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1331 | ERR_R_BN_LIB); | |
1332 | return 0; | |
1333 | } | |
1334 | } | |
1335 | felem_mul(tmp, z1, z2); | |
1336 | felem_reduce(z1, tmp); | |
1337 | felem_mul(tmp, y_in, z1); | |
1338 | felem_reduce(y_in, tmp); | |
1339 | felem_contract(y_out, y_in); | |
1340 | if (y != NULL) { | |
1341 | if (!felem_to_BN(y, y_out)) { | |
1342 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1343 | ERR_R_BN_LIB); | |
1344 | return 0; | |
1345 | } | |
1346 | } | |
1347 | return 1; | |
1348 | } | |
1349 | ||
1350 | static void make_points_affine(size_t num, felem points[ /* num */ ][3], | |
1351 | felem tmp_felems[ /* num+1 */ ]) | |
1352 | { | |
1353 | /* | |
1354 | * Runs in constant time, unless an input is the point at infinity (which | |
1355 | * normally shouldn't happen). | |
1356 | */ | |
1357 | ec_GFp_nistp_points_make_affine_internal(num, | |
1358 | points, | |
1359 | sizeof(felem), | |
1360 | tmp_felems, | |
1361 | (void (*)(void *))felem_one, | |
1362 | (int (*)(const void *)) | |
1363 | felem_is_zero_int, | |
1364 | (void (*)(void *, const void *)) | |
1365 | felem_assign, | |
1366 | (void (*)(void *, const void *)) | |
1367 | felem_square_reduce, (void (*) | |
1368 | (void *, | |
1369 | const void | |
1370 | *, | |
1371 | const void | |
1372 | *)) | |
1373 | felem_mul_reduce, | |
1374 | (void (*)(void *, const void *)) | |
1375 | felem_inv, | |
1376 | (void (*)(void *, const void *)) | |
1377 | felem_contract); | |
1378 | } | |
1379 | ||
1380 | /* | |
1381 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL | |
1382 | * values Result is stored in r (r can equal one of the inputs). | |
1383 | */ | |
04daec86 | 1384 | int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, |
0f113f3e MC |
1385 | const BIGNUM *scalar, size_t num, |
1386 | const EC_POINT *points[], | |
1387 | const BIGNUM *scalars[], BN_CTX *ctx) | |
1388 | { | |
1389 | int ret = 0; | |
1390 | int j; | |
1391 | unsigned i; | |
1392 | int mixed = 0; | |
1393 | BN_CTX *new_ctx = NULL; | |
1394 | BIGNUM *x, *y, *z, *tmp_scalar; | |
1395 | felem_bytearray g_secret; | |
1396 | felem_bytearray *secrets = NULL; | |
16f8d4eb | 1397 | felem (*pre_comp)[17][3] = NULL; |
0f113f3e MC |
1398 | felem *tmp_felems = NULL; |
1399 | felem_bytearray tmp; | |
1400 | unsigned num_bytes; | |
1401 | int have_pre_comp = 0; | |
1402 | size_t num_points = num; | |
1403 | felem x_in, y_in, z_in, x_out, y_out, z_out; | |
1404 | NISTP224_PRE_COMP *pre = NULL; | |
1405 | const felem(*g_pre_comp)[16][3] = NULL; | |
1406 | EC_POINT *generator = NULL; | |
1407 | const EC_POINT *p = NULL; | |
1408 | const BIGNUM *p_scalar = NULL; | |
1409 | ||
1410 | if (ctx == NULL) | |
1411 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1412 | return 0; | |
1413 | BN_CTX_start(ctx); | |
1414 | if (((x = BN_CTX_get(ctx)) == NULL) || | |
1415 | ((y = BN_CTX_get(ctx)) == NULL) || | |
1416 | ((z = BN_CTX_get(ctx)) == NULL) || | |
1417 | ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) | |
1418 | goto err; | |
1419 | ||
1420 | if (scalar != NULL) { | |
3aef36ff | 1421 | pre = group->pre_comp.nistp224; |
0f113f3e MC |
1422 | if (pre) |
1423 | /* we have precomputation, try to use it */ | |
1424 | g_pre_comp = (const felem(*)[16][3])pre->g_pre_comp; | |
1425 | else | |
1426 | /* try to use the standard precomputation */ | |
1427 | g_pre_comp = &gmul[0]; | |
1428 | generator = EC_POINT_new(group); | |
1429 | if (generator == NULL) | |
1430 | goto err; | |
1431 | /* get the generator from precomputation */ | |
1432 | if (!felem_to_BN(x, g_pre_comp[0][1][0]) || | |
1433 | !felem_to_BN(y, g_pre_comp[0][1][1]) || | |
1434 | !felem_to_BN(z, g_pre_comp[0][1][2])) { | |
1435 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1436 | goto err; | |
1437 | } | |
1438 | if (!EC_POINT_set_Jprojective_coordinates_GFp(group, | |
1439 | generator, x, y, z, | |
1440 | ctx)) | |
1441 | goto err; | |
1442 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
1443 | /* precomputation matches generator */ | |
1444 | have_pre_comp = 1; | |
1445 | else | |
1446 | /* | |
1447 | * we don't have valid precomputation: treat the generator as a | |
1448 | * random point | |
1449 | */ | |
1450 | num_points = num_points + 1; | |
1451 | } | |
1452 | ||
1453 | if (num_points > 0) { | |
1454 | if (num_points >= 3) { | |
1455 | /* | |
1456 | * unless we precompute multiples for just one or two points, | |
1457 | * converting those into affine form is time well spent | |
1458 | */ | |
1459 | mixed = 1; | |
1460 | } | |
b51bce94 RS |
1461 | secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); |
1462 | pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
1463 | if (mixed) |
1464 | tmp_felems = | |
16f8d4eb | 1465 | OPENSSL_malloc(sizeof(felem) * (num_points * 17 + 1)); |
0f113f3e MC |
1466 | if ((secrets == NULL) || (pre_comp == NULL) |
1467 | || (mixed && (tmp_felems == NULL))) { | |
1468 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
1469 | goto err; | |
1470 | } | |
1471 | ||
1472 | /* | |
1473 | * we treat NULL scalars as 0, and NULL points as points at infinity, | |
1474 | * i.e., they contribute nothing to the linear combination | |
1475 | */ | |
0f113f3e MC |
1476 | for (i = 0; i < num_points; ++i) { |
1477 | if (i == num) | |
1478 | /* the generator */ | |
1479 | { | |
1480 | p = EC_GROUP_get0_generator(group); | |
1481 | p_scalar = scalar; | |
1482 | } else | |
1483 | /* the i^th point */ | |
1484 | { | |
1485 | p = points[i]; | |
1486 | p_scalar = scalars[i]; | |
1487 | } | |
1488 | if ((p_scalar != NULL) && (p != NULL)) { | |
1489 | /* reduce scalar to 0 <= scalar < 2^224 */ | |
1490 | if ((BN_num_bits(p_scalar) > 224) | |
1491 | || (BN_is_negative(p_scalar))) { | |
1492 | /* | |
1493 | * this is an unusual input, and we don't guarantee | |
1494 | * constant-timeness | |
1495 | */ | |
ace8f546 | 1496 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
0f113f3e MC |
1497 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1498 | goto err; | |
1499 | } | |
1500 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1501 | } else | |
1502 | num_bytes = BN_bn2bin(p_scalar, tmp); | |
1503 | flip_endian(secrets[i], tmp, num_bytes); | |
1504 | /* precompute multiples */ | |
ace8f546 AP |
1505 | if ((!BN_to_felem(x_out, p->X)) || |
1506 | (!BN_to_felem(y_out, p->Y)) || | |
1507 | (!BN_to_felem(z_out, p->Z))) | |
0f113f3e MC |
1508 | goto err; |
1509 | felem_assign(pre_comp[i][1][0], x_out); | |
1510 | felem_assign(pre_comp[i][1][1], y_out); | |
1511 | felem_assign(pre_comp[i][1][2], z_out); | |
1512 | for (j = 2; j <= 16; ++j) { | |
1513 | if (j & 1) { | |
1514 | point_add(pre_comp[i][j][0], pre_comp[i][j][1], | |
1515 | pre_comp[i][j][2], pre_comp[i][1][0], | |
1516 | pre_comp[i][1][1], pre_comp[i][1][2], 0, | |
1517 | pre_comp[i][j - 1][0], | |
1518 | pre_comp[i][j - 1][1], | |
1519 | pre_comp[i][j - 1][2]); | |
1520 | } else { | |
1521 | point_double(pre_comp[i][j][0], pre_comp[i][j][1], | |
1522 | pre_comp[i][j][2], pre_comp[i][j / 2][0], | |
1523 | pre_comp[i][j / 2][1], | |
1524 | pre_comp[i][j / 2][2]); | |
1525 | } | |
1526 | } | |
1527 | } | |
1528 | } | |
1529 | if (mixed) | |
1530 | make_points_affine(num_points * 17, pre_comp[0], tmp_felems); | |
1531 | } | |
1532 | ||
1533 | /* the scalar for the generator */ | |
1534 | if ((scalar != NULL) && (have_pre_comp)) { | |
16f8d4eb | 1535 | memset(g_secret, 0, sizeof(g_secret)); |
0f113f3e MC |
1536 | /* reduce scalar to 0 <= scalar < 2^224 */ |
1537 | if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { | |
1538 | /* | |
1539 | * this is an unusual input, and we don't guarantee | |
1540 | * constant-timeness | |
1541 | */ | |
ace8f546 | 1542 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
0f113f3e MC |
1543 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1544 | goto err; | |
1545 | } | |
1546 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1547 | } else | |
1548 | num_bytes = BN_bn2bin(scalar, tmp); | |
1549 | flip_endian(g_secret, tmp, num_bytes); | |
1550 | /* do the multiplication with generator precomputation */ | |
1551 | batch_mul(x_out, y_out, z_out, | |
1552 | (const felem_bytearray(*))secrets, num_points, | |
1553 | g_secret, | |
1554 | mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); | |
1555 | } else | |
1556 | /* do the multiplication without generator precomputation */ | |
1557 | batch_mul(x_out, y_out, z_out, | |
1558 | (const felem_bytearray(*))secrets, num_points, | |
1559 | NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); | |
1560 | /* reduce the output to its unique minimal representation */ | |
1561 | felem_contract(x_in, x_out); | |
1562 | felem_contract(y_in, y_out); | |
1563 | felem_contract(z_in, z_out); | |
1564 | if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || | |
1565 | (!felem_to_BN(z, z_in))) { | |
1566 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1567 | goto err; | |
1568 | } | |
1569 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); | |
1570 | ||
1571 | err: | |
1572 | BN_CTX_end(ctx); | |
8fdc3734 | 1573 | EC_POINT_free(generator); |
23a1d5e9 | 1574 | BN_CTX_free(new_ctx); |
b548a1f1 RS |
1575 | OPENSSL_free(secrets); |
1576 | OPENSSL_free(pre_comp); | |
1577 | OPENSSL_free(tmp_felems); | |
0f113f3e MC |
1578 | return ret; |
1579 | } | |
04daec86 BM |
1580 | |
1581 | int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
0f113f3e MC |
1582 | { |
1583 | int ret = 0; | |
1584 | NISTP224_PRE_COMP *pre = NULL; | |
1585 | int i, j; | |
1586 | BN_CTX *new_ctx = NULL; | |
1587 | BIGNUM *x, *y; | |
1588 | EC_POINT *generator = NULL; | |
1589 | felem tmp_felems[32]; | |
1590 | ||
1591 | /* throw away old precomputation */ | |
2c52ac9b | 1592 | EC_pre_comp_free(group); |
0f113f3e MC |
1593 | if (ctx == NULL) |
1594 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1595 | return 0; | |
1596 | BN_CTX_start(ctx); | |
1597 | if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) | |
1598 | goto err; | |
1599 | /* get the generator */ | |
1600 | if (group->generator == NULL) | |
1601 | goto err; | |
1602 | generator = EC_POINT_new(group); | |
1603 | if (generator == NULL) | |
1604 | goto err; | |
1605 | BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); | |
1606 | BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); | |
1607 | if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) | |
1608 | goto err; | |
1609 | if ((pre = nistp224_pre_comp_new()) == NULL) | |
1610 | goto err; | |
1611 | /* | |
1612 | * if the generator is the standard one, use built-in precomputation | |
1613 | */ | |
1614 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { | |
1615 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
615614c8 | 1616 | goto done; |
0f113f3e | 1617 | } |
ace8f546 AP |
1618 | if ((!BN_to_felem(pre->g_pre_comp[0][1][0], group->generator->X)) || |
1619 | (!BN_to_felem(pre->g_pre_comp[0][1][1], group->generator->Y)) || | |
1620 | (!BN_to_felem(pre->g_pre_comp[0][1][2], group->generator->Z))) | |
0f113f3e MC |
1621 | goto err; |
1622 | /* | |
1623 | * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, | |
1624 | * 2^140*G, 2^196*G for the second one | |
1625 | */ | |
1626 | for (i = 1; i <= 8; i <<= 1) { | |
1627 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
1628 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], | |
1629 | pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); | |
1630 | for (j = 0; j < 27; ++j) { | |
1631 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
1632 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], | |
1633 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1634 | } | |
1635 | if (i == 8) | |
1636 | break; | |
1637 | point_double(pre->g_pre_comp[0][2 * i][0], | |
1638 | pre->g_pre_comp[0][2 * i][1], | |
1639 | pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], | |
1640 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1641 | for (j = 0; j < 27; ++j) { | |
1642 | point_double(pre->g_pre_comp[0][2 * i][0], | |
1643 | pre->g_pre_comp[0][2 * i][1], | |
1644 | pre->g_pre_comp[0][2 * i][2], | |
1645 | 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]); | |
1648 | } | |
1649 | } | |
1650 | for (i = 0; i < 2; i++) { | |
1651 | /* g_pre_comp[i][0] is the point at infinity */ | |
1652 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); | |
1653 | /* the remaining multiples */ | |
1654 | /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ | |
1655 | point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], | |
1656 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], | |
1657 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], | |
1658 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1659 | pre->g_pre_comp[i][2][2]); | |
1660 | /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ | |
1661 | point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], | |
1662 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], | |
1663 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1664 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1665 | pre->g_pre_comp[i][2][2]); | |
1666 | /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ | |
1667 | point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], | |
1668 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], | |
1669 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1670 | 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], | |
1671 | pre->g_pre_comp[i][4][2]); | |
1672 | /* | |
1673 | * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G | |
1674 | */ | |
1675 | point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], | |
1676 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], | |
1677 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], | |
1678 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1679 | pre->g_pre_comp[i][2][2]); | |
1680 | for (j = 1; j < 8; ++j) { | |
1681 | /* odd multiples: add G resp. 2^28*G */ | |
1682 | point_add(pre->g_pre_comp[i][2 * j + 1][0], | |
1683 | pre->g_pre_comp[i][2 * j + 1][1], | |
1684 | pre->g_pre_comp[i][2 * j + 1][2], | |
1685 | pre->g_pre_comp[i][2 * j][0], | |
1686 | pre->g_pre_comp[i][2 * j][1], | |
1687 | pre->g_pre_comp[i][2 * j][2], 0, | |
1688 | pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], | |
1689 | pre->g_pre_comp[i][1][2]); | |
1690 | } | |
1691 | } | |
1692 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); | |
1693 | ||
615614c8 | 1694 | done: |
3aef36ff | 1695 | SETPRECOMP(group, nistp224, pre); |
0f113f3e | 1696 | pre = NULL; |
3aef36ff | 1697 | ret = 1; |
04daec86 | 1698 | err: |
0f113f3e | 1699 | BN_CTX_end(ctx); |
8fdc3734 | 1700 | EC_POINT_free(generator); |
23a1d5e9 | 1701 | BN_CTX_free(new_ctx); |
3aef36ff | 1702 | EC_nistp224_pre_comp_free(pre); |
0f113f3e MC |
1703 | return ret; |
1704 | } | |
04daec86 BM |
1705 | |
1706 | int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) | |
0f113f3e | 1707 | { |
3aef36ff | 1708 | return HAVEPRECOMP(group, nistp224); |
0f113f3e | 1709 | } |
396cb565 | 1710 | |
04daec86 | 1711 | #endif |