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04daec86 BM |
1 | /* crypto/ec/ecp_nistp224.c */ |
2 | /* | |
3 | * Written by Emilia Kasper (Google) for the OpenSSL project. | |
4 | */ | |
3e00b4c9 | 5 | /* Copyright 2011 Google Inc. |
04daec86 | 6 | * |
3e00b4c9 | 7 | * Licensed under the Apache License, Version 2.0 (the "License"); |
04daec86 | 8 | * |
3e00b4c9 BM |
9 | * you may not use this file except in compliance with the License. |
10 | * You may obtain a copy of the License at | |
04daec86 | 11 | * |
3e00b4c9 | 12 | * http://www.apache.org/licenses/LICENSE-2.0 |
04daec86 | 13 | * |
3e00b4c9 BM |
14 | * Unless required by applicable law or agreed to in writing, software |
15 | * distributed under the License is distributed on an "AS IS" BASIS, | |
16 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
17 | * See the License for the specific language governing permissions and | |
18 | * limitations under the License. | |
04daec86 BM |
19 | */ |
20 | ||
21 | /* | |
22 | * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication | |
23 | * | |
24 | * Inspired by Daniel J. Bernstein's public domain nistp224 implementation | |
25 | * and Adam Langley's public domain 64-bit C implementation of curve25519 | |
26 | */ | |
e0d6132b BM |
27 | |
28 | #include <openssl/opensslconf.h> | |
29 | #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 | |
30 | ||
04daec86 BM |
31 | #include <stdint.h> |
32 | #include <string.h> | |
33 | #include <openssl/err.h> | |
34 | #include "ec_lcl.h" | |
35 | ||
396cb565 BM |
36 | #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) |
37 | /* even with gcc, the typedef won't work for 32-bit platforms */ | |
38 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ | |
39 | #else | |
40 | #error "Need GCC 3.1 or later to define type uint128_t" | |
41 | #endif | |
04daec86 BM |
42 | |
43 | typedef uint8_t u8; | |
3e00b4c9 BM |
44 | typedef uint64_t u64; |
45 | typedef int64_t s64; | |
04daec86 | 46 | |
04daec86 BM |
47 | |
48 | /******************************************************************************/ | |
49 | /* INTERNAL REPRESENTATION OF FIELD ELEMENTS | |
50 | * | |
51 | * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 | |
3e00b4c9 BM |
52 | * using 64-bit coefficients called 'limbs', |
53 | * and sometimes (for multiplication results) as | |
04daec86 | 54 | * 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 |
55 | * using 128-bit coefficients called 'widelimbs'. |
56 | * A 4-limb representation is an 'felem'; | |
57 | * a 7-widelimb representation is a 'widefelem'. | |
58 | * Even within felems, bits of adjacent limbs overlap, and we don't always | |
59 | * reduce the representations: we ensure that inputs to each felem | |
04daec86 BM |
60 | * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, |
61 | * and fit into a 128-bit word without overflow. The coefficients are then | |
3e00b4c9 BM |
62 | * again partially reduced to obtain an felem satisfying a_i < 2^57. |
63 | * We only reduce to the unique minimal representation at the end of the | |
64 | * computation. | |
04daec86 BM |
65 | */ |
66 | ||
3e00b4c9 BM |
67 | typedef uint64_t limb; |
68 | typedef uint128_t widelimb; | |
69 | ||
70 | typedef limb felem[4]; | |
71 | typedef widelimb widefelem[7]; | |
04daec86 | 72 | |
396cb565 | 73 | /* Field element represented as a byte arrary. |
3e00b4c9 BM |
74 | * 28*8 = 224 bits is also the group order size for the elliptic curve, |
75 | * and we also use this type for scalars for point multiplication. | |
76 | */ | |
396cb565 BM |
77 | typedef u8 felem_bytearray[28]; |
78 | ||
79 | static const felem_bytearray nistp224_curve_params[5] = { | |
80 | {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ | |
81 | 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, | |
82 | 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, | |
83 | {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ | |
84 | 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, | |
85 | 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, | |
86 | {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ | |
87 | 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, | |
88 | 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, | |
89 | {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ | |
90 | 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, | |
91 | 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, | |
92 | {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ | |
93 | 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, | |
94 | 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} | |
95 | }; | |
04daec86 BM |
96 | |
97 | /* Precomputed multiples of the standard generator | |
3e00b4c9 BM |
98 | * Points are given in coordinates (X, Y, Z) where Z normally is 1 |
99 | * (0 for the point at infinity). | |
100 | * For each field element, slice a_0 is word 0, etc. | |
101 | * | |
102 | * The table has 2 * 16 elements, starting with the following: | |
103 | * index | bits | point | |
104 | * ------+---------+------------------------------ | |
105 | * 0 | 0 0 0 0 | 0G | |
106 | * 1 | 0 0 0 1 | 1G | |
107 | * 2 | 0 0 1 0 | 2^56G | |
108 | * 3 | 0 0 1 1 | (2^56 + 1)G | |
109 | * 4 | 0 1 0 0 | 2^112G | |
110 | * 5 | 0 1 0 1 | (2^112 + 1)G | |
111 | * 6 | 0 1 1 0 | (2^112 + 2^56)G | |
112 | * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G | |
113 | * 8 | 1 0 0 0 | 2^168G | |
114 | * 9 | 1 0 0 1 | (2^168 + 1)G | |
115 | * 10 | 1 0 1 0 | (2^168 + 2^56)G | |
116 | * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G | |
117 | * 12 | 1 1 0 0 | (2^168 + 2^112)G | |
118 | * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G | |
119 | * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G | |
120 | * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G | |
121 | * followed by a copy of this with each element multiplied by 2^28. | |
122 | * | |
123 | * The reason for this is so that we can clock bits into four different | |
124 | * locations when doing simple scalar multiplies against the base point, | |
125 | * and then another four locations using the second 16 elements. | |
126 | */ | |
127 | static const felem gmul[2][16][3] = | |
128 | {{{{0, 0, 0, 0}, | |
129 | {0, 0, 0, 0}, | |
130 | {0, 0, 0, 0}}, | |
131 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, | |
132 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, | |
133 | {1, 0, 0, 0}}, | |
134 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, | |
135 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, | |
136 | {1, 0, 0, 0}}, | |
137 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, | |
138 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, | |
139 | {1, 0, 0, 0}}, | |
140 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, | |
141 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, | |
142 | {1, 0, 0, 0}}, | |
143 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, | |
144 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, | |
145 | {1, 0, 0, 0}}, | |
146 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, | |
147 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, | |
148 | {1, 0, 0, 0}}, | |
149 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, | |
150 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, | |
151 | {1, 0, 0, 0}}, | |
152 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, | |
153 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, | |
154 | {1, 0, 0, 0}}, | |
155 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, | |
156 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, | |
157 | {1, 0, 0, 0}}, | |
158 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, | |
159 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, | |
160 | {1, 0, 0, 0}}, | |
161 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, | |
162 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, | |
163 | {1, 0, 0, 0}}, | |
164 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, | |
165 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, | |
166 | {1, 0, 0, 0}}, | |
167 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, | |
168 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, | |
169 | {1, 0, 0, 0}}, | |
170 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, | |
171 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, | |
172 | {1, 0, 0, 0}}, | |
173 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, | |
174 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, | |
175 | {1, 0, 0, 0}}}, | |
176 | {{{0, 0, 0, 0}, | |
177 | {0, 0, 0, 0}, | |
178 | {0, 0, 0, 0}}, | |
179 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, | |
180 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, | |
181 | {1, 0, 0, 0}}, | |
182 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, | |
183 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, | |
184 | {1, 0, 0, 0}}, | |
185 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, | |
186 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, | |
187 | {1, 0, 0, 0}}, | |
188 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, | |
189 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, | |
190 | {1, 0, 0, 0}}, | |
191 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, | |
192 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, | |
193 | {1, 0, 0, 0}}, | |
194 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, | |
195 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, | |
196 | {1, 0, 0, 0}}, | |
197 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, | |
198 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, | |
199 | {1, 0, 0, 0}}, | |
200 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, | |
201 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, | |
202 | {1, 0, 0, 0}}, | |
203 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, | |
204 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, | |
205 | {1, 0, 0, 0}}, | |
206 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, | |
207 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, | |
208 | {1, 0, 0, 0}}, | |
209 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, | |
210 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, | |
211 | {1, 0, 0, 0}}, | |
212 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, | |
213 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, | |
214 | {1, 0, 0, 0}}, | |
215 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, | |
216 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, | |
217 | {1, 0, 0, 0}}, | |
218 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, | |
219 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, | |
220 | {1, 0, 0, 0}}, | |
221 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, | |
222 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, | |
223 | {1, 0, 0, 0}}}}; | |
04daec86 BM |
224 | |
225 | /* Precomputation for the group generator. */ | |
226 | typedef struct { | |
3e00b4c9 | 227 | felem g_pre_comp[2][16][3]; |
04daec86 BM |
228 | int references; |
229 | } NISTP224_PRE_COMP; | |
230 | ||
231 | const EC_METHOD *EC_GFp_nistp224_method(void) | |
232 | { | |
233 | static const EC_METHOD ret = { | |
3e00b4c9 | 234 | EC_FLAGS_DEFAULT_OCT, |
04daec86 BM |
235 | NID_X9_62_prime_field, |
236 | ec_GFp_nistp224_group_init, | |
237 | ec_GFp_simple_group_finish, | |
238 | ec_GFp_simple_group_clear_finish, | |
239 | ec_GFp_nist_group_copy, | |
240 | ec_GFp_nistp224_group_set_curve, | |
241 | ec_GFp_simple_group_get_curve, | |
242 | ec_GFp_simple_group_get_degree, | |
243 | ec_GFp_simple_group_check_discriminant, | |
244 | ec_GFp_simple_point_init, | |
245 | ec_GFp_simple_point_finish, | |
246 | ec_GFp_simple_point_clear_finish, | |
247 | ec_GFp_simple_point_copy, | |
248 | ec_GFp_simple_point_set_to_infinity, | |
249 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
250 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
251 | ec_GFp_simple_point_set_affine_coordinates, | |
252 | ec_GFp_nistp224_point_get_affine_coordinates, | |
e0d6132b BM |
253 | 0 /* point_set_compressed_coordinates */, |
254 | 0 /* point2oct */, | |
255 | 0 /* oct2point */, | |
04daec86 BM |
256 | ec_GFp_simple_add, |
257 | ec_GFp_simple_dbl, | |
258 | ec_GFp_simple_invert, | |
259 | ec_GFp_simple_is_at_infinity, | |
260 | ec_GFp_simple_is_on_curve, | |
261 | ec_GFp_simple_cmp, | |
262 | ec_GFp_simple_make_affine, | |
263 | ec_GFp_simple_points_make_affine, | |
264 | ec_GFp_nistp224_points_mul, | |
265 | ec_GFp_nistp224_precompute_mult, | |
266 | ec_GFp_nistp224_have_precompute_mult, | |
267 | ec_GFp_nist_field_mul, | |
268 | ec_GFp_nist_field_sqr, | |
269 | 0 /* field_div */, | |
270 | 0 /* field_encode */, | |
271 | 0 /* field_decode */, | |
272 | 0 /* field_set_to_one */ }; | |
273 | ||
274 | return &ret; | |
275 | } | |
276 | ||
277 | /* Helper functions to convert field elements to/from internal representation */ | |
3e00b4c9 | 278 | static void bin28_to_felem(felem out, const u8 in[28]) |
04daec86 BM |
279 | { |
280 | out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; | |
281 | out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; | |
282 | out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; | |
283 | out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; | |
284 | } | |
285 | ||
3e00b4c9 | 286 | static void felem_to_bin28(u8 out[28], const felem in) |
04daec86 BM |
287 | { |
288 | unsigned i; | |
289 | for (i = 0; i < 7; ++i) | |
290 | { | |
291 | out[i] = in[0]>>(8*i); | |
292 | out[i+7] = in[1]>>(8*i); | |
293 | out[i+14] = in[2]>>(8*i); | |
294 | out[i+21] = in[3]>>(8*i); | |
295 | } | |
296 | } | |
297 | ||
298 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ | |
299 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | |
300 | { | |
301 | unsigned i; | |
302 | for (i = 0; i < len; ++i) | |
303 | out[i] = in[len-1-i]; | |
304 | } | |
305 | ||
306 | /* From OpenSSL BIGNUM to internal representation */ | |
3e00b4c9 | 307 | static int BN_to_felem(felem out, const BIGNUM *bn) |
04daec86 | 308 | { |
3e00b4c9 | 309 | felem_bytearray b_in; |
396cb565 | 310 | felem_bytearray b_out; |
1b5af90b BM |
311 | unsigned num_bytes; |
312 | ||
04daec86 | 313 | /* BN_bn2bin eats leading zeroes */ |
396cb565 | 314 | memset(b_out, 0, sizeof b_out); |
1b5af90b | 315 | num_bytes = BN_num_bytes(bn); |
396cb565 | 316 | if (num_bytes > sizeof b_out) |
04daec86 BM |
317 | { |
318 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
319 | return 0; | |
320 | } | |
321 | if (BN_is_negative(bn)) | |
322 | { | |
323 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
324 | return 0; | |
325 | } | |
326 | num_bytes = BN_bn2bin(bn, b_in); | |
327 | flip_endian(b_out, b_in, num_bytes); | |
328 | bin28_to_felem(out, b_out); | |
329 | return 1; | |
330 | } | |
331 | ||
332 | /* From internal representation to OpenSSL BIGNUM */ | |
3e00b4c9 | 333 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) |
04daec86 | 334 | { |
396cb565 | 335 | felem_bytearray b_in, b_out; |
04daec86 | 336 | felem_to_bin28(b_in, in); |
396cb565 BM |
337 | flip_endian(b_out, b_in, sizeof b_out); |
338 | return BN_bin2bn(b_out, sizeof b_out, out); | |
04daec86 BM |
339 | } |
340 | ||
341 | /******************************************************************************/ | |
342 | /* FIELD OPERATIONS | |
343 | * | |
344 | * Field operations, using the internal representation of field elements. | |
345 | * NB! These operations are specific to our point multiplication and cannot be | |
346 | * expected to be correct in general - e.g., multiplication with a large scalar | |
347 | * will cause an overflow. | |
348 | * | |
349 | */ | |
350 | ||
3e00b4c9 BM |
351 | static void felem_one(felem out) |
352 | { | |
353 | out[0] = 1; | |
354 | out[1] = 0; | |
355 | out[2] = 0; | |
356 | out[3] = 0; | |
357 | } | |
358 | ||
359 | static void felem_assign(felem out, const felem in) | |
360 | { | |
361 | out[0] = in[0]; | |
362 | out[1] = in[1]; | |
363 | out[2] = in[2]; | |
364 | out[3] = in[3]; | |
365 | } | |
366 | ||
04daec86 | 367 | /* Sum two field elements: out += in */ |
3e00b4c9 | 368 | static void felem_sum(felem out, const felem in) |
04daec86 BM |
369 | { |
370 | out[0] += in[0]; | |
371 | out[1] += in[1]; | |
372 | out[2] += in[2]; | |
373 | out[3] += in[3]; | |
374 | } | |
375 | ||
3e00b4c9 BM |
376 | /* Get negative value: out = -in */ |
377 | /* Assumes in[i] < 2^57 */ | |
378 | static void felem_neg(felem out, const felem in) | |
379 | { | |
380 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); | |
381 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
382 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
383 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
384 | ||
385 | /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ | |
386 | out[0] = two58p2 - in[0]; | |
387 | out[1] = two58m42m2 - in[1]; | |
388 | out[2] = two58m2 - in[2]; | |
389 | out[3] = two58m2 - in[3]; | |
390 | } | |
391 | ||
04daec86 BM |
392 | /* Subtract field elements: out -= in */ |
393 | /* Assumes in[i] < 2^57 */ | |
3e00b4c9 | 394 | static void felem_diff(felem out, const felem in) |
04daec86 | 395 | { |
3e00b4c9 BM |
396 | static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); |
397 | static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); | |
398 | static const limb two58m42m2 = (((limb) 1) << 58) - | |
399 | (((limb) 1) << 42) - (((limb) 1) << 2); | |
04daec86 BM |
400 | |
401 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
402 | out[0] += two58p2; | |
403 | out[1] += two58m42m2; | |
404 | out[2] += two58m2; | |
405 | out[3] += two58m2; | |
406 | ||
407 | out[0] -= in[0]; | |
408 | out[1] -= in[1]; | |
409 | out[2] -= in[2]; | |
410 | out[3] -= in[3]; | |
411 | } | |
412 | ||
3e00b4c9 | 413 | /* Subtract in unreduced 128-bit mode: out -= in */ |
04daec86 | 414 | /* Assumes in[i] < 2^119 */ |
3e00b4c9 | 415 | static void widefelem_diff(widefelem out, const widefelem in) |
04daec86 | 416 | { |
3e00b4c9 BM |
417 | static const widelimb two120 = ((widelimb) 1) << 120; |
418 | static const widelimb two120m64 = (((widelimb) 1) << 120) - | |
419 | (((widelimb) 1) << 64); | |
420 | static const widelimb two120m104m64 = (((widelimb) 1) << 120) - | |
421 | (((widelimb) 1) << 104) - (((widelimb) 1) << 64); | |
04daec86 BM |
422 | |
423 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
424 | out[0] += two120; | |
425 | out[1] += two120m64; | |
426 | out[2] += two120m64; | |
427 | out[3] += two120; | |
428 | out[4] += two120m104m64; | |
429 | out[5] += two120m64; | |
430 | out[6] += two120m64; | |
431 | ||
432 | out[0] -= in[0]; | |
433 | out[1] -= in[1]; | |
434 | out[2] -= in[2]; | |
435 | out[3] -= in[3]; | |
436 | out[4] -= in[4]; | |
437 | out[5] -= in[5]; | |
438 | out[6] -= in[6]; | |
439 | } | |
440 | ||
441 | /* Subtract in mixed mode: out128 -= in64 */ | |
442 | /* in[i] < 2^63 */ | |
3e00b4c9 | 443 | static void felem_diff_128_64(widefelem out, const felem in) |
04daec86 | 444 | { |
3e00b4c9 BM |
445 | static const widelimb two64p8 = (((widelimb) 1) << 64) + |
446 | (((widelimb) 1) << 8); | |
447 | static const widelimb two64m8 = (((widelimb) 1) << 64) - | |
448 | (((widelimb) 1) << 8); | |
449 | static const widelimb two64m48m8 = (((widelimb) 1) << 64) - | |
450 | (((widelimb) 1) << 48) - (((widelimb) 1) << 8); | |
04daec86 BM |
451 | |
452 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ | |
453 | out[0] += two64p8; | |
454 | out[1] += two64m48m8; | |
455 | out[2] += two64m8; | |
456 | out[3] += two64m8; | |
457 | ||
458 | out[0] -= in[0]; | |
459 | out[1] -= in[1]; | |
460 | out[2] -= in[2]; | |
461 | out[3] -= in[3]; | |
462 | } | |
463 | ||
3e00b4c9 | 464 | /* Multiply a field element by a scalar: out = out * scalar |
04daec86 | 465 | * The scalars we actually use are small, so results fit without overflow */ |
3e00b4c9 | 466 | static void felem_scalar(felem out, const limb scalar) |
04daec86 BM |
467 | { |
468 | out[0] *= scalar; | |
469 | out[1] *= scalar; | |
470 | out[2] *= scalar; | |
471 | out[3] *= scalar; | |
472 | } | |
473 | ||
3e00b4c9 | 474 | /* Multiply an unreduced field element by a scalar: out = out * scalar |
04daec86 | 475 | * The scalars we actually use are small, so results fit without overflow */ |
3e00b4c9 | 476 | static void widefelem_scalar(widefelem out, const widelimb scalar) |
04daec86 BM |
477 | { |
478 | out[0] *= scalar; | |
479 | out[1] *= scalar; | |
480 | out[2] *= scalar; | |
481 | out[3] *= scalar; | |
482 | out[4] *= scalar; | |
483 | out[5] *= scalar; | |
484 | out[6] *= scalar; | |
485 | } | |
486 | ||
487 | /* Square a field element: out = in^2 */ | |
3e00b4c9 | 488 | static void felem_square(widefelem out, const felem in) |
04daec86 | 489 | { |
3e00b4c9 BM |
490 | limb tmp0, tmp1, tmp2; |
491 | tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; | |
492 | out[0] = ((widelimb) in[0]) * in[0]; | |
493 | out[1] = ((widelimb) in[0]) * tmp1; | |
494 | out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; | |
495 | out[3] = ((widelimb) in[3]) * tmp0 + | |
496 | ((widelimb) in[1]) * tmp2; | |
497 | out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; | |
498 | out[5] = ((widelimb) in[3]) * tmp2; | |
499 | out[6] = ((widelimb) in[3]) * in[3]; | |
04daec86 BM |
500 | } |
501 | ||
502 | /* Multiply two field elements: out = in1 * in2 */ | |
3e00b4c9 | 503 | static void felem_mul(widefelem out, const felem in1, const felem in2) |
04daec86 | 504 | { |
3e00b4c9 BM |
505 | out[0] = ((widelimb) in1[0]) * in2[0]; |
506 | out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; | |
507 | out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + | |
508 | ((widelimb) in1[2]) * in2[0]; | |
509 | out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + | |
510 | ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; | |
511 | out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + | |
512 | ((widelimb) in1[3]) * in2[1]; | |
513 | out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; | |
514 | out[6] = ((widelimb) in1[3]) * in2[3]; | |
04daec86 BM |
515 | } |
516 | ||
3e00b4c9 BM |
517 | /* Reduce seven 128-bit coefficients to four 64-bit coefficients. |
518 | * Requires in[i] < 2^126, | |
519 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ | |
520 | static void felem_reduce(felem out, const widefelem in) | |
04daec86 | 521 | { |
3e00b4c9 BM |
522 | static const widelimb two127p15 = (((widelimb) 1) << 127) + |
523 | (((widelimb) 1) << 15); | |
524 | static const widelimb two127m71 = (((widelimb) 1) << 127) - | |
525 | (((widelimb) 1) << 71); | |
526 | static const widelimb two127m71m55 = (((widelimb) 1) << 127) - | |
527 | (((widelimb) 1) << 71) - (((widelimb) 1) << 55); | |
528 | widelimb output[5]; | |
04daec86 BM |
529 | |
530 | /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ | |
531 | output[0] = in[0] + two127p15; | |
532 | output[1] = in[1] + two127m71m55; | |
533 | output[2] = in[2] + two127m71; | |
534 | output[3] = in[3]; | |
535 | output[4] = in[4]; | |
536 | ||
537 | /* Eliminate in[4], in[5], in[6] */ | |
538 | output[4] += in[6] >> 16; | |
3e00b4c9 | 539 | output[3] += (in[6] & 0xffff) << 40; |
04daec86 BM |
540 | output[2] -= in[6]; |
541 | ||
542 | output[3] += in[5] >> 16; | |
3e00b4c9 | 543 | output[2] += (in[5] & 0xffff) << 40; |
04daec86 BM |
544 | output[1] -= in[5]; |
545 | ||
546 | output[2] += output[4] >> 16; | |
3e00b4c9 | 547 | output[1] += (output[4] & 0xffff) << 40; |
04daec86 | 548 | output[0] -= output[4]; |
04daec86 BM |
549 | |
550 | /* Carry 2 -> 3 -> 4 */ | |
551 | output[3] += output[2] >> 56; | |
552 | output[2] &= 0x00ffffffffffffff; | |
553 | ||
3e00b4c9 | 554 | output[4] = output[3] >> 56; |
04daec86 BM |
555 | output[3] &= 0x00ffffffffffffff; |
556 | ||
3e00b4c9 | 557 | /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ |
04daec86 BM |
558 | |
559 | /* Eliminate output[4] */ | |
560 | output[2] += output[4] >> 16; | |
3e00b4c9 BM |
561 | /* output[2] < 2^56 + 2^56 = 2^57 */ |
562 | output[1] += (output[4] & 0xffff) << 40; | |
04daec86 BM |
563 | output[0] -= output[4]; |
564 | ||
565 | /* Carry 0 -> 1 -> 2 -> 3 */ | |
566 | output[1] += output[0] >> 56; | |
567 | out[0] = output[0] & 0x00ffffffffffffff; | |
568 | ||
569 | output[2] += output[1] >> 56; | |
3e00b4c9 | 570 | /* output[2] < 2^57 + 2^72 */ |
04daec86 BM |
571 | out[1] = output[1] & 0x00ffffffffffffff; |
572 | output[3] += output[2] >> 56; | |
3e00b4c9 | 573 | /* output[3] <= 2^56 + 2^16 */ |
04daec86 BM |
574 | out[2] = output[2] & 0x00ffffffffffffff; |
575 | ||
576 | /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, | |
3e00b4c9 BM |
577 | * out[3] <= 2^56 + 2^16 (due to final carry), |
578 | * so out < 2*p */ | |
04daec86 BM |
579 | out[3] = output[3]; |
580 | } | |
581 | ||
3e00b4c9 | 582 | static void felem_square_reduce(felem out, const felem in) |
04daec86 | 583 | { |
3e00b4c9 BM |
584 | widefelem tmp; |
585 | felem_square(tmp, in); | |
586 | felem_reduce(out, tmp); | |
587 | } | |
04daec86 | 588 | |
3e00b4c9 BM |
589 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) |
590 | { | |
591 | widefelem tmp; | |
592 | felem_mul(tmp, in1, in2); | |
593 | felem_reduce(out, tmp); | |
594 | } | |
04daec86 | 595 | |
3e00b4c9 BM |
596 | /* Reduce to unique minimal representation. |
597 | * Requires 0 <= in < 2*p (always call felem_reduce first) */ | |
598 | static void felem_contract(felem out, const felem in) | |
599 | { | |
600 | static const int64_t two56 = ((limb) 1) << 56; | |
601 | /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ | |
602 | /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ | |
603 | int64_t tmp[4], a; | |
604 | tmp[0] = in[0]; | |
605 | tmp[1] = in[1]; | |
606 | tmp[2] = in[2]; | |
607 | tmp[3] = in[3]; | |
608 | /* Case 1: a = 1 iff in >= 2^224 */ | |
609 | a = (in[3] >> 56); | |
610 | tmp[0] -= a; | |
611 | tmp[1] += a << 40; | |
04daec86 | 612 | tmp[3] &= 0x00ffffffffffffff; |
3e00b4c9 BM |
613 | /* Case 2: a = 0 iff p <= in < 2^224, i.e., |
614 | * the high 128 bits are all 1 and the lower part is non-zero */ | |
615 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | | |
616 | (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); | |
617 | a &= 0x00ffffffffffffff; | |
618 | /* turn a into an all-one mask (if a = 0) or an all-zero mask */ | |
619 | a = (a - 1) >> 63; | |
620 | /* subtract 2^224 - 2^96 + 1 if a is all-one*/ | |
621 | tmp[3] &= a ^ 0xffffffffffffffff; | |
622 | tmp[2] &= a ^ 0xffffffffffffffff; | |
623 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; | |
624 | tmp[0] -= 1 & a; | |
04daec86 | 625 | |
3e00b4c9 BM |
626 | /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must |
627 | * be non-zero, so we only need one step */ | |
04daec86 BM |
628 | a = tmp[0] >> 63; |
629 | tmp[0] += two56 & a; | |
630 | tmp[1] -= 1 & a; | |
631 | ||
04daec86 BM |
632 | /* carry 1 -> 2 -> 3 */ |
633 | tmp[2] += tmp[1] >> 56; | |
634 | tmp[1] &= 0x00ffffffffffffff; | |
635 | ||
636 | tmp[3] += tmp[2] >> 56; | |
637 | tmp[2] &= 0x00ffffffffffffff; | |
638 | ||
3e00b4c9 | 639 | /* Now 0 <= out < p */ |
04daec86 BM |
640 | out[0] = tmp[0]; |
641 | out[1] = tmp[1]; | |
642 | out[2] = tmp[2]; | |
643 | out[3] = tmp[3]; | |
644 | } | |
645 | ||
646 | /* Zero-check: returns 1 if input is 0, and 0 otherwise. | |
647 | * We know that field elements are reduced to in < 2^225, | |
648 | * so we only need to check three cases: 0, 2^224 - 2^96 + 1, | |
649 | * and 2^225 - 2^97 + 2 */ | |
3e00b4c9 | 650 | static limb felem_is_zero(const felem in) |
04daec86 | 651 | { |
3e00b4c9 | 652 | limb zero, two224m96p1, two225m97p2; |
1b5af90b BM |
653 | |
654 | zero = in[0] | in[1] | in[2] | in[3]; | |
04daec86 | 655 | zero = (((int64_t)(zero) - 1) >> 63) & 1; |
1b5af90b | 656 | two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) |
04daec86 BM |
657 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); |
658 | two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; | |
1b5af90b | 659 | two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) |
04daec86 BM |
660 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); |
661 | two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; | |
1b5af90b | 662 | return (zero | two224m96p1 | two225m97p2); |
04daec86 BM |
663 | } |
664 | ||
3e00b4c9 BM |
665 | static limb felem_is_zero_int(const felem in) |
666 | { | |
667 | return (int) (felem_is_zero(in) & ((limb)1)); | |
668 | } | |
669 | ||
04daec86 BM |
670 | /* Invert a field element */ |
671 | /* Computation chain copied from djb's code */ | |
3e00b4c9 | 672 | static void felem_inv(felem out, const felem in) |
04daec86 | 673 | { |
3e00b4c9 BM |
674 | felem ftmp, ftmp2, ftmp3, ftmp4; |
675 | widefelem tmp; | |
04daec86 | 676 | unsigned i; |
1b5af90b | 677 | |
04daec86 BM |
678 | felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ |
679 | felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ | |
680 | felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ | |
681 | felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ | |
682 | felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ | |
683 | felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ | |
684 | felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ | |
685 | felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ | |
686 | felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ | |
687 | for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ | |
688 | { | |
689 | felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); | |
690 | } | |
691 | felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ | |
692 | felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ | |
693 | for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ | |
694 | { | |
695 | felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); | |
696 | } | |
697 | felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ | |
698 | felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ | |
699 | for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ | |
700 | { | |
701 | felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); | |
702 | } | |
703 | felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ | |
704 | felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ | |
705 | for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ | |
706 | { | |
707 | felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); | |
708 | } | |
709 | felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ | |
710 | felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ | |
711 | for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ | |
712 | { | |
713 | felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); | |
714 | } | |
715 | felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ | |
716 | for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ | |
717 | { | |
718 | felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); | |
719 | } | |
720 | felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ | |
721 | felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ | |
722 | felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ | |
723 | for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ | |
724 | { | |
725 | felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); | |
726 | } | |
727 | felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ | |
728 | } | |
729 | ||
730 | /* Copy in constant time: | |
731 | * if icopy == 1, copy in to out, | |
732 | * if icopy == 0, copy out to itself. */ | |
733 | static void | |
3e00b4c9 | 734 | copy_conditional(felem out, const felem in, limb icopy) |
04daec86 BM |
735 | { |
736 | unsigned i; | |
737 | /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ | |
3e00b4c9 BM |
738 | const limb copy = -icopy; |
739 | for (i = 0; i < 4; ++i) | |
04daec86 | 740 | { |
3e00b4c9 | 741 | const limb tmp = copy & (in[i] ^ out[i]); |
04daec86 BM |
742 | out[i] ^= tmp; |
743 | } | |
744 | } | |
745 | ||
04daec86 BM |
746 | /******************************************************************************/ |
747 | /* ELLIPTIC CURVE POINT OPERATIONS | |
748 | * | |
749 | * Points are represented in Jacobian projective coordinates: | |
750 | * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), | |
751 | * or to the point at infinity if Z == 0. | |
752 | * | |
753 | */ | |
754 | ||
755 | /* Double an elliptic curve point: | |
756 | * (X', Y', Z') = 2 * (X, Y, Z), where | |
757 | * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 | |
758 | * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 | |
759 | * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z | |
760 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, | |
761 | * while x_out == y_in is not (maybe this works, but it's not tested). */ | |
762 | static void | |
3e00b4c9 BM |
763 | point_double(felem x_out, felem y_out, felem z_out, |
764 | const felem x_in, const felem y_in, const felem z_in) | |
04daec86 | 765 | { |
3e00b4c9 BM |
766 | widefelem tmp, tmp2; |
767 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
768 | ||
769 | felem_assign(ftmp, x_in); | |
770 | felem_assign(ftmp2, x_in); | |
04daec86 BM |
771 | |
772 | /* delta = z^2 */ | |
773 | felem_square(tmp, z_in); | |
774 | felem_reduce(delta, tmp); | |
775 | ||
776 | /* gamma = y^2 */ | |
777 | felem_square(tmp, y_in); | |
778 | felem_reduce(gamma, tmp); | |
779 | ||
780 | /* beta = x*gamma */ | |
781 | felem_mul(tmp, x_in, gamma); | |
782 | felem_reduce(beta, tmp); | |
783 | ||
784 | /* alpha = 3*(x-delta)*(x+delta) */ | |
3e00b4c9 | 785 | felem_diff(ftmp, delta); |
04daec86 | 786 | /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ |
3e00b4c9 | 787 | felem_sum(ftmp2, delta); |
04daec86 | 788 | /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ |
3e00b4c9 | 789 | felem_scalar(ftmp2, 3); |
04daec86 BM |
790 | /* ftmp2[i] < 3 * 2^58 < 2^60 */ |
791 | felem_mul(tmp, ftmp, ftmp2); | |
792 | /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ | |
793 | felem_reduce(alpha, tmp); | |
794 | ||
795 | /* x' = alpha^2 - 8*beta */ | |
796 | felem_square(tmp, alpha); | |
797 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
3e00b4c9 BM |
798 | felem_assign(ftmp, beta); |
799 | felem_scalar(ftmp, 8); | |
04daec86 BM |
800 | /* ftmp[i] < 8 * 2^57 = 2^60 */ |
801 | felem_diff_128_64(tmp, ftmp); | |
802 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
803 | felem_reduce(x_out, tmp); | |
804 | ||
805 | /* z' = (y + z)^2 - gamma - delta */ | |
3e00b4c9 | 806 | felem_sum(delta, gamma); |
04daec86 | 807 | /* delta[i] < 2^57 + 2^57 = 2^58 */ |
3e00b4c9 BM |
808 | felem_assign(ftmp, y_in); |
809 | felem_sum(ftmp, z_in); | |
04daec86 BM |
810 | /* ftmp[i] < 2^57 + 2^57 = 2^58 */ |
811 | felem_square(tmp, ftmp); | |
812 | /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ | |
813 | felem_diff_128_64(tmp, delta); | |
814 | /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ | |
815 | felem_reduce(z_out, tmp); | |
816 | ||
817 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
3e00b4c9 | 818 | felem_scalar(beta, 4); |
04daec86 | 819 | /* beta[i] < 4 * 2^57 = 2^59 */ |
3e00b4c9 | 820 | felem_diff(beta, x_out); |
04daec86 BM |
821 | /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ |
822 | felem_mul(tmp, alpha, beta); | |
823 | /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ | |
824 | felem_square(tmp2, gamma); | |
825 | /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
3e00b4c9 | 826 | widefelem_scalar(tmp2, 8); |
04daec86 | 827 | /* tmp2[i] < 8 * 2^116 = 2^119 */ |
3e00b4c9 | 828 | widefelem_diff(tmp, tmp2); |
04daec86 BM |
829 | /* tmp[i] < 2^119 + 2^120 < 2^121 */ |
830 | felem_reduce(y_out, tmp); | |
831 | } | |
832 | ||
833 | /* Add two elliptic curve points: | |
834 | * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where | |
835 | * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - | |
836 | * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 | |
837 | * 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) - | |
838 | * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 | |
3e00b4c9 BM |
839 | * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
840 | * | |
841 | * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. | |
842 | */ | |
04daec86 BM |
843 | |
844 | /* This function is not entirely constant-time: | |
845 | * it includes a branch for checking whether the two input points are equal, | |
846 | * (while not equal to the point at infinity). | |
847 | * This case never happens during single point multiplication, | |
848 | * so there is no timing leak for ECDH or ECDSA signing. */ | |
3e00b4c9 BM |
849 | static void point_add(felem x3, felem y3, felem z3, |
850 | const felem x1, const felem y1, const felem z1, | |
851 | const int mixed, const felem x2, const felem y2, const felem z2) | |
04daec86 | 852 | { |
3e00b4c9 BM |
853 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; |
854 | widefelem tmp, tmp2; | |
855 | limb z1_is_zero, z2_is_zero, x_equal, y_equal; | |
856 | ||
857 | if (!mixed) | |
858 | { | |
859 | /* ftmp2 = z2^2 */ | |
860 | felem_square(tmp, z2); | |
861 | felem_reduce(ftmp2, tmp); | |
862 | ||
863 | /* ftmp4 = z2^3 */ | |
864 | felem_mul(tmp, ftmp2, z2); | |
865 | felem_reduce(ftmp4, tmp); | |
866 | ||
867 | /* ftmp4 = z2^3*y1 */ | |
868 | felem_mul(tmp2, ftmp4, y1); | |
869 | felem_reduce(ftmp4, tmp2); | |
870 | ||
871 | /* ftmp2 = z2^2*x1 */ | |
872 | felem_mul(tmp2, ftmp2, x1); | |
873 | felem_reduce(ftmp2, tmp2); | |
874 | } | |
875 | else | |
876 | { | |
877 | /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ | |
878 | ||
879 | /* ftmp4 = z2^3*y1 */ | |
880 | felem_assign(ftmp4, y1); | |
881 | ||
882 | /* ftmp2 = z2^2*x1 */ | |
883 | felem_assign(ftmp2, x1); | |
884 | } | |
04daec86 BM |
885 | |
886 | /* ftmp = z1^2 */ | |
887 | felem_square(tmp, z1); | |
888 | felem_reduce(ftmp, tmp); | |
889 | ||
04daec86 BM |
890 | /* ftmp3 = z1^3 */ |
891 | felem_mul(tmp, ftmp, z1); | |
892 | felem_reduce(ftmp3, tmp); | |
893 | ||
3e00b4c9 | 894 | /* tmp = z1^3*y2 */ |
04daec86 BM |
895 | felem_mul(tmp, ftmp3, y2); |
896 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
897 | ||
04daec86 BM |
898 | /* ftmp3 = z1^3*y2 - z2^3*y1 */ |
899 | felem_diff_128_64(tmp, ftmp4); | |
900 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
901 | felem_reduce(ftmp3, tmp); | |
902 | ||
3e00b4c9 | 903 | /* tmp = z1^2*x2 */ |
04daec86 BM |
904 | felem_mul(tmp, ftmp, x2); |
905 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
906 | ||
04daec86 | 907 | /* ftmp = z1^2*x2 - z2^2*x1 */ |
3e00b4c9 | 908 | felem_diff_128_64(tmp, ftmp2); |
04daec86 BM |
909 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
910 | felem_reduce(ftmp, tmp); | |
911 | ||
912 | /* the formulae are incorrect if the points are equal | |
913 | * so we check for this and do doubling if this happens */ | |
914 | x_equal = felem_is_zero(ftmp); | |
915 | y_equal = felem_is_zero(ftmp3); | |
916 | z1_is_zero = felem_is_zero(z1); | |
917 | z2_is_zero = felem_is_zero(z2); | |
918 | /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ | |
919 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) | |
920 | { | |
921 | point_double(x3, y3, z3, x1, y1, z1); | |
922 | return; | |
923 | } | |
924 | ||
925 | /* ftmp5 = z1*z2 */ | |
3e00b4c9 BM |
926 | if (!mixed) |
927 | { | |
928 | felem_mul(tmp, z1, z2); | |
929 | felem_reduce(ftmp5, tmp); | |
930 | } | |
931 | else | |
932 | { | |
933 | /* special case z2 = 0 is handled later */ | |
934 | felem_assign(ftmp5, z1); | |
935 | } | |
04daec86 | 936 | |
3e00b4c9 | 937 | /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ |
04daec86 | 938 | felem_mul(tmp, ftmp, ftmp5); |
3e00b4c9 | 939 | felem_reduce(z_out, tmp); |
04daec86 BM |
940 | |
941 | /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ | |
3e00b4c9 | 942 | felem_assign(ftmp5, ftmp); |
04daec86 BM |
943 | felem_square(tmp, ftmp); |
944 | felem_reduce(ftmp, tmp); | |
945 | ||
946 | /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ | |
947 | felem_mul(tmp, ftmp, ftmp5); | |
948 | felem_reduce(ftmp5, tmp); | |
949 | ||
950 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
951 | felem_mul(tmp, ftmp2, ftmp); | |
952 | felem_reduce(ftmp2, tmp); | |
953 | ||
3e00b4c9 | 954 | /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
04daec86 BM |
955 | felem_mul(tmp, ftmp4, ftmp5); |
956 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ | |
957 | ||
958 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ | |
959 | felem_square(tmp2, ftmp3); | |
960 | /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ | |
961 | ||
962 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ | |
963 | felem_diff_128_64(tmp2, ftmp5); | |
964 | /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ | |
965 | ||
966 | /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ | |
3e00b4c9 BM |
967 | felem_assign(ftmp5, ftmp2); |
968 | felem_scalar(ftmp5, 2); | |
04daec86 BM |
969 | /* ftmp5[i] < 2 * 2^57 = 2^58 */ |
970 | ||
3e00b4c9 | 971 | /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - |
04daec86 BM |
972 | 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
973 | felem_diff_128_64(tmp2, ftmp5); | |
974 | /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ | |
3e00b4c9 | 975 | felem_reduce(x_out, tmp2); |
04daec86 | 976 | |
3e00b4c9 BM |
977 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ |
978 | felem_diff(ftmp2, x_out); | |
04daec86 BM |
979 | /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ |
980 | ||
3e00b4c9 | 981 | /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ |
04daec86 BM |
982 | felem_mul(tmp2, ftmp3, ftmp2); |
983 | /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ | |
984 | ||
3e00b4c9 | 985 | /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - |
04daec86 | 986 | z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
3e00b4c9 | 987 | widefelem_diff(tmp2, tmp); |
04daec86 | 988 | /* tmp2[i] < 2^118 + 2^120 < 2^121 */ |
3e00b4c9 | 989 | felem_reduce(y_out, tmp2); |
04daec86 | 990 | |
3e00b4c9 BM |
991 | /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is |
992 | * the point at infinity, so we need to check for this separately */ | |
04daec86 BM |
993 | |
994 | /* if point 1 is at infinity, copy point 2 to output, and vice versa */ | |
3e00b4c9 BM |
995 | copy_conditional(x_out, x2, z1_is_zero); |
996 | copy_conditional(x_out, x1, z2_is_zero); | |
997 | copy_conditional(y_out, y2, z1_is_zero); | |
998 | copy_conditional(y_out, y1, z2_is_zero); | |
999 | copy_conditional(z_out, z2, z1_is_zero); | |
1000 | copy_conditional(z_out, z1, z2_is_zero); | |
1001 | felem_assign(x3, x_out); | |
1002 | felem_assign(y3, y_out); | |
1003 | felem_assign(z3, z_out); | |
04daec86 BM |
1004 | } |
1005 | ||
e0d6132b | 1006 | /* select_point selects the |idx|th point from a precomputation table and |
3e00b4c9 | 1007 | * copies it to out. */ |
e0d6132b | 1008 | static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) |
04daec86 | 1009 | { |
3e00b4c9 BM |
1010 | unsigned i, j; |
1011 | limb *outlimbs = &out[0][0]; | |
1012 | memset(outlimbs, 0, 3 * sizeof(felem)); | |
1013 | ||
1014 | for (i = 0; i < size; i++) | |
1015 | { | |
1016 | const limb *inlimbs = &pre_comp[i][0][0]; | |
e0d6132b | 1017 | u64 mask = i ^ idx; |
3e00b4c9 BM |
1018 | mask |= mask >> 4; |
1019 | mask |= mask >> 2; | |
1020 | mask |= mask >> 1; | |
1021 | mask &= 1; | |
1022 | mask--; | |
1023 | for (j = 0; j < 4 * 3; j++) | |
1024 | outlimbs[j] |= inlimbs[j] & mask; | |
1025 | } | |
1026 | } | |
1027 | ||
1028 | /* get_bit returns the |i|th bit in |in| */ | |
1029 | static char get_bit(const felem_bytearray in, unsigned i) | |
1030 | { | |
1031 | if (i >= 224) | |
1032 | return 0; | |
1033 | return (in[i >> 3] >> (i & 7)) & 1; | |
04daec86 BM |
1034 | } |
1035 | ||
1036 | /* Interleaved point multiplication using precomputed point multiples: | |
3e00b4c9 | 1037 | * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], |
04daec86 BM |
1038 | * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple |
1039 | * of the generator, using certain (large) precomputed multiples in g_pre_comp. | |
1040 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ | |
3e00b4c9 | 1041 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
396cb565 | 1042 | const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, |
3e00b4c9 | 1043 | const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) |
04daec86 | 1044 | { |
3e00b4c9 BM |
1045 | int i, skip; |
1046 | unsigned num; | |
04daec86 | 1047 | unsigned gen_mul = (g_scalar != NULL); |
3e00b4c9 BM |
1048 | felem nq[3], tmp[4]; |
1049 | u64 bits; | |
1050 | u8 sign, digit; | |
04daec86 | 1051 | |
1b5af90b | 1052 | /* set nq to the point at infinity */ |
3e00b4c9 BM |
1053 | memset(nq, 0, 3 * sizeof(felem)); |
1054 | ||
1055 | /* Loop over all scalars msb-to-lsb, interleaving additions | |
1056 | * of multiples of the generator (two in each of the last 28 rounds) | |
1057 | * and additions of other points multiples (every 5th round). | |
1058 | */ | |
1059 | skip = 1; /* save two point operations in the first round */ | |
1060 | for (i = (num_points ? 220 : 27); i >= 0; --i) | |
04daec86 | 1061 | { |
3e00b4c9 BM |
1062 | /* double */ |
1063 | if (!skip) | |
1064 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1065 | ||
1066 | /* add multiples of the generator */ | |
1067 | if (gen_mul && (i <= 27)) | |
04daec86 | 1068 | { |
3e00b4c9 BM |
1069 | /* first, look 28 bits upwards */ |
1070 | bits = get_bit(g_scalar, i + 196) << 3; | |
1071 | bits |= get_bit(g_scalar, i + 140) << 2; | |
1072 | bits |= get_bit(g_scalar, i + 84) << 1; | |
1073 | bits |= get_bit(g_scalar, i + 28); | |
1074 | /* select the point to add, in constant time */ | |
1075 | select_point(bits, 16, g_pre_comp[1], tmp); | |
1076 | ||
1077 | if (!skip) | |
1078 | { | |
1079 | point_add(nq[0], nq[1], nq[2], | |
1080 | nq[0], nq[1], nq[2], | |
1081 | 1 /* mixed */, tmp[0], tmp[1], tmp[2]); | |
1082 | } | |
1083 | else | |
04daec86 | 1084 | { |
3e00b4c9 BM |
1085 | memcpy(nq, tmp, 3 * sizeof(felem)); |
1086 | skip = 0; | |
04daec86 | 1087 | } |
3e00b4c9 BM |
1088 | |
1089 | /* second, look at the current position */ | |
1090 | bits = get_bit(g_scalar, i + 168) << 3; | |
1091 | bits |= get_bit(g_scalar, i + 112) << 2; | |
1092 | bits |= get_bit(g_scalar, i + 56) << 1; | |
1093 | bits |= get_bit(g_scalar, i); | |
1094 | /* select the point to add, in constant time */ | |
1095 | select_point(bits, 16, g_pre_comp[0], tmp); | |
1096 | point_add(nq[0], nq[1], nq[2], | |
1097 | nq[0], nq[1], nq[2], | |
1098 | 1 /* mixed */, tmp[0], tmp[1], tmp[2]); | |
1099 | } | |
1100 | ||
1101 | /* do other additions every 5 doublings */ | |
1102 | if (num_points && (i % 5 == 0)) | |
1103 | { | |
1104 | /* loop over all scalars */ | |
1105 | for (num = 0; num < num_points; ++num) | |
04daec86 | 1106 | { |
3e00b4c9 BM |
1107 | bits = get_bit(scalars[num], i + 4) << 5; |
1108 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1109 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1110 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1111 | bits |= get_bit(scalars[num], i) << 1; | |
1112 | bits |= get_bit(scalars[num], i - 1); | |
1113 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1114 | ||
1115 | /* select the point to add or subtract */ | |
1116 | select_point(digit, 17, pre_comp[num], tmp); | |
1117 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ | |
1118 | copy_conditional(tmp[1], tmp[3], sign); | |
1119 | ||
1120 | if (!skip) | |
04daec86 | 1121 | { |
3e00b4c9 BM |
1122 | point_add(nq[0], nq[1], nq[2], |
1123 | nq[0], nq[1], nq[2], | |
1124 | mixed, tmp[0], tmp[1], tmp[2]); | |
1125 | } | |
1126 | else | |
1127 | { | |
1128 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1129 | skip = 0; | |
04daec86 BM |
1130 | } |
1131 | } | |
1132 | } | |
1133 | } | |
3e00b4c9 BM |
1134 | felem_assign(x_out, nq[0]); |
1135 | felem_assign(y_out, nq[1]); | |
1136 | felem_assign(z_out, nq[2]); | |
04daec86 BM |
1137 | } |
1138 | ||
1139 | /******************************************************************************/ | |
1140 | /* FUNCTIONS TO MANAGE PRECOMPUTATION | |
1141 | */ | |
1142 | ||
1143 | static NISTP224_PRE_COMP *nistp224_pre_comp_new() | |
1144 | { | |
1145 | NISTP224_PRE_COMP *ret = NULL; | |
3e00b4c9 | 1146 | ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); |
04daec86 BM |
1147 | if (!ret) |
1148 | { | |
1149 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1150 | return ret; | |
1151 | } | |
1152 | memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); | |
1153 | ret->references = 1; | |
1154 | return ret; | |
1155 | } | |
1156 | ||
1157 | static void *nistp224_pre_comp_dup(void *src_) | |
1158 | { | |
1159 | NISTP224_PRE_COMP *src = src_; | |
1160 | ||
1161 | /* no need to actually copy, these objects never change! */ | |
1162 | CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); | |
1163 | ||
1164 | return src_; | |
1165 | } | |
1166 | ||
1167 | static void nistp224_pre_comp_free(void *pre_) | |
1168 | { | |
1169 | int i; | |
1170 | NISTP224_PRE_COMP *pre = pre_; | |
1171 | ||
1172 | if (!pre) | |
1173 | return; | |
1174 | ||
1175 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); | |
1176 | if (i > 0) | |
1177 | return; | |
1178 | ||
1179 | OPENSSL_free(pre); | |
1180 | } | |
1181 | ||
1182 | static void nistp224_pre_comp_clear_free(void *pre_) | |
1183 | { | |
1184 | int i; | |
1185 | NISTP224_PRE_COMP *pre = pre_; | |
1186 | ||
1187 | if (!pre) | |
1188 | return; | |
1189 | ||
1190 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); | |
1191 | if (i > 0) | |
1192 | return; | |
1193 | ||
1194 | OPENSSL_cleanse(pre, sizeof *pre); | |
1195 | OPENSSL_free(pre); | |
1196 | } | |
1197 | ||
1198 | /******************************************************************************/ | |
1199 | /* OPENSSL EC_METHOD FUNCTIONS | |
1200 | */ | |
1201 | ||
1202 | int ec_GFp_nistp224_group_init(EC_GROUP *group) | |
1203 | { | |
1204 | int ret; | |
1205 | ret = ec_GFp_simple_group_init(group); | |
1206 | group->a_is_minus3 = 1; | |
1207 | return ret; | |
1208 | } | |
1209 | ||
1210 | int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
1211 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
1212 | { | |
04daec86 BM |
1213 | int ret = 0; |
1214 | BN_CTX *new_ctx = NULL; | |
1215 | BIGNUM *curve_p, *curve_a, *curve_b; | |
1b5af90b | 1216 | |
04daec86 BM |
1217 | if (ctx == NULL) |
1218 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; | |
1219 | BN_CTX_start(ctx); | |
1220 | if (((curve_p = BN_CTX_get(ctx)) == NULL) || | |
1221 | ((curve_a = BN_CTX_get(ctx)) == NULL) || | |
1222 | ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; | |
396cb565 BM |
1223 | BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); |
1224 | BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1225 | BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); | |
04daec86 BM |
1226 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || |
1227 | (BN_cmp(curve_b, b))) | |
1228 | { | |
1229 | ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, | |
1230 | EC_R_WRONG_CURVE_PARAMETERS); | |
1231 | goto err; | |
1232 | } | |
1233 | group->field_mod_func = BN_nist_mod_224; | |
1234 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1235 | err: | |
1236 | BN_CTX_end(ctx); | |
1237 | if (new_ctx != NULL) | |
1238 | BN_CTX_free(new_ctx); | |
1239 | return ret; | |
1240 | } | |
1241 | ||
1242 | /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns | |
1243 | * (X', Y') = (X/Z^2, Y/Z^3) */ | |
1244 | int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, | |
1245 | const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) | |
1246 | { | |
3e00b4c9 BM |
1247 | felem z1, z2, x_in, y_in, x_out, y_out; |
1248 | widefelem tmp; | |
1b5af90b | 1249 | |
04daec86 BM |
1250 | if (EC_POINT_is_at_infinity(group, point)) |
1251 | { | |
1252 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1253 | EC_R_POINT_AT_INFINITY); | |
1254 | return 0; | |
1255 | } | |
1256 | if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || | |
1257 | (!BN_to_felem(z1, &point->Z))) return 0; | |
1258 | felem_inv(z2, z1); | |
1259 | felem_square(tmp, z2); felem_reduce(z1, tmp); | |
1260 | felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); | |
1261 | felem_contract(x_out, x_in); | |
1262 | if (x != NULL) | |
1263 | { | |
1264 | if (!felem_to_BN(x, x_out)) { | |
1265 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1266 | ERR_R_BN_LIB); | |
1267 | return 0; | |
1268 | } | |
1269 | } | |
1270 | felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); | |
1271 | felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); | |
1272 | felem_contract(y_out, y_in); | |
1273 | if (y != NULL) | |
1274 | { | |
1275 | if (!felem_to_BN(y, y_out)) { | |
1276 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, | |
1277 | ERR_R_BN_LIB); | |
1278 | return 0; | |
1279 | } | |
1280 | } | |
1281 | return 1; | |
1282 | } | |
1283 | ||
3e00b4c9 BM |
1284 | static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) |
1285 | { | |
1286 | /* Runs in constant time, unless an input is the point at infinity | |
1287 | * (which normally shouldn't happen). */ | |
1288 | ec_GFp_nistp_points_make_affine_internal( | |
1289 | num, | |
1290 | points, | |
1291 | sizeof(felem), | |
1292 | tmp_felems, | |
1293 | (void (*)(void *)) felem_one, | |
1294 | (int (*)(const void *)) felem_is_zero_int, | |
1295 | (void (*)(void *, const void *)) felem_assign, | |
1296 | (void (*)(void *, const void *)) felem_square_reduce, | |
1297 | (void (*)(void *, const void *, const void *)) felem_mul_reduce, | |
1298 | (void (*)(void *, const void *)) felem_inv, | |
1299 | (void (*)(void *, const void *)) felem_contract); | |
1300 | } | |
1301 | ||
04daec86 BM |
1302 | /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values |
1303 | * Result is stored in r (r can equal one of the inputs). */ | |
1304 | int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, | |
1305 | const BIGNUM *scalar, size_t num, const EC_POINT *points[], | |
1306 | const BIGNUM *scalars[], BN_CTX *ctx) | |
1307 | { | |
1308 | int ret = 0; | |
3e00b4c9 BM |
1309 | int j; |
1310 | unsigned i; | |
1311 | int mixed = 0; | |
04daec86 BM |
1312 | BN_CTX *new_ctx = NULL; |
1313 | BIGNUM *x, *y, *z, *tmp_scalar; | |
396cb565 BM |
1314 | felem_bytearray g_secret; |
1315 | felem_bytearray *secrets = NULL; | |
3e00b4c9 BM |
1316 | felem (*pre_comp)[17][3] = NULL; |
1317 | felem *tmp_felems = NULL; | |
396cb565 | 1318 | felem_bytearray tmp; |
04daec86 BM |
1319 | unsigned num_bytes; |
1320 | int have_pre_comp = 0; | |
1321 | size_t num_points = num; | |
3e00b4c9 | 1322 | felem x_in, y_in, z_in, x_out, y_out, z_out; |
04daec86 | 1323 | NISTP224_PRE_COMP *pre = NULL; |
3e00b4c9 | 1324 | const felem (*g_pre_comp)[16][3] = NULL; |
04daec86 BM |
1325 | EC_POINT *generator = NULL; |
1326 | const EC_POINT *p = NULL; | |
1327 | const BIGNUM *p_scalar = NULL; | |
1b5af90b | 1328 | |
04daec86 BM |
1329 | if (ctx == NULL) |
1330 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; | |
1331 | BN_CTX_start(ctx); | |
1332 | if (((x = BN_CTX_get(ctx)) == NULL) || | |
1333 | ((y = BN_CTX_get(ctx)) == NULL) || | |
1334 | ((z = BN_CTX_get(ctx)) == NULL) || | |
1335 | ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) | |
1336 | goto err; | |
1337 | ||
1338 | if (scalar != NULL) | |
1339 | { | |
1340 | pre = EC_EX_DATA_get_data(group->extra_data, | |
1341 | nistp224_pre_comp_dup, nistp224_pre_comp_free, | |
1342 | nistp224_pre_comp_clear_free); | |
1343 | if (pre) | |
1344 | /* we have precomputation, try to use it */ | |
3e00b4c9 | 1345 | g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; |
04daec86 BM |
1346 | else |
1347 | /* try to use the standard precomputation */ | |
3e00b4c9 | 1348 | g_pre_comp = &gmul[0]; |
04daec86 BM |
1349 | generator = EC_POINT_new(group); |
1350 | if (generator == NULL) | |
1351 | goto err; | |
1352 | /* get the generator from precomputation */ | |
3e00b4c9 BM |
1353 | if (!felem_to_BN(x, g_pre_comp[0][1][0]) || |
1354 | !felem_to_BN(y, g_pre_comp[0][1][1]) || | |
1355 | !felem_to_BN(z, g_pre_comp[0][1][2])) | |
04daec86 BM |
1356 | { |
1357 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1358 | goto err; | |
1359 | } | |
1360 | if (!EC_POINT_set_Jprojective_coordinates_GFp(group, | |
1361 | generator, x, y, z, ctx)) | |
1362 | goto err; | |
1363 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
1364 | /* precomputation matches generator */ | |
1365 | have_pre_comp = 1; | |
1366 | else | |
1367 | /* we don't have valid precomputation: | |
1368 | * treat the generator as a random point */ | |
1369 | num_points = num_points + 1; | |
1370 | } | |
04daec86 | 1371 | |
3e00b4c9 | 1372 | if (num_points > 0) |
04daec86 | 1373 | { |
3e00b4c9 | 1374 | if (num_points >= 3) |
04daec86 | 1375 | { |
3e00b4c9 BM |
1376 | /* unless we precompute multiples for just one or two points, |
1377 | * converting those into affine form is time well spent */ | |
1378 | mixed = 1; | |
04daec86 | 1379 | } |
3e00b4c9 BM |
1380 | secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); |
1381 | pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); | |
1382 | if (mixed) | |
1383 | tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); | |
1384 | if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) | |
04daec86 | 1385 | { |
3e00b4c9 BM |
1386 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); |
1387 | goto err; | |
04daec86 | 1388 | } |
3e00b4c9 BM |
1389 | |
1390 | /* we treat NULL scalars as 0, and NULL points as points at infinity, | |
1391 | * i.e., they contribute nothing to the linear combination */ | |
1392 | memset(secrets, 0, num_points * sizeof(felem_bytearray)); | |
1393 | memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); | |
1394 | for (i = 0; i < num_points; ++i) | |
04daec86 | 1395 | { |
3e00b4c9 BM |
1396 | if (i == num) |
1397 | /* the generator */ | |
04daec86 | 1398 | { |
3e00b4c9 BM |
1399 | p = EC_GROUP_get0_generator(group); |
1400 | p_scalar = scalar; | |
04daec86 BM |
1401 | } |
1402 | else | |
3e00b4c9 | 1403 | /* the i^th point */ |
04daec86 | 1404 | { |
3e00b4c9 BM |
1405 | p = points[i]; |
1406 | p_scalar = scalars[i]; | |
1407 | } | |
1408 | if ((p_scalar != NULL) && (p != NULL)) | |
1409 | { | |
1410 | /* reduce scalar to 0 <= scalar < 2^224 */ | |
1411 | if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) | |
1412 | { | |
1413 | /* this is an unusual input, and we don't guarantee | |
1414 | * constant-timeness */ | |
1415 | if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) | |
1416 | { | |
1417 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1418 | goto err; | |
1419 | } | |
1420 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1421 | } | |
1422 | else | |
1423 | num_bytes = BN_bn2bin(p_scalar, tmp); | |
1424 | flip_endian(secrets[i], tmp, num_bytes); | |
1425 | /* precompute multiples */ | |
1426 | if ((!BN_to_felem(x_out, &p->X)) || | |
1427 | (!BN_to_felem(y_out, &p->Y)) || | |
1428 | (!BN_to_felem(z_out, &p->Z))) goto err; | |
1429 | felem_assign(pre_comp[i][1][0], x_out); | |
1430 | felem_assign(pre_comp[i][1][1], y_out); | |
1431 | felem_assign(pre_comp[i][1][2], z_out); | |
1432 | for (j = 2; j <= 16; ++j) | |
1433 | { | |
1434 | if (j & 1) | |
1435 | { | |
1436 | point_add( | |
1437 | pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], | |
1438 | pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], | |
1439 | 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); | |
1440 | } | |
1441 | else | |
1442 | { | |
1443 | point_double( | |
1444 | pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], | |
1445 | pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); | |
1446 | } | |
1447 | } | |
04daec86 BM |
1448 | } |
1449 | } | |
3e00b4c9 BM |
1450 | if (mixed) |
1451 | make_points_affine(num_points * 17, pre_comp[0], tmp_felems); | |
04daec86 BM |
1452 | } |
1453 | ||
1454 | /* the scalar for the generator */ | |
1455 | if ((scalar != NULL) && (have_pre_comp)) | |
1456 | { | |
396cb565 | 1457 | memset(g_secret, 0, sizeof g_secret); |
04daec86 | 1458 | /* reduce scalar to 0 <= scalar < 2^224 */ |
3e00b4c9 | 1459 | if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) |
04daec86 BM |
1460 | { |
1461 | /* this is an unusual input, and we don't guarantee | |
1462 | * constant-timeness */ | |
1463 | if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) | |
1464 | { | |
1465 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1466 | goto err; | |
1467 | } | |
1468 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
1469 | } | |
1470 | else | |
3e00b4c9 | 1471 | num_bytes = BN_bn2bin(scalar, tmp); |
04daec86 BM |
1472 | flip_endian(g_secret, tmp, num_bytes); |
1473 | /* do the multiplication with generator precomputation*/ | |
1474 | batch_mul(x_out, y_out, z_out, | |
396cb565 | 1475 | (const felem_bytearray (*)) secrets, num_points, |
3e00b4c9 BM |
1476 | g_secret, |
1477 | mixed, (const felem (*)[17][3]) pre_comp, | |
1478 | g_pre_comp); | |
04daec86 BM |
1479 | } |
1480 | else | |
1481 | /* do the multiplication without generator precomputation */ | |
1482 | batch_mul(x_out, y_out, z_out, | |
396cb565 | 1483 | (const felem_bytearray (*)) secrets, num_points, |
3e00b4c9 | 1484 | NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); |
04daec86 BM |
1485 | /* reduce the output to its unique minimal representation */ |
1486 | felem_contract(x_in, x_out); | |
1487 | felem_contract(y_in, y_out); | |
1488 | felem_contract(z_in, z_out); | |
1489 | if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || | |
1490 | (!felem_to_BN(z, z_in))) | |
1491 | { | |
1492 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); | |
1493 | goto err; | |
1494 | } | |
1495 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); | |
1496 | ||
1497 | err: | |
1498 | BN_CTX_end(ctx); | |
1499 | if (generator != NULL) | |
1500 | EC_POINT_free(generator); | |
1501 | if (new_ctx != NULL) | |
1502 | BN_CTX_free(new_ctx); | |
1503 | if (secrets != NULL) | |
1504 | OPENSSL_free(secrets); | |
1505 | if (pre_comp != NULL) | |
1506 | OPENSSL_free(pre_comp); | |
3e00b4c9 BM |
1507 | if (tmp_felems != NULL) |
1508 | OPENSSL_free(tmp_felems); | |
04daec86 BM |
1509 | return ret; |
1510 | } | |
1511 | ||
1512 | int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
1513 | { | |
1514 | int ret = 0; | |
1515 | NISTP224_PRE_COMP *pre = NULL; | |
1516 | int i, j; | |
1517 | BN_CTX *new_ctx = NULL; | |
1518 | BIGNUM *x, *y; | |
1519 | EC_POINT *generator = NULL; | |
3e00b4c9 | 1520 | felem tmp_felems[32]; |
1b5af90b | 1521 | |
04daec86 BM |
1522 | /* throw away old precomputation */ |
1523 | EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, | |
1524 | nistp224_pre_comp_free, nistp224_pre_comp_clear_free); | |
1525 | if (ctx == NULL) | |
1526 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; | |
1527 | BN_CTX_start(ctx); | |
1528 | if (((x = BN_CTX_get(ctx)) == NULL) || | |
1529 | ((y = BN_CTX_get(ctx)) == NULL)) | |
1530 | goto err; | |
1531 | /* get the generator */ | |
1532 | if (group->generator == NULL) goto err; | |
1533 | generator = EC_POINT_new(group); | |
1534 | if (generator == NULL) | |
1535 | goto err; | |
396cb565 BM |
1536 | BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); |
1537 | BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); | |
04daec86 BM |
1538 | if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) |
1539 | goto err; | |
1540 | if ((pre = nistp224_pre_comp_new()) == NULL) | |
1541 | goto err; | |
1542 | /* if the generator is the standard one, use built-in precomputation */ | |
1543 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
1544 | { | |
1545 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
1546 | ret = 1; | |
1547 | goto err; | |
1548 | } | |
3e00b4c9 BM |
1549 | if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || |
1550 | (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || | |
1551 | (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) | |
04daec86 | 1552 | goto err; |
3e00b4c9 BM |
1553 | /* compute 2^56*G, 2^112*G, 2^168*G for the first table, |
1554 | * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one | |
1555 | */ | |
1556 | for (i = 1; i <= 8; i <<= 1) | |
04daec86 | 1557 | { |
3e00b4c9 BM |
1558 | point_double( |
1559 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], | |
1560 | pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); | |
1561 | for (j = 0; j < 27; ++j) | |
04daec86 | 1562 | { |
3e00b4c9 BM |
1563 | point_double( |
1564 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], | |
1565 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1566 | } | |
1567 | if (i == 8) | |
1568 | break; | |
1569 | point_double( | |
1570 | pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], | |
1571 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); | |
1572 | for (j = 0; j < 27; ++j) | |
1573 | { | |
1574 | point_double( | |
1575 | pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], | |
1576 | pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); | |
04daec86 BM |
1577 | } |
1578 | } | |
3e00b4c9 | 1579 | for (i = 0; i < 2; i++) |
04daec86 | 1580 | { |
3e00b4c9 BM |
1581 | /* g_pre_comp[i][0] is the point at infinity */ |
1582 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); | |
1583 | /* the remaining multiples */ | |
1584 | /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ | |
1585 | point_add( | |
1586 | pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], | |
1587 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], | |
1588 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], | |
1589 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1590 | pre->g_pre_comp[i][2][2]); | |
1591 | /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ | |
1592 | point_add( | |
1593 | pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], | |
1594 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], | |
1595 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1596 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1597 | pre->g_pre_comp[i][2][2]); | |
1598 | /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ | |
1599 | point_add( | |
1600 | pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], | |
1601 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], | |
1602 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
1603 | 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], | |
1604 | pre->g_pre_comp[i][4][2]); | |
1605 | /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ | |
1606 | point_add( | |
1607 | pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], | |
1608 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], | |
1609 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], | |
1610 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
1611 | pre->g_pre_comp[i][2][2]); | |
1612 | for (j = 1; j < 8; ++j) | |
1613 | { | |
1614 | /* odd multiples: add G resp. 2^28*G */ | |
1615 | point_add( | |
1616 | pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], | |
1617 | pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], | |
1618 | pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], | |
1619 | 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], | |
1620 | pre->g_pre_comp[i][1][2]); | |
1621 | } | |
04daec86 | 1622 | } |
3e00b4c9 | 1623 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); |
04daec86 BM |
1624 | |
1625 | if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, | |
1626 | nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) | |
1627 | goto err; | |
1628 | ret = 1; | |
1629 | pre = NULL; | |
1630 | err: | |
1631 | BN_CTX_end(ctx); | |
1632 | if (generator != NULL) | |
1633 | EC_POINT_free(generator); | |
1634 | if (new_ctx != NULL) | |
1635 | BN_CTX_free(new_ctx); | |
1636 | if (pre) | |
1637 | nistp224_pre_comp_free(pre); | |
1638 | return ret; | |
1639 | } | |
1640 | ||
1641 | int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) | |
1642 | { | |
1643 | if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, | |
1644 | nistp224_pre_comp_free, nistp224_pre_comp_clear_free) | |
1645 | != NULL) | |
1646 | return 1; | |
1647 | else | |
1648 | return 0; | |
1649 | } | |
396cb565 BM |
1650 | |
1651 | #else | |
1652 | static void *dummy=&dummy; | |
04daec86 | 1653 | #endif |