1 | /* |
2 | * Copyright 2010-2018 The OpenSSL Project Authors. All Rights Reserved. |
3 | * |
4 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
5 | * this file except in compliance with the License. You can obtain a copy |
6 | * in the file LICENSE in the source distribution or at |
7 | * https://www.openssl.org/source/license.html |
8 | */ |
9 | |
10 | /* Copyright 2011 Google Inc. |
11 | * |
12 | * Licensed under the Apache License, Version 2.0 (the "License"); |
13 | * |
14 | * you may not use this file except in compliance with the License. |
15 | * You may obtain a copy of the License at |
16 | * |
17 | * http://www.apache.org/licenses/LICENSE-2.0 |
18 | * |
19 | * Unless required by applicable law or agreed to in writing, software |
20 | * distributed under the License is distributed on an "AS IS" BASIS, |
21 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
22 | * See the License for the specific language governing permissions and |
23 | * limitations under the License. |
24 | */ |
25 | |
26 | /* |
27 | * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication |
28 | * |
29 | * Inspired by Daniel J. Bernstein's public domain nistp224 implementation |
30 | * and Adam Langley's public domain 64-bit C implementation of curve25519 |
31 | */ |
32 | |
33 | #include <openssl/opensslconf.h> |
34 | #ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 |
35 | NON_EMPTY_TRANSLATION_UNIT |
36 | #else |
37 | |
38 | # include <stdint.h> |
39 | # include <string.h> |
40 | # include <openssl/err.h> |
41 | # include "ec_local.h" |
42 | |
43 | # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 |
44 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
45 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
46 | * platforms */ |
47 | # else |
48 | # error "Your compiler doesn't appear to support 128-bit integer types" |
49 | # endif |
50 | |
51 | typedef uint8_t u8; |
52 | typedef uint64_t u64; |
53 | |
54 | /******************************************************************************/ |
55 | /*- |
56 | * INTERNAL REPRESENTATION OF FIELD ELEMENTS |
57 | * |
58 | * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 |
59 | * using 64-bit coefficients called 'limbs', |
60 | * and sometimes (for multiplication results) as |
61 | * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 |
62 | * using 128-bit coefficients called 'widelimbs'. |
63 | * A 4-limb representation is an 'felem'; |
64 | * a 7-widelimb representation is a 'widefelem'. |
65 | * Even within felems, bits of adjacent limbs overlap, and we don't always |
66 | * reduce the representations: we ensure that inputs to each felem |
67 | * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, |
68 | * and fit into a 128-bit word without overflow. The coefficients are then |
69 | * again partially reduced to obtain an felem satisfying a_i < 2^57. |
70 | * We only reduce to the unique minimal representation at the end of the |
71 | * computation. |
72 | */ |
73 | |
74 | typedef uint64_t limb; |
75 | typedef uint128_t widelimb; |
76 | |
77 | typedef limb felem[4]; |
78 | typedef widelimb widefelem[7]; |
79 | |
80 | /* |
81 | * Field element represented as a byte array. 28*8 = 224 bits is also the |
82 | * group order size for the elliptic curve, and we also use this type for |
83 | * scalars for point multiplication. |
84 | */ |
85 | typedef u8 felem_bytearray[28]; |
86 | |
87 | static const felem_bytearray nistp224_curve_params[5] = { |
88 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ |
89 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, |
90 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, |
91 | {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ |
92 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, |
93 | 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, |
94 | {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ |
95 | 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, |
96 | 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, |
97 | {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ |
98 | 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, |
99 | 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, |
100 | {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ |
101 | 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, |
102 | 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} |
103 | }; |
104 | |
105 | /*- |
106 | * Precomputed multiples of the standard generator |
107 | * Points are given in coordinates (X, Y, Z) where Z normally is 1 |
108 | * (0 for the point at infinity). |
109 | * For each field element, slice a_0 is word 0, etc. |
110 | * |
111 | * The table has 2 * 16 elements, starting with the following: |
112 | * index | bits | point |
113 | * ------+---------+------------------------------ |
114 | * 0 | 0 0 0 0 | 0G |
115 | * 1 | 0 0 0 1 | 1G |
116 | * 2 | 0 0 1 0 | 2^56G |
117 | * 3 | 0 0 1 1 | (2^56 + 1)G |
118 | * 4 | 0 1 0 0 | 2^112G |
119 | * 5 | 0 1 0 1 | (2^112 + 1)G |
120 | * 6 | 0 1 1 0 | (2^112 + 2^56)G |
121 | * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G |
122 | * 8 | 1 0 0 0 | 2^168G |
123 | * 9 | 1 0 0 1 | (2^168 + 1)G |
124 | * 10 | 1 0 1 0 | (2^168 + 2^56)G |
125 | * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G |
126 | * 12 | 1 1 0 0 | (2^168 + 2^112)G |
127 | * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G |
128 | * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G |
129 | * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G |
130 | * followed by a copy of this with each element multiplied by 2^28. |
131 | * |
132 | * The reason for this is so that we can clock bits into four different |
133 | * locations when doing simple scalar multiplies against the base point, |
134 | * and then another four locations using the second 16 elements. |
135 | */ |
136 | static const felem gmul[2][16][3] = { |
137 | {{{0, 0, 0, 0}, |
138 | {0, 0, 0, 0}, |
139 | {0, 0, 0, 0}}, |
140 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, |
141 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, |
142 | {1, 0, 0, 0}}, |
143 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, |
144 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, |
145 | {1, 0, 0, 0}}, |
146 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, |
147 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, |
148 | {1, 0, 0, 0}}, |
149 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, |
150 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, |
151 | {1, 0, 0, 0}}, |
152 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, |
153 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, |
154 | {1, 0, 0, 0}}, |
155 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, |
156 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, |
157 | {1, 0, 0, 0}}, |
158 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, |
159 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, |
160 | {1, 0, 0, 0}}, |
161 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, |
162 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, |
163 | {1, 0, 0, 0}}, |
164 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, |
165 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, |
166 | {1, 0, 0, 0}}, |
167 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, |
168 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, |
169 | {1, 0, 0, 0}}, |
170 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, |
171 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, |
172 | {1, 0, 0, 0}}, |
173 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, |
174 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, |
175 | {1, 0, 0, 0}}, |
176 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, |
177 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, |
178 | {1, 0, 0, 0}}, |
179 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, |
180 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, |
181 | {1, 0, 0, 0}}, |
182 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, |
183 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, |
184 | {1, 0, 0, 0}}}, |
185 | {{{0, 0, 0, 0}, |
186 | {0, 0, 0, 0}, |
187 | {0, 0, 0, 0}}, |
188 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, |
189 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, |
190 | {1, 0, 0, 0}}, |
191 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, |
192 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, |
193 | {1, 0, 0, 0}}, |
194 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, |
195 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, |
196 | {1, 0, 0, 0}}, |
197 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, |
198 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, |
199 | {1, 0, 0, 0}}, |
200 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, |
201 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, |
202 | {1, 0, 0, 0}}, |
203 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, |
204 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, |
205 | {1, 0, 0, 0}}, |
206 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, |
207 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, |
208 | {1, 0, 0, 0}}, |
209 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, |
210 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, |
211 | {1, 0, 0, 0}}, |
212 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, |
213 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, |
214 | {1, 0, 0, 0}}, |
215 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, |
216 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, |
217 | {1, 0, 0, 0}}, |
218 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, |
219 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, |
220 | {1, 0, 0, 0}}, |
221 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, |
222 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, |
223 | {1, 0, 0, 0}}, |
224 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, |
225 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, |
226 | {1, 0, 0, 0}}, |
227 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, |
228 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, |
229 | {1, 0, 0, 0}}, |
230 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, |
231 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, |
232 | {1, 0, 0, 0}}} |
233 | }; |
234 | |
235 | /* Precomputation for the group generator. */ |
236 | struct nistp224_pre_comp_st { |
237 | felem g_pre_comp[2][16][3]; |
238 | CRYPTO_REF_COUNT references; |
239 | CRYPTO_RWLOCK *lock; |
240 | }; |
241 | |
242 | const EC_METHOD *EC_GFp_nistp224_method(void) |
243 | { |
244 | static const EC_METHOD ret = { |
245 | EC_FLAGS_DEFAULT_OCT, |
246 | NID_X9_62_prime_field, |
247 | ec_GFp_nistp224_group_init, |
248 | ec_GFp_simple_group_finish, |
249 | ec_GFp_simple_group_clear_finish, |
250 | ec_GFp_nist_group_copy, |
251 | ec_GFp_nistp224_group_set_curve, |
252 | ec_GFp_simple_group_get_curve, |
253 | ec_GFp_simple_group_get_degree, |
254 | ec_group_simple_order_bits, |
255 | ec_GFp_simple_group_check_discriminant, |
256 | ec_GFp_simple_point_init, |
257 | ec_GFp_simple_point_finish, |
258 | ec_GFp_simple_point_clear_finish, |
259 | ec_GFp_simple_point_copy, |
260 | ec_GFp_simple_point_set_to_infinity, |
261 | ec_GFp_simple_set_Jprojective_coordinates_GFp, |
262 | ec_GFp_simple_get_Jprojective_coordinates_GFp, |
263 | ec_GFp_simple_point_set_affine_coordinates, |
264 | ec_GFp_nistp224_point_get_affine_coordinates, |
265 | 0 /* point_set_compressed_coordinates */ , |
266 | 0 /* point2oct */ , |
267 | 0 /* oct2point */ , |
268 | ec_GFp_simple_add, |
269 | ec_GFp_simple_dbl, |
270 | ec_GFp_simple_invert, |
271 | ec_GFp_simple_is_at_infinity, |
272 | ec_GFp_simple_is_on_curve, |
273 | ec_GFp_simple_cmp, |
274 | ec_GFp_simple_make_affine, |
275 | ec_GFp_simple_points_make_affine, |
276 | ec_GFp_nistp224_points_mul, |
277 | ec_GFp_nistp224_precompute_mult, |
278 | ec_GFp_nistp224_have_precompute_mult, |
279 | ec_GFp_nist_field_mul, |
280 | ec_GFp_nist_field_sqr, |
281 | 0 /* field_div */ , |
282 | ec_GFp_simple_field_inv, |
283 | 0 /* field_encode */ , |
284 | 0 /* field_decode */ , |
285 | 0, /* field_set_to_one */ |
286 | ec_key_simple_priv2oct, |
287 | ec_key_simple_oct2priv, |
288 | 0, /* set private */ |
289 | ec_key_simple_generate_key, |
290 | ec_key_simple_check_key, |
291 | ec_key_simple_generate_public_key, |
292 | 0, /* keycopy */ |
293 | 0, /* keyfinish */ |
294 | ecdh_simple_compute_key, |
295 | ecdsa_simple_sign_setup, |
296 | ecdsa_simple_sign_sig, |
297 | ecdsa_simple_verify_sig, |
298 | 0, /* field_inverse_mod_ord */ |
299 | 0, /* blind_coordinates */ |
300 | 0, /* ladder_pre */ |
301 | 0, /* ladder_step */ |
302 | 0 /* ladder_post */ |
303 | }; |
304 | |
305 | return &ret; |
306 | } |
307 | |
308 | /* |
309 | * Helper functions to convert field elements to/from internal representation |
310 | */ |
311 | static void bin28_to_felem(felem out, const u8 in[28]) |
312 | { |
313 | out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; |
314 | out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; |
315 | out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; |
316 | out[3] = (*((const uint64_t *)(in+20))) >> 8; |
317 | } |
318 | |
319 | static void felem_to_bin28(u8 out[28], const felem in) |
320 | { |
321 | unsigned i; |
322 | for (i = 0; i < 7; ++i) { |
323 | out[i] = in[0] >> (8 * i); |
324 | out[i + 7] = in[1] >> (8 * i); |
325 | out[i + 14] = in[2] >> (8 * i); |
326 | out[i + 21] = in[3] >> (8 * i); |
327 | } |
328 | } |
329 | |
330 | /* From OpenSSL BIGNUM to internal representation */ |
331 | static int BN_to_felem(felem out, const BIGNUM *bn) |
332 | { |
333 | felem_bytearray b_out; |
334 | int num_bytes; |
335 | |
336 | if (BN_is_negative(bn)) { |
337 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
338 | return 0; |
339 | } |
340 | num_bytes = BN_bn2lebinpad(bn, b_out, sizeof(b_out)); |
341 | if (num_bytes < 0) { |
342 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
343 | return 0; |
344 | } |
345 | bin28_to_felem(out, b_out); |
346 | return 1; |
347 | } |
348 | |
349 | /* From internal representation to OpenSSL BIGNUM */ |
350 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) |
351 | { |
352 | felem_bytearray b_out; |
353 | felem_to_bin28(b_out, in); |
354 | return BN_lebin2bn(b_out, sizeof(b_out), out); |
355 | } |
356 | |
357 | /******************************************************************************/ |
358 | /*- |
359 | * FIELD OPERATIONS |
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 | |
368 | static void felem_one(felem out) |
369 | { |
370 | out[0] = 1; |
371 | out[1] = 0; |
372 | out[2] = 0; |
373 | out[3] = 0; |
374 | } |
375 | |
376 | static void felem_assign(felem out, const felem in) |
377 | { |
378 | out[0] = in[0]; |
379 | out[1] = in[1]; |
380 | out[2] = in[2]; |
381 | out[3] = in[3]; |
382 | } |
383 | |
384 | /* Sum two field elements: out += in */ |
385 | static void felem_sum(felem out, const felem in) |
386 | { |
387 | out[0] += in[0]; |
388 | out[1] += in[1]; |
389 | out[2] += in[2]; |
390 | out[3] += in[3]; |
391 | } |
392 | |
393 | /* Subtract field elements: out -= in */ |
394 | /* Assumes in[i] < 2^57 */ |
395 | static void felem_diff(felem out, const felem in) |
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 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
403 | out[0] += two58p2; |
404 | out[1] += two58m42m2; |
405 | out[2] += two58m2; |
406 | out[3] += two58m2; |
407 | |
408 | out[0] -= in[0]; |
409 | out[1] -= in[1]; |
410 | out[2] -= in[2]; |
411 | out[3] -= in[3]; |
412 | } |
413 | |
414 | /* Subtract in unreduced 128-bit mode: out -= in */ |
415 | /* Assumes in[i] < 2^119 */ |
416 | static void widefelem_diff(widefelem out, const widefelem in) |
417 | { |
418 | static const widelimb two120 = ((widelimb) 1) << 120; |
419 | static const widelimb two120m64 = (((widelimb) 1) << 120) - |
420 | (((widelimb) 1) << 64); |
421 | static const widelimb two120m104m64 = (((widelimb) 1) << 120) - |
422 | (((widelimb) 1) << 104) - (((widelimb) 1) << 64); |
423 | |
424 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
425 | out[0] += two120; |
426 | out[1] += two120m64; |
427 | out[2] += two120m64; |
428 | out[3] += two120; |
429 | out[4] += two120m104m64; |
430 | out[5] += two120m64; |
431 | out[6] += two120m64; |
432 | |
433 | out[0] -= in[0]; |
434 | out[1] -= in[1]; |
435 | out[2] -= in[2]; |
436 | out[3] -= in[3]; |
437 | out[4] -= in[4]; |
438 | out[5] -= in[5]; |
439 | out[6] -= in[6]; |
440 | } |
441 | |
442 | /* Subtract in mixed mode: out128 -= in64 */ |
443 | /* in[i] < 2^63 */ |
444 | static void felem_diff_128_64(widefelem out, const felem in) |
445 | { |
446 | static const widelimb two64p8 = (((widelimb) 1) << 64) + |
447 | (((widelimb) 1) << 8); |
448 | static const widelimb two64m8 = (((widelimb) 1) << 64) - |
449 | (((widelimb) 1) << 8); |
450 | static const widelimb two64m48m8 = (((widelimb) 1) << 64) - |
451 | (((widelimb) 1) << 48) - (((widelimb) 1) << 8); |
452 | |
453 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
454 | out[0] += two64p8; |
455 | out[1] += two64m48m8; |
456 | out[2] += two64m8; |
457 | out[3] += two64m8; |
458 | |
459 | out[0] -= in[0]; |
460 | out[1] -= in[1]; |
461 | out[2] -= in[2]; |
462 | out[3] -= in[3]; |
463 | } |
464 | |
465 | /* |
466 | * Multiply a field element by a scalar: out = out * scalar The scalars we |
467 | * actually use are small, so results fit without overflow |
468 | */ |
469 | static void felem_scalar(felem out, const limb scalar) |
470 | { |
471 | out[0] *= scalar; |
472 | out[1] *= scalar; |
473 | out[2] *= scalar; |
474 | out[3] *= scalar; |
475 | } |
476 | |
477 | /* |
478 | * Multiply an unreduced field element by a scalar: out = out * scalar The |
479 | * scalars we actually use are small, so results fit without overflow |
480 | */ |
481 | static void widefelem_scalar(widefelem out, const widelimb scalar) |
482 | { |
483 | out[0] *= scalar; |
484 | out[1] *= scalar; |
485 | out[2] *= scalar; |
486 | out[3] *= scalar; |
487 | out[4] *= scalar; |
488 | out[5] *= scalar; |
489 | out[6] *= scalar; |
490 | } |
491 | |
492 | /* Square a field element: out = in^2 */ |
493 | static void felem_square(widefelem out, const felem in) |
494 | { |
495 | limb tmp0, tmp1, tmp2; |
496 | tmp0 = 2 * in[0]; |
497 | tmp1 = 2 * in[1]; |
498 | tmp2 = 2 * in[2]; |
499 | out[0] = ((widelimb) in[0]) * in[0]; |
500 | out[1] = ((widelimb) in[0]) * tmp1; |
501 | out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; |
502 | out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; |
503 | out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; |
504 | out[5] = ((widelimb) in[3]) * tmp2; |
505 | out[6] = ((widelimb) in[3]) * in[3]; |
506 | } |
507 | |
508 | /* Multiply two field elements: out = in1 * in2 */ |
509 | static void felem_mul(widefelem out, const felem in1, const felem in2) |
510 | { |
511 | out[0] = ((widelimb) in1[0]) * in2[0]; |
512 | out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; |
513 | out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + |
514 | ((widelimb) in1[2]) * in2[0]; |
515 | out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + |
516 | ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; |
517 | out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + |
518 | ((widelimb) in1[3]) * in2[1]; |
519 | out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; |
520 | out[6] = ((widelimb) in1[3]) * in2[3]; |
521 | } |
522 | |
523 | /*- |
524 | * Reduce seven 128-bit coefficients to four 64-bit coefficients. |
525 | * Requires in[i] < 2^126, |
526 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ |
527 | static void felem_reduce(felem out, const widefelem in) |
528 | { |
529 | static const widelimb two127p15 = (((widelimb) 1) << 127) + |
530 | (((widelimb) 1) << 15); |
531 | static const widelimb two127m71 = (((widelimb) 1) << 127) - |
532 | (((widelimb) 1) << 71); |
533 | static const widelimb two127m71m55 = (((widelimb) 1) << 127) - |
534 | (((widelimb) 1) << 71) - (((widelimb) 1) << 55); |
535 | widelimb output[5]; |
536 | |
537 | /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ |
538 | output[0] = in[0] + two127p15; |
539 | output[1] = in[1] + two127m71m55; |
540 | output[2] = in[2] + two127m71; |
541 | output[3] = in[3]; |
542 | output[4] = in[4]; |
543 | |
544 | /* Eliminate in[4], in[5], in[6] */ |
545 | output[4] += in[6] >> 16; |
546 | output[3] += (in[6] & 0xffff) << 40; |
547 | output[2] -= in[6]; |
548 | |
549 | output[3] += in[5] >> 16; |
550 | output[2] += (in[5] & 0xffff) << 40; |
551 | output[1] -= in[5]; |
552 | |
553 | output[2] += output[4] >> 16; |
554 | output[1] += (output[4] & 0xffff) << 40; |
555 | output[0] -= output[4]; |
556 | |
557 | /* Carry 2 -> 3 -> 4 */ |
558 | output[3] += output[2] >> 56; |
559 | output[2] &= 0x00ffffffffffffff; |
560 | |
561 | output[4] = output[3] >> 56; |
562 | output[3] &= 0x00ffffffffffffff; |
563 | |
564 | /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ |
565 | |
566 | /* Eliminate output[4] */ |
567 | output[2] += output[4] >> 16; |
568 | /* output[2] < 2^56 + 2^56 = 2^57 */ |
569 | output[1] += (output[4] & 0xffff) << 40; |
570 | output[0] -= output[4]; |
571 | |
572 | /* Carry 0 -> 1 -> 2 -> 3 */ |
573 | output[1] += output[0] >> 56; |
574 | out[0] = output[0] & 0x00ffffffffffffff; |
575 | |
576 | output[2] += output[1] >> 56; |
577 | /* output[2] < 2^57 + 2^72 */ |
578 | out[1] = output[1] & 0x00ffffffffffffff; |
579 | output[3] += output[2] >> 56; |
580 | /* output[3] <= 2^56 + 2^16 */ |
581 | out[2] = output[2] & 0x00ffffffffffffff; |
582 | |
583 | /*- |
584 | * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, |
585 | * out[3] <= 2^56 + 2^16 (due to final carry), |
586 | * so out < 2*p |
587 | */ |
588 | out[3] = output[3]; |
589 | } |
590 | |
591 | static void felem_square_reduce(felem out, const felem in) |
592 | { |
593 | widefelem tmp; |
594 | felem_square(tmp, in); |
595 | felem_reduce(out, tmp); |
596 | } |
597 | |
598 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) |
599 | { |
600 | widefelem tmp; |
601 | felem_mul(tmp, in1, in2); |
602 | felem_reduce(out, tmp); |
603 | } |
604 | |
605 | /* |
606 | * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always |
607 | * call felem_reduce first) |
608 | */ |
609 | static void felem_contract(felem out, const felem in) |
610 | { |
611 | static const int64_t two56 = ((limb) 1) << 56; |
612 | /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ |
613 | /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ |
614 | int64_t tmp[4], a; |
615 | tmp[0] = in[0]; |
616 | tmp[1] = in[1]; |
617 | tmp[2] = in[2]; |
618 | tmp[3] = in[3]; |
619 | /* Case 1: a = 1 iff in >= 2^224 */ |
620 | a = (in[3] >> 56); |
621 | tmp[0] -= a; |
622 | tmp[1] += a << 40; |
623 | tmp[3] &= 0x00ffffffffffffff; |
624 | /* |
625 | * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 |
626 | * and the lower part is non-zero |
627 | */ |
628 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | |
629 | (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); |
630 | a &= 0x00ffffffffffffff; |
631 | /* turn a into an all-one mask (if a = 0) or an all-zero mask */ |
632 | a = (a - 1) >> 63; |
633 | /* subtract 2^224 - 2^96 + 1 if a is all-one */ |
634 | tmp[3] &= a ^ 0xffffffffffffffff; |
635 | tmp[2] &= a ^ 0xffffffffffffffff; |
636 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; |
637 | tmp[0] -= 1 & a; |
638 | |
639 | /* |
640 | * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be |
641 | * non-zero, so we only need one step |
642 | */ |
643 | a = tmp[0] >> 63; |
644 | tmp[0] += two56 & a; |
645 | tmp[1] -= 1 & a; |
646 | |
647 | /* carry 1 -> 2 -> 3 */ |
648 | tmp[2] += tmp[1] >> 56; |
649 | tmp[1] &= 0x00ffffffffffffff; |
650 | |
651 | tmp[3] += tmp[2] >> 56; |
652 | tmp[2] &= 0x00ffffffffffffff; |
653 | |
654 | /* Now 0 <= out < p */ |
655 | out[0] = tmp[0]; |
656 | out[1] = tmp[1]; |
657 | out[2] = tmp[2]; |
658 | out[3] = tmp[3]; |
659 | } |
660 | |
661 | /* |
662 | * Get negative value: out = -in |
663 | * Requires in[i] < 2^63, |
664 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 |
665 | */ |
666 | static void felem_neg(felem out, const felem in) |
667 | { |
668 | widefelem tmp; |
669 | |
670 | memset(tmp, 0, sizeof(tmp)); |
671 | felem_diff_128_64(tmp, in); |
672 | felem_reduce(out, tmp); |
673 | } |
674 | |
675 | /* |
676 | * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field |
677 | * elements are reduced to in < 2^225, so we only need to check three cases: |
678 | * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 |
679 | */ |
680 | static limb felem_is_zero(const felem in) |
681 | { |
682 | limb zero, two224m96p1, two225m97p2; |
683 | |
684 | zero = in[0] | in[1] | in[2] | in[3]; |
685 | zero = (((int64_t) (zero) - 1) >> 63) & 1; |
686 | two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) |
687 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); |
688 | two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; |
689 | two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) |
690 | | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); |
691 | two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; |
692 | return (zero | two224m96p1 | two225m97p2); |
693 | } |
694 | |
695 | static int felem_is_zero_int(const void *in) |
696 | { |
697 | return (int)(felem_is_zero(in) & ((limb) 1)); |
698 | } |
699 | |
700 | /* Invert a field element */ |
701 | /* Computation chain copied from djb's code */ |
702 | static void felem_inv(felem out, const felem in) |
703 | { |
704 | felem ftmp, ftmp2, ftmp3, ftmp4; |
705 | widefelem tmp; |
706 | unsigned i; |
707 | |
708 | felem_square(tmp, in); |
709 | felem_reduce(ftmp, tmp); /* 2 */ |
710 | felem_mul(tmp, in, ftmp); |
711 | felem_reduce(ftmp, tmp); /* 2^2 - 1 */ |
712 | felem_square(tmp, ftmp); |
713 | felem_reduce(ftmp, tmp); /* 2^3 - 2 */ |
714 | felem_mul(tmp, in, ftmp); |
715 | felem_reduce(ftmp, tmp); /* 2^3 - 1 */ |
716 | felem_square(tmp, ftmp); |
717 | felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ |
718 | felem_square(tmp, ftmp2); |
719 | felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ |
720 | felem_square(tmp, ftmp2); |
721 | felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ |
722 | felem_mul(tmp, ftmp2, ftmp); |
723 | felem_reduce(ftmp, tmp); /* 2^6 - 1 */ |
724 | felem_square(tmp, ftmp); |
725 | felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ |
726 | for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ |
727 | felem_square(tmp, ftmp2); |
728 | felem_reduce(ftmp2, tmp); |
729 | } |
730 | felem_mul(tmp, ftmp2, ftmp); |
731 | felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ |
732 | felem_square(tmp, ftmp2); |
733 | felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ |
734 | for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ |
735 | felem_square(tmp, ftmp3); |
736 | felem_reduce(ftmp3, tmp); |
737 | } |
738 | felem_mul(tmp, ftmp3, ftmp2); |
739 | felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ |
740 | felem_square(tmp, ftmp2); |
741 | felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ |
742 | for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ |
743 | felem_square(tmp, ftmp3); |
744 | felem_reduce(ftmp3, tmp); |
745 | } |
746 | felem_mul(tmp, ftmp3, ftmp2); |
747 | felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ |
748 | felem_square(tmp, ftmp3); |
749 | felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ |
750 | for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ |
751 | felem_square(tmp, ftmp4); |
752 | felem_reduce(ftmp4, tmp); |
753 | } |
754 | felem_mul(tmp, ftmp3, ftmp4); |
755 | felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ |
756 | felem_square(tmp, ftmp3); |
757 | felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ |
758 | for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ |
759 | felem_square(tmp, ftmp4); |
760 | felem_reduce(ftmp4, tmp); |
761 | } |
762 | felem_mul(tmp, ftmp2, ftmp4); |
763 | felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ |
764 | for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ |
765 | felem_square(tmp, ftmp2); |
766 | felem_reduce(ftmp2, tmp); |
767 | } |
768 | felem_mul(tmp, ftmp2, ftmp); |
769 | felem_reduce(ftmp, tmp); /* 2^126 - 1 */ |
770 | felem_square(tmp, ftmp); |
771 | felem_reduce(ftmp, tmp); /* 2^127 - 2 */ |
772 | felem_mul(tmp, ftmp, in); |
773 | felem_reduce(ftmp, tmp); /* 2^127 - 1 */ |
774 | for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ |
775 | felem_square(tmp, ftmp); |
776 | felem_reduce(ftmp, tmp); |
777 | } |
778 | felem_mul(tmp, ftmp, ftmp3); |
779 | felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ |
780 | } |
781 | |
782 | /* |
783 | * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy |
784 | * out to itself. |
785 | */ |
786 | static void copy_conditional(felem out, const felem in, limb icopy) |
787 | { |
788 | unsigned i; |
789 | /* |
790 | * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one |
791 | */ |
792 | const limb copy = -icopy; |
793 | for (i = 0; i < 4; ++i) { |
794 | const limb tmp = copy & (in[i] ^ out[i]); |
795 | out[i] ^= tmp; |
796 | } |
797 | } |
798 | |
799 | /******************************************************************************/ |
800 | /*- |
801 | * ELLIPTIC CURVE POINT OPERATIONS |
802 | * |
803 | * Points are represented in Jacobian projective coordinates: |
804 | * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), |
805 | * or to the point at infinity if Z == 0. |
806 | * |
807 | */ |
808 | |
809 | /*- |
810 | * Double an elliptic curve point: |
811 | * (X', Y', Z') = 2 * (X, Y, Z), where |
812 | * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 |
813 | * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^4 |
814 | * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z |
815 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, |
816 | * while x_out == y_in is not (maybe this works, but it's not tested). |
817 | */ |
818 | static void |
819 | point_double(felem x_out, felem y_out, felem z_out, |
820 | const felem x_in, const felem y_in, const felem z_in) |
821 | { |
822 | widefelem tmp, tmp2; |
823 | felem delta, gamma, beta, alpha, ftmp, ftmp2; |
824 | |
825 | felem_assign(ftmp, x_in); |
826 | felem_assign(ftmp2, x_in); |
827 | |
828 | /* delta = z^2 */ |
829 | felem_square(tmp, z_in); |
830 | felem_reduce(delta, tmp); |
831 | |
832 | /* gamma = y^2 */ |
833 | felem_square(tmp, y_in); |
834 | felem_reduce(gamma, tmp); |
835 | |
836 | /* beta = x*gamma */ |
837 | felem_mul(tmp, x_in, gamma); |
838 | felem_reduce(beta, tmp); |
839 | |
840 | /* alpha = 3*(x-delta)*(x+delta) */ |
841 | felem_diff(ftmp, delta); |
842 | /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ |
843 | felem_sum(ftmp2, delta); |
844 | /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ |
845 | felem_scalar(ftmp2, 3); |
846 | /* ftmp2[i] < 3 * 2^58 < 2^60 */ |
847 | felem_mul(tmp, ftmp, ftmp2); |
848 | /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ |
849 | felem_reduce(alpha, tmp); |
850 | |
851 | /* x' = alpha^2 - 8*beta */ |
852 | felem_square(tmp, alpha); |
853 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
854 | felem_assign(ftmp, beta); |
855 | felem_scalar(ftmp, 8); |
856 | /* ftmp[i] < 8 * 2^57 = 2^60 */ |
857 | felem_diff_128_64(tmp, ftmp); |
858 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
859 | felem_reduce(x_out, tmp); |
860 | |
861 | /* z' = (y + z)^2 - gamma - delta */ |
862 | felem_sum(delta, gamma); |
863 | /* delta[i] < 2^57 + 2^57 = 2^58 */ |
864 | felem_assign(ftmp, y_in); |
865 | felem_sum(ftmp, z_in); |
866 | /* ftmp[i] < 2^57 + 2^57 = 2^58 */ |
867 | felem_square(tmp, ftmp); |
868 | /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ |
869 | felem_diff_128_64(tmp, delta); |
870 | /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ |
871 | felem_reduce(z_out, tmp); |
872 | |
873 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ |
874 | felem_scalar(beta, 4); |
875 | /* beta[i] < 4 * 2^57 = 2^59 */ |
876 | felem_diff(beta, x_out); |
877 | /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ |
878 | felem_mul(tmp, alpha, beta); |
879 | /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ |
880 | felem_square(tmp2, gamma); |
881 | /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ |
882 | widefelem_scalar(tmp2, 8); |
883 | /* tmp2[i] < 8 * 2^116 = 2^119 */ |
884 | widefelem_diff(tmp, tmp2); |
885 | /* tmp[i] < 2^119 + 2^120 < 2^121 */ |
886 | felem_reduce(y_out, tmp); |
887 | } |
888 | |
889 | /*- |
890 | * Add two elliptic curve points: |
891 | * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where |
892 | * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - |
893 | * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 |
894 | * 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) - |
895 | * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 |
896 | * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
897 | * |
898 | * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. |
899 | */ |
900 | |
901 | /* |
902 | * This function is not entirely constant-time: it includes a branch for |
903 | * checking whether the two input points are equal, (while not equal to the |
904 | * point at infinity). This case never happens during single point |
905 | * multiplication, so there is no timing leak for ECDH or ECDSA signing. |
906 | */ |
907 | static void point_add(felem x3, felem y3, felem z3, |
908 | const felem x1, const felem y1, const felem z1, |
909 | const int mixed, const felem x2, const felem y2, |
910 | const felem z2) |
911 | { |
912 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; |
913 | widefelem tmp, tmp2; |
914 | limb z1_is_zero, z2_is_zero, x_equal, y_equal; |
915 | |
916 | if (!mixed) { |
917 | /* ftmp2 = z2^2 */ |
918 | felem_square(tmp, z2); |
919 | felem_reduce(ftmp2, tmp); |
920 | |
921 | /* ftmp4 = z2^3 */ |
922 | felem_mul(tmp, ftmp2, z2); |
923 | felem_reduce(ftmp4, tmp); |
924 | |
925 | /* ftmp4 = z2^3*y1 */ |
926 | felem_mul(tmp2, ftmp4, y1); |
927 | felem_reduce(ftmp4, tmp2); |
928 | |
929 | /* ftmp2 = z2^2*x1 */ |
930 | felem_mul(tmp2, ftmp2, x1); |
931 | felem_reduce(ftmp2, tmp2); |
932 | } else { |
933 | /* |
934 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) |
935 | */ |
936 | |
937 | /* ftmp4 = z2^3*y1 */ |
938 | felem_assign(ftmp4, y1); |
939 | |
940 | /* ftmp2 = z2^2*x1 */ |
941 | felem_assign(ftmp2, x1); |
942 | } |
943 | |
944 | /* ftmp = z1^2 */ |
945 | felem_square(tmp, z1); |
946 | felem_reduce(ftmp, tmp); |
947 | |
948 | /* ftmp3 = z1^3 */ |
949 | felem_mul(tmp, ftmp, z1); |
950 | felem_reduce(ftmp3, tmp); |
951 | |
952 | /* tmp = z1^3*y2 */ |
953 | felem_mul(tmp, ftmp3, y2); |
954 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
955 | |
956 | /* ftmp3 = z1^3*y2 - z2^3*y1 */ |
957 | felem_diff_128_64(tmp, ftmp4); |
958 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
959 | felem_reduce(ftmp3, tmp); |
960 | |
961 | /* tmp = z1^2*x2 */ |
962 | felem_mul(tmp, ftmp, x2); |
963 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
964 | |
965 | /* ftmp = z1^2*x2 - z2^2*x1 */ |
966 | felem_diff_128_64(tmp, ftmp2); |
967 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
968 | felem_reduce(ftmp, tmp); |
969 | |
970 | /* |
971 | * the formulae are incorrect if the points are equal so we check for |
972 | * this and do doubling if this happens |
973 | */ |
974 | x_equal = felem_is_zero(ftmp); |
975 | y_equal = felem_is_zero(ftmp3); |
976 | z1_is_zero = felem_is_zero(z1); |
977 | z2_is_zero = felem_is_zero(z2); |
978 | /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ |
979 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { |
980 | point_double(x3, y3, z3, x1, y1, z1); |
981 | return; |
982 | } |
983 | |
984 | /* ftmp5 = z1*z2 */ |
985 | if (!mixed) { |
986 | felem_mul(tmp, z1, z2); |
987 | felem_reduce(ftmp5, tmp); |
988 | } else { |
989 | /* special case z2 = 0 is handled later */ |
990 | felem_assign(ftmp5, z1); |
991 | } |
992 | |
993 | /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ |
994 | felem_mul(tmp, ftmp, ftmp5); |
995 | felem_reduce(z_out, tmp); |
996 | |
997 | /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ |
998 | felem_assign(ftmp5, ftmp); |
999 | felem_square(tmp, ftmp); |
1000 | felem_reduce(ftmp, tmp); |
1001 | |
1002 | /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ |
1003 | felem_mul(tmp, ftmp, ftmp5); |
1004 | felem_reduce(ftmp5, tmp); |
1005 | |
1006 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
1007 | felem_mul(tmp, ftmp2, ftmp); |
1008 | felem_reduce(ftmp2, tmp); |
1009 | |
1010 | /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
1011 | felem_mul(tmp, ftmp4, ftmp5); |
1012 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
1013 | |
1014 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ |
1015 | felem_square(tmp2, ftmp3); |
1016 | /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ |
1017 | |
1018 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ |
1019 | felem_diff_128_64(tmp2, ftmp5); |
1020 | /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ |
1021 | |
1022 | /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
1023 | felem_assign(ftmp5, ftmp2); |
1024 | felem_scalar(ftmp5, 2); |
1025 | /* ftmp5[i] < 2 * 2^57 = 2^58 */ |
1026 | |
1027 | /*- |
1028 | * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - |
1029 | * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 |
1030 | */ |
1031 | felem_diff_128_64(tmp2, ftmp5); |
1032 | /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ |
1033 | felem_reduce(x_out, tmp2); |
1034 | |
1035 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ |
1036 | felem_diff(ftmp2, x_out); |
1037 | /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ |
1038 | |
1039 | /* |
1040 | * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) |
1041 | */ |
1042 | felem_mul(tmp2, ftmp3, ftmp2); |
1043 | /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ |
1044 | |
1045 | /*- |
1046 | * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - |
1047 | * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 |
1048 | */ |
1049 | widefelem_diff(tmp2, tmp); |
1050 | /* tmp2[i] < 2^118 + 2^120 < 2^121 */ |
1051 | felem_reduce(y_out, tmp2); |
1052 | |
1053 | /* |
1054 | * the result (x_out, y_out, z_out) is incorrect if one of the inputs is |
1055 | * the point at infinity, so we need to check for this separately |
1056 | */ |
1057 | |
1058 | /* |
1059 | * if point 1 is at infinity, copy point 2 to output, and vice versa |
1060 | */ |
1061 | copy_conditional(x_out, x2, z1_is_zero); |
1062 | copy_conditional(x_out, x1, z2_is_zero); |
1063 | copy_conditional(y_out, y2, z1_is_zero); |
1064 | copy_conditional(y_out, y1, z2_is_zero); |
1065 | copy_conditional(z_out, z2, z1_is_zero); |
1066 | copy_conditional(z_out, z1, z2_is_zero); |
1067 | felem_assign(x3, x_out); |
1068 | felem_assign(y3, y_out); |
1069 | felem_assign(z3, z_out); |
1070 | } |
1071 | |
1072 | /* |
1073 | * select_point selects the |idx|th point from a precomputation table and |
1074 | * copies it to out. |
1075 | * The pre_comp array argument should be size of |size| argument |
1076 | */ |
1077 | static void select_point(const u64 idx, unsigned int size, |
1078 | const felem pre_comp[][3], felem out[3]) |
1079 | { |
1080 | unsigned i, j; |
1081 | limb *outlimbs = &out[0][0]; |
1082 | |
1083 | memset(out, 0, sizeof(*out) * 3); |
1084 | for (i = 0; i < size; i++) { |
1085 | const limb *inlimbs = &pre_comp[i][0][0]; |
1086 | u64 mask = i ^ idx; |
1087 | mask |= mask >> 4; |
1088 | mask |= mask >> 2; |
1089 | mask |= mask >> 1; |
1090 | mask &= 1; |
1091 | mask--; |
1092 | for (j = 0; j < 4 * 3; j++) |
1093 | outlimbs[j] |= inlimbs[j] & mask; |
1094 | } |
1095 | } |
1096 | |
1097 | /* get_bit returns the |i|th bit in |in| */ |
1098 | static char get_bit(const felem_bytearray in, unsigned i) |
1099 | { |
1100 | if (i >= 224) |
1101 | return 0; |
1102 | return (in[i >> 3] >> (i & 7)) & 1; |
1103 | } |
1104 | |
1105 | /* |
1106 | * Interleaved point multiplication using precomputed point multiples: The |
1107 | * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars |
1108 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the |
1109 | * generator, using certain (large) precomputed multiples in g_pre_comp. |
1110 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out |
1111 | */ |
1112 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
1113 | const felem_bytearray scalars[], |
1114 | const unsigned num_points, const u8 *g_scalar, |
1115 | const int mixed, const felem pre_comp[][17][3], |
1116 | const felem g_pre_comp[2][16][3]) |
1117 | { |
1118 | int i, skip; |
1119 | unsigned num; |
1120 | unsigned gen_mul = (g_scalar != NULL); |
1121 | felem nq[3], tmp[4]; |
1122 | u64 bits; |
1123 | u8 sign, digit; |
1124 | |
1125 | /* set nq to the point at infinity */ |
1126 | memset(nq, 0, sizeof(nq)); |
1127 | |
1128 | /* |
1129 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples |
1130 | * of the generator (two in each of the last 28 rounds) and additions of |
1131 | * other points multiples (every 5th round). |
1132 | */ |
1133 | skip = 1; /* save two point operations in the first |
1134 | * round */ |
1135 | for (i = (num_points ? 220 : 27); i >= 0; --i) { |
1136 | /* double */ |
1137 | if (!skip) |
1138 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
1139 | |
1140 | /* add multiples of the generator */ |
1141 | if (gen_mul && (i <= 27)) { |
1142 | /* first, look 28 bits upwards */ |
1143 | bits = get_bit(g_scalar, i + 196) << 3; |
1144 | bits |= get_bit(g_scalar, i + 140) << 2; |
1145 | bits |= get_bit(g_scalar, i + 84) << 1; |
1146 | bits |= get_bit(g_scalar, i + 28); |
1147 | /* select the point to add, in constant time */ |
1148 | select_point(bits, 16, g_pre_comp[1], tmp); |
1149 | |
1150 | if (!skip) { |
1151 | /* value 1 below is argument for "mixed" */ |
1152 | point_add(nq[0], nq[1], nq[2], |
1153 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); |
1154 | } else { |
1155 | memcpy(nq, tmp, 3 * sizeof(felem)); |
1156 | skip = 0; |
1157 | } |
1158 | |
1159 | /* second, look at the current position */ |
1160 | bits = get_bit(g_scalar, i + 168) << 3; |
1161 | bits |= get_bit(g_scalar, i + 112) << 2; |
1162 | bits |= get_bit(g_scalar, i + 56) << 1; |
1163 | bits |= get_bit(g_scalar, i); |
1164 | /* select the point to add, in constant time */ |
1165 | select_point(bits, 16, g_pre_comp[0], tmp); |
1166 | point_add(nq[0], nq[1], nq[2], |
1167 | nq[0], nq[1], nq[2], |
1168 | 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); |
1169 | } |
1170 | |
1171 | /* do other additions every 5 doublings */ |
1172 | if (num_points && (i % 5 == 0)) { |
1173 | /* loop over all scalars */ |
1174 | for (num = 0; num < num_points; ++num) { |
1175 | bits = get_bit(scalars[num], i + 4) << 5; |
1176 | bits |= get_bit(scalars[num], i + 3) << 4; |
1177 | bits |= get_bit(scalars[num], i + 2) << 3; |
1178 | bits |= get_bit(scalars[num], i + 1) << 2; |
1179 | bits |= get_bit(scalars[num], i) << 1; |
1180 | bits |= get_bit(scalars[num], i - 1); |
1181 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); |
1182 | |
1183 | /* select the point to add or subtract */ |
1184 | select_point(digit, 17, pre_comp[num], tmp); |
1185 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative |
1186 | * point */ |
1187 | copy_conditional(tmp[1], tmp[3], sign); |
1188 | |
1189 | if (!skip) { |
1190 | point_add(nq[0], nq[1], nq[2], |
1191 | nq[0], nq[1], nq[2], |
1192 | mixed, tmp[0], tmp[1], tmp[2]); |
1193 | } else { |
1194 | memcpy(nq, tmp, 3 * sizeof(felem)); |
1195 | skip = 0; |
1196 | } |
1197 | } |
1198 | } |
1199 | } |
1200 | felem_assign(x_out, nq[0]); |
1201 | felem_assign(y_out, nq[1]); |
1202 | felem_assign(z_out, nq[2]); |
1203 | } |
1204 | |
1205 | /******************************************************************************/ |
1206 | /* |
1207 | * FUNCTIONS TO MANAGE PRECOMPUTATION |
1208 | */ |
1209 | |
1210 | static NISTP224_PRE_COMP *nistp224_pre_comp_new(void) |
1211 | { |
1212 | NISTP224_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
1213 | |
1214 | if (!ret) { |
1215 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
1216 | return ret; |
1217 | } |
1218 | |
1219 | ret->references = 1; |
1220 | |
1221 | ret->lock = CRYPTO_THREAD_lock_new(); |
1222 | if (ret->lock == NULL) { |
1223 | ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
1224 | OPENSSL_free(ret); |
1225 | return NULL; |
1226 | } |
1227 | return ret; |
1228 | } |
1229 | |
1230 | NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *p) |
1231 | { |
1232 | int i; |
1233 | if (p != NULL) |
1234 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
1235 | return p; |
1236 | } |
1237 | |
1238 | void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *p) |
1239 | { |
1240 | int i; |
1241 | |
1242 | if (p == NULL) |
1243 | return; |
1244 | |
1245 | CRYPTO_DOWN_REF(&p->references, &i, p->lock); |
1246 | REF_PRINT_COUNT("EC_nistp224" , x); |
1247 | if (i > 0) |
1248 | return; |
1249 | REF_ASSERT_ISNT(i < 0); |
1250 | |
1251 | CRYPTO_THREAD_lock_free(p->lock); |
1252 | OPENSSL_free(p); |
1253 | } |
1254 | |
1255 | /******************************************************************************/ |
1256 | /* |
1257 | * OPENSSL EC_METHOD FUNCTIONS |
1258 | */ |
1259 | |
1260 | int ec_GFp_nistp224_group_init(EC_GROUP *group) |
1261 | { |
1262 | int ret; |
1263 | ret = ec_GFp_simple_group_init(group); |
1264 | group->a_is_minus3 = 1; |
1265 | return ret; |
1266 | } |
1267 | |
1268 | int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
1269 | const BIGNUM *a, const BIGNUM *b, |
1270 | BN_CTX *ctx) |
1271 | { |
1272 | int ret = 0; |
1273 | BIGNUM *curve_p, *curve_a, *curve_b; |
1274 | #ifndef FIPS_MODE |
1275 | BN_CTX *new_ctx = NULL; |
1276 | |
1277 | if (ctx == NULL) |
1278 | ctx = new_ctx = BN_CTX_new(); |
1279 | #endif |
1280 | if (ctx == NULL) |
1281 | return 0; |
1282 | |
1283 | BN_CTX_start(ctx); |
1284 | curve_p = BN_CTX_get(ctx); |
1285 | curve_a = BN_CTX_get(ctx); |
1286 | curve_b = BN_CTX_get(ctx); |
1287 | if (curve_b == NULL) |
1288 | goto err; |
1289 | BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); |
1290 | BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); |
1291 | BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); |
1292 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { |
1293 | ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, |
1294 | EC_R_WRONG_CURVE_PARAMETERS); |
1295 | goto err; |
1296 | } |
1297 | group->field_mod_func = BN_nist_mod_224; |
1298 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); |
1299 | err: |
1300 | BN_CTX_end(ctx); |
1301 | #ifndef FIPS_MODE |
1302 | BN_CTX_free(new_ctx); |
1303 | #endif |
1304 | return ret; |
1305 | } |
1306 | |
1307 | /* |
1308 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = |
1309 | * (X/Z^2, Y/Z^3) |
1310 | */ |
1311 | int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, |
1312 | const EC_POINT *point, |
1313 | BIGNUM *x, BIGNUM *y, |
1314 | BN_CTX *ctx) |
1315 | { |
1316 | felem z1, z2, x_in, y_in, x_out, y_out; |
1317 | widefelem tmp; |
1318 | |
1319 | if (EC_POINT_is_at_infinity(group, point)) { |
1320 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, |
1321 | EC_R_POINT_AT_INFINITY); |
1322 | return 0; |
1323 | } |
1324 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1325 | (!BN_to_felem(z1, point->Z))) |
1326 | return 0; |
1327 | felem_inv(z2, z1); |
1328 | felem_square(tmp, z2); |
1329 | felem_reduce(z1, tmp); |
1330 | felem_mul(tmp, x_in, z1); |
1331 | felem_reduce(x_in, tmp); |
1332 | felem_contract(x_out, x_in); |
1333 | if (x != NULL) { |
1334 | if (!felem_to_BN(x, x_out)) { |
1335 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, |
1336 | ERR_R_BN_LIB); |
1337 | return 0; |
1338 | } |
1339 | } |
1340 | felem_mul(tmp, z1, z2); |
1341 | felem_reduce(z1, tmp); |
1342 | felem_mul(tmp, y_in, z1); |
1343 | felem_reduce(y_in, tmp); |
1344 | felem_contract(y_out, y_in); |
1345 | if (y != NULL) { |
1346 | if (!felem_to_BN(y, y_out)) { |
1347 | ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, |
1348 | ERR_R_BN_LIB); |
1349 | return 0; |
1350 | } |
1351 | } |
1352 | return 1; |
1353 | } |
1354 | |
1355 | static void make_points_affine(size_t num, felem points[ /* num */ ][3], |
1356 | felem tmp_felems[ /* num+1 */ ]) |
1357 | { |
1358 | /* |
1359 | * Runs in constant time, unless an input is the point at infinity (which |
1360 | * normally shouldn't happen). |
1361 | */ |
1362 | ec_GFp_nistp_points_make_affine_internal(num, |
1363 | points, |
1364 | sizeof(felem), |
1365 | tmp_felems, |
1366 | (void (*)(void *))felem_one, |
1367 | felem_is_zero_int, |
1368 | (void (*)(void *, const void *)) |
1369 | felem_assign, |
1370 | (void (*)(void *, const void *)) |
1371 | felem_square_reduce, (void (*) |
1372 | (void *, |
1373 | const void |
1374 | *, |
1375 | const void |
1376 | *)) |
1377 | felem_mul_reduce, |
1378 | (void (*)(void *, const void *)) |
1379 | felem_inv, |
1380 | (void (*)(void *, const void *)) |
1381 | felem_contract); |
1382 | } |
1383 | |
1384 | /* |
1385 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL |
1386 | * values Result is stored in r (r can equal one of the inputs). |
1387 | */ |
1388 | int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, |
1389 | const BIGNUM *scalar, size_t num, |
1390 | const EC_POINT *points[], |
1391 | const BIGNUM *scalars[], BN_CTX *ctx) |
1392 | { |
1393 | int ret = 0; |
1394 | int j; |
1395 | unsigned i; |
1396 | int mixed = 0; |
1397 | BIGNUM *x, *y, *z, *tmp_scalar; |
1398 | felem_bytearray g_secret; |
1399 | felem_bytearray *secrets = NULL; |
1400 | felem (*pre_comp)[17][3] = NULL; |
1401 | felem *tmp_felems = NULL; |
1402 | int num_bytes; |
1403 | int have_pre_comp = 0; |
1404 | size_t num_points = num; |
1405 | felem x_in, y_in, z_in, x_out, y_out, z_out; |
1406 | NISTP224_PRE_COMP *pre = NULL; |
1407 | const felem(*g_pre_comp)[16][3] = NULL; |
1408 | EC_POINT *generator = NULL; |
1409 | const EC_POINT *p = NULL; |
1410 | const BIGNUM *p_scalar = NULL; |
1411 | |
1412 | BN_CTX_start(ctx); |
1413 | x = BN_CTX_get(ctx); |
1414 | y = BN_CTX_get(ctx); |
1415 | z = BN_CTX_get(ctx); |
1416 | tmp_scalar = BN_CTX_get(ctx); |
1417 | if (tmp_scalar == NULL) |
1418 | goto err; |
1419 | |
1420 | if (scalar != NULL) { |
1421 | pre = group->pre_comp.nistp224; |
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 | } |
1461 | secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); |
1462 | pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); |
1463 | if (mixed) |
1464 | tmp_felems = |
1465 | OPENSSL_malloc(sizeof(felem) * (num_points * 17 + 1)); |
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 | */ |
1476 | for (i = 0; i < num_points; ++i) { |
1477 | if (i == num) { |
1478 | /* the generator */ |
1479 | p = EC_GROUP_get0_generator(group); |
1480 | p_scalar = scalar; |
1481 | } else { |
1482 | /* the i^th point */ |
1483 | p = points[i]; |
1484 | p_scalar = scalars[i]; |
1485 | } |
1486 | if ((p_scalar != NULL) && (p != NULL)) { |
1487 | /* reduce scalar to 0 <= scalar < 2^224 */ |
1488 | if ((BN_num_bits(p_scalar) > 224) |
1489 | || (BN_is_negative(p_scalar))) { |
1490 | /* |
1491 | * this is an unusual input, and we don't guarantee |
1492 | * constant-timeness |
1493 | */ |
1494 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
1495 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1496 | goto err; |
1497 | } |
1498 | num_bytes = BN_bn2lebinpad(tmp_scalar, |
1499 | secrets[i], sizeof(secrets[i])); |
1500 | } else { |
1501 | num_bytes = BN_bn2lebinpad(p_scalar, |
1502 | secrets[i], sizeof(secrets[i])); |
1503 | } |
1504 | if (num_bytes < 0) { |
1505 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1506 | goto err; |
1507 | } |
1508 | /* precompute multiples */ |
1509 | if ((!BN_to_felem(x_out, p->X)) || |
1510 | (!BN_to_felem(y_out, p->Y)) || |
1511 | (!BN_to_felem(z_out, p->Z))) |
1512 | goto err; |
1513 | felem_assign(pre_comp[i][1][0], x_out); |
1514 | felem_assign(pre_comp[i][1][1], y_out); |
1515 | felem_assign(pre_comp[i][1][2], z_out); |
1516 | for (j = 2; j <= 16; ++j) { |
1517 | if (j & 1) { |
1518 | point_add(pre_comp[i][j][0], pre_comp[i][j][1], |
1519 | pre_comp[i][j][2], pre_comp[i][1][0], |
1520 | pre_comp[i][1][1], pre_comp[i][1][2], 0, |
1521 | pre_comp[i][j - 1][0], |
1522 | pre_comp[i][j - 1][1], |
1523 | pre_comp[i][j - 1][2]); |
1524 | } else { |
1525 | point_double(pre_comp[i][j][0], pre_comp[i][j][1], |
1526 | pre_comp[i][j][2], pre_comp[i][j / 2][0], |
1527 | pre_comp[i][j / 2][1], |
1528 | pre_comp[i][j / 2][2]); |
1529 | } |
1530 | } |
1531 | } |
1532 | } |
1533 | if (mixed) |
1534 | make_points_affine(num_points * 17, pre_comp[0], tmp_felems); |
1535 | } |
1536 | |
1537 | /* the scalar for the generator */ |
1538 | if ((scalar != NULL) && (have_pre_comp)) { |
1539 | memset(g_secret, 0, sizeof(g_secret)); |
1540 | /* reduce scalar to 0 <= scalar < 2^224 */ |
1541 | if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { |
1542 | /* |
1543 | * this is an unusual input, and we don't guarantee |
1544 | * constant-timeness |
1545 | */ |
1546 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
1547 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1548 | goto err; |
1549 | } |
1550 | num_bytes = BN_bn2lebinpad(tmp_scalar, g_secret, sizeof(g_secret)); |
1551 | } else { |
1552 | num_bytes = BN_bn2lebinpad(scalar, g_secret, sizeof(g_secret)); |
1553 | } |
1554 | /* do the multiplication with generator precomputation */ |
1555 | batch_mul(x_out, y_out, z_out, |
1556 | (const felem_bytearray(*))secrets, num_points, |
1557 | g_secret, |
1558 | mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); |
1559 | } else { |
1560 | /* do the multiplication without generator precomputation */ |
1561 | batch_mul(x_out, y_out, z_out, |
1562 | (const felem_bytearray(*))secrets, num_points, |
1563 | NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); |
1564 | } |
1565 | /* reduce the output to its unique minimal representation */ |
1566 | felem_contract(x_in, x_out); |
1567 | felem_contract(y_in, y_out); |
1568 | felem_contract(z_in, z_out); |
1569 | if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || |
1570 | (!felem_to_BN(z, z_in))) { |
1571 | ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); |
1572 | goto err; |
1573 | } |
1574 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); |
1575 | |
1576 | err: |
1577 | BN_CTX_end(ctx); |
1578 | EC_POINT_free(generator); |
1579 | OPENSSL_free(secrets); |
1580 | OPENSSL_free(pre_comp); |
1581 | OPENSSL_free(tmp_felems); |
1582 | return ret; |
1583 | } |
1584 | |
1585 | int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
1586 | { |
1587 | int ret = 0; |
1588 | NISTP224_PRE_COMP *pre = NULL; |
1589 | int i, j; |
1590 | BIGNUM *x, *y; |
1591 | EC_POINT *generator = NULL; |
1592 | felem tmp_felems[32]; |
1593 | #ifndef FIPS_MODE |
1594 | BN_CTX *new_ctx = NULL; |
1595 | #endif |
1596 | |
1597 | /* throw away old precomputation */ |
1598 | EC_pre_comp_free(group); |
1599 | |
1600 | #ifndef FIPS_MODE |
1601 | if (ctx == NULL) |
1602 | ctx = new_ctx = BN_CTX_new(); |
1603 | #endif |
1604 | if (ctx == NULL) |
1605 | return 0; |
1606 | |
1607 | BN_CTX_start(ctx); |
1608 | x = BN_CTX_get(ctx); |
1609 | y = BN_CTX_get(ctx); |
1610 | if (y == NULL) |
1611 | goto err; |
1612 | /* get the generator */ |
1613 | if (group->generator == NULL) |
1614 | goto err; |
1615 | generator = EC_POINT_new(group); |
1616 | if (generator == NULL) |
1617 | goto err; |
1618 | BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); |
1619 | BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); |
1620 | if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx)) |
1621 | goto err; |
1622 | if ((pre = nistp224_pre_comp_new()) == NULL) |
1623 | goto err; |
1624 | /* |
1625 | * if the generator is the standard one, use built-in precomputation |
1626 | */ |
1627 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { |
1628 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); |
1629 | goto done; |
1630 | } |
1631 | if ((!BN_to_felem(pre->g_pre_comp[0][1][0], group->generator->X)) || |
1632 | (!BN_to_felem(pre->g_pre_comp[0][1][1], group->generator->Y)) || |
1633 | (!BN_to_felem(pre->g_pre_comp[0][1][2], group->generator->Z))) |
1634 | goto err; |
1635 | /* |
1636 | * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, |
1637 | * 2^140*G, 2^196*G for the second one |
1638 | */ |
1639 | for (i = 1; i <= 8; i <<= 1) { |
1640 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], |
1641 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], |
1642 | pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); |
1643 | for (j = 0; j < 27; ++j) { |
1644 | point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], |
1645 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], |
1646 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); |
1647 | } |
1648 | if (i == 8) |
1649 | break; |
1650 | point_double(pre->g_pre_comp[0][2 * i][0], |
1651 | pre->g_pre_comp[0][2 * i][1], |
1652 | pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], |
1653 | pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); |
1654 | for (j = 0; j < 27; ++j) { |
1655 | point_double(pre->g_pre_comp[0][2 * i][0], |
1656 | pre->g_pre_comp[0][2 * i][1], |
1657 | pre->g_pre_comp[0][2 * i][2], |
1658 | pre->g_pre_comp[0][2 * i][0], |
1659 | pre->g_pre_comp[0][2 * i][1], |
1660 | pre->g_pre_comp[0][2 * i][2]); |
1661 | } |
1662 | } |
1663 | for (i = 0; i < 2; i++) { |
1664 | /* g_pre_comp[i][0] is the point at infinity */ |
1665 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); |
1666 | /* the remaining multiples */ |
1667 | /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ |
1668 | point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], |
1669 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], |
1670 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], |
1671 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], |
1672 | pre->g_pre_comp[i][2][2]); |
1673 | /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ |
1674 | point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], |
1675 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], |
1676 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], |
1677 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], |
1678 | pre->g_pre_comp[i][2][2]); |
1679 | /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ |
1680 | point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], |
1681 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], |
1682 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], |
1683 | 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], |
1684 | pre->g_pre_comp[i][4][2]); |
1685 | /* |
1686 | * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G |
1687 | */ |
1688 | point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], |
1689 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], |
1690 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], |
1691 | 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], |
1692 | pre->g_pre_comp[i][2][2]); |
1693 | for (j = 1; j < 8; ++j) { |
1694 | /* odd multiples: add G resp. 2^28*G */ |
1695 | point_add(pre->g_pre_comp[i][2 * j + 1][0], |
1696 | pre->g_pre_comp[i][2 * j + 1][1], |
1697 | pre->g_pre_comp[i][2 * j + 1][2], |
1698 | pre->g_pre_comp[i][2 * j][0], |
1699 | pre->g_pre_comp[i][2 * j][1], |
1700 | pre->g_pre_comp[i][2 * j][2], 0, |
1701 | pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], |
1702 | pre->g_pre_comp[i][1][2]); |
1703 | } |
1704 | } |
1705 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); |
1706 | |
1707 | done: |
1708 | SETPRECOMP(group, nistp224, pre); |
1709 | pre = NULL; |
1710 | ret = 1; |
1711 | err: |
1712 | BN_CTX_end(ctx); |
1713 | EC_POINT_free(generator); |
1714 | #ifndef FIPS_MODE |
1715 | BN_CTX_free(new_ctx); |
1716 | #endif |
1717 | EC_nistp224_pre_comp_free(pre); |
1718 | return ret; |
1719 | } |
1720 | |
1721 | int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) |
1722 | { |
1723 | return HAVEPRECOMP(group, nistp224); |
1724 | } |
1725 | |
1726 | #endif |
1727 | |