1 /* crypto/ec/ecp_nistp224.c */ 2 /* 3 * Written by Emilia Kasper (Google) for the OpenSSL project. 4 */ 5 /* Copyright 2011 Google Inc. 6 * 7 * Licensed under the Apache License, Version 2.0 (the "License"); 8 * 9 * you may not use this file except in compliance with the License. 10 * You may obtain a copy of the License at 11 * 12 * http://www.apache.org/licenses/LICENSE-2.0 13 * 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. 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 */ 27 28 #include <openssl/opensslconf.h> 29 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 30 31 #ifndef OPENSSL_SYS_VMS 32 #include <stdint.h> 33 #else 34 #include <inttypes.h> 35 #endif 36 37 #include <string.h> 38 #include <openssl/err.h> 39 #include "ec_lcl.h" 40 41 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) 42 /* even with gcc, the typedef won't work for 32-bit platforms */ 43 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ 44 #else 45 #error "Need GCC 3.1 or later to define type uint128_t" 46 #endif 47 48 typedef uint8_t u8; 49 typedef uint64_t u64; 50 typedef int64_t s64; 51 52 53 /******************************************************************************/ 54 /* INTERNAL REPRESENTATION OF FIELD ELEMENTS 55 * 56 * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 57 * using 64-bit coefficients called 'limbs', 58 * and sometimes (for multiplication results) as 59 * 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 60 * using 128-bit coefficients called 'widelimbs'. 61 * A 4-limb representation is an 'felem'; 62 * a 7-widelimb representation is a 'widefelem'. 63 * Even within felems, bits of adjacent limbs overlap, and we don't always 64 * reduce the representations: we ensure that inputs to each felem 65 * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, 66 * and fit into a 128-bit word without overflow. The coefficients are then 67 * again partially reduced to obtain an felem satisfying a_i < 2^57. 68 * We only reduce to the unique minimal representation at the end of the 69 * computation. 70 */ 71 72 typedef uint64_t limb; 73 typedef uint128_t widelimb; 74 75 typedef limb felem[4]; 76 typedef widelimb widefelem[7]; 77 78 /* Field element represented as a byte arrary. 79 * 28*8 = 224 bits is also the group order size for the elliptic curve, 80 * and we also use this type for scalars for point multiplication. 81 */ 82 typedef u8 felem_bytearray[28]; 83 84 static const felem_bytearray nistp224_curve_params[5] = { 85 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ 86 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, 87 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, 88 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ 89 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, 90 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, 91 {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ 92 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, 93 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, 94 {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ 95 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, 96 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, 97 {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ 98 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, 99 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} 100 }; 101 102 /* Precomputed multiples of the standard generator 103 * Points are given in coordinates (X, Y, Z) where Z normally is 1 104 * (0 for the point at infinity). 105 * For each field element, slice a_0 is word 0, etc. 106 * 107 * The table has 2 * 16 elements, starting with the following: 108 * index | bits | point 109 * ------+---------+------------------------------ 110 * 0 | 0 0 0 0 | 0G 111 * 1 | 0 0 0 1 | 1G 112 * 2 | 0 0 1 0 | 2^56G 113 * 3 | 0 0 1 1 | (2^56 + 1)G 114 * 4 | 0 1 0 0 | 2^112G 115 * 5 | 0 1 0 1 | (2^112 + 1)G 116 * 6 | 0 1 1 0 | (2^112 + 2^56)G 117 * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G 118 * 8 | 1 0 0 0 | 2^168G 119 * 9 | 1 0 0 1 | (2^168 + 1)G 120 * 10 | 1 0 1 0 | (2^168 + 2^56)G 121 * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G 122 * 12 | 1 1 0 0 | (2^168 + 2^112)G 123 * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G 124 * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G 125 * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G 126 * followed by a copy of this with each element multiplied by 2^28. 127 * 128 * The reason for this is so that we can clock bits into four different 129 * locations when doing simple scalar multiplies against the base point, 130 * and then another four locations using the second 16 elements. 131 */ 132 static const felem gmul[2][16][3] = 133 {{{{0, 0, 0, 0}, 134 {0, 0, 0, 0}, 135 {0, 0, 0, 0}}, 136 {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, 137 {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, 138 {1, 0, 0, 0}}, 139 {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, 140 {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, 141 {1, 0, 0, 0}}, 142 {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, 143 {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, 144 {1, 0, 0, 0}}, 145 {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, 146 {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, 147 {1, 0, 0, 0}}, 148 {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, 149 {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, 150 {1, 0, 0, 0}}, 151 {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, 152 {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, 153 {1, 0, 0, 0}}, 154 {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, 155 {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, 156 {1, 0, 0, 0}}, 157 {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, 158 {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, 159 {1, 0, 0, 0}}, 160 {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, 161 {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, 162 {1, 0, 0, 0}}, 163 {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, 164 {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, 165 {1, 0, 0, 0}}, 166 {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, 167 {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, 168 {1, 0, 0, 0}}, 169 {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, 170 {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, 171 {1, 0, 0, 0}}, 172 {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, 173 {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, 174 {1, 0, 0, 0}}, 175 {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, 176 {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, 177 {1, 0, 0, 0}}, 178 {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, 179 {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, 180 {1, 0, 0, 0}}}, 181 {{{0, 0, 0, 0}, 182 {0, 0, 0, 0}, 183 {0, 0, 0, 0}}, 184 {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, 185 {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, 186 {1, 0, 0, 0}}, 187 {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, 188 {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, 189 {1, 0, 0, 0}}, 190 {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, 191 {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, 192 {1, 0, 0, 0}}, 193 {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, 194 {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, 195 {1, 0, 0, 0}}, 196 {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, 197 {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, 198 {1, 0, 0, 0}}, 199 {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, 200 {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, 201 {1, 0, 0, 0}}, 202 {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, 203 {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, 204 {1, 0, 0, 0}}, 205 {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, 206 {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, 207 {1, 0, 0, 0}}, 208 {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, 209 {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, 210 {1, 0, 0, 0}}, 211 {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, 212 {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, 213 {1, 0, 0, 0}}, 214 {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, 215 {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, 216 {1, 0, 0, 0}}, 217 {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, 218 {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, 219 {1, 0, 0, 0}}, 220 {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, 221 {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, 222 {1, 0, 0, 0}}, 223 {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, 224 {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, 225 {1, 0, 0, 0}}, 226 {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, 227 {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, 228 {1, 0, 0, 0}}}}; 229 230 /* Precomputation for the group generator. */ 231 typedef struct { 232 felem g_pre_comp[2][16][3]; 233 int references; 234 } NISTP224_PRE_COMP; 235 236 const EC_METHOD *EC_GFp_nistp224_method(void) 237 { 238 static const EC_METHOD ret = { 239 EC_FLAGS_DEFAULT_OCT, 240 NID_X9_62_prime_field, 241 ec_GFp_nistp224_group_init, 242 ec_GFp_simple_group_finish, 243 ec_GFp_simple_group_clear_finish, 244 ec_GFp_nist_group_copy, 245 ec_GFp_nistp224_group_set_curve, 246 ec_GFp_simple_group_get_curve, 247 ec_GFp_simple_group_get_degree, 248 ec_GFp_simple_group_check_discriminant, 249 ec_GFp_simple_point_init, 250 ec_GFp_simple_point_finish, 251 ec_GFp_simple_point_clear_finish, 252 ec_GFp_simple_point_copy, 253 ec_GFp_simple_point_set_to_infinity, 254 ec_GFp_simple_set_Jprojective_coordinates_GFp, 255 ec_GFp_simple_get_Jprojective_coordinates_GFp, 256 ec_GFp_simple_point_set_affine_coordinates, 257 ec_GFp_nistp224_point_get_affine_coordinates, 258 0 /* point_set_compressed_coordinates */, 259 0 /* point2oct */, 260 0 /* oct2point */, 261 ec_GFp_simple_add, 262 ec_GFp_simple_dbl, 263 ec_GFp_simple_invert, 264 ec_GFp_simple_is_at_infinity, 265 ec_GFp_simple_is_on_curve, 266 ec_GFp_simple_cmp, 267 ec_GFp_simple_make_affine, 268 ec_GFp_simple_points_make_affine, 269 ec_GFp_nistp224_points_mul, 270 ec_GFp_nistp224_precompute_mult, 271 ec_GFp_nistp224_have_precompute_mult, 272 ec_GFp_nist_field_mul, 273 ec_GFp_nist_field_sqr, 274 0 /* field_div */, 275 0 /* field_encode */, 276 0 /* field_decode */, 277 0 /* field_set_to_one */ }; 278 279 return &ret; 280 } 281 282 /* Helper functions to convert field elements to/from internal representation */ 283 static void bin28_to_felem(felem out, const u8 in[28]) 284 { 285 out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; 286 out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; 287 out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; 288 out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; 289 } 290 291 static void felem_to_bin28(u8 out[28], const felem in) 292 { 293 unsigned i; 294 for (i = 0; i < 7; ++i) 295 { 296 out[i] = in[0]>>(8*i); 297 out[i+7] = in[1]>>(8*i); 298 out[i+14] = in[2]>>(8*i); 299 out[i+21] = in[3]>>(8*i); 300 } 301 } 302 303 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ 304 static void flip_endian(u8 *out, const u8 *in, unsigned len) 305 { 306 unsigned i; 307 for (i = 0; i < len; ++i) 308 out[i] = in[len-1-i]; 309 } 310 311 /* From OpenSSL BIGNUM to internal representation */ 312 static int BN_to_felem(felem out, const BIGNUM *bn) 313 { 314 felem_bytearray b_in; 315 felem_bytearray b_out; 316 unsigned num_bytes; 317 318 /* BN_bn2bin eats leading zeroes */ 319 memset(b_out, 0, sizeof b_out); 320 num_bytes = BN_num_bytes(bn); 321 if (num_bytes > sizeof b_out) 322 { 323 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 324 return 0; 325 } 326 if (BN_is_negative(bn)) 327 { 328 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 329 return 0; 330 } 331 num_bytes = BN_bn2bin(bn, b_in); 332 flip_endian(b_out, b_in, num_bytes); 333 bin28_to_felem(out, b_out); 334 return 1; 335 } 336 337 /* From internal representation to OpenSSL BIGNUM */ 338 static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) 339 { 340 felem_bytearray b_in, b_out; 341 felem_to_bin28(b_in, in); 342 flip_endian(b_out, b_in, sizeof b_out); 343 return BN_bin2bn(b_out, sizeof b_out, out); 344 } 345 346 /******************************************************************************/ 347 /* FIELD OPERATIONS 348 * 349 * Field operations, using the internal representation of field elements. 350 * NB! These operations are specific to our point multiplication and cannot be 351 * expected to be correct in general - e.g., multiplication with a large scalar 352 * will cause an overflow. 353 * 354 */ 355 356 static void felem_one(felem out) 357 { 358 out[0] = 1; 359 out[1] = 0; 360 out[2] = 0; 361 out[3] = 0; 362 } 363 364 static void felem_assign(felem out, const felem in) 365 { 366 out[0] = in[0]; 367 out[1] = in[1]; 368 out[2] = in[2]; 369 out[3] = in[3]; 370 } 371 372 /* Sum two field elements: out += in */ 373 static void felem_sum(felem out, const felem in) 374 { 375 out[0] += in[0]; 376 out[1] += in[1]; 377 out[2] += in[2]; 378 out[3] += in[3]; 379 } 380 381 /* Get negative value: out = -in */ 382 /* Assumes in[i] < 2^57 */ 383 static void felem_neg(felem out, const felem in) 384 { 385 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); 386 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); 387 static const limb two58m42m2 = (((limb) 1) << 58) - 388 (((limb) 1) << 42) - (((limb) 1) << 2); 389 390 /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ 391 out[0] = two58p2 - in[0]; 392 out[1] = two58m42m2 - in[1]; 393 out[2] = two58m2 - in[2]; 394 out[3] = two58m2 - in[3]; 395 } 396 397 /* Subtract field elements: out -= in */ 398 /* Assumes in[i] < 2^57 */ 399 static void felem_diff(felem out, const felem in) 400 { 401 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); 402 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); 403 static const limb two58m42m2 = (((limb) 1) << 58) - 404 (((limb) 1) << 42) - (((limb) 1) << 2); 405 406 /* Add 0 mod 2^224-2^96+1 to ensure out > in */ 407 out[0] += two58p2; 408 out[1] += two58m42m2; 409 out[2] += two58m2; 410 out[3] += two58m2; 411 412 out[0] -= in[0]; 413 out[1] -= in[1]; 414 out[2] -= in[2]; 415 out[3] -= in[3]; 416 } 417 418 /* Subtract in unreduced 128-bit mode: out -= in */ 419 /* Assumes in[i] < 2^119 */ 420 static void widefelem_diff(widefelem out, const widefelem in) 421 { 422 static const widelimb two120 = ((widelimb) 1) << 120; 423 static const widelimb two120m64 = (((widelimb) 1) << 120) - 424 (((widelimb) 1) << 64); 425 static const widelimb two120m104m64 = (((widelimb) 1) << 120) - 426 (((widelimb) 1) << 104) - (((widelimb) 1) << 64); 427 428 /* Add 0 mod 2^224-2^96+1 to ensure out > in */ 429 out[0] += two120; 430 out[1] += two120m64; 431 out[2] += two120m64; 432 out[3] += two120; 433 out[4] += two120m104m64; 434 out[5] += two120m64; 435 out[6] += two120m64; 436 437 out[0] -= in[0]; 438 out[1] -= in[1]; 439 out[2] -= in[2]; 440 out[3] -= in[3]; 441 out[4] -= in[4]; 442 out[5] -= in[5]; 443 out[6] -= in[6]; 444 } 445 446 /* Subtract in mixed mode: out128 -= in64 */ 447 /* in[i] < 2^63 */ 448 static void felem_diff_128_64(widefelem out, const felem in) 449 { 450 static const widelimb two64p8 = (((widelimb) 1) << 64) + 451 (((widelimb) 1) << 8); 452 static const widelimb two64m8 = (((widelimb) 1) << 64) - 453 (((widelimb) 1) << 8); 454 static const widelimb two64m48m8 = (((widelimb) 1) << 64) - 455 (((widelimb) 1) << 48) - (((widelimb) 1) << 8); 456 457 /* Add 0 mod 2^224-2^96+1 to ensure out > in */ 458 out[0] += two64p8; 459 out[1] += two64m48m8; 460 out[2] += two64m8; 461 out[3] += two64m8; 462 463 out[0] -= in[0]; 464 out[1] -= in[1]; 465 out[2] -= in[2]; 466 out[3] -= in[3]; 467 } 468 469 /* Multiply a field element by a scalar: out = out * scalar 470 * The scalars we actually use are small, so results fit without overflow */ 471 static void felem_scalar(felem out, const limb scalar) 472 { 473 out[0] *= scalar; 474 out[1] *= scalar; 475 out[2] *= scalar; 476 out[3] *= scalar; 477 } 478 479 /* Multiply an unreduced field element by a scalar: out = out * scalar 480 * The scalars we actually use are small, so results fit without overflow */ 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]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; 497 out[0] = ((widelimb) in[0]) * in[0]; 498 out[1] = ((widelimb) in[0]) * tmp1; 499 out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; 500 out[3] = ((widelimb) in[3]) * tmp0 + 501 ((widelimb) in[1]) * tmp2; 502 out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; 503 out[5] = ((widelimb) in[3]) * tmp2; 504 out[6] = ((widelimb) in[3]) * in[3]; 505 } 506 507 /* Multiply two field elements: out = in1 * in2 */ 508 static void felem_mul(widefelem out, const felem in1, const felem in2) 509 { 510 out[0] = ((widelimb) in1[0]) * in2[0]; 511 out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; 512 out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + 513 ((widelimb) in1[2]) * in2[0]; 514 out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + 515 ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; 516 out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + 517 ((widelimb) in1[3]) * in2[1]; 518 out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; 519 out[6] = ((widelimb) in1[3]) * in2[3]; 520 } 521 522 /* Reduce seven 128-bit coefficients to four 64-bit coefficients. 523 * Requires in[i] < 2^126, 524 * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ 525 static void felem_reduce(felem out, const widefelem in) 526 { 527 static const widelimb two127p15 = (((widelimb) 1) << 127) + 528 (((widelimb) 1) << 15); 529 static const widelimb two127m71 = (((widelimb) 1) << 127) - 530 (((widelimb) 1) << 71); 531 static const widelimb two127m71m55 = (((widelimb) 1) << 127) - 532 (((widelimb) 1) << 71) - (((widelimb) 1) << 55); 533 widelimb output[5]; 534 535 /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ 536 output[0] = in[0] + two127p15; 537 output[1] = in[1] + two127m71m55; 538 output[2] = in[2] + two127m71; 539 output[3] = in[3]; 540 output[4] = in[4]; 541 542 /* Eliminate in[4], in[5], in[6] */ 543 output[4] += in[6] >> 16; 544 output[3] += (in[6] & 0xffff) << 40; 545 output[2] -= in[6]; 546 547 output[3] += in[5] >> 16; 548 output[2] += (in[5] & 0xffff) << 40; 549 output[1] -= in[5]; 550 551 output[2] += output[4] >> 16; 552 output[1] += (output[4] & 0xffff) << 40; 553 output[0] -= output[4]; 554 555 /* Carry 2 -> 3 -> 4 */ 556 output[3] += output[2] >> 56; 557 output[2] &= 0x00ffffffffffffff; 558 559 output[4] = output[3] >> 56; 560 output[3] &= 0x00ffffffffffffff; 561 562 /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ 563 564 /* Eliminate output[4] */ 565 output[2] += output[4] >> 16; 566 /* output[2] < 2^56 + 2^56 = 2^57 */ 567 output[1] += (output[4] & 0xffff) << 40; 568 output[0] -= output[4]; 569 570 /* Carry 0 -> 1 -> 2 -> 3 */ 571 output[1] += output[0] >> 56; 572 out[0] = output[0] & 0x00ffffffffffffff; 573 574 output[2] += output[1] >> 56; 575 /* output[2] < 2^57 + 2^72 */ 576 out[1] = output[1] & 0x00ffffffffffffff; 577 output[3] += output[2] >> 56; 578 /* output[3] <= 2^56 + 2^16 */ 579 out[2] = output[2] & 0x00ffffffffffffff; 580 581 /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, 582 * out[3] <= 2^56 + 2^16 (due to final carry), 583 * so out < 2*p */ 584 out[3] = output[3]; 585 } 586 587 static void felem_square_reduce(felem out, const felem in) 588 { 589 widefelem tmp; 590 felem_square(tmp, in); 591 felem_reduce(out, tmp); 592 } 593 594 static void felem_mul_reduce(felem out, const felem in1, const felem in2) 595 { 596 widefelem tmp; 597 felem_mul(tmp, in1, in2); 598 felem_reduce(out, tmp); 599 } 600 601 /* Reduce to unique minimal representation. 602 * Requires 0 <= in < 2*p (always call felem_reduce first) */ 603 static void felem_contract(felem out, const felem in) 604 { 605 static const int64_t two56 = ((limb) 1) << 56; 606 /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ 607 /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ 608 int64_t tmp[4], a; 609 tmp[0] = in[0]; 610 tmp[1] = in[1]; 611 tmp[2] = in[2]; 612 tmp[3] = in[3]; 613 /* Case 1: a = 1 iff in >= 2^224 */ 614 a = (in[3] >> 56); 615 tmp[0] -= a; 616 tmp[1] += a << 40; 617 tmp[3] &= 0x00ffffffffffffff; 618 /* Case 2: a = 0 iff p <= in < 2^224, i.e., 619 * the high 128 bits are all 1 and the lower part is non-zero */ 620 a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | 621 (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); 622 a &= 0x00ffffffffffffff; 623 /* turn a into an all-one mask (if a = 0) or an all-zero mask */ 624 a = (a - 1) >> 63; 625 /* subtract 2^224 - 2^96 + 1 if a is all-one*/ 626 tmp[3] &= a ^ 0xffffffffffffffff; 627 tmp[2] &= a ^ 0xffffffffffffffff; 628 tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; 629 tmp[0] -= 1 & a; 630 631 /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must 632 * be non-zero, so we only need one step */ 633 a = tmp[0] >> 63; 634 tmp[0] += two56 & a; 635 tmp[1] -= 1 & a; 636 637 /* carry 1 -> 2 -> 3 */ 638 tmp[2] += tmp[1] >> 56; 639 tmp[1] &= 0x00ffffffffffffff; 640 641 tmp[3] += tmp[2] >> 56; 642 tmp[2] &= 0x00ffffffffffffff; 643 644 /* Now 0 <= out < p */ 645 out[0] = tmp[0]; 646 out[1] = tmp[1]; 647 out[2] = tmp[2]; 648 out[3] = tmp[3]; 649 } 650 651 /* Zero-check: returns 1 if input is 0, and 0 otherwise. 652 * We know that field elements are reduced to in < 2^225, 653 * so we only need to check three cases: 0, 2^224 - 2^96 + 1, 654 * and 2^225 - 2^97 + 2 */ 655 static limb felem_is_zero(const felem in) 656 { 657 limb zero, two224m96p1, two225m97p2; 658 659 zero = in[0] | in[1] | in[2] | in[3]; 660 zero = (((int64_t)(zero) - 1) >> 63) & 1; 661 two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) 662 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); 663 two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; 664 two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) 665 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); 666 two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; 667 return (zero | two224m96p1 | two225m97p2); 668 } 669 670 static limb felem_is_zero_int(const felem in) 671 { 672 return (int) (felem_is_zero(in) & ((limb)1)); 673 } 674 675 /* Invert a field element */ 676 /* Computation chain copied from djb's code */ 677 static void felem_inv(felem out, const felem in) 678 { 679 felem ftmp, ftmp2, ftmp3, ftmp4; 680 widefelem tmp; 681 unsigned i; 682 683 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ 684 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ 685 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ 686 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ 687 felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ 688 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ 689 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ 690 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ 691 felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ 692 for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ 693 { 694 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 695 } 696 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ 697 felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ 698 for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ 699 { 700 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); 701 } 702 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ 703 felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ 704 for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ 705 { 706 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); 707 } 708 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ 709 felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ 710 for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ 711 { 712 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); 713 } 714 felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ 715 felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ 716 for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ 717 { 718 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); 719 } 720 felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ 721 for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ 722 { 723 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 724 } 725 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ 726 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ 727 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ 728 for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ 729 { 730 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 731 } 732 felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ 733 } 734 735 /* Copy in constant time: 736 * if icopy == 1, copy in to out, 737 * if icopy == 0, copy out to itself. */ 738 static void 739 copy_conditional(felem out, const felem in, limb icopy) 740 { 741 unsigned i; 742 /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ 743 const limb copy = -icopy; 744 for (i = 0; i < 4; ++i) 745 { 746 const limb tmp = copy & (in[i] ^ out[i]); 747 out[i] ^= tmp; 748 } 749 } 750 751 /******************************************************************************/ 752 /* ELLIPTIC CURVE POINT OPERATIONS 753 * 754 * Points are represented in Jacobian projective coordinates: 755 * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), 756 * or to the point at infinity if Z == 0. 757 * 758 */ 759 760 /* Double an elliptic curve point: 761 * (X', Y', Z') = 2 * (X, Y, Z), where 762 * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 763 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 764 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z 765 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, 766 * while x_out == y_in is not (maybe this works, but it's not tested). */ 767 static void 768 point_double(felem x_out, felem y_out, felem z_out, 769 const felem x_in, const felem y_in, const felem z_in) 770 { 771 widefelem tmp, tmp2; 772 felem delta, gamma, beta, alpha, ftmp, ftmp2; 773 774 felem_assign(ftmp, x_in); 775 felem_assign(ftmp2, x_in); 776 777 /* delta = z^2 */ 778 felem_square(tmp, z_in); 779 felem_reduce(delta, tmp); 780 781 /* gamma = y^2 */ 782 felem_square(tmp, y_in); 783 felem_reduce(gamma, tmp); 784 785 /* beta = x*gamma */ 786 felem_mul(tmp, x_in, gamma); 787 felem_reduce(beta, tmp); 788 789 /* alpha = 3*(x-delta)*(x+delta) */ 790 felem_diff(ftmp, delta); 791 /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ 792 felem_sum(ftmp2, delta); 793 /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ 794 felem_scalar(ftmp2, 3); 795 /* ftmp2[i] < 3 * 2^58 < 2^60 */ 796 felem_mul(tmp, ftmp, ftmp2); 797 /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ 798 felem_reduce(alpha, tmp); 799 800 /* x' = alpha^2 - 8*beta */ 801 felem_square(tmp, alpha); 802 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ 803 felem_assign(ftmp, beta); 804 felem_scalar(ftmp, 8); 805 /* ftmp[i] < 8 * 2^57 = 2^60 */ 806 felem_diff_128_64(tmp, ftmp); 807 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ 808 felem_reduce(x_out, tmp); 809 810 /* z' = (y + z)^2 - gamma - delta */ 811 felem_sum(delta, gamma); 812 /* delta[i] < 2^57 + 2^57 = 2^58 */ 813 felem_assign(ftmp, y_in); 814 felem_sum(ftmp, z_in); 815 /* ftmp[i] < 2^57 + 2^57 = 2^58 */ 816 felem_square(tmp, ftmp); 817 /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ 818 felem_diff_128_64(tmp, delta); 819 /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ 820 felem_reduce(z_out, tmp); 821 822 /* y' = alpha*(4*beta - x') - 8*gamma^2 */ 823 felem_scalar(beta, 4); 824 /* beta[i] < 4 * 2^57 = 2^59 */ 825 felem_diff(beta, x_out); 826 /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ 827 felem_mul(tmp, alpha, beta); 828 /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ 829 felem_square(tmp2, gamma); 830 /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ 831 widefelem_scalar(tmp2, 8); 832 /* tmp2[i] < 8 * 2^116 = 2^119 */ 833 widefelem_diff(tmp, tmp2); 834 /* tmp[i] < 2^119 + 2^120 < 2^121 */ 835 felem_reduce(y_out, tmp); 836 } 837 838 /* Add two elliptic curve points: 839 * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where 840 * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - 841 * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 842 * 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) - 843 * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 844 * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) 845 * 846 * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. 847 */ 848 849 /* This function is not entirely constant-time: 850 * it includes a branch for checking whether the two input points are equal, 851 * (while not equal to the point at infinity). 852 * This case never happens during single point multiplication, 853 * so there is no timing leak for ECDH or ECDSA signing. */ 854 static void point_add(felem x3, felem y3, felem z3, 855 const felem x1, const felem y1, const felem z1, 856 const int mixed, const felem x2, const felem y2, const felem z2) 857 { 858 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; 859 widefelem tmp, tmp2; 860 limb z1_is_zero, z2_is_zero, x_equal, y_equal; 861 862 if (!mixed) 863 { 864 /* ftmp2 = z2^2 */ 865 felem_square(tmp, z2); 866 felem_reduce(ftmp2, tmp); 867 868 /* ftmp4 = z2^3 */ 869 felem_mul(tmp, ftmp2, z2); 870 felem_reduce(ftmp4, tmp); 871 872 /* ftmp4 = z2^3*y1 */ 873 felem_mul(tmp2, ftmp4, y1); 874 felem_reduce(ftmp4, tmp2); 875 876 /* ftmp2 = z2^2*x1 */ 877 felem_mul(tmp2, ftmp2, x1); 878 felem_reduce(ftmp2, tmp2); 879 } 880 else 881 { 882 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ 883 884 /* ftmp4 = z2^3*y1 */ 885 felem_assign(ftmp4, y1); 886 887 /* ftmp2 = z2^2*x1 */ 888 felem_assign(ftmp2, x1); 889 } 890 891 /* ftmp = z1^2 */ 892 felem_square(tmp, z1); 893 felem_reduce(ftmp, tmp); 894 895 /* ftmp3 = z1^3 */ 896 felem_mul(tmp, ftmp, z1); 897 felem_reduce(ftmp3, tmp); 898 899 /* tmp = z1^3*y2 */ 900 felem_mul(tmp, ftmp3, y2); 901 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ 902 903 /* ftmp3 = z1^3*y2 - z2^3*y1 */ 904 felem_diff_128_64(tmp, ftmp4); 905 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ 906 felem_reduce(ftmp3, tmp); 907 908 /* tmp = z1^2*x2 */ 909 felem_mul(tmp, ftmp, x2); 910 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ 911 912 /* ftmp = z1^2*x2 - z2^2*x1 */ 913 felem_diff_128_64(tmp, ftmp2); 914 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ 915 felem_reduce(ftmp, tmp); 916 917 /* the formulae are incorrect if the points are equal 918 * so we check for this and do doubling if this happens */ 919 x_equal = felem_is_zero(ftmp); 920 y_equal = felem_is_zero(ftmp3); 921 z1_is_zero = felem_is_zero(z1); 922 z2_is_zero = felem_is_zero(z2); 923 /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ 924 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) 925 { 926 point_double(x3, y3, z3, x1, y1, z1); 927 return; 928 } 929 930 /* ftmp5 = z1*z2 */ 931 if (!mixed) 932 { 933 felem_mul(tmp, z1, z2); 934 felem_reduce(ftmp5, tmp); 935 } 936 else 937 { 938 /* special case z2 = 0 is handled later */ 939 felem_assign(ftmp5, z1); 940 } 941 942 /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ 943 felem_mul(tmp, ftmp, ftmp5); 944 felem_reduce(z_out, tmp); 945 946 /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ 947 felem_assign(ftmp5, ftmp); 948 felem_square(tmp, ftmp); 949 felem_reduce(ftmp, tmp); 950 951 /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ 952 felem_mul(tmp, ftmp, ftmp5); 953 felem_reduce(ftmp5, tmp); 954 955 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ 956 felem_mul(tmp, ftmp2, ftmp); 957 felem_reduce(ftmp2, tmp); 958 959 /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ 960 felem_mul(tmp, ftmp4, ftmp5); 961 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ 962 963 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ 964 felem_square(tmp2, ftmp3); 965 /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ 966 967 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ 968 felem_diff_128_64(tmp2, ftmp5); 969 /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ 970 971 /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ 972 felem_assign(ftmp5, ftmp2); 973 felem_scalar(ftmp5, 2); 974 /* ftmp5[i] < 2 * 2^57 = 2^58 */ 975 976 /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - 977 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ 978 felem_diff_128_64(tmp2, ftmp5); 979 /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ 980 felem_reduce(x_out, tmp2); 981 982 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ 983 felem_diff(ftmp2, x_out); 984 /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ 985 986 /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ 987 felem_mul(tmp2, ftmp3, ftmp2); 988 /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ 989 990 /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - 991 z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ 992 widefelem_diff(tmp2, tmp); 993 /* tmp2[i] < 2^118 + 2^120 < 2^121 */ 994 felem_reduce(y_out, tmp2); 995 996 /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is 997 * the point at infinity, so we need to check for this separately */ 998 999 /* if point 1 is at infinity, copy point 2 to output, and vice versa */ 1000 copy_conditional(x_out, x2, z1_is_zero); 1001 copy_conditional(x_out, x1, z2_is_zero); 1002 copy_conditional(y_out, y2, z1_is_zero); 1003 copy_conditional(y_out, y1, z2_is_zero); 1004 copy_conditional(z_out, z2, z1_is_zero); 1005 copy_conditional(z_out, z1, z2_is_zero); 1006 felem_assign(x3, x_out); 1007 felem_assign(y3, y_out); 1008 felem_assign(z3, z_out); 1009 } 1010 1011 /* select_point selects the |idx|th point from a precomputation table and 1012 * copies it to out. */ 1013 static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) 1014 { 1015 unsigned i, j; 1016 limb *outlimbs = &out[0][0]; 1017 memset(outlimbs, 0, 3 * sizeof(felem)); 1018 1019 for (i = 0; i < size; i++) 1020 { 1021 const limb *inlimbs = &pre_comp[i][0][0]; 1022 u64 mask = i ^ idx; 1023 mask |= mask >> 4; 1024 mask |= mask >> 2; 1025 mask |= mask >> 1; 1026 mask &= 1; 1027 mask--; 1028 for (j = 0; j < 4 * 3; j++) 1029 outlimbs[j] |= inlimbs[j] & mask; 1030 } 1031 } 1032 1033 /* get_bit returns the |i|th bit in |in| */ 1034 static char get_bit(const felem_bytearray in, unsigned i) 1035 { 1036 if (i >= 224) 1037 return 0; 1038 return (in[i >> 3] >> (i & 7)) & 1; 1039 } 1040 1041 /* Interleaved point multiplication using precomputed point multiples: 1042 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], 1043 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple 1044 * of the generator, using certain (large) precomputed multiples in g_pre_comp. 1045 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ 1046 static void batch_mul(felem x_out, felem y_out, felem z_out, 1047 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, 1048 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) 1049 { 1050 int i, skip; 1051 unsigned num; 1052 unsigned gen_mul = (g_scalar != NULL); 1053 felem nq[3], tmp[4]; 1054 u64 bits; 1055 u8 sign, digit; 1056 1057 /* set nq to the point at infinity */ 1058 memset(nq, 0, 3 * sizeof(felem)); 1059 1060 /* Loop over all scalars msb-to-lsb, interleaving additions 1061 * of multiples of the generator (two in each of the last 28 rounds) 1062 * and additions of other points multiples (every 5th round). 1063 */ 1064 skip = 1; /* save two point operations in the first round */ 1065 for (i = (num_points ? 220 : 27); i >= 0; --i) 1066 { 1067 /* double */ 1068 if (!skip) 1069 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); 1070 1071 /* add multiples of the generator */ 1072 if (gen_mul && (i <= 27)) 1073 { 1074 /* first, look 28 bits upwards */ 1075 bits = get_bit(g_scalar, i + 196) << 3; 1076 bits |= get_bit(g_scalar, i + 140) << 2; 1077 bits |= get_bit(g_scalar, i + 84) << 1; 1078 bits |= get_bit(g_scalar, i + 28); 1079 /* select the point to add, in constant time */ 1080 select_point(bits, 16, g_pre_comp[1], tmp); 1081 1082 if (!skip) 1083 { 1084 point_add(nq[0], nq[1], nq[2], 1085 nq[0], nq[1], nq[2], 1086 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1087 } 1088 else 1089 { 1090 memcpy(nq, tmp, 3 * sizeof(felem)); 1091 skip = 0; 1092 } 1093 1094 /* second, look at the current position */ 1095 bits = get_bit(g_scalar, i + 168) << 3; 1096 bits |= get_bit(g_scalar, i + 112) << 2; 1097 bits |= get_bit(g_scalar, i + 56) << 1; 1098 bits |= get_bit(g_scalar, i); 1099 /* select the point to add, in constant time */ 1100 select_point(bits, 16, g_pre_comp[0], tmp); 1101 point_add(nq[0], nq[1], nq[2], 1102 nq[0], nq[1], nq[2], 1103 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1104 } 1105 1106 /* do other additions every 5 doublings */ 1107 if (num_points && (i % 5 == 0)) 1108 { 1109 /* loop over all scalars */ 1110 for (num = 0; num < num_points; ++num) 1111 { 1112 bits = get_bit(scalars[num], i + 4) << 5; 1113 bits |= get_bit(scalars[num], i + 3) << 4; 1114 bits |= get_bit(scalars[num], i + 2) << 3; 1115 bits |= get_bit(scalars[num], i + 1) << 2; 1116 bits |= get_bit(scalars[num], i) << 1; 1117 bits |= get_bit(scalars[num], i - 1); 1118 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); 1119 1120 /* select the point to add or subtract */ 1121 select_point(digit, 17, pre_comp[num], tmp); 1122 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ 1123 copy_conditional(tmp[1], tmp[3], sign); 1124 1125 if (!skip) 1126 { 1127 point_add(nq[0], nq[1], nq[2], 1128 nq[0], nq[1], nq[2], 1129 mixed, tmp[0], tmp[1], tmp[2]); 1130 } 1131 else 1132 { 1133 memcpy(nq, tmp, 3 * sizeof(felem)); 1134 skip = 0; 1135 } 1136 } 1137 } 1138 } 1139 felem_assign(x_out, nq[0]); 1140 felem_assign(y_out, nq[1]); 1141 felem_assign(z_out, nq[2]); 1142 } 1143 1144 /******************************************************************************/ 1145 /* FUNCTIONS TO MANAGE PRECOMPUTATION 1146 */ 1147 1148 static NISTP224_PRE_COMP *nistp224_pre_comp_new() 1149 { 1150 NISTP224_PRE_COMP *ret = NULL; 1151 ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); 1152 if (!ret) 1153 { 1154 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 1155 return ret; 1156 } 1157 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); 1158 ret->references = 1; 1159 return ret; 1160 } 1161 1162 static void *nistp224_pre_comp_dup(void *src_) 1163 { 1164 NISTP224_PRE_COMP *src = src_; 1165 1166 /* no need to actually copy, these objects never change! */ 1167 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 1168 1169 return src_; 1170 } 1171 1172 static void nistp224_pre_comp_free(void *pre_) 1173 { 1174 int i; 1175 NISTP224_PRE_COMP *pre = pre_; 1176 1177 if (!pre) 1178 return; 1179 1180 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1181 if (i > 0) 1182 return; 1183 1184 OPENSSL_free(pre); 1185 } 1186 1187 static void nistp224_pre_comp_clear_free(void *pre_) 1188 { 1189 int i; 1190 NISTP224_PRE_COMP *pre = pre_; 1191 1192 if (!pre) 1193 return; 1194 1195 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1196 if (i > 0) 1197 return; 1198 1199 OPENSSL_cleanse(pre, sizeof *pre); 1200 OPENSSL_free(pre); 1201 } 1202 1203 /******************************************************************************/ 1204 /* OPENSSL EC_METHOD FUNCTIONS 1205 */ 1206 1207 int ec_GFp_nistp224_group_init(EC_GROUP *group) 1208 { 1209 int ret; 1210 ret = ec_GFp_simple_group_init(group); 1211 group->a_is_minus3 = 1; 1212 return ret; 1213 } 1214 1215 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, 1216 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1217 { 1218 int ret = 0; 1219 BN_CTX *new_ctx = NULL; 1220 BIGNUM *curve_p, *curve_a, *curve_b; 1221 1222 if (ctx == NULL) 1223 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1224 BN_CTX_start(ctx); 1225 if (((curve_p = BN_CTX_get(ctx)) == NULL) || 1226 ((curve_a = BN_CTX_get(ctx)) == NULL) || 1227 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; 1228 BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); 1229 BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); 1230 BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); 1231 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || 1232 (BN_cmp(curve_b, b))) 1233 { 1234 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, 1235 EC_R_WRONG_CURVE_PARAMETERS); 1236 goto err; 1237 } 1238 group->field_mod_func = BN_nist_mod_224; 1239 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); 1240 err: 1241 BN_CTX_end(ctx); 1242 if (new_ctx != NULL) 1243 BN_CTX_free(new_ctx); 1244 return ret; 1245 } 1246 1247 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns 1248 * (X', Y') = (X/Z^2, Y/Z^3) */ 1249 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, 1250 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 1251 { 1252 felem z1, z2, x_in, y_in, x_out, y_out; 1253 widefelem tmp; 1254 1255 if (EC_POINT_is_at_infinity(group, point)) 1256 { 1257 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, 1258 EC_R_POINT_AT_INFINITY); 1259 return 0; 1260 } 1261 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || 1262 (!BN_to_felem(z1, &point->Z))) return 0; 1263 felem_inv(z2, z1); 1264 felem_square(tmp, z2); felem_reduce(z1, tmp); 1265 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); 1266 felem_contract(x_out, x_in); 1267 if (x != NULL) 1268 { 1269 if (!felem_to_BN(x, x_out)) { 1270 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, 1271 ERR_R_BN_LIB); 1272 return 0; 1273 } 1274 } 1275 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); 1276 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); 1277 felem_contract(y_out, y_in); 1278 if (y != NULL) 1279 { 1280 if (!felem_to_BN(y, y_out)) { 1281 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, 1282 ERR_R_BN_LIB); 1283 return 0; 1284 } 1285 } 1286 return 1; 1287 } 1288 1289 static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) 1290 { 1291 /* Runs in constant time, unless an input is the point at infinity 1292 * (which normally shouldn't happen). */ 1293 ec_GFp_nistp_points_make_affine_internal( 1294 num, 1295 points, 1296 sizeof(felem), 1297 tmp_felems, 1298 (void (*)(void *)) felem_one, 1299 (int (*)(const void *)) felem_is_zero_int, 1300 (void (*)(void *, const void *)) felem_assign, 1301 (void (*)(void *, const void *)) felem_square_reduce, 1302 (void (*)(void *, const void *, const void *)) felem_mul_reduce, 1303 (void (*)(void *, const void *)) felem_inv, 1304 (void (*)(void *, const void *)) felem_contract); 1305 } 1306 1307 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values 1308 * Result is stored in r (r can equal one of the inputs). */ 1309 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, 1310 const BIGNUM *scalar, size_t num, const EC_POINT *points[], 1311 const BIGNUM *scalars[], BN_CTX *ctx) 1312 { 1313 int ret = 0; 1314 int j; 1315 unsigned i; 1316 int mixed = 0; 1317 BN_CTX *new_ctx = NULL; 1318 BIGNUM *x, *y, *z, *tmp_scalar; 1319 felem_bytearray g_secret; 1320 felem_bytearray *secrets = NULL; 1321 felem (*pre_comp)[17][3] = NULL; 1322 felem *tmp_felems = NULL; 1323 felem_bytearray tmp; 1324 unsigned num_bytes; 1325 int have_pre_comp = 0; 1326 size_t num_points = num; 1327 felem x_in, y_in, z_in, x_out, y_out, z_out; 1328 NISTP224_PRE_COMP *pre = NULL; 1329 const felem (*g_pre_comp)[16][3] = NULL; 1330 EC_POINT *generator = NULL; 1331 const EC_POINT *p = NULL; 1332 const BIGNUM *p_scalar = NULL; 1333 1334 if (ctx == NULL) 1335 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1336 BN_CTX_start(ctx); 1337 if (((x = BN_CTX_get(ctx)) == NULL) || 1338 ((y = BN_CTX_get(ctx)) == NULL) || 1339 ((z = BN_CTX_get(ctx)) == NULL) || 1340 ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) 1341 goto err; 1342 1343 if (scalar != NULL) 1344 { 1345 pre = EC_EX_DATA_get_data(group->extra_data, 1346 nistp224_pre_comp_dup, nistp224_pre_comp_free, 1347 nistp224_pre_comp_clear_free); 1348 if (pre) 1349 /* we have precomputation, try to use it */ 1350 g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; 1351 else 1352 /* try to use the standard precomputation */ 1353 g_pre_comp = &gmul[0]; 1354 generator = EC_POINT_new(group); 1355 if (generator == NULL) 1356 goto err; 1357 /* get the generator from precomputation */ 1358 if (!felem_to_BN(x, g_pre_comp[0][1][0]) || 1359 !felem_to_BN(y, g_pre_comp[0][1][1]) || 1360 !felem_to_BN(z, g_pre_comp[0][1][2])) 1361 { 1362 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); 1363 goto err; 1364 } 1365 if (!EC_POINT_set_Jprojective_coordinates_GFp(group, 1366 generator, x, y, z, ctx)) 1367 goto err; 1368 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 1369 /* precomputation matches generator */ 1370 have_pre_comp = 1; 1371 else 1372 /* we don't have valid precomputation: 1373 * treat the generator as a random point */ 1374 num_points = num_points + 1; 1375 } 1376 1377 if (num_points > 0) 1378 { 1379 if (num_points >= 3) 1380 { 1381 /* unless we precompute multiples for just one or two points, 1382 * converting those into affine form is time well spent */ 1383 mixed = 1; 1384 } 1385 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); 1386 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); 1387 if (mixed) 1388 tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); 1389 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) 1390 { 1391 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1392 goto err; 1393 } 1394 1395 /* we treat NULL scalars as 0, and NULL points as points at infinity, 1396 * i.e., they contribute nothing to the linear combination */ 1397 memset(secrets, 0, num_points * sizeof(felem_bytearray)); 1398 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); 1399 for (i = 0; i < num_points; ++i) 1400 { 1401 if (i == num) 1402 /* the generator */ 1403 { 1404 p = EC_GROUP_get0_generator(group); 1405 p_scalar = scalar; 1406 } 1407 else 1408 /* the i^th point */ 1409 { 1410 p = points[i]; 1411 p_scalar = scalars[i]; 1412 } 1413 if ((p_scalar != NULL) && (p != NULL)) 1414 { 1415 /* reduce scalar to 0 <= scalar < 2^224 */ 1416 if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) 1417 { 1418 /* this is an unusual input, and we don't guarantee 1419 * constant-timeness */ 1420 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) 1421 { 1422 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); 1423 goto err; 1424 } 1425 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1426 } 1427 else 1428 num_bytes = BN_bn2bin(p_scalar, tmp); 1429 flip_endian(secrets[i], tmp, num_bytes); 1430 /* precompute multiples */ 1431 if ((!BN_to_felem(x_out, &p->X)) || 1432 (!BN_to_felem(y_out, &p->Y)) || 1433 (!BN_to_felem(z_out, &p->Z))) goto err; 1434 felem_assign(pre_comp[i][1][0], x_out); 1435 felem_assign(pre_comp[i][1][1], y_out); 1436 felem_assign(pre_comp[i][1][2], z_out); 1437 for (j = 2; j <= 16; ++j) 1438 { 1439 if (j & 1) 1440 { 1441 point_add( 1442 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1443 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 1444 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); 1445 } 1446 else 1447 { 1448 point_double( 1449 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1450 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); 1451 } 1452 } 1453 } 1454 } 1455 if (mixed) 1456 make_points_affine(num_points * 17, pre_comp[0], tmp_felems); 1457 } 1458 1459 /* the scalar for the generator */ 1460 if ((scalar != NULL) && (have_pre_comp)) 1461 { 1462 memset(g_secret, 0, sizeof g_secret); 1463 /* reduce scalar to 0 <= scalar < 2^224 */ 1464 if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) 1465 { 1466 /* this is an unusual input, and we don't guarantee 1467 * constant-timeness */ 1468 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) 1469 { 1470 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); 1471 goto err; 1472 } 1473 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1474 } 1475 else 1476 num_bytes = BN_bn2bin(scalar, tmp); 1477 flip_endian(g_secret, tmp, num_bytes); 1478 /* do the multiplication with generator precomputation*/ 1479 batch_mul(x_out, y_out, z_out, 1480 (const felem_bytearray (*)) secrets, num_points, 1481 g_secret, 1482 mixed, (const felem (*)[17][3]) pre_comp, 1483 g_pre_comp); 1484 } 1485 else 1486 /* do the multiplication without generator precomputation */ 1487 batch_mul(x_out, y_out, z_out, 1488 (const felem_bytearray (*)) secrets, num_points, 1489 NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); 1490 /* reduce the output to its unique minimal representation */ 1491 felem_contract(x_in, x_out); 1492 felem_contract(y_in, y_out); 1493 felem_contract(z_in, z_out); 1494 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || 1495 (!felem_to_BN(z, z_in))) 1496 { 1497 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); 1498 goto err; 1499 } 1500 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); 1501 1502 err: 1503 BN_CTX_end(ctx); 1504 if (generator != NULL) 1505 EC_POINT_free(generator); 1506 if (new_ctx != NULL) 1507 BN_CTX_free(new_ctx); 1508 if (secrets != NULL) 1509 OPENSSL_free(secrets); 1510 if (pre_comp != NULL) 1511 OPENSSL_free(pre_comp); 1512 if (tmp_felems != NULL) 1513 OPENSSL_free(tmp_felems); 1514 return ret; 1515 } 1516 1517 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 1518 { 1519 int ret = 0; 1520 NISTP224_PRE_COMP *pre = NULL; 1521 int i, j; 1522 BN_CTX *new_ctx = NULL; 1523 BIGNUM *x, *y; 1524 EC_POINT *generator = NULL; 1525 felem tmp_felems[32]; 1526 1527 /* throw away old precomputation */ 1528 EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, 1529 nistp224_pre_comp_free, nistp224_pre_comp_clear_free); 1530 if (ctx == NULL) 1531 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1532 BN_CTX_start(ctx); 1533 if (((x = BN_CTX_get(ctx)) == NULL) || 1534 ((y = BN_CTX_get(ctx)) == NULL)) 1535 goto err; 1536 /* get the generator */ 1537 if (group->generator == NULL) goto err; 1538 generator = EC_POINT_new(group); 1539 if (generator == NULL) 1540 goto err; 1541 BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); 1542 BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); 1543 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) 1544 goto err; 1545 if ((pre = nistp224_pre_comp_new()) == NULL) 1546 goto err; 1547 /* if the generator is the standard one, use built-in precomputation */ 1548 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 1549 { 1550 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); 1551 ret = 1; 1552 goto err; 1553 } 1554 if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || 1555 (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || 1556 (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) 1557 goto err; 1558 /* compute 2^56*G, 2^112*G, 2^168*G for the first table, 1559 * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one 1560 */ 1561 for (i = 1; i <= 8; i <<= 1) 1562 { 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[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); 1566 for (j = 0; j < 27; ++j) 1567 { 1568 point_double( 1569 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], 1570 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 1571 } 1572 if (i == 8) 1573 break; 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[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 1577 for (j = 0; j < 27; ++j) 1578 { 1579 point_double( 1580 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], 1581 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); 1582 } 1583 } 1584 for (i = 0; i < 2; i++) 1585 { 1586 /* g_pre_comp[i][0] is the point at infinity */ 1587 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); 1588 /* the remaining multiples */ 1589 /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ 1590 point_add( 1591 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], 1592 pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], 1593 pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], 1594 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], 1595 pre->g_pre_comp[i][2][2]); 1596 /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ 1597 point_add( 1598 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], 1599 pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], 1600 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 1601 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], 1602 pre->g_pre_comp[i][2][2]); 1603 /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ 1604 point_add( 1605 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], 1606 pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], 1607 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 1608 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], 1609 pre->g_pre_comp[i][4][2]); 1610 /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ 1611 point_add( 1612 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], 1613 pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], 1614 pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], 1615 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], 1616 pre->g_pre_comp[i][2][2]); 1617 for (j = 1; j < 8; ++j) 1618 { 1619 /* odd multiples: add G resp. 2^28*G */ 1620 point_add( 1621 pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], 1622 pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], 1623 pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], 1624 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], 1625 pre->g_pre_comp[i][1][2]); 1626 } 1627 } 1628 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); 1629 1630 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, 1631 nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) 1632 goto err; 1633 ret = 1; 1634 pre = NULL; 1635 err: 1636 BN_CTX_end(ctx); 1637 if (generator != NULL) 1638 EC_POINT_free(generator); 1639 if (new_ctx != NULL) 1640 BN_CTX_free(new_ctx); 1641 if (pre) 1642 nistp224_pre_comp_free(pre); 1643 return ret; 1644 } 1645 1646 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) 1647 { 1648 if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, 1649 nistp224_pre_comp_free, nistp224_pre_comp_clear_free) 1650 != NULL) 1651 return 1; 1652 else 1653 return 0; 1654 } 1655 1656 #else 1657 static void *dummy=&dummy; 1658 #endif 1659