1 /* crypto/ec/ecp_nistp256.c */ 2 /* 3 * Written by Adam Langley (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-256 elliptic curve point multiplication 23 * 24 * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. 25 * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 26 * work which got its smarts from Daniel J. Bernstein's work on the same. 27 */ 28 29 #include <openssl/opensslconf.h> 30 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 31 32 #ifndef OPENSSL_SYS_VMS 33 #include <stdint.h> 34 #else 35 #include <inttypes.h> 36 #endif 37 38 #include <string.h> 39 #include <openssl/err.h> 40 #include "ec_lcl.h" 41 42 #if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) 43 /* even with gcc, the typedef won't work for 32-bit platforms */ 44 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ 45 typedef __int128_t int128_t; 46 #else 47 #error "Need GCC 3.1 or later to define type uint128_t" 48 #endif 49 50 typedef uint8_t u8; 51 typedef uint32_t u32; 52 typedef uint64_t u64; 53 typedef int64_t s64; 54 55 /* The underlying field. 56 * 57 * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element 58 * of this field into 32 bytes. We call this an felem_bytearray. */ 59 60 typedef u8 felem_bytearray[32]; 61 62 /* These are the parameters of P256, taken from FIPS 186-3, page 86. These 63 * values are big-endian. */ 64 static const felem_bytearray nistp256_curve_params[5] = { 65 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ 66 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 67 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 68 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, 69 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ 70 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 71 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 72 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ 73 {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, 74 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, 75 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, 76 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, 77 {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ 78 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, 79 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, 80 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, 81 {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ 82 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, 83 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, 84 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} 85 }; 86 87 /* The representation of field elements. 88 * ------------------------------------ 89 * 90 * We represent field elements with either four 128-bit values, eight 128-bit 91 * values, or four 64-bit values. The field element represented is: 92 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p) 93 * or: 94 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p) 95 * 96 * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits 97 * apart, but are 128-bits wide, the most significant bits of each limb overlap 98 * with the least significant bits of the next. 99 * 100 * A field element with four limbs is an 'felem'. One with eight limbs is a 101 * 'longfelem' 102 * 103 * A field element with four, 64-bit values is called a 'smallfelem'. Small 104 * values are used as intermediate values before multiplication. 105 */ 106 107 #define NLIMBS 4 108 109 typedef uint128_t limb; 110 typedef limb felem[NLIMBS]; 111 typedef limb longfelem[NLIMBS * 2]; 112 typedef u64 smallfelem[NLIMBS]; 113 114 /* This is the value of the prime as four 64-bit words, little-endian. */ 115 static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; 116 static const limb bottom32bits = 0xffffffff; 117 static const u64 bottom63bits = 0x7ffffffffffffffful; 118 119 /* bin32_to_felem takes a little-endian byte array and converts it into felem 120 * form. This assumes that the CPU is little-endian. */ 121 static void bin32_to_felem(felem out, const u8 in[32]) 122 { 123 out[0] = *((u64*) &in[0]); 124 out[1] = *((u64*) &in[8]); 125 out[2] = *((u64*) &in[16]); 126 out[3] = *((u64*) &in[24]); 127 } 128 129 /* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, 130 * 32 byte array. This assumes that the CPU is little-endian. */ 131 static void smallfelem_to_bin32(u8 out[32], const smallfelem in) 132 { 133 *((u64*) &out[0]) = in[0]; 134 *((u64*) &out[8]) = in[1]; 135 *((u64*) &out[16]) = in[2]; 136 *((u64*) &out[24]) = in[3]; 137 } 138 139 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ 140 static void flip_endian(u8 *out, const u8 *in, unsigned len) 141 { 142 unsigned i; 143 for (i = 0; i < len; ++i) 144 out[i] = in[len-1-i]; 145 } 146 147 /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ 148 static int BN_to_felem(felem out, const BIGNUM *bn) 149 { 150 felem_bytearray b_in; 151 felem_bytearray b_out; 152 unsigned num_bytes; 153 154 /* BN_bn2bin eats leading zeroes */ 155 memset(b_out, 0, sizeof b_out); 156 num_bytes = BN_num_bytes(bn); 157 if (num_bytes > sizeof b_out) 158 { 159 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 160 return 0; 161 } 162 if (BN_is_negative(bn)) 163 { 164 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 165 return 0; 166 } 167 num_bytes = BN_bn2bin(bn, b_in); 168 flip_endian(b_out, b_in, num_bytes); 169 bin32_to_felem(out, b_out); 170 return 1; 171 } 172 173 /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ 174 static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) 175 { 176 felem_bytearray b_in, b_out; 177 smallfelem_to_bin32(b_in, in); 178 flip_endian(b_out, b_in, sizeof b_out); 179 return BN_bin2bn(b_out, sizeof b_out, out); 180 } 181 182 183 /* Field operations 184 * ---------------- */ 185 186 static void smallfelem_one(smallfelem out) 187 { 188 out[0] = 1; 189 out[1] = 0; 190 out[2] = 0; 191 out[3] = 0; 192 } 193 194 static void smallfelem_assign(smallfelem out, const smallfelem in) 195 { 196 out[0] = in[0]; 197 out[1] = in[1]; 198 out[2] = in[2]; 199 out[3] = in[3]; 200 } 201 202 static void felem_assign(felem out, const felem in) 203 { 204 out[0] = in[0]; 205 out[1] = in[1]; 206 out[2] = in[2]; 207 out[3] = in[3]; 208 } 209 210 /* felem_sum sets out = out + in. */ 211 static void felem_sum(felem out, const felem in) 212 { 213 out[0] += in[0]; 214 out[1] += in[1]; 215 out[2] += in[2]; 216 out[3] += in[3]; 217 } 218 219 /* felem_small_sum sets out = out + in. */ 220 static void felem_small_sum(felem out, const smallfelem in) 221 { 222 out[0] += in[0]; 223 out[1] += in[1]; 224 out[2] += in[2]; 225 out[3] += in[3]; 226 } 227 228 /* felem_scalar sets out = out * scalar */ 229 static void felem_scalar(felem out, const u64 scalar) 230 { 231 out[0] *= scalar; 232 out[1] *= scalar; 233 out[2] *= scalar; 234 out[3] *= scalar; 235 } 236 237 /* longfelem_scalar sets out = out * scalar */ 238 static void longfelem_scalar(longfelem out, const u64 scalar) 239 { 240 out[0] *= scalar; 241 out[1] *= scalar; 242 out[2] *= scalar; 243 out[3] *= scalar; 244 out[4] *= scalar; 245 out[5] *= scalar; 246 out[6] *= scalar; 247 out[7] *= scalar; 248 } 249 250 #define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) 251 #define two105 (((limb)1) << 105) 252 #define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) 253 254 /* zero105 is 0 mod p */ 255 static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; 256 257 /* smallfelem_neg sets |out| to |-small| 258 * On exit: 259 * out[i] < out[i] + 2^105 260 */ 261 static void smallfelem_neg(felem out, const smallfelem small) 262 { 263 /* In order to prevent underflow, we subtract from 0 mod p. */ 264 out[0] = zero105[0] - small[0]; 265 out[1] = zero105[1] - small[1]; 266 out[2] = zero105[2] - small[2]; 267 out[3] = zero105[3] - small[3]; 268 } 269 270 /* felem_diff subtracts |in| from |out| 271 * On entry: 272 * in[i] < 2^104 273 * On exit: 274 * out[i] < out[i] + 2^105 275 */ 276 static void felem_diff(felem out, const felem in) 277 { 278 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 279 out[0] += zero105[0]; 280 out[1] += zero105[1]; 281 out[2] += zero105[2]; 282 out[3] += zero105[3]; 283 284 out[0] -= in[0]; 285 out[1] -= in[1]; 286 out[2] -= in[2]; 287 out[3] -= in[3]; 288 } 289 290 #define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) 291 #define two107 (((limb)1) << 107) 292 #define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) 293 294 /* zero107 is 0 mod p */ 295 static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; 296 297 /* An alternative felem_diff for larger inputs |in| 298 * felem_diff_zero107 subtracts |in| from |out| 299 * On entry: 300 * in[i] < 2^106 301 * On exit: 302 * out[i] < out[i] + 2^107 303 */ 304 static void felem_diff_zero107(felem out, const felem in) 305 { 306 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 307 out[0] += zero107[0]; 308 out[1] += zero107[1]; 309 out[2] += zero107[2]; 310 out[3] += zero107[3]; 311 312 out[0] -= in[0]; 313 out[1] -= in[1]; 314 out[2] -= in[2]; 315 out[3] -= in[3]; 316 } 317 318 /* longfelem_diff subtracts |in| from |out| 319 * On entry: 320 * in[i] < 7*2^67 321 * On exit: 322 * out[i] < out[i] + 2^70 + 2^40 323 */ 324 static void longfelem_diff(longfelem out, const longfelem in) 325 { 326 static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); 327 static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); 328 static const limb two70 = (((limb)1) << 70); 329 static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); 330 static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); 331 332 /* add 0 mod p to avoid underflow */ 333 out[0] += two70m8p6; 334 out[1] += two70p40; 335 out[2] += two70; 336 out[3] += two70m40m38p6; 337 out[4] += two70m6; 338 out[5] += two70m6; 339 out[6] += two70m6; 340 out[7] += two70m6; 341 342 /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ 343 out[0] -= in[0]; 344 out[1] -= in[1]; 345 out[2] -= in[2]; 346 out[3] -= in[3]; 347 out[4] -= in[4]; 348 out[5] -= in[5]; 349 out[6] -= in[6]; 350 out[7] -= in[7]; 351 } 352 353 #define two64m0 (((limb)1) << 64) - 1 354 #define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 355 #define two64m46 (((limb)1) << 64) - (((limb)1) << 46) 356 #define two64m32 (((limb)1) << 64) - (((limb)1) << 32) 357 358 /* zero110 is 0 mod p */ 359 static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; 360 361 /* felem_shrink converts an felem into a smallfelem. The result isn't quite 362 * minimal as the value may be greater than p. 363 * 364 * On entry: 365 * in[i] < 2^109 366 * On exit: 367 * out[i] < 2^64 368 */ 369 static void felem_shrink(smallfelem out, const felem in) 370 { 371 felem tmp; 372 u64 a, b, mask; 373 s64 high, low; 374 static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ 375 376 /* Carry 2->3 */ 377 tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); 378 /* tmp[3] < 2^110 */ 379 380 tmp[2] = zero110[2] + (u64) in[2]; 381 tmp[0] = zero110[0] + in[0]; 382 tmp[1] = zero110[1] + in[1]; 383 /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ 384 385 /* We perform two partial reductions where we eliminate the 386 * high-word of tmp[3]. We don't update the other words till the end. 387 */ 388 a = tmp[3] >> 64; /* a < 2^46 */ 389 tmp[3] = (u64) tmp[3]; 390 tmp[3] -= a; 391 tmp[3] += ((limb)a) << 32; 392 /* tmp[3] < 2^79 */ 393 394 b = a; 395 a = tmp[3] >> 64; /* a < 2^15 */ 396 b += a; /* b < 2^46 + 2^15 < 2^47 */ 397 tmp[3] = (u64) tmp[3]; 398 tmp[3] -= a; 399 tmp[3] += ((limb)a) << 32; 400 /* tmp[3] < 2^64 + 2^47 */ 401 402 /* This adjusts the other two words to complete the two partial 403 * reductions. */ 404 tmp[0] += b; 405 tmp[1] -= (((limb)b) << 32); 406 407 /* In order to make space in tmp[3] for the carry from 2 -> 3, we 408 * conditionally subtract kPrime if tmp[3] is large enough. */ 409 high = tmp[3] >> 64; 410 /* As tmp[3] < 2^65, high is either 1 or 0 */ 411 high <<= 63; 412 high >>= 63; 413 /* high is: 414 * all ones if the high word of tmp[3] is 1 415 * all zeros if the high word of tmp[3] if 0 */ 416 low = tmp[3]; 417 mask = low >> 63; 418 /* mask is: 419 * all ones if the MSB of low is 1 420 * all zeros if the MSB of low if 0 */ 421 low &= bottom63bits; 422 low -= kPrime3Test; 423 /* if low was greater than kPrime3Test then the MSB is zero */ 424 low = ~low; 425 low >>= 63; 426 /* low is: 427 * all ones if low was > kPrime3Test 428 * all zeros if low was <= kPrime3Test */ 429 mask = (mask & low) | high; 430 tmp[0] -= mask & kPrime[0]; 431 tmp[1] -= mask & kPrime[1]; 432 /* kPrime[2] is zero, so omitted */ 433 tmp[3] -= mask & kPrime[3]; 434 /* tmp[3] < 2**64 - 2**32 + 1 */ 435 436 tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; 437 tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; 438 tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; 439 /* tmp[i] < 2^64 */ 440 441 out[0] = tmp[0]; 442 out[1] = tmp[1]; 443 out[2] = tmp[2]; 444 out[3] = tmp[3]; 445 } 446 447 /* smallfelem_expand converts a smallfelem to an felem */ 448 static void smallfelem_expand(felem out, const smallfelem in) 449 { 450 out[0] = in[0]; 451 out[1] = in[1]; 452 out[2] = in[2]; 453 out[3] = in[3]; 454 } 455 456 /* smallfelem_square sets |out| = |small|^2 457 * On entry: 458 * small[i] < 2^64 459 * On exit: 460 * out[i] < 7 * 2^64 < 2^67 461 */ 462 static void smallfelem_square(longfelem out, const smallfelem small) 463 { 464 limb a; 465 u64 high, low; 466 467 a = ((uint128_t) small[0]) * small[0]; 468 low = a; 469 high = a >> 64; 470 out[0] = low; 471 out[1] = high; 472 473 a = ((uint128_t) small[0]) * small[1]; 474 low = a; 475 high = a >> 64; 476 out[1] += low; 477 out[1] += low; 478 out[2] = high; 479 480 a = ((uint128_t) small[0]) * small[2]; 481 low = a; 482 high = a >> 64; 483 out[2] += low; 484 out[2] *= 2; 485 out[3] = high; 486 487 a = ((uint128_t) small[0]) * small[3]; 488 low = a; 489 high = a >> 64; 490 out[3] += low; 491 out[4] = high; 492 493 a = ((uint128_t) small[1]) * small[2]; 494 low = a; 495 high = a >> 64; 496 out[3] += low; 497 out[3] *= 2; 498 out[4] += high; 499 500 a = ((uint128_t) small[1]) * small[1]; 501 low = a; 502 high = a >> 64; 503 out[2] += low; 504 out[3] += high; 505 506 a = ((uint128_t) small[1]) * small[3]; 507 low = a; 508 high = a >> 64; 509 out[4] += low; 510 out[4] *= 2; 511 out[5] = high; 512 513 a = ((uint128_t) small[2]) * small[3]; 514 low = a; 515 high = a >> 64; 516 out[5] += low; 517 out[5] *= 2; 518 out[6] = high; 519 out[6] += high; 520 521 a = ((uint128_t) small[2]) * small[2]; 522 low = a; 523 high = a >> 64; 524 out[4] += low; 525 out[5] += high; 526 527 a = ((uint128_t) small[3]) * small[3]; 528 low = a; 529 high = a >> 64; 530 out[6] += low; 531 out[7] = high; 532 } 533 534 /* felem_square sets |out| = |in|^2 535 * On entry: 536 * in[i] < 2^109 537 * On exit: 538 * out[i] < 7 * 2^64 < 2^67 539 */ 540 static void felem_square(longfelem out, const felem in) 541 { 542 u64 small[4]; 543 felem_shrink(small, in); 544 smallfelem_square(out, small); 545 } 546 547 /* smallfelem_mul sets |out| = |small1| * |small2| 548 * On entry: 549 * small1[i] < 2^64 550 * small2[i] < 2^64 551 * On exit: 552 * out[i] < 7 * 2^64 < 2^67 553 */ 554 static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) 555 { 556 limb a; 557 u64 high, low; 558 559 a = ((uint128_t) small1[0]) * small2[0]; 560 low = a; 561 high = a >> 64; 562 out[0] = low; 563 out[1] = high; 564 565 566 a = ((uint128_t) small1[0]) * small2[1]; 567 low = a; 568 high = a >> 64; 569 out[1] += low; 570 out[2] = high; 571 572 a = ((uint128_t) small1[1]) * small2[0]; 573 low = a; 574 high = a >> 64; 575 out[1] += low; 576 out[2] += high; 577 578 579 a = ((uint128_t) small1[0]) * small2[2]; 580 low = a; 581 high = a >> 64; 582 out[2] += low; 583 out[3] = high; 584 585 a = ((uint128_t) small1[1]) * small2[1]; 586 low = a; 587 high = a >> 64; 588 out[2] += low; 589 out[3] += high; 590 591 a = ((uint128_t) small1[2]) * small2[0]; 592 low = a; 593 high = a >> 64; 594 out[2] += low; 595 out[3] += high; 596 597 598 a = ((uint128_t) small1[0]) * small2[3]; 599 low = a; 600 high = a >> 64; 601 out[3] += low; 602 out[4] = high; 603 604 a = ((uint128_t) small1[1]) * small2[2]; 605 low = a; 606 high = a >> 64; 607 out[3] += low; 608 out[4] += high; 609 610 a = ((uint128_t) small1[2]) * small2[1]; 611 low = a; 612 high = a >> 64; 613 out[3] += low; 614 out[4] += high; 615 616 a = ((uint128_t) small1[3]) * small2[0]; 617 low = a; 618 high = a >> 64; 619 out[3] += low; 620 out[4] += high; 621 622 623 a = ((uint128_t) small1[1]) * small2[3]; 624 low = a; 625 high = a >> 64; 626 out[4] += low; 627 out[5] = high; 628 629 a = ((uint128_t) small1[2]) * small2[2]; 630 low = a; 631 high = a >> 64; 632 out[4] += low; 633 out[5] += high; 634 635 a = ((uint128_t) small1[3]) * small2[1]; 636 low = a; 637 high = a >> 64; 638 out[4] += low; 639 out[5] += high; 640 641 642 a = ((uint128_t) small1[2]) * small2[3]; 643 low = a; 644 high = a >> 64; 645 out[5] += low; 646 out[6] = high; 647 648 a = ((uint128_t) small1[3]) * small2[2]; 649 low = a; 650 high = a >> 64; 651 out[5] += low; 652 out[6] += high; 653 654 655 a = ((uint128_t) small1[3]) * small2[3]; 656 low = a; 657 high = a >> 64; 658 out[6] += low; 659 out[7] = high; 660 } 661 662 /* felem_mul sets |out| = |in1| * |in2| 663 * On entry: 664 * in1[i] < 2^109 665 * in2[i] < 2^109 666 * On exit: 667 * out[i] < 7 * 2^64 < 2^67 668 */ 669 static void felem_mul(longfelem out, const felem in1, const felem in2) 670 { 671 smallfelem small1, small2; 672 felem_shrink(small1, in1); 673 felem_shrink(small2, in2); 674 smallfelem_mul(out, small1, small2); 675 } 676 677 /* felem_small_mul sets |out| = |small1| * |in2| 678 * On entry: 679 * small1[i] < 2^64 680 * in2[i] < 2^109 681 * On exit: 682 * out[i] < 7 * 2^64 < 2^67 683 */ 684 static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) 685 { 686 smallfelem small2; 687 felem_shrink(small2, in2); 688 smallfelem_mul(out, small1, small2); 689 } 690 691 #define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) 692 #define two100 (((limb)1) << 100) 693 #define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) 694 /* zero100 is 0 mod p */ 695 static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; 696 697 /* Internal function for the different flavours of felem_reduce. 698 * felem_reduce_ reduces the higher coefficients in[4]-in[7]. 699 * On entry: 700 * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] 701 * out[1] >= in[7] + 2^32*in[4] 702 * out[2] >= in[5] + 2^32*in[5] 703 * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] 704 * On exit: 705 * out[0] <= out[0] + in[4] + 2^32*in[5] 706 * out[1] <= out[1] + in[5] + 2^33*in[6] 707 * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] 708 * out[3] <= out[3] + 2^32*in[4] + 3*in[7] 709 */ 710 static void felem_reduce_(felem out, const longfelem in) 711 { 712 int128_t c; 713 /* combine common terms from below */ 714 c = in[4] + (in[5] << 32); 715 out[0] += c; 716 out[3] -= c; 717 718 c = in[5] - in[7]; 719 out[1] += c; 720 out[2] -= c; 721 722 /* the remaining terms */ 723 /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ 724 out[1] -= (in[4] << 32); 725 out[3] += (in[4] << 32); 726 727 /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ 728 out[2] -= (in[5] << 32); 729 730 /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ 731 out[0] -= in[6]; 732 out[0] -= (in[6] << 32); 733 out[1] += (in[6] << 33); 734 out[2] += (in[6] * 2); 735 out[3] -= (in[6] << 32); 736 737 /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ 738 out[0] -= in[7]; 739 out[0] -= (in[7] << 32); 740 out[2] += (in[7] << 33); 741 out[3] += (in[7] * 3); 742 } 743 744 /* felem_reduce converts a longfelem into an felem. 745 * To be called directly after felem_square or felem_mul. 746 * On entry: 747 * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 748 * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 749 * On exit: 750 * out[i] < 2^101 751 */ 752 static void felem_reduce(felem out, const longfelem in) 753 { 754 out[0] = zero100[0] + in[0]; 755 out[1] = zero100[1] + in[1]; 756 out[2] = zero100[2] + in[2]; 757 out[3] = zero100[3] + in[3]; 758 759 felem_reduce_(out, in); 760 761 /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 762 * out[1] > 2^100 - 2^64 - 7*2^96 > 0 763 * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 764 * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 765 * 766 * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 767 * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 768 * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 769 * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 770 */ 771 } 772 773 /* felem_reduce_zero105 converts a larger longfelem into an felem. 774 * On entry: 775 * in[0] < 2^71 776 * On exit: 777 * out[i] < 2^106 778 */ 779 static void felem_reduce_zero105(felem out, const longfelem in) 780 { 781 out[0] = zero105[0] + in[0]; 782 out[1] = zero105[1] + in[1]; 783 out[2] = zero105[2] + in[2]; 784 out[3] = zero105[3] + in[3]; 785 786 felem_reduce_(out, in); 787 788 /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 789 * out[1] > 2^105 - 2^71 - 2^103 > 0 790 * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 791 * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 792 * 793 * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 794 * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 795 * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 796 * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 797 */ 798 } 799 800 /* subtract_u64 sets *result = *result - v and *carry to one if the subtraction 801 * underflowed. */ 802 static void subtract_u64(u64* result, u64* carry, u64 v) 803 { 804 uint128_t r = *result; 805 r -= v; 806 *carry = (r >> 64) & 1; 807 *result = (u64) r; 808 } 809 810 /* felem_contract converts |in| to its unique, minimal representation. 811 * On entry: 812 * in[i] < 2^109 813 */ 814 static void felem_contract(smallfelem out, const felem in) 815 { 816 unsigned i; 817 u64 all_equal_so_far = 0, result = 0, carry; 818 819 felem_shrink(out, in); 820 /* small is minimal except that the value might be > p */ 821 822 all_equal_so_far--; 823 /* We are doing a constant time test if out >= kPrime. We need to 824 * compare each u64, from most-significant to least significant. For 825 * each one, if all words so far have been equal (m is all ones) then a 826 * non-equal result is the answer. Otherwise we continue. */ 827 for (i = 3; i < 4; i--) 828 { 829 u64 equal; 830 uint128_t a = ((uint128_t) kPrime[i]) - out[i]; 831 /* if out[i] > kPrime[i] then a will underflow and the high 832 * 64-bits will all be set. */ 833 result |= all_equal_so_far & ((u64) (a >> 64)); 834 835 /* if kPrime[i] == out[i] then |equal| will be all zeros and 836 * the decrement will make it all ones. */ 837 equal = kPrime[i] ^ out[i]; 838 equal--; 839 equal &= equal << 32; 840 equal &= equal << 16; 841 equal &= equal << 8; 842 equal &= equal << 4; 843 equal &= equal << 2; 844 equal &= equal << 1; 845 equal = ((s64) equal) >> 63; 846 847 all_equal_so_far &= equal; 848 } 849 850 /* if all_equal_so_far is still all ones then the two values are equal 851 * and so out >= kPrime is true. */ 852 result |= all_equal_so_far; 853 854 /* if out >= kPrime then we subtract kPrime. */ 855 subtract_u64(&out[0], &carry, result & kPrime[0]); 856 subtract_u64(&out[1], &carry, carry); 857 subtract_u64(&out[2], &carry, carry); 858 subtract_u64(&out[3], &carry, carry); 859 860 subtract_u64(&out[1], &carry, result & kPrime[1]); 861 subtract_u64(&out[2], &carry, carry); 862 subtract_u64(&out[3], &carry, carry); 863 864 subtract_u64(&out[2], &carry, result & kPrime[2]); 865 subtract_u64(&out[3], &carry, carry); 866 867 subtract_u64(&out[3], &carry, result & kPrime[3]); 868 } 869 870 static void smallfelem_square_contract(smallfelem out, const smallfelem in) 871 { 872 longfelem longtmp; 873 felem tmp; 874 875 smallfelem_square(longtmp, in); 876 felem_reduce(tmp, longtmp); 877 felem_contract(out, tmp); 878 } 879 880 static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) 881 { 882 longfelem longtmp; 883 felem tmp; 884 885 smallfelem_mul(longtmp, in1, in2); 886 felem_reduce(tmp, longtmp); 887 felem_contract(out, tmp); 888 } 889 890 /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 891 * otherwise. 892 * On entry: 893 * small[i] < 2^64 894 */ 895 static limb smallfelem_is_zero(const smallfelem small) 896 { 897 limb result; 898 u64 is_p; 899 900 u64 is_zero = small[0] | small[1] | small[2] | small[3]; 901 is_zero--; 902 is_zero &= is_zero << 32; 903 is_zero &= is_zero << 16; 904 is_zero &= is_zero << 8; 905 is_zero &= is_zero << 4; 906 is_zero &= is_zero << 2; 907 is_zero &= is_zero << 1; 908 is_zero = ((s64) is_zero) >> 63; 909 910 is_p = (small[0] ^ kPrime[0]) | 911 (small[1] ^ kPrime[1]) | 912 (small[2] ^ kPrime[2]) | 913 (small[3] ^ kPrime[3]); 914 is_p--; 915 is_p &= is_p << 32; 916 is_p &= is_p << 16; 917 is_p &= is_p << 8; 918 is_p &= is_p << 4; 919 is_p &= is_p << 2; 920 is_p &= is_p << 1; 921 is_p = ((s64) is_p) >> 63; 922 923 is_zero |= is_p; 924 925 result = is_zero; 926 result |= ((limb) is_zero) << 64; 927 return result; 928 } 929 930 static int smallfelem_is_zero_int(const smallfelem small) 931 { 932 return (int) (smallfelem_is_zero(small) & ((limb)1)); 933 } 934 935 /* felem_inv calculates |out| = |in|^{-1} 936 * 937 * Based on Fermat's Little Theorem: 938 * a^p = a (mod p) 939 * a^{p-1} = 1 (mod p) 940 * a^{p-2} = a^{-1} (mod p) 941 */ 942 static void felem_inv(felem out, const felem in) 943 { 944 felem ftmp, ftmp2; 945 /* each e_I will hold |in|^{2^I - 1} */ 946 felem e2, e4, e8, e16, e32, e64; 947 longfelem tmp; 948 unsigned i; 949 950 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ 951 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ 952 felem_assign(e2, ftmp); 953 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ 954 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ 955 felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ 956 felem_assign(e4, ftmp); 957 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ 958 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ 959 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ 960 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ 961 felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ 962 felem_assign(e8, ftmp); 963 for (i = 0; i < 8; i++) { 964 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 965 } /* 2^16 - 2^8 */ 966 felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ 967 felem_assign(e16, ftmp); 968 for (i = 0; i < 16; i++) { 969 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 970 } /* 2^32 - 2^16 */ 971 felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ 972 felem_assign(e32, ftmp); 973 for (i = 0; i < 32; i++) { 974 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 975 } /* 2^64 - 2^32 */ 976 felem_assign(e64, ftmp); 977 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ 978 for (i = 0; i < 192; i++) { 979 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 980 } /* 2^256 - 2^224 + 2^192 */ 981 982 felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ 983 for (i = 0; i < 16; i++) { 984 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 985 } /* 2^80 - 2^16 */ 986 felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ 987 for (i = 0; i < 8; i++) { 988 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 989 } /* 2^88 - 2^8 */ 990 felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ 991 for (i = 0; i < 4; i++) { 992 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 993 } /* 2^92 - 2^4 */ 994 felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ 995 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ 996 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ 997 felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ 998 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ 999 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ 1000 felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ 1001 1002 felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ 1003 } 1004 1005 static void smallfelem_inv_contract(smallfelem out, const smallfelem in) 1006 { 1007 felem tmp; 1008 1009 smallfelem_expand(tmp, in); 1010 felem_inv(tmp, tmp); 1011 felem_contract(out, tmp); 1012 } 1013 1014 /* Group operations 1015 * ---------------- 1016 * 1017 * Building on top of the field operations we have the operations on the 1018 * elliptic curve group itself. Points on the curve are represented in Jacobian 1019 * coordinates */ 1020 1021 /* point_double calculates 2*(x_in, y_in, z_in) 1022 * 1023 * The method is taken from: 1024 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b 1025 * 1026 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. 1027 * while x_out == y_in is not (maybe this works, but it's not tested). */ 1028 static void 1029 point_double(felem x_out, felem y_out, felem z_out, 1030 const felem x_in, const felem y_in, const felem z_in) 1031 { 1032 longfelem tmp, tmp2; 1033 felem delta, gamma, beta, alpha, ftmp, ftmp2; 1034 smallfelem small1, small2; 1035 1036 felem_assign(ftmp, x_in); 1037 /* ftmp[i] < 2^106 */ 1038 felem_assign(ftmp2, x_in); 1039 /* ftmp2[i] < 2^106 */ 1040 1041 /* delta = z^2 */ 1042 felem_square(tmp, z_in); 1043 felem_reduce(delta, tmp); 1044 /* delta[i] < 2^101 */ 1045 1046 /* gamma = y^2 */ 1047 felem_square(tmp, y_in); 1048 felem_reduce(gamma, tmp); 1049 /* gamma[i] < 2^101 */ 1050 felem_shrink(small1, gamma); 1051 1052 /* beta = x*gamma */ 1053 felem_small_mul(tmp, small1, x_in); 1054 felem_reduce(beta, tmp); 1055 /* beta[i] < 2^101 */ 1056 1057 /* alpha = 3*(x-delta)*(x+delta) */ 1058 felem_diff(ftmp, delta); 1059 /* ftmp[i] < 2^105 + 2^106 < 2^107 */ 1060 felem_sum(ftmp2, delta); 1061 /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ 1062 felem_scalar(ftmp2, 3); 1063 /* ftmp2[i] < 3 * 2^107 < 2^109 */ 1064 felem_mul(tmp, ftmp, ftmp2); 1065 felem_reduce(alpha, tmp); 1066 /* alpha[i] < 2^101 */ 1067 felem_shrink(small2, alpha); 1068 1069 /* x' = alpha^2 - 8*beta */ 1070 smallfelem_square(tmp, small2); 1071 felem_reduce(x_out, tmp); 1072 felem_assign(ftmp, beta); 1073 felem_scalar(ftmp, 8); 1074 /* ftmp[i] < 8 * 2^101 = 2^104 */ 1075 felem_diff(x_out, ftmp); 1076 /* x_out[i] < 2^105 + 2^101 < 2^106 */ 1077 1078 /* z' = (y + z)^2 - gamma - delta */ 1079 felem_sum(delta, gamma); 1080 /* delta[i] < 2^101 + 2^101 = 2^102 */ 1081 felem_assign(ftmp, y_in); 1082 felem_sum(ftmp, z_in); 1083 /* ftmp[i] < 2^106 + 2^106 = 2^107 */ 1084 felem_square(tmp, ftmp); 1085 felem_reduce(z_out, tmp); 1086 felem_diff(z_out, delta); 1087 /* z_out[i] < 2^105 + 2^101 < 2^106 */ 1088 1089 /* y' = alpha*(4*beta - x') - 8*gamma^2 */ 1090 felem_scalar(beta, 4); 1091 /* beta[i] < 4 * 2^101 = 2^103 */ 1092 felem_diff_zero107(beta, x_out); 1093 /* beta[i] < 2^107 + 2^103 < 2^108 */ 1094 felem_small_mul(tmp, small2, beta); 1095 /* tmp[i] < 7 * 2^64 < 2^67 */ 1096 smallfelem_square(tmp2, small1); 1097 /* tmp2[i] < 7 * 2^64 */ 1098 longfelem_scalar(tmp2, 8); 1099 /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ 1100 longfelem_diff(tmp, tmp2); 1101 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ 1102 felem_reduce_zero105(y_out, tmp); 1103 /* y_out[i] < 2^106 */ 1104 } 1105 1106 /* point_double_small is the same as point_double, except that it operates on 1107 * smallfelems */ 1108 static void 1109 point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, 1110 const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) 1111 { 1112 felem felem_x_out, felem_y_out, felem_z_out; 1113 felem felem_x_in, felem_y_in, felem_z_in; 1114 1115 smallfelem_expand(felem_x_in, x_in); 1116 smallfelem_expand(felem_y_in, y_in); 1117 smallfelem_expand(felem_z_in, z_in); 1118 point_double(felem_x_out, felem_y_out, felem_z_out, 1119 felem_x_in, felem_y_in, felem_z_in); 1120 felem_shrink(x_out, felem_x_out); 1121 felem_shrink(y_out, felem_y_out); 1122 felem_shrink(z_out, felem_z_out); 1123 } 1124 1125 /* copy_conditional copies in to out iff mask is all ones. */ 1126 static void 1127 copy_conditional(felem out, const felem in, limb mask) 1128 { 1129 unsigned i; 1130 for (i = 0; i < NLIMBS; ++i) 1131 { 1132 const limb tmp = mask & (in[i] ^ out[i]); 1133 out[i] ^= tmp; 1134 } 1135 } 1136 1137 /* copy_small_conditional copies in to out iff mask is all ones. */ 1138 static void 1139 copy_small_conditional(felem out, const smallfelem in, limb mask) 1140 { 1141 unsigned i; 1142 const u64 mask64 = mask; 1143 for (i = 0; i < NLIMBS; ++i) 1144 { 1145 out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); 1146 } 1147 } 1148 1149 /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) 1150 * 1151 * The method is taken from: 1152 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, 1153 * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). 1154 * 1155 * This function includes a branch for checking whether the two input points 1156 * are equal, (while not equal to the point at infinity). This case never 1157 * happens during single point multiplication, so there is no timing leak for 1158 * ECDH or ECDSA signing. */ 1159 static void point_add(felem x3, felem y3, felem z3, 1160 const felem x1, const felem y1, const felem z1, 1161 const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) 1162 { 1163 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; 1164 longfelem tmp, tmp2; 1165 smallfelem small1, small2, small3, small4, small5; 1166 limb x_equal, y_equal, z1_is_zero, z2_is_zero; 1167 1168 felem_shrink(small3, z1); 1169 1170 z1_is_zero = smallfelem_is_zero(small3); 1171 z2_is_zero = smallfelem_is_zero(z2); 1172 1173 /* ftmp = z1z1 = z1**2 */ 1174 smallfelem_square(tmp, small3); 1175 felem_reduce(ftmp, tmp); 1176 /* ftmp[i] < 2^101 */ 1177 felem_shrink(small1, ftmp); 1178 1179 if(!mixed) 1180 { 1181 /* ftmp2 = z2z2 = z2**2 */ 1182 smallfelem_square(tmp, z2); 1183 felem_reduce(ftmp2, tmp); 1184 /* ftmp2[i] < 2^101 */ 1185 felem_shrink(small2, ftmp2); 1186 1187 felem_shrink(small5, x1); 1188 1189 /* u1 = ftmp3 = x1*z2z2 */ 1190 smallfelem_mul(tmp, small5, small2); 1191 felem_reduce(ftmp3, tmp); 1192 /* ftmp3[i] < 2^101 */ 1193 1194 /* ftmp5 = z1 + z2 */ 1195 felem_assign(ftmp5, z1); 1196 felem_small_sum(ftmp5, z2); 1197 /* ftmp5[i] < 2^107 */ 1198 1199 /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ 1200 felem_square(tmp, ftmp5); 1201 felem_reduce(ftmp5, tmp); 1202 /* ftmp2 = z2z2 + z1z1 */ 1203 felem_sum(ftmp2, ftmp); 1204 /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ 1205 felem_diff(ftmp5, ftmp2); 1206 /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ 1207 1208 /* ftmp2 = z2 * z2z2 */ 1209 smallfelem_mul(tmp, small2, z2); 1210 felem_reduce(ftmp2, tmp); 1211 1212 /* s1 = ftmp2 = y1 * z2**3 */ 1213 felem_mul(tmp, y1, ftmp2); 1214 felem_reduce(ftmp6, tmp); 1215 /* ftmp6[i] < 2^101 */ 1216 } 1217 else 1218 { 1219 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ 1220 1221 /* u1 = ftmp3 = x1*z2z2 */ 1222 felem_assign(ftmp3, x1); 1223 /* ftmp3[i] < 2^106 */ 1224 1225 /* ftmp5 = 2z1z2 */ 1226 felem_assign(ftmp5, z1); 1227 felem_scalar(ftmp5, 2); 1228 /* ftmp5[i] < 2*2^106 = 2^107 */ 1229 1230 /* s1 = ftmp2 = y1 * z2**3 */ 1231 felem_assign(ftmp6, y1); 1232 /* ftmp6[i] < 2^106 */ 1233 } 1234 1235 /* u2 = x2*z1z1 */ 1236 smallfelem_mul(tmp, x2, small1); 1237 felem_reduce(ftmp4, tmp); 1238 1239 /* h = ftmp4 = u2 - u1 */ 1240 felem_diff_zero107(ftmp4, ftmp3); 1241 /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ 1242 felem_shrink(small4, ftmp4); 1243 1244 x_equal = smallfelem_is_zero(small4); 1245 1246 /* z_out = ftmp5 * h */ 1247 felem_small_mul(tmp, small4, ftmp5); 1248 felem_reduce(z_out, tmp); 1249 /* z_out[i] < 2^101 */ 1250 1251 /* ftmp = z1 * z1z1 */ 1252 smallfelem_mul(tmp, small1, small3); 1253 felem_reduce(ftmp, tmp); 1254 1255 /* s2 = tmp = y2 * z1**3 */ 1256 felem_small_mul(tmp, y2, ftmp); 1257 felem_reduce(ftmp5, tmp); 1258 1259 /* r = ftmp5 = (s2 - s1)*2 */ 1260 felem_diff_zero107(ftmp5, ftmp6); 1261 /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ 1262 felem_scalar(ftmp5, 2); 1263 /* ftmp5[i] < 2^109 */ 1264 felem_shrink(small1, ftmp5); 1265 y_equal = smallfelem_is_zero(small1); 1266 1267 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) 1268 { 1269 point_double(x3, y3, z3, x1, y1, z1); 1270 return; 1271 } 1272 1273 /* I = ftmp = (2h)**2 */ 1274 felem_assign(ftmp, ftmp4); 1275 felem_scalar(ftmp, 2); 1276 /* ftmp[i] < 2*2^108 = 2^109 */ 1277 felem_square(tmp, ftmp); 1278 felem_reduce(ftmp, tmp); 1279 1280 /* J = ftmp2 = h * I */ 1281 felem_mul(tmp, ftmp4, ftmp); 1282 felem_reduce(ftmp2, tmp); 1283 1284 /* V = ftmp4 = U1 * I */ 1285 felem_mul(tmp, ftmp3, ftmp); 1286 felem_reduce(ftmp4, tmp); 1287 1288 /* x_out = r**2 - J - 2V */ 1289 smallfelem_square(tmp, small1); 1290 felem_reduce(x_out, tmp); 1291 felem_assign(ftmp3, ftmp4); 1292 felem_scalar(ftmp4, 2); 1293 felem_sum(ftmp4, ftmp2); 1294 /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ 1295 felem_diff(x_out, ftmp4); 1296 /* x_out[i] < 2^105 + 2^101 */ 1297 1298 /* y_out = r(V-x_out) - 2 * s1 * J */ 1299 felem_diff_zero107(ftmp3, x_out); 1300 /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ 1301 felem_small_mul(tmp, small1, ftmp3); 1302 felem_mul(tmp2, ftmp6, ftmp2); 1303 longfelem_scalar(tmp2, 2); 1304 /* tmp2[i] < 2*2^67 = 2^68 */ 1305 longfelem_diff(tmp, tmp2); 1306 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ 1307 felem_reduce_zero105(y_out, tmp); 1308 /* y_out[i] < 2^106 */ 1309 1310 copy_small_conditional(x_out, x2, z1_is_zero); 1311 copy_conditional(x_out, x1, z2_is_zero); 1312 copy_small_conditional(y_out, y2, z1_is_zero); 1313 copy_conditional(y_out, y1, z2_is_zero); 1314 copy_small_conditional(z_out, z2, z1_is_zero); 1315 copy_conditional(z_out, z1, z2_is_zero); 1316 felem_assign(x3, x_out); 1317 felem_assign(y3, y_out); 1318 felem_assign(z3, z_out); 1319 } 1320 1321 /* point_add_small is the same as point_add, except that it operates on 1322 * smallfelems */ 1323 static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, 1324 smallfelem x1, smallfelem y1, smallfelem z1, 1325 smallfelem x2, smallfelem y2, smallfelem z2) 1326 { 1327 felem felem_x3, felem_y3, felem_z3; 1328 felem felem_x1, felem_y1, felem_z1; 1329 smallfelem_expand(felem_x1, x1); 1330 smallfelem_expand(felem_y1, y1); 1331 smallfelem_expand(felem_z1, z1); 1332 point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2); 1333 felem_shrink(x3, felem_x3); 1334 felem_shrink(y3, felem_y3); 1335 felem_shrink(z3, felem_z3); 1336 } 1337 1338 /* Base point pre computation 1339 * -------------------------- 1340 * 1341 * Two different sorts of precomputed tables are used in the following code. 1342 * Each contain various points on the curve, where each point is three field 1343 * elements (x, y, z). 1344 * 1345 * For the base point table, z is usually 1 (0 for the point at infinity). 1346 * This table has 2 * 16 elements, starting with the following: 1347 * index | bits | point 1348 * ------+---------+------------------------------ 1349 * 0 | 0 0 0 0 | 0G 1350 * 1 | 0 0 0 1 | 1G 1351 * 2 | 0 0 1 0 | 2^64G 1352 * 3 | 0 0 1 1 | (2^64 + 1)G 1353 * 4 | 0 1 0 0 | 2^128G 1354 * 5 | 0 1 0 1 | (2^128 + 1)G 1355 * 6 | 0 1 1 0 | (2^128 + 2^64)G 1356 * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G 1357 * 8 | 1 0 0 0 | 2^192G 1358 * 9 | 1 0 0 1 | (2^192 + 1)G 1359 * 10 | 1 0 1 0 | (2^192 + 2^64)G 1360 * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G 1361 * 12 | 1 1 0 0 | (2^192 + 2^128)G 1362 * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G 1363 * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G 1364 * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G 1365 * followed by a copy of this with each element multiplied by 2^32. 1366 * 1367 * The reason for this is so that we can clock bits into four different 1368 * locations when doing simple scalar multiplies against the base point, 1369 * and then another four locations using the second 16 elements. 1370 * 1371 * Tables for other points have table[i] = iG for i in 0 .. 16. */ 1372 1373 /* gmul is the table of precomputed base points */ 1374 static const smallfelem gmul[2][16][3] = 1375 {{{{0, 0, 0, 0}, 1376 {0, 0, 0, 0}, 1377 {0, 0, 0, 0}}, 1378 {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, 1379 {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, 1380 {1, 0, 0, 0}}, 1381 {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, 1382 {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, 1383 {1, 0, 0, 0}}, 1384 {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, 1385 {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, 1386 {1, 0, 0, 0}}, 1387 {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, 1388 {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, 1389 {1, 0, 0, 0}}, 1390 {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, 1391 {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, 1392 {1, 0, 0, 0}}, 1393 {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, 1394 {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, 1395 {1, 0, 0, 0}}, 1396 {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, 1397 {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, 1398 {1, 0, 0, 0}}, 1399 {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, 1400 {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, 1401 {1, 0, 0, 0}}, 1402 {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, 1403 {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, 1404 {1, 0, 0, 0}}, 1405 {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, 1406 {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, 1407 {1, 0, 0, 0}}, 1408 {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, 1409 {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, 1410 {1, 0, 0, 0}}, 1411 {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, 1412 {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, 1413 {1, 0, 0, 0}}, 1414 {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, 1415 {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, 1416 {1, 0, 0, 0}}, 1417 {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, 1418 {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, 1419 {1, 0, 0, 0}}, 1420 {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, 1421 {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, 1422 {1, 0, 0, 0}}}, 1423 {{{0, 0, 0, 0}, 1424 {0, 0, 0, 0}, 1425 {0, 0, 0, 0}}, 1426 {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, 1427 {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, 1428 {1, 0, 0, 0}}, 1429 {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, 1430 {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, 1431 {1, 0, 0, 0}}, 1432 {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, 1433 {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, 1434 {1, 0, 0, 0}}, 1435 {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, 1436 {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, 1437 {1, 0, 0, 0}}, 1438 {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, 1439 {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, 1440 {1, 0, 0, 0}}, 1441 {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, 1442 {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, 1443 {1, 0, 0, 0}}, 1444 {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, 1445 {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, 1446 {1, 0, 0, 0}}, 1447 {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, 1448 {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, 1449 {1, 0, 0, 0}}, 1450 {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, 1451 {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, 1452 {1, 0, 0, 0}}, 1453 {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, 1454 {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, 1455 {1, 0, 0, 0}}, 1456 {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, 1457 {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, 1458 {1, 0, 0, 0}}, 1459 {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, 1460 {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, 1461 {1, 0, 0, 0}}, 1462 {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, 1463 {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, 1464 {1, 0, 0, 0}}, 1465 {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, 1466 {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, 1467 {1, 0, 0, 0}}, 1468 {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, 1469 {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, 1470 {1, 0, 0, 0}}}}; 1471 1472 /* select_point selects the |idx|th point from a precomputation table and 1473 * copies it to out. */ 1474 static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) 1475 { 1476 unsigned i, j; 1477 u64 *outlimbs = &out[0][0]; 1478 memset(outlimbs, 0, 3 * sizeof(smallfelem)); 1479 1480 for (i = 0; i < size; i++) 1481 { 1482 const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; 1483 u64 mask = i ^ idx; 1484 mask |= mask >> 4; 1485 mask |= mask >> 2; 1486 mask |= mask >> 1; 1487 mask &= 1; 1488 mask--; 1489 for (j = 0; j < NLIMBS * 3; j++) 1490 outlimbs[j] |= inlimbs[j] & mask; 1491 } 1492 } 1493 1494 /* get_bit returns the |i|th bit in |in| */ 1495 static char get_bit(const felem_bytearray in, int i) 1496 { 1497 if ((i < 0) || (i >= 256)) 1498 return 0; 1499 return (in[i >> 3] >> (i & 7)) & 1; 1500 } 1501 1502 /* Interleaved point multiplication using precomputed point multiples: 1503 * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], 1504 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple 1505 * of the generator, using certain (large) precomputed multiples in g_pre_comp. 1506 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ 1507 static void batch_mul(felem x_out, felem y_out, felem z_out, 1508 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, 1509 const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) 1510 { 1511 int i, skip; 1512 unsigned num, gen_mul = (g_scalar != NULL); 1513 felem nq[3], ftmp; 1514 smallfelem tmp[3]; 1515 u64 bits; 1516 u8 sign, digit; 1517 1518 /* set nq to the point at infinity */ 1519 memset(nq, 0, 3 * sizeof(felem)); 1520 1521 /* Loop over all scalars msb-to-lsb, interleaving additions 1522 * of multiples of the generator (two in each of the last 32 rounds) 1523 * and additions of other points multiples (every 5th round). 1524 */ 1525 skip = 1; /* save two point operations in the first round */ 1526 for (i = (num_points ? 255 : 31); i >= 0; --i) 1527 { 1528 /* double */ 1529 if (!skip) 1530 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); 1531 1532 /* add multiples of the generator */ 1533 if (gen_mul && (i <= 31)) 1534 { 1535 /* first, look 32 bits upwards */ 1536 bits = get_bit(g_scalar, i + 224) << 3; 1537 bits |= get_bit(g_scalar, i + 160) << 2; 1538 bits |= get_bit(g_scalar, i + 96) << 1; 1539 bits |= get_bit(g_scalar, i + 32); 1540 /* select the point to add, in constant time */ 1541 select_point(bits, 16, g_pre_comp[1], tmp); 1542 1543 if (!skip) 1544 { 1545 point_add(nq[0], nq[1], nq[2], 1546 nq[0], nq[1], nq[2], 1547 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1548 } 1549 else 1550 { 1551 smallfelem_expand(nq[0], tmp[0]); 1552 smallfelem_expand(nq[1], tmp[1]); 1553 smallfelem_expand(nq[2], tmp[2]); 1554 skip = 0; 1555 } 1556 1557 /* second, look at the current position */ 1558 bits = get_bit(g_scalar, i + 192) << 3; 1559 bits |= get_bit(g_scalar, i + 128) << 2; 1560 bits |= get_bit(g_scalar, i + 64) << 1; 1561 bits |= get_bit(g_scalar, i); 1562 /* select the point to add, in constant time */ 1563 select_point(bits, 16, g_pre_comp[0], tmp); 1564 point_add(nq[0], nq[1], nq[2], 1565 nq[0], nq[1], nq[2], 1566 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1567 } 1568 1569 /* do other additions every 5 doublings */ 1570 if (num_points && (i % 5 == 0)) 1571 { 1572 /* loop over all scalars */ 1573 for (num = 0; num < num_points; ++num) 1574 { 1575 bits = get_bit(scalars[num], i + 4) << 5; 1576 bits |= get_bit(scalars[num], i + 3) << 4; 1577 bits |= get_bit(scalars[num], i + 2) << 3; 1578 bits |= get_bit(scalars[num], i + 1) << 2; 1579 bits |= get_bit(scalars[num], i) << 1; 1580 bits |= get_bit(scalars[num], i - 1); 1581 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); 1582 1583 /* select the point to add or subtract, in constant time */ 1584 select_point(digit, 17, pre_comp[num], tmp); 1585 smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ 1586 copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); 1587 felem_contract(tmp[1], ftmp); 1588 1589 if (!skip) 1590 { 1591 point_add(nq[0], nq[1], nq[2], 1592 nq[0], nq[1], nq[2], 1593 mixed, tmp[0], tmp[1], tmp[2]); 1594 } 1595 else 1596 { 1597 smallfelem_expand(nq[0], tmp[0]); 1598 smallfelem_expand(nq[1], tmp[1]); 1599 smallfelem_expand(nq[2], tmp[2]); 1600 skip = 0; 1601 } 1602 } 1603 } 1604 } 1605 felem_assign(x_out, nq[0]); 1606 felem_assign(y_out, nq[1]); 1607 felem_assign(z_out, nq[2]); 1608 } 1609 1610 /* Precomputation for the group generator. */ 1611 typedef struct { 1612 smallfelem g_pre_comp[2][16][3]; 1613 int references; 1614 } NISTP256_PRE_COMP; 1615 1616 const EC_METHOD *EC_GFp_nistp256_method(void) 1617 { 1618 static const EC_METHOD ret = { 1619 EC_FLAGS_DEFAULT_OCT, 1620 NID_X9_62_prime_field, 1621 ec_GFp_nistp256_group_init, 1622 ec_GFp_simple_group_finish, 1623 ec_GFp_simple_group_clear_finish, 1624 ec_GFp_nist_group_copy, 1625 ec_GFp_nistp256_group_set_curve, 1626 ec_GFp_simple_group_get_curve, 1627 ec_GFp_simple_group_get_degree, 1628 ec_GFp_simple_group_check_discriminant, 1629 ec_GFp_simple_point_init, 1630 ec_GFp_simple_point_finish, 1631 ec_GFp_simple_point_clear_finish, 1632 ec_GFp_simple_point_copy, 1633 ec_GFp_simple_point_set_to_infinity, 1634 ec_GFp_simple_set_Jprojective_coordinates_GFp, 1635 ec_GFp_simple_get_Jprojective_coordinates_GFp, 1636 ec_GFp_simple_point_set_affine_coordinates, 1637 ec_GFp_nistp256_point_get_affine_coordinates, 1638 0 /* point_set_compressed_coordinates */, 1639 0 /* point2oct */, 1640 0 /* oct2point */, 1641 ec_GFp_simple_add, 1642 ec_GFp_simple_dbl, 1643 ec_GFp_simple_invert, 1644 ec_GFp_simple_is_at_infinity, 1645 ec_GFp_simple_is_on_curve, 1646 ec_GFp_simple_cmp, 1647 ec_GFp_simple_make_affine, 1648 ec_GFp_simple_points_make_affine, 1649 ec_GFp_nistp256_points_mul, 1650 ec_GFp_nistp256_precompute_mult, 1651 ec_GFp_nistp256_have_precompute_mult, 1652 ec_GFp_nist_field_mul, 1653 ec_GFp_nist_field_sqr, 1654 0 /* field_div */, 1655 0 /* field_encode */, 1656 0 /* field_decode */, 1657 0 /* field_set_to_one */ }; 1658 1659 return &ret; 1660 } 1661 1662 /******************************************************************************/ 1663 /* FUNCTIONS TO MANAGE PRECOMPUTATION 1664 */ 1665 1666 static NISTP256_PRE_COMP *nistp256_pre_comp_new() 1667 { 1668 NISTP256_PRE_COMP *ret = NULL; 1669 ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); 1670 if (!ret) 1671 { 1672 ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 1673 return ret; 1674 } 1675 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); 1676 ret->references = 1; 1677 return ret; 1678 } 1679 1680 static void *nistp256_pre_comp_dup(void *src_) 1681 { 1682 NISTP256_PRE_COMP *src = src_; 1683 1684 /* no need to actually copy, these objects never change! */ 1685 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 1686 1687 return src_; 1688 } 1689 1690 static void nistp256_pre_comp_free(void *pre_) 1691 { 1692 int i; 1693 NISTP256_PRE_COMP *pre = pre_; 1694 1695 if (!pre) 1696 return; 1697 1698 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1699 if (i > 0) 1700 return; 1701 1702 OPENSSL_free(pre); 1703 } 1704 1705 static void nistp256_pre_comp_clear_free(void *pre_) 1706 { 1707 int i; 1708 NISTP256_PRE_COMP *pre = pre_; 1709 1710 if (!pre) 1711 return; 1712 1713 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1714 if (i > 0) 1715 return; 1716 1717 OPENSSL_cleanse(pre, sizeof *pre); 1718 OPENSSL_free(pre); 1719 } 1720 1721 /******************************************************************************/ 1722 /* OPENSSL EC_METHOD FUNCTIONS 1723 */ 1724 1725 int ec_GFp_nistp256_group_init(EC_GROUP *group) 1726 { 1727 int ret; 1728 ret = ec_GFp_simple_group_init(group); 1729 group->a_is_minus3 = 1; 1730 return ret; 1731 } 1732 1733 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, 1734 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1735 { 1736 int ret = 0; 1737 BN_CTX *new_ctx = NULL; 1738 BIGNUM *curve_p, *curve_a, *curve_b; 1739 1740 if (ctx == NULL) 1741 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1742 BN_CTX_start(ctx); 1743 if (((curve_p = BN_CTX_get(ctx)) == NULL) || 1744 ((curve_a = BN_CTX_get(ctx)) == NULL) || 1745 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; 1746 BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); 1747 BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); 1748 BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); 1749 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || 1750 (BN_cmp(curve_b, b))) 1751 { 1752 ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, 1753 EC_R_WRONG_CURVE_PARAMETERS); 1754 goto err; 1755 } 1756 group->field_mod_func = BN_nist_mod_256; 1757 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); 1758 err: 1759 BN_CTX_end(ctx); 1760 if (new_ctx != NULL) 1761 BN_CTX_free(new_ctx); 1762 return ret; 1763 } 1764 1765 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns 1766 * (X', Y') = (X/Z^2, Y/Z^3) */ 1767 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 1768 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 1769 { 1770 felem z1, z2, x_in, y_in; 1771 smallfelem x_out, y_out; 1772 longfelem tmp; 1773 1774 if (EC_POINT_is_at_infinity(group, point)) 1775 { 1776 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1777 EC_R_POINT_AT_INFINITY); 1778 return 0; 1779 } 1780 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || 1781 (!BN_to_felem(z1, &point->Z))) return 0; 1782 felem_inv(z2, z1); 1783 felem_square(tmp, z2); felem_reduce(z1, tmp); 1784 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); 1785 felem_contract(x_out, x_in); 1786 if (x != NULL) 1787 { 1788 if (!smallfelem_to_BN(x, x_out)) { 1789 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1790 ERR_R_BN_LIB); 1791 return 0; 1792 } 1793 } 1794 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); 1795 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); 1796 felem_contract(y_out, y_in); 1797 if (y != NULL) 1798 { 1799 if (!smallfelem_to_BN(y, y_out)) 1800 { 1801 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1802 ERR_R_BN_LIB); 1803 return 0; 1804 } 1805 } 1806 return 1; 1807 } 1808 1809 static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) 1810 { 1811 /* Runs in constant time, unless an input is the point at infinity 1812 * (which normally shouldn't happen). */ 1813 ec_GFp_nistp_points_make_affine_internal( 1814 num, 1815 points, 1816 sizeof(smallfelem), 1817 tmp_smallfelems, 1818 (void (*)(void *)) smallfelem_one, 1819 (int (*)(const void *)) smallfelem_is_zero_int, 1820 (void (*)(void *, const void *)) smallfelem_assign, 1821 (void (*)(void *, const void *)) smallfelem_square_contract, 1822 (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, 1823 (void (*)(void *, const void *)) smallfelem_inv_contract, 1824 (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); 1825 } 1826 1827 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values 1828 * Result is stored in r (r can equal one of the inputs). */ 1829 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 1830 const BIGNUM *scalar, size_t num, const EC_POINT *points[], 1831 const BIGNUM *scalars[], BN_CTX *ctx) 1832 { 1833 int ret = 0; 1834 int j; 1835 int mixed = 0; 1836 BN_CTX *new_ctx = NULL; 1837 BIGNUM *x, *y, *z, *tmp_scalar; 1838 felem_bytearray g_secret; 1839 felem_bytearray *secrets = NULL; 1840 smallfelem (*pre_comp)[17][3] = NULL; 1841 smallfelem *tmp_smallfelems = NULL; 1842 felem_bytearray tmp; 1843 unsigned i, num_bytes; 1844 int have_pre_comp = 0; 1845 size_t num_points = num; 1846 smallfelem x_in, y_in, z_in; 1847 felem x_out, y_out, z_out; 1848 NISTP256_PRE_COMP *pre = NULL; 1849 const smallfelem (*g_pre_comp)[16][3] = NULL; 1850 EC_POINT *generator = NULL; 1851 const EC_POINT *p = NULL; 1852 const BIGNUM *p_scalar = NULL; 1853 1854 if (ctx == NULL) 1855 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1856 BN_CTX_start(ctx); 1857 if (((x = BN_CTX_get(ctx)) == NULL) || 1858 ((y = BN_CTX_get(ctx)) == NULL) || 1859 ((z = BN_CTX_get(ctx)) == NULL) || 1860 ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) 1861 goto err; 1862 1863 if (scalar != NULL) 1864 { 1865 pre = EC_EX_DATA_get_data(group->extra_data, 1866 nistp256_pre_comp_dup, nistp256_pre_comp_free, 1867 nistp256_pre_comp_clear_free); 1868 if (pre) 1869 /* we have precomputation, try to use it */ 1870 g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; 1871 else 1872 /* try to use the standard precomputation */ 1873 g_pre_comp = &gmul[0]; 1874 generator = EC_POINT_new(group); 1875 if (generator == NULL) 1876 goto err; 1877 /* get the generator from precomputation */ 1878 if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || 1879 !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || 1880 !smallfelem_to_BN(z, g_pre_comp[0][1][2])) 1881 { 1882 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1883 goto err; 1884 } 1885 if (!EC_POINT_set_Jprojective_coordinates_GFp(group, 1886 generator, x, y, z, ctx)) 1887 goto err; 1888 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 1889 /* precomputation matches generator */ 1890 have_pre_comp = 1; 1891 else 1892 /* we don't have valid precomputation: 1893 * treat the generator as a random point */ 1894 num_points++; 1895 } 1896 if (num_points > 0) 1897 { 1898 if (num_points >= 3) 1899 { 1900 /* unless we precompute multiples for just one or two points, 1901 * converting those into affine form is time well spent */ 1902 mixed = 1; 1903 } 1904 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); 1905 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem)); 1906 if (mixed) 1907 tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); 1908 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) 1909 { 1910 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1911 goto err; 1912 } 1913 1914 /* we treat NULL scalars as 0, and NULL points as points at infinity, 1915 * i.e., they contribute nothing to the linear combination */ 1916 memset(secrets, 0, num_points * sizeof(felem_bytearray)); 1917 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); 1918 for (i = 0; i < num_points; ++i) 1919 { 1920 if (i == num) 1921 /* we didn't have a valid precomputation, so we pick 1922 * the generator */ 1923 { 1924 p = EC_GROUP_get0_generator(group); 1925 p_scalar = scalar; 1926 } 1927 else 1928 /* the i^th point */ 1929 { 1930 p = points[i]; 1931 p_scalar = scalars[i]; 1932 } 1933 if ((p_scalar != NULL) && (p != NULL)) 1934 { 1935 /* reduce scalar to 0 <= scalar < 2^256 */ 1936 if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) 1937 { 1938 /* this is an unusual input, and we don't guarantee 1939 * constant-timeness */ 1940 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) 1941 { 1942 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1943 goto err; 1944 } 1945 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1946 } 1947 else 1948 num_bytes = BN_bn2bin(p_scalar, tmp); 1949 flip_endian(secrets[i], tmp, num_bytes); 1950 /* precompute multiples */ 1951 if ((!BN_to_felem(x_out, &p->X)) || 1952 (!BN_to_felem(y_out, &p->Y)) || 1953 (!BN_to_felem(z_out, &p->Z))) goto err; 1954 felem_shrink(pre_comp[i][1][0], x_out); 1955 felem_shrink(pre_comp[i][1][1], y_out); 1956 felem_shrink(pre_comp[i][1][2], z_out); 1957 for (j = 2; j <= 16; ++j) 1958 { 1959 if (j & 1) 1960 { 1961 point_add_small( 1962 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1963 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 1964 pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); 1965 } 1966 else 1967 { 1968 point_double_small( 1969 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1970 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); 1971 } 1972 } 1973 } 1974 } 1975 if (mixed) 1976 make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); 1977 } 1978 1979 /* the scalar for the generator */ 1980 if ((scalar != NULL) && (have_pre_comp)) 1981 { 1982 memset(g_secret, 0, sizeof(g_secret)); 1983 /* reduce scalar to 0 <= scalar < 2^256 */ 1984 if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) 1985 { 1986 /* this is an unusual input, and we don't guarantee 1987 * constant-timeness */ 1988 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) 1989 { 1990 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1991 goto err; 1992 } 1993 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1994 } 1995 else 1996 num_bytes = BN_bn2bin(scalar, tmp); 1997 flip_endian(g_secret, tmp, num_bytes); 1998 /* do the multiplication with generator precomputation*/ 1999 batch_mul(x_out, y_out, z_out, 2000 (const felem_bytearray (*)) secrets, num_points, 2001 g_secret, 2002 mixed, (const smallfelem (*)[17][3]) pre_comp, 2003 g_pre_comp); 2004 } 2005 else 2006 /* do the multiplication without generator precomputation */ 2007 batch_mul(x_out, y_out, z_out, 2008 (const felem_bytearray (*)) secrets, num_points, 2009 NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); 2010 /* reduce the output to its unique minimal representation */ 2011 felem_contract(x_in, x_out); 2012 felem_contract(y_in, y_out); 2013 felem_contract(z_in, z_out); 2014 if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || 2015 (!smallfelem_to_BN(z, z_in))) 2016 { 2017 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 2018 goto err; 2019 } 2020 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); 2021 2022 err: 2023 BN_CTX_end(ctx); 2024 if (generator != NULL) 2025 EC_POINT_free(generator); 2026 if (new_ctx != NULL) 2027 BN_CTX_free(new_ctx); 2028 if (secrets != NULL) 2029 OPENSSL_free(secrets); 2030 if (pre_comp != NULL) 2031 OPENSSL_free(pre_comp); 2032 if (tmp_smallfelems != NULL) 2033 OPENSSL_free(tmp_smallfelems); 2034 return ret; 2035 } 2036 2037 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 2038 { 2039 int ret = 0; 2040 NISTP256_PRE_COMP *pre = NULL; 2041 int i, j; 2042 BN_CTX *new_ctx = NULL; 2043 BIGNUM *x, *y; 2044 EC_POINT *generator = NULL; 2045 smallfelem tmp_smallfelems[32]; 2046 felem x_tmp, y_tmp, z_tmp; 2047 2048 /* throw away old precomputation */ 2049 EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, 2050 nistp256_pre_comp_free, nistp256_pre_comp_clear_free); 2051 if (ctx == NULL) 2052 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 2053 BN_CTX_start(ctx); 2054 if (((x = BN_CTX_get(ctx)) == NULL) || 2055 ((y = BN_CTX_get(ctx)) == NULL)) 2056 goto err; 2057 /* get the generator */ 2058 if (group->generator == NULL) goto err; 2059 generator = EC_POINT_new(group); 2060 if (generator == NULL) 2061 goto err; 2062 BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); 2063 BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); 2064 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) 2065 goto err; 2066 if ((pre = nistp256_pre_comp_new()) == NULL) 2067 goto err; 2068 /* if the generator is the standard one, use built-in precomputation */ 2069 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 2070 { 2071 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); 2072 ret = 1; 2073 goto err; 2074 } 2075 if ((!BN_to_felem(x_tmp, &group->generator->X)) || 2076 (!BN_to_felem(y_tmp, &group->generator->Y)) || 2077 (!BN_to_felem(z_tmp, &group->generator->Z))) 2078 goto err; 2079 felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); 2080 felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); 2081 felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); 2082 /* compute 2^64*G, 2^128*G, 2^192*G for the first table, 2083 * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one 2084 */ 2085 for (i = 1; i <= 8; i <<= 1) 2086 { 2087 point_double_small( 2088 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], 2089 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); 2090 for (j = 0; j < 31; ++j) 2091 { 2092 point_double_small( 2093 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], 2094 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 2095 } 2096 if (i == 8) 2097 break; 2098 point_double_small( 2099 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], 2100 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 2101 for (j = 0; j < 31; ++j) 2102 { 2103 point_double_small( 2104 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], 2105 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); 2106 } 2107 } 2108 for (i = 0; i < 2; i++) 2109 { 2110 /* g_pre_comp[i][0] is the point at infinity */ 2111 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); 2112 /* the remaining multiples */ 2113 /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ 2114 point_add_small( 2115 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], 2116 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], 2117 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2118 /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ 2119 point_add_small( 2120 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], 2121 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 2122 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2123 /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ 2124 point_add_small( 2125 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], 2126 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 2127 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); 2128 /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ 2129 point_add_small( 2130 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], 2131 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], 2132 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2133 for (j = 1; j < 8; ++j) 2134 { 2135 /* odd multiples: add G resp. 2^32*G */ 2136 point_add_small( 2137 pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], pre->g_pre_comp[i][2*j+1][2], 2138 pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], 2139 pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); 2140 } 2141 } 2142 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); 2143 2144 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, 2145 nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) 2146 goto err; 2147 ret = 1; 2148 pre = NULL; 2149 err: 2150 BN_CTX_end(ctx); 2151 if (generator != NULL) 2152 EC_POINT_free(generator); 2153 if (new_ctx != NULL) 2154 BN_CTX_free(new_ctx); 2155 if (pre) 2156 nistp256_pre_comp_free(pre); 2157 return ret; 2158 } 2159 2160 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) 2161 { 2162 if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, 2163 nistp256_pre_comp_free, nistp256_pre_comp_clear_free) 2164 != NULL) 2165 return 1; 2166 else 2167 return 0; 2168 } 2169 #else 2170 static void *dummy=&dummy; 2171 #endif 2172