ecp_nistp256.c revision 279264
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 50typedef uint8_t u8; 51typedef uint32_t u32; 52typedef uint64_t u64; 53typedef 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 60typedef 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. */ 64static 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 109typedef uint128_t limb; 110typedef limb felem[NLIMBS]; 111typedef limb longfelem[NLIMBS * 2]; 112typedef u64 smallfelem[NLIMBS]; 113 114/* This is the value of the prime as four 64-bit words, little-endian. */ 115static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; 116static const u64 bottom63bits = 0x7ffffffffffffffful; 117 118/* bin32_to_felem takes a little-endian byte array and converts it into felem 119 * form. This assumes that the CPU is little-endian. */ 120static void bin32_to_felem(felem out, const u8 in[32]) 121 { 122 out[0] = *((u64*) &in[0]); 123 out[1] = *((u64*) &in[8]); 124 out[2] = *((u64*) &in[16]); 125 out[3] = *((u64*) &in[24]); 126 } 127 128/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, 129 * 32 byte array. This assumes that the CPU is little-endian. */ 130static void smallfelem_to_bin32(u8 out[32], const smallfelem in) 131 { 132 *((u64*) &out[0]) = in[0]; 133 *((u64*) &out[8]) = in[1]; 134 *((u64*) &out[16]) = in[2]; 135 *((u64*) &out[24]) = in[3]; 136 } 137 138/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ 139static void flip_endian(u8 *out, const u8 *in, unsigned len) 140 { 141 unsigned i; 142 for (i = 0; i < len; ++i) 143 out[i] = in[len-1-i]; 144 } 145 146/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ 147static int BN_to_felem(felem out, const BIGNUM *bn) 148 { 149 felem_bytearray b_in; 150 felem_bytearray b_out; 151 unsigned num_bytes; 152 153 /* BN_bn2bin eats leading zeroes */ 154 memset(b_out, 0, sizeof b_out); 155 num_bytes = BN_num_bytes(bn); 156 if (num_bytes > sizeof b_out) 157 { 158 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 159 return 0; 160 } 161 if (BN_is_negative(bn)) 162 { 163 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); 164 return 0; 165 } 166 num_bytes = BN_bn2bin(bn, b_in); 167 flip_endian(b_out, b_in, num_bytes); 168 bin32_to_felem(out, b_out); 169 return 1; 170 } 171 172/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ 173static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) 174 { 175 felem_bytearray b_in, b_out; 176 smallfelem_to_bin32(b_in, in); 177 flip_endian(b_out, b_in, sizeof b_out); 178 return BN_bin2bn(b_out, sizeof b_out, out); 179 } 180 181 182/* Field operations 183 * ---------------- */ 184 185static void smallfelem_one(smallfelem out) 186 { 187 out[0] = 1; 188 out[1] = 0; 189 out[2] = 0; 190 out[3] = 0; 191 } 192 193static void smallfelem_assign(smallfelem out, const smallfelem in) 194 { 195 out[0] = in[0]; 196 out[1] = in[1]; 197 out[2] = in[2]; 198 out[3] = in[3]; 199 } 200 201static void felem_assign(felem out, const felem in) 202 { 203 out[0] = in[0]; 204 out[1] = in[1]; 205 out[2] = in[2]; 206 out[3] = in[3]; 207 } 208 209/* felem_sum sets out = out + in. */ 210static void felem_sum(felem out, const felem in) 211 { 212 out[0] += in[0]; 213 out[1] += in[1]; 214 out[2] += in[2]; 215 out[3] += in[3]; 216 } 217 218/* felem_small_sum sets out = out + in. */ 219static void felem_small_sum(felem out, const smallfelem in) 220 { 221 out[0] += in[0]; 222 out[1] += in[1]; 223 out[2] += in[2]; 224 out[3] += in[3]; 225 } 226 227/* felem_scalar sets out = out * scalar */ 228static void felem_scalar(felem out, const u64 scalar) 229 { 230 out[0] *= scalar; 231 out[1] *= scalar; 232 out[2] *= scalar; 233 out[3] *= scalar; 234 } 235 236/* longfelem_scalar sets out = out * scalar */ 237static void longfelem_scalar(longfelem out, const u64 scalar) 238 { 239 out[0] *= scalar; 240 out[1] *= scalar; 241 out[2] *= scalar; 242 out[3] *= scalar; 243 out[4] *= scalar; 244 out[5] *= scalar; 245 out[6] *= scalar; 246 out[7] *= scalar; 247 } 248 249#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) 250#define two105 (((limb)1) << 105) 251#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) 252 253/* zero105 is 0 mod p */ 254static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; 255 256/* smallfelem_neg sets |out| to |-small| 257 * On exit: 258 * out[i] < out[i] + 2^105 259 */ 260static void smallfelem_neg(felem out, const smallfelem small) 261 { 262 /* In order to prevent underflow, we subtract from 0 mod p. */ 263 out[0] = zero105[0] - small[0]; 264 out[1] = zero105[1] - small[1]; 265 out[2] = zero105[2] - small[2]; 266 out[3] = zero105[3] - small[3]; 267 } 268 269/* felem_diff subtracts |in| from |out| 270 * On entry: 271 * in[i] < 2^104 272 * On exit: 273 * out[i] < out[i] + 2^105 274 */ 275static void felem_diff(felem out, const felem in) 276 { 277 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 278 out[0] += zero105[0]; 279 out[1] += zero105[1]; 280 out[2] += zero105[2]; 281 out[3] += zero105[3]; 282 283 out[0] -= in[0]; 284 out[1] -= in[1]; 285 out[2] -= in[2]; 286 out[3] -= in[3]; 287 } 288 289#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) 290#define two107 (((limb)1) << 107) 291#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) 292 293/* zero107 is 0 mod p */ 294static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; 295 296/* An alternative felem_diff for larger inputs |in| 297 * felem_diff_zero107 subtracts |in| from |out| 298 * On entry: 299 * in[i] < 2^106 300 * On exit: 301 * out[i] < out[i] + 2^107 302 */ 303static void felem_diff_zero107(felem out, const felem in) 304 { 305 /* In order to prevent underflow, we add 0 mod p before subtracting. */ 306 out[0] += zero107[0]; 307 out[1] += zero107[1]; 308 out[2] += zero107[2]; 309 out[3] += zero107[3]; 310 311 out[0] -= in[0]; 312 out[1] -= in[1]; 313 out[2] -= in[2]; 314 out[3] -= in[3]; 315 } 316 317/* longfelem_diff subtracts |in| from |out| 318 * On entry: 319 * in[i] < 7*2^67 320 * On exit: 321 * out[i] < out[i] + 2^70 + 2^40 322 */ 323static void longfelem_diff(longfelem out, const longfelem in) 324 { 325 static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); 326 static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); 327 static const limb two70 = (((limb)1) << 70); 328 static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); 329 static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); 330 331 /* add 0 mod p to avoid underflow */ 332 out[0] += two70m8p6; 333 out[1] += two70p40; 334 out[2] += two70; 335 out[3] += two70m40m38p6; 336 out[4] += two70m6; 337 out[5] += two70m6; 338 out[6] += two70m6; 339 out[7] += two70m6; 340 341 /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ 342 out[0] -= in[0]; 343 out[1] -= in[1]; 344 out[2] -= in[2]; 345 out[3] -= in[3]; 346 out[4] -= in[4]; 347 out[5] -= in[5]; 348 out[6] -= in[6]; 349 out[7] -= in[7]; 350 } 351 352#define two64m0 (((limb)1) << 64) - 1 353#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 354#define two64m46 (((limb)1) << 64) - (((limb)1) << 46) 355#define two64m32 (((limb)1) << 64) - (((limb)1) << 32) 356 357/* zero110 is 0 mod p */ 358static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; 359 360/* felem_shrink converts an felem into a smallfelem. The result isn't quite 361 * minimal as the value may be greater than p. 362 * 363 * On entry: 364 * in[i] < 2^109 365 * On exit: 366 * out[i] < 2^64 367 */ 368static void felem_shrink(smallfelem out, const felem in) 369 { 370 felem tmp; 371 u64 a, b, mask; 372 s64 high, low; 373 static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ 374 375 /* Carry 2->3 */ 376 tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); 377 /* tmp[3] < 2^110 */ 378 379 tmp[2] = zero110[2] + (u64) in[2]; 380 tmp[0] = zero110[0] + in[0]; 381 tmp[1] = zero110[1] + in[1]; 382 /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ 383 384 /* We perform two partial reductions where we eliminate the 385 * high-word of tmp[3]. We don't update the other words till the end. 386 */ 387 a = tmp[3] >> 64; /* a < 2^46 */ 388 tmp[3] = (u64) tmp[3]; 389 tmp[3] -= a; 390 tmp[3] += ((limb)a) << 32; 391 /* tmp[3] < 2^79 */ 392 393 b = a; 394 a = tmp[3] >> 64; /* a < 2^15 */ 395 b += a; /* b < 2^46 + 2^15 < 2^47 */ 396 tmp[3] = (u64) tmp[3]; 397 tmp[3] -= a; 398 tmp[3] += ((limb)a) << 32; 399 /* tmp[3] < 2^64 + 2^47 */ 400 401 /* This adjusts the other two words to complete the two partial 402 * reductions. */ 403 tmp[0] += b; 404 tmp[1] -= (((limb)b) << 32); 405 406 /* In order to make space in tmp[3] for the carry from 2 -> 3, we 407 * conditionally subtract kPrime if tmp[3] is large enough. */ 408 high = tmp[3] >> 64; 409 /* As tmp[3] < 2^65, high is either 1 or 0 */ 410 high <<= 63; 411 high >>= 63; 412 /* high is: 413 * all ones if the high word of tmp[3] is 1 414 * all zeros if the high word of tmp[3] if 0 */ 415 low = tmp[3]; 416 mask = low >> 63; 417 /* mask is: 418 * all ones if the MSB of low is 1 419 * all zeros if the MSB of low if 0 */ 420 low &= bottom63bits; 421 low -= kPrime3Test; 422 /* if low was greater than kPrime3Test then the MSB is zero */ 423 low = ~low; 424 low >>= 63; 425 /* low is: 426 * all ones if low was > kPrime3Test 427 * all zeros if low was <= kPrime3Test */ 428 mask = (mask & low) | high; 429 tmp[0] -= mask & kPrime[0]; 430 tmp[1] -= mask & kPrime[1]; 431 /* kPrime[2] is zero, so omitted */ 432 tmp[3] -= mask & kPrime[3]; 433 /* tmp[3] < 2**64 - 2**32 + 1 */ 434 435 tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; 436 tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; 437 tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; 438 /* tmp[i] < 2^64 */ 439 440 out[0] = tmp[0]; 441 out[1] = tmp[1]; 442 out[2] = tmp[2]; 443 out[3] = tmp[3]; 444 } 445 446/* smallfelem_expand converts a smallfelem to an felem */ 447static void smallfelem_expand(felem out, const smallfelem in) 448 { 449 out[0] = in[0]; 450 out[1] = in[1]; 451 out[2] = in[2]; 452 out[3] = in[3]; 453 } 454 455/* smallfelem_square sets |out| = |small|^2 456 * On entry: 457 * small[i] < 2^64 458 * On exit: 459 * out[i] < 7 * 2^64 < 2^67 460 */ 461static void smallfelem_square(longfelem out, const smallfelem small) 462 { 463 limb a; 464 u64 high, low; 465 466 a = ((uint128_t) small[0]) * small[0]; 467 low = a; 468 high = a >> 64; 469 out[0] = low; 470 out[1] = high; 471 472 a = ((uint128_t) small[0]) * small[1]; 473 low = a; 474 high = a >> 64; 475 out[1] += low; 476 out[1] += low; 477 out[2] = high; 478 479 a = ((uint128_t) small[0]) * small[2]; 480 low = a; 481 high = a >> 64; 482 out[2] += low; 483 out[2] *= 2; 484 out[3] = high; 485 486 a = ((uint128_t) small[0]) * small[3]; 487 low = a; 488 high = a >> 64; 489 out[3] += low; 490 out[4] = high; 491 492 a = ((uint128_t) small[1]) * small[2]; 493 low = a; 494 high = a >> 64; 495 out[3] += low; 496 out[3] *= 2; 497 out[4] += high; 498 499 a = ((uint128_t) small[1]) * small[1]; 500 low = a; 501 high = a >> 64; 502 out[2] += low; 503 out[3] += high; 504 505 a = ((uint128_t) small[1]) * small[3]; 506 low = a; 507 high = a >> 64; 508 out[4] += low; 509 out[4] *= 2; 510 out[5] = high; 511 512 a = ((uint128_t) small[2]) * small[3]; 513 low = a; 514 high = a >> 64; 515 out[5] += low; 516 out[5] *= 2; 517 out[6] = high; 518 out[6] += high; 519 520 a = ((uint128_t) small[2]) * small[2]; 521 low = a; 522 high = a >> 64; 523 out[4] += low; 524 out[5] += high; 525 526 a = ((uint128_t) small[3]) * small[3]; 527 low = a; 528 high = a >> 64; 529 out[6] += low; 530 out[7] = high; 531 } 532 533/* felem_square sets |out| = |in|^2 534 * On entry: 535 * in[i] < 2^109 536 * On exit: 537 * out[i] < 7 * 2^64 < 2^67 538 */ 539static void felem_square(longfelem out, const felem in) 540 { 541 u64 small[4]; 542 felem_shrink(small, in); 543 smallfelem_square(out, small); 544 } 545 546/* smallfelem_mul sets |out| = |small1| * |small2| 547 * On entry: 548 * small1[i] < 2^64 549 * small2[i] < 2^64 550 * On exit: 551 * out[i] < 7 * 2^64 < 2^67 552 */ 553static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) 554 { 555 limb a; 556 u64 high, low; 557 558 a = ((uint128_t) small1[0]) * small2[0]; 559 low = a; 560 high = a >> 64; 561 out[0] = low; 562 out[1] = high; 563 564 565 a = ((uint128_t) small1[0]) * small2[1]; 566 low = a; 567 high = a >> 64; 568 out[1] += low; 569 out[2] = high; 570 571 a = ((uint128_t) small1[1]) * small2[0]; 572 low = a; 573 high = a >> 64; 574 out[1] += low; 575 out[2] += high; 576 577 578 a = ((uint128_t) small1[0]) * small2[2]; 579 low = a; 580 high = a >> 64; 581 out[2] += low; 582 out[3] = high; 583 584 a = ((uint128_t) small1[1]) * small2[1]; 585 low = a; 586 high = a >> 64; 587 out[2] += low; 588 out[3] += high; 589 590 a = ((uint128_t) small1[2]) * small2[0]; 591 low = a; 592 high = a >> 64; 593 out[2] += low; 594 out[3] += high; 595 596 597 a = ((uint128_t) small1[0]) * small2[3]; 598 low = a; 599 high = a >> 64; 600 out[3] += low; 601 out[4] = high; 602 603 a = ((uint128_t) small1[1]) * small2[2]; 604 low = a; 605 high = a >> 64; 606 out[3] += low; 607 out[4] += high; 608 609 a = ((uint128_t) small1[2]) * small2[1]; 610 low = a; 611 high = a >> 64; 612 out[3] += low; 613 out[4] += high; 614 615 a = ((uint128_t) small1[3]) * small2[0]; 616 low = a; 617 high = a >> 64; 618 out[3] += low; 619 out[4] += high; 620 621 622 a = ((uint128_t) small1[1]) * small2[3]; 623 low = a; 624 high = a >> 64; 625 out[4] += low; 626 out[5] = high; 627 628 a = ((uint128_t) small1[2]) * small2[2]; 629 low = a; 630 high = a >> 64; 631 out[4] += low; 632 out[5] += high; 633 634 a = ((uint128_t) small1[3]) * small2[1]; 635 low = a; 636 high = a >> 64; 637 out[4] += low; 638 out[5] += high; 639 640 641 a = ((uint128_t) small1[2]) * small2[3]; 642 low = a; 643 high = a >> 64; 644 out[5] += low; 645 out[6] = high; 646 647 a = ((uint128_t) small1[3]) * small2[2]; 648 low = a; 649 high = a >> 64; 650 out[5] += low; 651 out[6] += high; 652 653 654 a = ((uint128_t) small1[3]) * small2[3]; 655 low = a; 656 high = a >> 64; 657 out[6] += low; 658 out[7] = high; 659 } 660 661/* felem_mul sets |out| = |in1| * |in2| 662 * On entry: 663 * in1[i] < 2^109 664 * in2[i] < 2^109 665 * On exit: 666 * out[i] < 7 * 2^64 < 2^67 667 */ 668static void felem_mul(longfelem out, const felem in1, const felem in2) 669 { 670 smallfelem small1, small2; 671 felem_shrink(small1, in1); 672 felem_shrink(small2, in2); 673 smallfelem_mul(out, small1, small2); 674 } 675 676/* felem_small_mul sets |out| = |small1| * |in2| 677 * On entry: 678 * small1[i] < 2^64 679 * in2[i] < 2^109 680 * On exit: 681 * out[i] < 7 * 2^64 < 2^67 682 */ 683static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) 684 { 685 smallfelem small2; 686 felem_shrink(small2, in2); 687 smallfelem_mul(out, small1, small2); 688 } 689 690#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) 691#define two100 (((limb)1) << 100) 692#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) 693/* zero100 is 0 mod p */ 694static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; 695 696/* Internal function for the different flavours of felem_reduce. 697 * felem_reduce_ reduces the higher coefficients in[4]-in[7]. 698 * On entry: 699 * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] 700 * out[1] >= in[7] + 2^32*in[4] 701 * out[2] >= in[5] + 2^32*in[5] 702 * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] 703 * On exit: 704 * out[0] <= out[0] + in[4] + 2^32*in[5] 705 * out[1] <= out[1] + in[5] + 2^33*in[6] 706 * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] 707 * out[3] <= out[3] + 2^32*in[4] + 3*in[7] 708 */ 709static void felem_reduce_(felem out, const longfelem in) 710 { 711 int128_t c; 712 /* combine common terms from below */ 713 c = in[4] + (in[5] << 32); 714 out[0] += c; 715 out[3] -= c; 716 717 c = in[5] - in[7]; 718 out[1] += c; 719 out[2] -= c; 720 721 /* the remaining terms */ 722 /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ 723 out[1] -= (in[4] << 32); 724 out[3] += (in[4] << 32); 725 726 /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ 727 out[2] -= (in[5] << 32); 728 729 /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ 730 out[0] -= in[6]; 731 out[0] -= (in[6] << 32); 732 out[1] += (in[6] << 33); 733 out[2] += (in[6] * 2); 734 out[3] -= (in[6] << 32); 735 736 /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ 737 out[0] -= in[7]; 738 out[0] -= (in[7] << 32); 739 out[2] += (in[7] << 33); 740 out[3] += (in[7] * 3); 741 } 742 743/* felem_reduce converts a longfelem into an felem. 744 * To be called directly after felem_square or felem_mul. 745 * On entry: 746 * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 747 * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 748 * On exit: 749 * out[i] < 2^101 750 */ 751static void felem_reduce(felem out, const longfelem in) 752 { 753 out[0] = zero100[0] + in[0]; 754 out[1] = zero100[1] + in[1]; 755 out[2] = zero100[2] + in[2]; 756 out[3] = zero100[3] + in[3]; 757 758 felem_reduce_(out, in); 759 760 /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 761 * out[1] > 2^100 - 2^64 - 7*2^96 > 0 762 * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 763 * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 764 * 765 * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 766 * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 767 * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 768 * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 769 */ 770 } 771 772/* felem_reduce_zero105 converts a larger longfelem into an felem. 773 * On entry: 774 * in[0] < 2^71 775 * On exit: 776 * out[i] < 2^106 777 */ 778static void felem_reduce_zero105(felem out, const longfelem in) 779 { 780 out[0] = zero105[0] + in[0]; 781 out[1] = zero105[1] + in[1]; 782 out[2] = zero105[2] + in[2]; 783 out[3] = zero105[3] + in[3]; 784 785 felem_reduce_(out, in); 786 787 /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 788 * out[1] > 2^105 - 2^71 - 2^103 > 0 789 * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 790 * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 791 * 792 * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 793 * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 794 * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 795 * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 796 */ 797 } 798 799/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction 800 * underflowed. */ 801static void subtract_u64(u64* result, u64* carry, u64 v) 802 { 803 uint128_t r = *result; 804 r -= v; 805 *carry = (r >> 64) & 1; 806 *result = (u64) r; 807 } 808 809/* felem_contract converts |in| to its unique, minimal representation. 810 * On entry: 811 * in[i] < 2^109 812 */ 813static void felem_contract(smallfelem out, const felem in) 814 { 815 unsigned i; 816 u64 all_equal_so_far = 0, result = 0, carry; 817 818 felem_shrink(out, in); 819 /* small is minimal except that the value might be > p */ 820 821 all_equal_so_far--; 822 /* We are doing a constant time test if out >= kPrime. We need to 823 * compare each u64, from most-significant to least significant. For 824 * each one, if all words so far have been equal (m is all ones) then a 825 * non-equal result is the answer. Otherwise we continue. */ 826 for (i = 3; i < 4; i--) 827 { 828 u64 equal; 829 uint128_t a = ((uint128_t) kPrime[i]) - out[i]; 830 /* if out[i] > kPrime[i] then a will underflow and the high 831 * 64-bits will all be set. */ 832 result |= all_equal_so_far & ((u64) (a >> 64)); 833 834 /* if kPrime[i] == out[i] then |equal| will be all zeros and 835 * the decrement will make it all ones. */ 836 equal = kPrime[i] ^ out[i]; 837 equal--; 838 equal &= equal << 32; 839 equal &= equal << 16; 840 equal &= equal << 8; 841 equal &= equal << 4; 842 equal &= equal << 2; 843 equal &= equal << 1; 844 equal = ((s64) equal) >> 63; 845 846 all_equal_so_far &= equal; 847 } 848 849 /* if all_equal_so_far is still all ones then the two values are equal 850 * and so out >= kPrime is true. */ 851 result |= all_equal_so_far; 852 853 /* if out >= kPrime then we subtract kPrime. */ 854 subtract_u64(&out[0], &carry, result & kPrime[0]); 855 subtract_u64(&out[1], &carry, carry); 856 subtract_u64(&out[2], &carry, carry); 857 subtract_u64(&out[3], &carry, carry); 858 859 subtract_u64(&out[1], &carry, result & kPrime[1]); 860 subtract_u64(&out[2], &carry, carry); 861 subtract_u64(&out[3], &carry, carry); 862 863 subtract_u64(&out[2], &carry, result & kPrime[2]); 864 subtract_u64(&out[3], &carry, carry); 865 866 subtract_u64(&out[3], &carry, result & kPrime[3]); 867 } 868 869static void smallfelem_square_contract(smallfelem out, const smallfelem in) 870 { 871 longfelem longtmp; 872 felem tmp; 873 874 smallfelem_square(longtmp, in); 875 felem_reduce(tmp, longtmp); 876 felem_contract(out, tmp); 877 } 878 879static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) 880 { 881 longfelem longtmp; 882 felem tmp; 883 884 smallfelem_mul(longtmp, in1, in2); 885 felem_reduce(tmp, longtmp); 886 felem_contract(out, tmp); 887 } 888 889/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 890 * otherwise. 891 * On entry: 892 * small[i] < 2^64 893 */ 894static limb smallfelem_is_zero(const smallfelem small) 895 { 896 limb result; 897 u64 is_p; 898 899 u64 is_zero = small[0] | small[1] | small[2] | small[3]; 900 is_zero--; 901 is_zero &= is_zero << 32; 902 is_zero &= is_zero << 16; 903 is_zero &= is_zero << 8; 904 is_zero &= is_zero << 4; 905 is_zero &= is_zero << 2; 906 is_zero &= is_zero << 1; 907 is_zero = ((s64) is_zero) >> 63; 908 909 is_p = (small[0] ^ kPrime[0]) | 910 (small[1] ^ kPrime[1]) | 911 (small[2] ^ kPrime[2]) | 912 (small[3] ^ kPrime[3]); 913 is_p--; 914 is_p &= is_p << 32; 915 is_p &= is_p << 16; 916 is_p &= is_p << 8; 917 is_p &= is_p << 4; 918 is_p &= is_p << 2; 919 is_p &= is_p << 1; 920 is_p = ((s64) is_p) >> 63; 921 922 is_zero |= is_p; 923 924 result = is_zero; 925 result |= ((limb) is_zero) << 64; 926 return result; 927 } 928 929static int smallfelem_is_zero_int(const smallfelem small) 930 { 931 return (int) (smallfelem_is_zero(small) & ((limb)1)); 932 } 933 934/* felem_inv calculates |out| = |in|^{-1} 935 * 936 * Based on Fermat's Little Theorem: 937 * a^p = a (mod p) 938 * a^{p-1} = 1 (mod p) 939 * a^{p-2} = a^{-1} (mod p) 940 */ 941static void felem_inv(felem out, const felem in) 942 { 943 felem ftmp, ftmp2; 944 /* each e_I will hold |in|^{2^I - 1} */ 945 felem e2, e4, e8, e16, e32, e64; 946 longfelem tmp; 947 unsigned i; 948 949 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ 950 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ 951 felem_assign(e2, ftmp); 952 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ 953 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ 954 felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ 955 felem_assign(e4, ftmp); 956 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ 957 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ 958 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ 959 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ 960 felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ 961 felem_assign(e8, ftmp); 962 for (i = 0; i < 8; i++) { 963 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 964 } /* 2^16 - 2^8 */ 965 felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ 966 felem_assign(e16, ftmp); 967 for (i = 0; i < 16; i++) { 968 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 969 } /* 2^32 - 2^16 */ 970 felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ 971 felem_assign(e32, ftmp); 972 for (i = 0; i < 32; i++) { 973 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 974 } /* 2^64 - 2^32 */ 975 felem_assign(e64, ftmp); 976 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ 977 for (i = 0; i < 192; i++) { 978 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); 979 } /* 2^256 - 2^224 + 2^192 */ 980 981 felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ 982 for (i = 0; i < 16; i++) { 983 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 984 } /* 2^80 - 2^16 */ 985 felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ 986 for (i = 0; i < 8; i++) { 987 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 988 } /* 2^88 - 2^8 */ 989 felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ 990 for (i = 0; i < 4; i++) { 991 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); 992 } /* 2^92 - 2^4 */ 993 felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ 994 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ 995 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ 996 felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ 997 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ 998 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ 999 felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ 1000 1001 felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ 1002 } 1003 1004static void smallfelem_inv_contract(smallfelem out, const smallfelem in) 1005 { 1006 felem tmp; 1007 1008 smallfelem_expand(tmp, in); 1009 felem_inv(tmp, tmp); 1010 felem_contract(out, tmp); 1011 } 1012 1013/* Group operations 1014 * ---------------- 1015 * 1016 * Building on top of the field operations we have the operations on the 1017 * elliptic curve group itself. Points on the curve are represented in Jacobian 1018 * coordinates */ 1019 1020/* point_double calculates 2*(x_in, y_in, z_in) 1021 * 1022 * The method is taken from: 1023 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b 1024 * 1025 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. 1026 * while x_out == y_in is not (maybe this works, but it's not tested). */ 1027static void 1028point_double(felem x_out, felem y_out, felem z_out, 1029 const felem x_in, const felem y_in, const felem z_in) 1030 { 1031 longfelem tmp, tmp2; 1032 felem delta, gamma, beta, alpha, ftmp, ftmp2; 1033 smallfelem small1, small2; 1034 1035 felem_assign(ftmp, x_in); 1036 /* ftmp[i] < 2^106 */ 1037 felem_assign(ftmp2, x_in); 1038 /* ftmp2[i] < 2^106 */ 1039 1040 /* delta = z^2 */ 1041 felem_square(tmp, z_in); 1042 felem_reduce(delta, tmp); 1043 /* delta[i] < 2^101 */ 1044 1045 /* gamma = y^2 */ 1046 felem_square(tmp, y_in); 1047 felem_reduce(gamma, tmp); 1048 /* gamma[i] < 2^101 */ 1049 felem_shrink(small1, gamma); 1050 1051 /* beta = x*gamma */ 1052 felem_small_mul(tmp, small1, x_in); 1053 felem_reduce(beta, tmp); 1054 /* beta[i] < 2^101 */ 1055 1056 /* alpha = 3*(x-delta)*(x+delta) */ 1057 felem_diff(ftmp, delta); 1058 /* ftmp[i] < 2^105 + 2^106 < 2^107 */ 1059 felem_sum(ftmp2, delta); 1060 /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ 1061 felem_scalar(ftmp2, 3); 1062 /* ftmp2[i] < 3 * 2^107 < 2^109 */ 1063 felem_mul(tmp, ftmp, ftmp2); 1064 felem_reduce(alpha, tmp); 1065 /* alpha[i] < 2^101 */ 1066 felem_shrink(small2, alpha); 1067 1068 /* x' = alpha^2 - 8*beta */ 1069 smallfelem_square(tmp, small2); 1070 felem_reduce(x_out, tmp); 1071 felem_assign(ftmp, beta); 1072 felem_scalar(ftmp, 8); 1073 /* ftmp[i] < 8 * 2^101 = 2^104 */ 1074 felem_diff(x_out, ftmp); 1075 /* x_out[i] < 2^105 + 2^101 < 2^106 */ 1076 1077 /* z' = (y + z)^2 - gamma - delta */ 1078 felem_sum(delta, gamma); 1079 /* delta[i] < 2^101 + 2^101 = 2^102 */ 1080 felem_assign(ftmp, y_in); 1081 felem_sum(ftmp, z_in); 1082 /* ftmp[i] < 2^106 + 2^106 = 2^107 */ 1083 felem_square(tmp, ftmp); 1084 felem_reduce(z_out, tmp); 1085 felem_diff(z_out, delta); 1086 /* z_out[i] < 2^105 + 2^101 < 2^106 */ 1087 1088 /* y' = alpha*(4*beta - x') - 8*gamma^2 */ 1089 felem_scalar(beta, 4); 1090 /* beta[i] < 4 * 2^101 = 2^103 */ 1091 felem_diff_zero107(beta, x_out); 1092 /* beta[i] < 2^107 + 2^103 < 2^108 */ 1093 felem_small_mul(tmp, small2, beta); 1094 /* tmp[i] < 7 * 2^64 < 2^67 */ 1095 smallfelem_square(tmp2, small1); 1096 /* tmp2[i] < 7 * 2^64 */ 1097 longfelem_scalar(tmp2, 8); 1098 /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ 1099 longfelem_diff(tmp, tmp2); 1100 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ 1101 felem_reduce_zero105(y_out, tmp); 1102 /* y_out[i] < 2^106 */ 1103 } 1104 1105/* point_double_small is the same as point_double, except that it operates on 1106 * smallfelems */ 1107static void 1108point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, 1109 const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) 1110 { 1111 felem felem_x_out, felem_y_out, felem_z_out; 1112 felem felem_x_in, felem_y_in, felem_z_in; 1113 1114 smallfelem_expand(felem_x_in, x_in); 1115 smallfelem_expand(felem_y_in, y_in); 1116 smallfelem_expand(felem_z_in, z_in); 1117 point_double(felem_x_out, felem_y_out, felem_z_out, 1118 felem_x_in, felem_y_in, felem_z_in); 1119 felem_shrink(x_out, felem_x_out); 1120 felem_shrink(y_out, felem_y_out); 1121 felem_shrink(z_out, felem_z_out); 1122 } 1123 1124/* copy_conditional copies in to out iff mask is all ones. */ 1125static void 1126copy_conditional(felem out, const felem in, limb mask) 1127 { 1128 unsigned i; 1129 for (i = 0; i < NLIMBS; ++i) 1130 { 1131 const limb tmp = mask & (in[i] ^ out[i]); 1132 out[i] ^= tmp; 1133 } 1134 } 1135 1136/* copy_small_conditional copies in to out iff mask is all ones. */ 1137static void 1138copy_small_conditional(felem out, const smallfelem in, limb mask) 1139 { 1140 unsigned i; 1141 const u64 mask64 = mask; 1142 for (i = 0; i < NLIMBS; ++i) 1143 { 1144 out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); 1145 } 1146 } 1147 1148/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) 1149 * 1150 * The method is taken from: 1151 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, 1152 * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). 1153 * 1154 * This function includes a branch for checking whether the two input points 1155 * are equal, (while not equal to the point at infinity). This case never 1156 * happens during single point multiplication, so there is no timing leak for 1157 * ECDH or ECDSA signing. */ 1158static void point_add(felem x3, felem y3, felem z3, 1159 const felem x1, const felem y1, const felem z1, 1160 const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) 1161 { 1162 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; 1163 longfelem tmp, tmp2; 1164 smallfelem small1, small2, small3, small4, small5; 1165 limb x_equal, y_equal, z1_is_zero, z2_is_zero; 1166 1167 felem_shrink(small3, z1); 1168 1169 z1_is_zero = smallfelem_is_zero(small3); 1170 z2_is_zero = smallfelem_is_zero(z2); 1171 1172 /* ftmp = z1z1 = z1**2 */ 1173 smallfelem_square(tmp, small3); 1174 felem_reduce(ftmp, tmp); 1175 /* ftmp[i] < 2^101 */ 1176 felem_shrink(small1, ftmp); 1177 1178 if(!mixed) 1179 { 1180 /* ftmp2 = z2z2 = z2**2 */ 1181 smallfelem_square(tmp, z2); 1182 felem_reduce(ftmp2, tmp); 1183 /* ftmp2[i] < 2^101 */ 1184 felem_shrink(small2, ftmp2); 1185 1186 felem_shrink(small5, x1); 1187 1188 /* u1 = ftmp3 = x1*z2z2 */ 1189 smallfelem_mul(tmp, small5, small2); 1190 felem_reduce(ftmp3, tmp); 1191 /* ftmp3[i] < 2^101 */ 1192 1193 /* ftmp5 = z1 + z2 */ 1194 felem_assign(ftmp5, z1); 1195 felem_small_sum(ftmp5, z2); 1196 /* ftmp5[i] < 2^107 */ 1197 1198 /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ 1199 felem_square(tmp, ftmp5); 1200 felem_reduce(ftmp5, tmp); 1201 /* ftmp2 = z2z2 + z1z1 */ 1202 felem_sum(ftmp2, ftmp); 1203 /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ 1204 felem_diff(ftmp5, ftmp2); 1205 /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ 1206 1207 /* ftmp2 = z2 * z2z2 */ 1208 smallfelem_mul(tmp, small2, z2); 1209 felem_reduce(ftmp2, tmp); 1210 1211 /* s1 = ftmp2 = y1 * z2**3 */ 1212 felem_mul(tmp, y1, ftmp2); 1213 felem_reduce(ftmp6, tmp); 1214 /* ftmp6[i] < 2^101 */ 1215 } 1216 else 1217 { 1218 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ 1219 1220 /* u1 = ftmp3 = x1*z2z2 */ 1221 felem_assign(ftmp3, x1); 1222 /* ftmp3[i] < 2^106 */ 1223 1224 /* ftmp5 = 2z1z2 */ 1225 felem_assign(ftmp5, z1); 1226 felem_scalar(ftmp5, 2); 1227 /* ftmp5[i] < 2*2^106 = 2^107 */ 1228 1229 /* s1 = ftmp2 = y1 * z2**3 */ 1230 felem_assign(ftmp6, y1); 1231 /* ftmp6[i] < 2^106 */ 1232 } 1233 1234 /* u2 = x2*z1z1 */ 1235 smallfelem_mul(tmp, x2, small1); 1236 felem_reduce(ftmp4, tmp); 1237 1238 /* h = ftmp4 = u2 - u1 */ 1239 felem_diff_zero107(ftmp4, ftmp3); 1240 /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ 1241 felem_shrink(small4, ftmp4); 1242 1243 x_equal = smallfelem_is_zero(small4); 1244 1245 /* z_out = ftmp5 * h */ 1246 felem_small_mul(tmp, small4, ftmp5); 1247 felem_reduce(z_out, tmp); 1248 /* z_out[i] < 2^101 */ 1249 1250 /* ftmp = z1 * z1z1 */ 1251 smallfelem_mul(tmp, small1, small3); 1252 felem_reduce(ftmp, tmp); 1253 1254 /* s2 = tmp = y2 * z1**3 */ 1255 felem_small_mul(tmp, y2, ftmp); 1256 felem_reduce(ftmp5, tmp); 1257 1258 /* r = ftmp5 = (s2 - s1)*2 */ 1259 felem_diff_zero107(ftmp5, ftmp6); 1260 /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ 1261 felem_scalar(ftmp5, 2); 1262 /* ftmp5[i] < 2^109 */ 1263 felem_shrink(small1, ftmp5); 1264 y_equal = smallfelem_is_zero(small1); 1265 1266 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) 1267 { 1268 point_double(x3, y3, z3, x1, y1, z1); 1269 return; 1270 } 1271 1272 /* I = ftmp = (2h)**2 */ 1273 felem_assign(ftmp, ftmp4); 1274 felem_scalar(ftmp, 2); 1275 /* ftmp[i] < 2*2^108 = 2^109 */ 1276 felem_square(tmp, ftmp); 1277 felem_reduce(ftmp, tmp); 1278 1279 /* J = ftmp2 = h * I */ 1280 felem_mul(tmp, ftmp4, ftmp); 1281 felem_reduce(ftmp2, tmp); 1282 1283 /* V = ftmp4 = U1 * I */ 1284 felem_mul(tmp, ftmp3, ftmp); 1285 felem_reduce(ftmp4, tmp); 1286 1287 /* x_out = r**2 - J - 2V */ 1288 smallfelem_square(tmp, small1); 1289 felem_reduce(x_out, tmp); 1290 felem_assign(ftmp3, ftmp4); 1291 felem_scalar(ftmp4, 2); 1292 felem_sum(ftmp4, ftmp2); 1293 /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ 1294 felem_diff(x_out, ftmp4); 1295 /* x_out[i] < 2^105 + 2^101 */ 1296 1297 /* y_out = r(V-x_out) - 2 * s1 * J */ 1298 felem_diff_zero107(ftmp3, x_out); 1299 /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ 1300 felem_small_mul(tmp, small1, ftmp3); 1301 felem_mul(tmp2, ftmp6, ftmp2); 1302 longfelem_scalar(tmp2, 2); 1303 /* tmp2[i] < 2*2^67 = 2^68 */ 1304 longfelem_diff(tmp, tmp2); 1305 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ 1306 felem_reduce_zero105(y_out, tmp); 1307 /* y_out[i] < 2^106 */ 1308 1309 copy_small_conditional(x_out, x2, z1_is_zero); 1310 copy_conditional(x_out, x1, z2_is_zero); 1311 copy_small_conditional(y_out, y2, z1_is_zero); 1312 copy_conditional(y_out, y1, z2_is_zero); 1313 copy_small_conditional(z_out, z2, z1_is_zero); 1314 copy_conditional(z_out, z1, z2_is_zero); 1315 felem_assign(x3, x_out); 1316 felem_assign(y3, y_out); 1317 felem_assign(z3, z_out); 1318 } 1319 1320/* point_add_small is the same as point_add, except that it operates on 1321 * smallfelems */ 1322static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, 1323 smallfelem x1, smallfelem y1, smallfelem z1, 1324 smallfelem x2, smallfelem y2, smallfelem z2) 1325 { 1326 felem felem_x3, felem_y3, felem_z3; 1327 felem felem_x1, felem_y1, felem_z1; 1328 smallfelem_expand(felem_x1, x1); 1329 smallfelem_expand(felem_y1, y1); 1330 smallfelem_expand(felem_z1, z1); 1331 point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2); 1332 felem_shrink(x3, felem_x3); 1333 felem_shrink(y3, felem_y3); 1334 felem_shrink(z3, felem_z3); 1335 } 1336 1337/* Base point pre computation 1338 * -------------------------- 1339 * 1340 * Two different sorts of precomputed tables are used in the following code. 1341 * Each contain various points on the curve, where each point is three field 1342 * elements (x, y, z). 1343 * 1344 * For the base point table, z is usually 1 (0 for the point at infinity). 1345 * This table has 2 * 16 elements, starting with the following: 1346 * index | bits | point 1347 * ------+---------+------------------------------ 1348 * 0 | 0 0 0 0 | 0G 1349 * 1 | 0 0 0 1 | 1G 1350 * 2 | 0 0 1 0 | 2^64G 1351 * 3 | 0 0 1 1 | (2^64 + 1)G 1352 * 4 | 0 1 0 0 | 2^128G 1353 * 5 | 0 1 0 1 | (2^128 + 1)G 1354 * 6 | 0 1 1 0 | (2^128 + 2^64)G 1355 * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G 1356 * 8 | 1 0 0 0 | 2^192G 1357 * 9 | 1 0 0 1 | (2^192 + 1)G 1358 * 10 | 1 0 1 0 | (2^192 + 2^64)G 1359 * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G 1360 * 12 | 1 1 0 0 | (2^192 + 2^128)G 1361 * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G 1362 * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G 1363 * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G 1364 * followed by a copy of this with each element multiplied by 2^32. 1365 * 1366 * The reason for this is so that we can clock bits into four different 1367 * locations when doing simple scalar multiplies against the base point, 1368 * and then another four locations using the second 16 elements. 1369 * 1370 * Tables for other points have table[i] = iG for i in 0 .. 16. */ 1371 1372/* gmul is the table of precomputed base points */ 1373static const smallfelem gmul[2][16][3] = 1374{{{{0, 0, 0, 0}, 1375 {0, 0, 0, 0}, 1376 {0, 0, 0, 0}}, 1377 {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, 1378 {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, 1379 {1, 0, 0, 0}}, 1380 {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, 1381 {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, 1382 {1, 0, 0, 0}}, 1383 {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, 1384 {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, 1385 {1, 0, 0, 0}}, 1386 {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, 1387 {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, 1388 {1, 0, 0, 0}}, 1389 {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, 1390 {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, 1391 {1, 0, 0, 0}}, 1392 {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, 1393 {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, 1394 {1, 0, 0, 0}}, 1395 {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, 1396 {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, 1397 {1, 0, 0, 0}}, 1398 {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, 1399 {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, 1400 {1, 0, 0, 0}}, 1401 {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, 1402 {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, 1403 {1, 0, 0, 0}}, 1404 {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, 1405 {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, 1406 {1, 0, 0, 0}}, 1407 {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, 1408 {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, 1409 {1, 0, 0, 0}}, 1410 {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, 1411 {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, 1412 {1, 0, 0, 0}}, 1413 {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, 1414 {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, 1415 {1, 0, 0, 0}}, 1416 {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, 1417 {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, 1418 {1, 0, 0, 0}}, 1419 {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, 1420 {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, 1421 {1, 0, 0, 0}}}, 1422 {{{0, 0, 0, 0}, 1423 {0, 0, 0, 0}, 1424 {0, 0, 0, 0}}, 1425 {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, 1426 {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, 1427 {1, 0, 0, 0}}, 1428 {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, 1429 {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, 1430 {1, 0, 0, 0}}, 1431 {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, 1432 {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, 1433 {1, 0, 0, 0}}, 1434 {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, 1435 {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, 1436 {1, 0, 0, 0}}, 1437 {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, 1438 {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, 1439 {1, 0, 0, 0}}, 1440 {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, 1441 {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, 1442 {1, 0, 0, 0}}, 1443 {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, 1444 {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, 1445 {1, 0, 0, 0}}, 1446 {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, 1447 {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, 1448 {1, 0, 0, 0}}, 1449 {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, 1450 {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, 1451 {1, 0, 0, 0}}, 1452 {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, 1453 {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, 1454 {1, 0, 0, 0}}, 1455 {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, 1456 {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, 1457 {1, 0, 0, 0}}, 1458 {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, 1459 {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, 1460 {1, 0, 0, 0}}, 1461 {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, 1462 {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, 1463 {1, 0, 0, 0}}, 1464 {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, 1465 {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, 1466 {1, 0, 0, 0}}, 1467 {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, 1468 {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, 1469 {1, 0, 0, 0}}}}; 1470 1471/* select_point selects the |idx|th point from a precomputation table and 1472 * copies it to out. */ 1473static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) 1474 { 1475 unsigned i, j; 1476 u64 *outlimbs = &out[0][0]; 1477 memset(outlimbs, 0, 3 * sizeof(smallfelem)); 1478 1479 for (i = 0; i < size; i++) 1480 { 1481 const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; 1482 u64 mask = i ^ idx; 1483 mask |= mask >> 4; 1484 mask |= mask >> 2; 1485 mask |= mask >> 1; 1486 mask &= 1; 1487 mask--; 1488 for (j = 0; j < NLIMBS * 3; j++) 1489 outlimbs[j] |= inlimbs[j] & mask; 1490 } 1491 } 1492 1493/* get_bit returns the |i|th bit in |in| */ 1494static char get_bit(const felem_bytearray in, int i) 1495 { 1496 if ((i < 0) || (i >= 256)) 1497 return 0; 1498 return (in[i >> 3] >> (i & 7)) & 1; 1499 } 1500 1501/* Interleaved point multiplication using precomputed point multiples: 1502 * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], 1503 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple 1504 * of the generator, using certain (large) precomputed multiples in g_pre_comp. 1505 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ 1506static void batch_mul(felem x_out, felem y_out, felem z_out, 1507 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, 1508 const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) 1509 { 1510 int i, skip; 1511 unsigned num, gen_mul = (g_scalar != NULL); 1512 felem nq[3], ftmp; 1513 smallfelem tmp[3]; 1514 u64 bits; 1515 u8 sign, digit; 1516 1517 /* set nq to the point at infinity */ 1518 memset(nq, 0, 3 * sizeof(felem)); 1519 1520 /* Loop over all scalars msb-to-lsb, interleaving additions 1521 * of multiples of the generator (two in each of the last 32 rounds) 1522 * and additions of other points multiples (every 5th round). 1523 */ 1524 skip = 1; /* save two point operations in the first round */ 1525 for (i = (num_points ? 255 : 31); i >= 0; --i) 1526 { 1527 /* double */ 1528 if (!skip) 1529 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); 1530 1531 /* add multiples of the generator */ 1532 if (gen_mul && (i <= 31)) 1533 { 1534 /* first, look 32 bits upwards */ 1535 bits = get_bit(g_scalar, i + 224) << 3; 1536 bits |= get_bit(g_scalar, i + 160) << 2; 1537 bits |= get_bit(g_scalar, i + 96) << 1; 1538 bits |= get_bit(g_scalar, i + 32); 1539 /* select the point to add, in constant time */ 1540 select_point(bits, 16, g_pre_comp[1], tmp); 1541 1542 if (!skip) 1543 { 1544 point_add(nq[0], nq[1], nq[2], 1545 nq[0], nq[1], nq[2], 1546 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1547 } 1548 else 1549 { 1550 smallfelem_expand(nq[0], tmp[0]); 1551 smallfelem_expand(nq[1], tmp[1]); 1552 smallfelem_expand(nq[2], tmp[2]); 1553 skip = 0; 1554 } 1555 1556 /* second, look at the current position */ 1557 bits = get_bit(g_scalar, i + 192) << 3; 1558 bits |= get_bit(g_scalar, i + 128) << 2; 1559 bits |= get_bit(g_scalar, i + 64) << 1; 1560 bits |= get_bit(g_scalar, i); 1561 /* select the point to add, in constant time */ 1562 select_point(bits, 16, g_pre_comp[0], tmp); 1563 point_add(nq[0], nq[1], nq[2], 1564 nq[0], nq[1], nq[2], 1565 1 /* mixed */, tmp[0], tmp[1], tmp[2]); 1566 } 1567 1568 /* do other additions every 5 doublings */ 1569 if (num_points && (i % 5 == 0)) 1570 { 1571 /* loop over all scalars */ 1572 for (num = 0; num < num_points; ++num) 1573 { 1574 bits = get_bit(scalars[num], i + 4) << 5; 1575 bits |= get_bit(scalars[num], i + 3) << 4; 1576 bits |= get_bit(scalars[num], i + 2) << 3; 1577 bits |= get_bit(scalars[num], i + 1) << 2; 1578 bits |= get_bit(scalars[num], i) << 1; 1579 bits |= get_bit(scalars[num], i - 1); 1580 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); 1581 1582 /* select the point to add or subtract, in constant time */ 1583 select_point(digit, 17, pre_comp[num], tmp); 1584 smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ 1585 copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); 1586 felem_contract(tmp[1], ftmp); 1587 1588 if (!skip) 1589 { 1590 point_add(nq[0], nq[1], nq[2], 1591 nq[0], nq[1], nq[2], 1592 mixed, tmp[0], tmp[1], tmp[2]); 1593 } 1594 else 1595 { 1596 smallfelem_expand(nq[0], tmp[0]); 1597 smallfelem_expand(nq[1], tmp[1]); 1598 smallfelem_expand(nq[2], tmp[2]); 1599 skip = 0; 1600 } 1601 } 1602 } 1603 } 1604 felem_assign(x_out, nq[0]); 1605 felem_assign(y_out, nq[1]); 1606 felem_assign(z_out, nq[2]); 1607 } 1608 1609/* Precomputation for the group generator. */ 1610typedef struct { 1611 smallfelem g_pre_comp[2][16][3]; 1612 int references; 1613} NISTP256_PRE_COMP; 1614 1615const EC_METHOD *EC_GFp_nistp256_method(void) 1616 { 1617 static const EC_METHOD ret = { 1618 EC_FLAGS_DEFAULT_OCT, 1619 NID_X9_62_prime_field, 1620 ec_GFp_nistp256_group_init, 1621 ec_GFp_simple_group_finish, 1622 ec_GFp_simple_group_clear_finish, 1623 ec_GFp_nist_group_copy, 1624 ec_GFp_nistp256_group_set_curve, 1625 ec_GFp_simple_group_get_curve, 1626 ec_GFp_simple_group_get_degree, 1627 ec_GFp_simple_group_check_discriminant, 1628 ec_GFp_simple_point_init, 1629 ec_GFp_simple_point_finish, 1630 ec_GFp_simple_point_clear_finish, 1631 ec_GFp_simple_point_copy, 1632 ec_GFp_simple_point_set_to_infinity, 1633 ec_GFp_simple_set_Jprojective_coordinates_GFp, 1634 ec_GFp_simple_get_Jprojective_coordinates_GFp, 1635 ec_GFp_simple_point_set_affine_coordinates, 1636 ec_GFp_nistp256_point_get_affine_coordinates, 1637 0 /* point_set_compressed_coordinates */, 1638 0 /* point2oct */, 1639 0 /* oct2point */, 1640 ec_GFp_simple_add, 1641 ec_GFp_simple_dbl, 1642 ec_GFp_simple_invert, 1643 ec_GFp_simple_is_at_infinity, 1644 ec_GFp_simple_is_on_curve, 1645 ec_GFp_simple_cmp, 1646 ec_GFp_simple_make_affine, 1647 ec_GFp_simple_points_make_affine, 1648 ec_GFp_nistp256_points_mul, 1649 ec_GFp_nistp256_precompute_mult, 1650 ec_GFp_nistp256_have_precompute_mult, 1651 ec_GFp_nist_field_mul, 1652 ec_GFp_nist_field_sqr, 1653 0 /* field_div */, 1654 0 /* field_encode */, 1655 0 /* field_decode */, 1656 0 /* field_set_to_one */ }; 1657 1658 return &ret; 1659 } 1660 1661/******************************************************************************/ 1662/* FUNCTIONS TO MANAGE PRECOMPUTATION 1663 */ 1664 1665static NISTP256_PRE_COMP *nistp256_pre_comp_new() 1666 { 1667 NISTP256_PRE_COMP *ret = NULL; 1668 ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); 1669 if (!ret) 1670 { 1671 ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 1672 return ret; 1673 } 1674 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); 1675 ret->references = 1; 1676 return ret; 1677 } 1678 1679static void *nistp256_pre_comp_dup(void *src_) 1680 { 1681 NISTP256_PRE_COMP *src = src_; 1682 1683 /* no need to actually copy, these objects never change! */ 1684 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 1685 1686 return src_; 1687 } 1688 1689static void nistp256_pre_comp_free(void *pre_) 1690 { 1691 int i; 1692 NISTP256_PRE_COMP *pre = pre_; 1693 1694 if (!pre) 1695 return; 1696 1697 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1698 if (i > 0) 1699 return; 1700 1701 OPENSSL_free(pre); 1702 } 1703 1704static void nistp256_pre_comp_clear_free(void *pre_) 1705 { 1706 int i; 1707 NISTP256_PRE_COMP *pre = pre_; 1708 1709 if (!pre) 1710 return; 1711 1712 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1713 if (i > 0) 1714 return; 1715 1716 OPENSSL_cleanse(pre, sizeof *pre); 1717 OPENSSL_free(pre); 1718 } 1719 1720/******************************************************************************/ 1721/* OPENSSL EC_METHOD FUNCTIONS 1722 */ 1723 1724int ec_GFp_nistp256_group_init(EC_GROUP *group) 1725 { 1726 int ret; 1727 ret = ec_GFp_simple_group_init(group); 1728 group->a_is_minus3 = 1; 1729 return ret; 1730 } 1731 1732int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, 1733 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1734 { 1735 int ret = 0; 1736 BN_CTX *new_ctx = NULL; 1737 BIGNUM *curve_p, *curve_a, *curve_b; 1738 1739 if (ctx == NULL) 1740 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1741 BN_CTX_start(ctx); 1742 if (((curve_p = BN_CTX_get(ctx)) == NULL) || 1743 ((curve_a = BN_CTX_get(ctx)) == NULL) || 1744 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; 1745 BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); 1746 BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); 1747 BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); 1748 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || 1749 (BN_cmp(curve_b, b))) 1750 { 1751 ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, 1752 EC_R_WRONG_CURVE_PARAMETERS); 1753 goto err; 1754 } 1755 group->field_mod_func = BN_nist_mod_256; 1756 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); 1757err: 1758 BN_CTX_end(ctx); 1759 if (new_ctx != NULL) 1760 BN_CTX_free(new_ctx); 1761 return ret; 1762 } 1763 1764/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns 1765 * (X', Y') = (X/Z^2, Y/Z^3) */ 1766int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 1767 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 1768 { 1769 felem z1, z2, x_in, y_in; 1770 smallfelem x_out, y_out; 1771 longfelem tmp; 1772 1773 if (EC_POINT_is_at_infinity(group, point)) 1774 { 1775 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1776 EC_R_POINT_AT_INFINITY); 1777 return 0; 1778 } 1779 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || 1780 (!BN_to_felem(z1, &point->Z))) return 0; 1781 felem_inv(z2, z1); 1782 felem_square(tmp, z2); felem_reduce(z1, tmp); 1783 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); 1784 felem_contract(x_out, x_in); 1785 if (x != NULL) 1786 { 1787 if (!smallfelem_to_BN(x, x_out)) { 1788 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1789 ERR_R_BN_LIB); 1790 return 0; 1791 } 1792 } 1793 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); 1794 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); 1795 felem_contract(y_out, y_in); 1796 if (y != NULL) 1797 { 1798 if (!smallfelem_to_BN(y, y_out)) 1799 { 1800 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, 1801 ERR_R_BN_LIB); 1802 return 0; 1803 } 1804 } 1805 return 1; 1806 } 1807 1808static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) 1809 { 1810 /* Runs in constant time, unless an input is the point at infinity 1811 * (which normally shouldn't happen). */ 1812 ec_GFp_nistp_points_make_affine_internal( 1813 num, 1814 points, 1815 sizeof(smallfelem), 1816 tmp_smallfelems, 1817 (void (*)(void *)) smallfelem_one, 1818 (int (*)(const void *)) smallfelem_is_zero_int, 1819 (void (*)(void *, const void *)) smallfelem_assign, 1820 (void (*)(void *, const void *)) smallfelem_square_contract, 1821 (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, 1822 (void (*)(void *, const void *)) smallfelem_inv_contract, 1823 (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); 1824 } 1825 1826/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values 1827 * Result is stored in r (r can equal one of the inputs). */ 1828int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 1829 const BIGNUM *scalar, size_t num, const EC_POINT *points[], 1830 const BIGNUM *scalars[], BN_CTX *ctx) 1831 { 1832 int ret = 0; 1833 int j; 1834 int mixed = 0; 1835 BN_CTX *new_ctx = NULL; 1836 BIGNUM *x, *y, *z, *tmp_scalar; 1837 felem_bytearray g_secret; 1838 felem_bytearray *secrets = NULL; 1839 smallfelem (*pre_comp)[17][3] = NULL; 1840 smallfelem *tmp_smallfelems = NULL; 1841 felem_bytearray tmp; 1842 unsigned i, num_bytes; 1843 int have_pre_comp = 0; 1844 size_t num_points = num; 1845 smallfelem x_in, y_in, z_in; 1846 felem x_out, y_out, z_out; 1847 NISTP256_PRE_COMP *pre = NULL; 1848 const smallfelem (*g_pre_comp)[16][3] = NULL; 1849 EC_POINT *generator = NULL; 1850 const EC_POINT *p = NULL; 1851 const BIGNUM *p_scalar = NULL; 1852 1853 if (ctx == NULL) 1854 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 1855 BN_CTX_start(ctx); 1856 if (((x = BN_CTX_get(ctx)) == NULL) || 1857 ((y = BN_CTX_get(ctx)) == NULL) || 1858 ((z = BN_CTX_get(ctx)) == NULL) || 1859 ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) 1860 goto err; 1861 1862 if (scalar != NULL) 1863 { 1864 pre = EC_EX_DATA_get_data(group->extra_data, 1865 nistp256_pre_comp_dup, nistp256_pre_comp_free, 1866 nistp256_pre_comp_clear_free); 1867 if (pre) 1868 /* we have precomputation, try to use it */ 1869 g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; 1870 else 1871 /* try to use the standard precomputation */ 1872 g_pre_comp = &gmul[0]; 1873 generator = EC_POINT_new(group); 1874 if (generator == NULL) 1875 goto err; 1876 /* get the generator from precomputation */ 1877 if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || 1878 !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || 1879 !smallfelem_to_BN(z, g_pre_comp[0][1][2])) 1880 { 1881 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1882 goto err; 1883 } 1884 if (!EC_POINT_set_Jprojective_coordinates_GFp(group, 1885 generator, x, y, z, ctx)) 1886 goto err; 1887 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 1888 /* precomputation matches generator */ 1889 have_pre_comp = 1; 1890 else 1891 /* we don't have valid precomputation: 1892 * treat the generator as a random point */ 1893 num_points++; 1894 } 1895 if (num_points > 0) 1896 { 1897 if (num_points >= 3) 1898 { 1899 /* unless we precompute multiples for just one or two points, 1900 * converting those into affine form is time well spent */ 1901 mixed = 1; 1902 } 1903 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); 1904 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem)); 1905 if (mixed) 1906 tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); 1907 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) 1908 { 1909 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1910 goto err; 1911 } 1912 1913 /* we treat NULL scalars as 0, and NULL points as points at infinity, 1914 * i.e., they contribute nothing to the linear combination */ 1915 memset(secrets, 0, num_points * sizeof(felem_bytearray)); 1916 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); 1917 for (i = 0; i < num_points; ++i) 1918 { 1919 if (i == num) 1920 /* we didn't have a valid precomputation, so we pick 1921 * the generator */ 1922 { 1923 p = EC_GROUP_get0_generator(group); 1924 p_scalar = scalar; 1925 } 1926 else 1927 /* the i^th point */ 1928 { 1929 p = points[i]; 1930 p_scalar = scalars[i]; 1931 } 1932 if ((p_scalar != NULL) && (p != NULL)) 1933 { 1934 /* reduce scalar to 0 <= scalar < 2^256 */ 1935 if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) 1936 { 1937 /* this is an unusual input, and we don't guarantee 1938 * constant-timeness */ 1939 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) 1940 { 1941 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1942 goto err; 1943 } 1944 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1945 } 1946 else 1947 num_bytes = BN_bn2bin(p_scalar, tmp); 1948 flip_endian(secrets[i], tmp, num_bytes); 1949 /* precompute multiples */ 1950 if ((!BN_to_felem(x_out, &p->X)) || 1951 (!BN_to_felem(y_out, &p->Y)) || 1952 (!BN_to_felem(z_out, &p->Z))) goto err; 1953 felem_shrink(pre_comp[i][1][0], x_out); 1954 felem_shrink(pre_comp[i][1][1], y_out); 1955 felem_shrink(pre_comp[i][1][2], z_out); 1956 for (j = 2; j <= 16; ++j) 1957 { 1958 if (j & 1) 1959 { 1960 point_add_small( 1961 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1962 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 1963 pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); 1964 } 1965 else 1966 { 1967 point_double_small( 1968 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], 1969 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); 1970 } 1971 } 1972 } 1973 } 1974 if (mixed) 1975 make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); 1976 } 1977 1978 /* the scalar for the generator */ 1979 if ((scalar != NULL) && (have_pre_comp)) 1980 { 1981 memset(g_secret, 0, sizeof(g_secret)); 1982 /* reduce scalar to 0 <= scalar < 2^256 */ 1983 if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) 1984 { 1985 /* this is an unusual input, and we don't guarantee 1986 * constant-timeness */ 1987 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) 1988 { 1989 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 1990 goto err; 1991 } 1992 num_bytes = BN_bn2bin(tmp_scalar, tmp); 1993 } 1994 else 1995 num_bytes = BN_bn2bin(scalar, tmp); 1996 flip_endian(g_secret, tmp, num_bytes); 1997 /* do the multiplication with generator precomputation*/ 1998 batch_mul(x_out, y_out, z_out, 1999 (const felem_bytearray (*)) secrets, num_points, 2000 g_secret, 2001 mixed, (const smallfelem (*)[17][3]) pre_comp, 2002 g_pre_comp); 2003 } 2004 else 2005 /* do the multiplication without generator precomputation */ 2006 batch_mul(x_out, y_out, z_out, 2007 (const felem_bytearray (*)) secrets, num_points, 2008 NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); 2009 /* reduce the output to its unique minimal representation */ 2010 felem_contract(x_in, x_out); 2011 felem_contract(y_in, y_out); 2012 felem_contract(z_in, z_out); 2013 if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || 2014 (!smallfelem_to_BN(z, z_in))) 2015 { 2016 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); 2017 goto err; 2018 } 2019 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); 2020 2021err: 2022 BN_CTX_end(ctx); 2023 if (generator != NULL) 2024 EC_POINT_free(generator); 2025 if (new_ctx != NULL) 2026 BN_CTX_free(new_ctx); 2027 if (secrets != NULL) 2028 OPENSSL_free(secrets); 2029 if (pre_comp != NULL) 2030 OPENSSL_free(pre_comp); 2031 if (tmp_smallfelems != NULL) 2032 OPENSSL_free(tmp_smallfelems); 2033 return ret; 2034 } 2035 2036int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 2037 { 2038 int ret = 0; 2039 NISTP256_PRE_COMP *pre = NULL; 2040 int i, j; 2041 BN_CTX *new_ctx = NULL; 2042 BIGNUM *x, *y; 2043 EC_POINT *generator = NULL; 2044 smallfelem tmp_smallfelems[32]; 2045 felem x_tmp, y_tmp, z_tmp; 2046 2047 /* throw away old precomputation */ 2048 EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, 2049 nistp256_pre_comp_free, nistp256_pre_comp_clear_free); 2050 if (ctx == NULL) 2051 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; 2052 BN_CTX_start(ctx); 2053 if (((x = BN_CTX_get(ctx)) == NULL) || 2054 ((y = BN_CTX_get(ctx)) == NULL)) 2055 goto err; 2056 /* get the generator */ 2057 if (group->generator == NULL) goto err; 2058 generator = EC_POINT_new(group); 2059 if (generator == NULL) 2060 goto err; 2061 BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); 2062 BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); 2063 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) 2064 goto err; 2065 if ((pre = nistp256_pre_comp_new()) == NULL) 2066 goto err; 2067 /* if the generator is the standard one, use built-in precomputation */ 2068 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) 2069 { 2070 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); 2071 ret = 1; 2072 goto err; 2073 } 2074 if ((!BN_to_felem(x_tmp, &group->generator->X)) || 2075 (!BN_to_felem(y_tmp, &group->generator->Y)) || 2076 (!BN_to_felem(z_tmp, &group->generator->Z))) 2077 goto err; 2078 felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); 2079 felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); 2080 felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); 2081 /* compute 2^64*G, 2^128*G, 2^192*G for the first table, 2082 * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one 2083 */ 2084 for (i = 1; i <= 8; i <<= 1) 2085 { 2086 point_double_small( 2087 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], 2088 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); 2089 for (j = 0; j < 31; ++j) 2090 { 2091 point_double_small( 2092 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], 2093 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 2094 } 2095 if (i == 8) 2096 break; 2097 point_double_small( 2098 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], 2099 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); 2100 for (j = 0; j < 31; ++j) 2101 { 2102 point_double_small( 2103 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], 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 } 2106 } 2107 for (i = 0; i < 2; i++) 2108 { 2109 /* g_pre_comp[i][0] is the point at infinity */ 2110 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); 2111 /* the remaining multiples */ 2112 /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ 2113 point_add_small( 2114 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], 2115 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], 2116 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2117 /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ 2118 point_add_small( 2119 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], 2120 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 2121 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2122 /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ 2123 point_add_small( 2124 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], 2125 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], 2126 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); 2127 /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ 2128 point_add_small( 2129 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], 2130 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], 2131 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); 2132 for (j = 1; j < 8; ++j) 2133 { 2134 /* odd multiples: add G resp. 2^32*G */ 2135 point_add_small( 2136 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], 2137 pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], 2138 pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); 2139 } 2140 } 2141 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); 2142 2143 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, 2144 nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) 2145 goto err; 2146 ret = 1; 2147 pre = NULL; 2148 err: 2149 BN_CTX_end(ctx); 2150 if (generator != NULL) 2151 EC_POINT_free(generator); 2152 if (new_ctx != NULL) 2153 BN_CTX_free(new_ctx); 2154 if (pre) 2155 nistp256_pre_comp_free(pre); 2156 return ret; 2157 } 2158 2159int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) 2160 { 2161 if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, 2162 nistp256_pre_comp_free, nistp256_pre_comp_clear_free) 2163 != NULL) 2164 return 1; 2165 else 2166 return 0; 2167 } 2168#else 2169static void *dummy=&dummy; 2170#endif 2171