1 /* crypto/ec/ecp_smpl.c */ 2 /* Includes code written by Lenka Fibikova <fibikova (at) exp-math.uni-essen.de> 3 * for the OpenSSL project. 4 * Includes code written by Bodo Moeller for the OpenSSL project. 5 */ 6 /* ==================================================================== 7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. 8 * 9 * Redistribution and use in source and binary forms, with or without 10 * modification, are permitted provided that the following conditions 11 * are met: 12 * 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 16 * 2. Redistributions in binary form must reproduce the above copyright 17 * notice, this list of conditions and the following disclaimer in 18 * the documentation and/or other materials provided with the 19 * distribution. 20 * 21 * 3. All advertising materials mentioning features or use of this 22 * software must display the following acknowledgment: 23 * "This product includes software developed by the OpenSSL Project 24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 25 * 26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 27 * endorse or promote products derived from this software without 28 * prior written permission. For written permission, please contact 29 * openssl-core (at) openssl.org. 30 * 31 * 5. Products derived from this software may not be called "OpenSSL" 32 * nor may "OpenSSL" appear in their names without prior written 33 * permission of the OpenSSL Project. 34 * 35 * 6. Redistributions of any form whatsoever must retain the following 36 * acknowledgment: 37 * "This product includes software developed by the OpenSSL Project 38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 39 * 40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 51 * OF THE POSSIBILITY OF SUCH DAMAGE. 52 * ==================================================================== 53 * 54 * This product includes cryptographic software written by Eric Young 55 * (eay (at) cryptsoft.com). This product includes software written by Tim 56 * Hudson (tjh (at) cryptsoft.com). 57 * 58 */ 59 /* ==================================================================== 60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 61 * Portions of this software developed by SUN MICROSYSTEMS, INC., 62 * and contributed to the OpenSSL project. 63 */ 64 65 #include <openssl/err.h> 66 #include <openssl/symhacks.h> 67 68 #ifdef OPENSSL_FIPS 69 #include <openssl/fips.h> 70 #endif 71 72 #include "ec_lcl.h" 73 74 const EC_METHOD *EC_GFp_simple_method(void) 75 { 76 #ifdef OPENSSL_FIPS 77 return fips_ec_gfp_simple_method(); 78 #else 79 static const EC_METHOD ret = { 80 EC_FLAGS_DEFAULT_OCT, 81 NID_X9_62_prime_field, 82 ec_GFp_simple_group_init, 83 ec_GFp_simple_group_finish, 84 ec_GFp_simple_group_clear_finish, 85 ec_GFp_simple_group_copy, 86 ec_GFp_simple_group_set_curve, 87 ec_GFp_simple_group_get_curve, 88 ec_GFp_simple_group_get_degree, 89 ec_GFp_simple_group_check_discriminant, 90 ec_GFp_simple_point_init, 91 ec_GFp_simple_point_finish, 92 ec_GFp_simple_point_clear_finish, 93 ec_GFp_simple_point_copy, 94 ec_GFp_simple_point_set_to_infinity, 95 ec_GFp_simple_set_Jprojective_coordinates_GFp, 96 ec_GFp_simple_get_Jprojective_coordinates_GFp, 97 ec_GFp_simple_point_set_affine_coordinates, 98 ec_GFp_simple_point_get_affine_coordinates, 99 0,0,0, 100 ec_GFp_simple_add, 101 ec_GFp_simple_dbl, 102 ec_GFp_simple_invert, 103 ec_GFp_simple_is_at_infinity, 104 ec_GFp_simple_is_on_curve, 105 ec_GFp_simple_cmp, 106 ec_GFp_simple_make_affine, 107 ec_GFp_simple_points_make_affine, 108 0 /* mul */, 109 0 /* precompute_mult */, 110 0 /* have_precompute_mult */, 111 ec_GFp_simple_field_mul, 112 ec_GFp_simple_field_sqr, 113 0 /* field_div */, 114 0 /* field_encode */, 115 0 /* field_decode */, 116 0 /* field_set_to_one */ }; 117 118 return &ret; 119 #endif 120 } 121 122 123 /* Most method functions in this file are designed to work with 124 * non-trivial representations of field elements if necessary 125 * (see ecp_mont.c): while standard modular addition and subtraction 126 * are used, the field_mul and field_sqr methods will be used for 127 * multiplication, and field_encode and field_decode (if defined) 128 * will be used for converting between representations. 129 130 * Functions ec_GFp_simple_points_make_affine() and 131 * ec_GFp_simple_point_get_affine_coordinates() specifically assume 132 * that if a non-trivial representation is used, it is a Montgomery 133 * representation (i.e. 'encoding' means multiplying by some factor R). 134 */ 135 136 137 int ec_GFp_simple_group_init(EC_GROUP *group) 138 { 139 BN_init(&group->field); 140 BN_init(&group->a); 141 BN_init(&group->b); 142 group->a_is_minus3 = 0; 143 return 1; 144 } 145 146 147 void ec_GFp_simple_group_finish(EC_GROUP *group) 148 { 149 BN_free(&group->field); 150 BN_free(&group->a); 151 BN_free(&group->b); 152 } 153 154 155 void ec_GFp_simple_group_clear_finish(EC_GROUP *group) 156 { 157 BN_clear_free(&group->field); 158 BN_clear_free(&group->a); 159 BN_clear_free(&group->b); 160 } 161 162 163 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) 164 { 165 if (!BN_copy(&dest->field, &src->field)) return 0; 166 if (!BN_copy(&dest->a, &src->a)) return 0; 167 if (!BN_copy(&dest->b, &src->b)) return 0; 168 169 dest->a_is_minus3 = src->a_is_minus3; 170 171 return 1; 172 } 173 174 175 int ec_GFp_simple_group_set_curve(EC_GROUP *group, 176 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 177 { 178 int ret = 0; 179 BN_CTX *new_ctx = NULL; 180 BIGNUM *tmp_a; 181 182 /* p must be a prime > 3 */ 183 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) 184 { 185 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); 186 return 0; 187 } 188 189 if (ctx == NULL) 190 { 191 ctx = new_ctx = BN_CTX_new(); 192 if (ctx == NULL) 193 return 0; 194 } 195 196 BN_CTX_start(ctx); 197 tmp_a = BN_CTX_get(ctx); 198 if (tmp_a == NULL) goto err; 199 200 /* group->field */ 201 if (!BN_copy(&group->field, p)) goto err; 202 BN_set_negative(&group->field, 0); 203 204 /* group->a */ 205 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; 206 if (group->meth->field_encode) 207 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; } 208 else 209 if (!BN_copy(&group->a, tmp_a)) goto err; 210 211 /* group->b */ 212 if (!BN_nnmod(&group->b, b, p, ctx)) goto err; 213 if (group->meth->field_encode) 214 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err; 215 216 /* group->a_is_minus3 */ 217 if (!BN_add_word(tmp_a, 3)) goto err; 218 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); 219 220 ret = 1; 221 222 err: 223 BN_CTX_end(ctx); 224 if (new_ctx != NULL) 225 BN_CTX_free(new_ctx); 226 return ret; 227 } 228 229 230 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 231 { 232 int ret = 0; 233 BN_CTX *new_ctx = NULL; 234 235 if (p != NULL) 236 { 237 if (!BN_copy(p, &group->field)) return 0; 238 } 239 240 if (a != NULL || b != NULL) 241 { 242 if (group->meth->field_decode) 243 { 244 if (ctx == NULL) 245 { 246 ctx = new_ctx = BN_CTX_new(); 247 if (ctx == NULL) 248 return 0; 249 } 250 if (a != NULL) 251 { 252 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; 253 } 254 if (b != NULL) 255 { 256 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; 257 } 258 } 259 else 260 { 261 if (a != NULL) 262 { 263 if (!BN_copy(a, &group->a)) goto err; 264 } 265 if (b != NULL) 266 { 267 if (!BN_copy(b, &group->b)) goto err; 268 } 269 } 270 } 271 272 ret = 1; 273 274 err: 275 if (new_ctx) 276 BN_CTX_free(new_ctx); 277 return ret; 278 } 279 280 281 int ec_GFp_simple_group_get_degree(const EC_GROUP *group) 282 { 283 return BN_num_bits(&group->field); 284 } 285 286 287 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) 288 { 289 int ret = 0; 290 BIGNUM *a,*b,*order,*tmp_1,*tmp_2; 291 const BIGNUM *p = &group->field; 292 BN_CTX *new_ctx = NULL; 293 294 if (ctx == NULL) 295 { 296 ctx = new_ctx = BN_CTX_new(); 297 if (ctx == NULL) 298 { 299 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); 300 goto err; 301 } 302 } 303 BN_CTX_start(ctx); 304 a = BN_CTX_get(ctx); 305 b = BN_CTX_get(ctx); 306 tmp_1 = BN_CTX_get(ctx); 307 tmp_2 = BN_CTX_get(ctx); 308 order = BN_CTX_get(ctx); 309 if (order == NULL) goto err; 310 311 if (group->meth->field_decode) 312 { 313 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; 314 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; 315 } 316 else 317 { 318 if (!BN_copy(a, &group->a)) goto err; 319 if (!BN_copy(b, &group->b)) goto err; 320 } 321 322 /* check the discriminant: 323 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) 324 * 0 =< a, b < p */ 325 if (BN_is_zero(a)) 326 { 327 if (BN_is_zero(b)) goto err; 328 } 329 else if (!BN_is_zero(b)) 330 { 331 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err; 332 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err; 333 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err; 334 /* tmp_1 = 4*a^3 */ 335 336 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err; 337 if (!BN_mul_word(tmp_2, 27)) goto err; 338 /* tmp_2 = 27*b^2 */ 339 340 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err; 341 if (BN_is_zero(a)) goto err; 342 } 343 ret = 1; 344 345 err: 346 if (ctx != NULL) 347 BN_CTX_end(ctx); 348 if (new_ctx != NULL) 349 BN_CTX_free(new_ctx); 350 return ret; 351 } 352 353 354 int ec_GFp_simple_point_init(EC_POINT *point) 355 { 356 BN_init(&point->X); 357 BN_init(&point->Y); 358 BN_init(&point->Z); 359 point->Z_is_one = 0; 360 361 return 1; 362 } 363 364 365 void ec_GFp_simple_point_finish(EC_POINT *point) 366 { 367 BN_free(&point->X); 368 BN_free(&point->Y); 369 BN_free(&point->Z); 370 } 371 372 373 void ec_GFp_simple_point_clear_finish(EC_POINT *point) 374 { 375 BN_clear_free(&point->X); 376 BN_clear_free(&point->Y); 377 BN_clear_free(&point->Z); 378 point->Z_is_one = 0; 379 } 380 381 382 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) 383 { 384 if (!BN_copy(&dest->X, &src->X)) return 0; 385 if (!BN_copy(&dest->Y, &src->Y)) return 0; 386 if (!BN_copy(&dest->Z, &src->Z)) return 0; 387 dest->Z_is_one = src->Z_is_one; 388 389 return 1; 390 } 391 392 393 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) 394 { 395 point->Z_is_one = 0; 396 BN_zero(&point->Z); 397 return 1; 398 } 399 400 401 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, 402 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) 403 { 404 BN_CTX *new_ctx = NULL; 405 int ret = 0; 406 407 if (ctx == NULL) 408 { 409 ctx = new_ctx = BN_CTX_new(); 410 if (ctx == NULL) 411 return 0; 412 } 413 414 if (x != NULL) 415 { 416 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err; 417 if (group->meth->field_encode) 418 { 419 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err; 420 } 421 } 422 423 if (y != NULL) 424 { 425 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err; 426 if (group->meth->field_encode) 427 { 428 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err; 429 } 430 } 431 432 if (z != NULL) 433 { 434 int Z_is_one; 435 436 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err; 437 Z_is_one = BN_is_one(&point->Z); 438 if (group->meth->field_encode) 439 { 440 if (Z_is_one && (group->meth->field_set_to_one != 0)) 441 { 442 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err; 443 } 444 else 445 { 446 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err; 447 } 448 } 449 point->Z_is_one = Z_is_one; 450 } 451 452 ret = 1; 453 454 err: 455 if (new_ctx != NULL) 456 BN_CTX_free(new_ctx); 457 return ret; 458 } 459 460 461 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, 462 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) 463 { 464 BN_CTX *new_ctx = NULL; 465 int ret = 0; 466 467 if (group->meth->field_decode != 0) 468 { 469 if (ctx == NULL) 470 { 471 ctx = new_ctx = BN_CTX_new(); 472 if (ctx == NULL) 473 return 0; 474 } 475 476 if (x != NULL) 477 { 478 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; 479 } 480 if (y != NULL) 481 { 482 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; 483 } 484 if (z != NULL) 485 { 486 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err; 487 } 488 } 489 else 490 { 491 if (x != NULL) 492 { 493 if (!BN_copy(x, &point->X)) goto err; 494 } 495 if (y != NULL) 496 { 497 if (!BN_copy(y, &point->Y)) goto err; 498 } 499 if (z != NULL) 500 { 501 if (!BN_copy(z, &point->Z)) goto err; 502 } 503 } 504 505 ret = 1; 506 507 err: 508 if (new_ctx != NULL) 509 BN_CTX_free(new_ctx); 510 return ret; 511 } 512 513 514 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, 515 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) 516 { 517 if (x == NULL || y == NULL) 518 { 519 /* unlike for projective coordinates, we do not tolerate this */ 520 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); 521 return 0; 522 } 523 524 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); 525 } 526 527 528 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, 529 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 530 { 531 BN_CTX *new_ctx = NULL; 532 BIGNUM *Z, *Z_1, *Z_2, *Z_3; 533 const BIGNUM *Z_; 534 int ret = 0; 535 536 if (EC_POINT_is_at_infinity(group, point)) 537 { 538 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); 539 return 0; 540 } 541 542 if (ctx == NULL) 543 { 544 ctx = new_ctx = BN_CTX_new(); 545 if (ctx == NULL) 546 return 0; 547 } 548 549 BN_CTX_start(ctx); 550 Z = BN_CTX_get(ctx); 551 Z_1 = BN_CTX_get(ctx); 552 Z_2 = BN_CTX_get(ctx); 553 Z_3 = BN_CTX_get(ctx); 554 if (Z_3 == NULL) goto err; 555 556 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ 557 558 if (group->meth->field_decode) 559 { 560 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err; 561 Z_ = Z; 562 } 563 else 564 { 565 Z_ = &point->Z; 566 } 567 568 if (BN_is_one(Z_)) 569 { 570 if (group->meth->field_decode) 571 { 572 if (x != NULL) 573 { 574 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; 575 } 576 if (y != NULL) 577 { 578 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; 579 } 580 } 581 else 582 { 583 if (x != NULL) 584 { 585 if (!BN_copy(x, &point->X)) goto err; 586 } 587 if (y != NULL) 588 { 589 if (!BN_copy(y, &point->Y)) goto err; 590 } 591 } 592 } 593 else 594 { 595 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) 596 { 597 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); 598 goto err; 599 } 600 601 if (group->meth->field_encode == 0) 602 { 603 /* field_sqr works on standard representation */ 604 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err; 605 } 606 else 607 { 608 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err; 609 } 610 611 if (x != NULL) 612 { 613 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */ 614 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err; 615 } 616 617 if (y != NULL) 618 { 619 if (group->meth->field_encode == 0) 620 { 621 /* field_mul works on standard representation */ 622 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err; 623 } 624 else 625 { 626 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err; 627 } 628 629 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */ 630 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err; 631 } 632 } 633 634 ret = 1; 635 636 err: 637 BN_CTX_end(ctx); 638 if (new_ctx != NULL) 639 BN_CTX_free(new_ctx); 640 return ret; 641 } 642 643 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 644 { 645 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 646 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 647 const BIGNUM *p; 648 BN_CTX *new_ctx = NULL; 649 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; 650 int ret = 0; 651 652 if (a == b) 653 return EC_POINT_dbl(group, r, a, ctx); 654 if (EC_POINT_is_at_infinity(group, a)) 655 return EC_POINT_copy(r, b); 656 if (EC_POINT_is_at_infinity(group, b)) 657 return EC_POINT_copy(r, a); 658 659 field_mul = group->meth->field_mul; 660 field_sqr = group->meth->field_sqr; 661 p = &group->field; 662 663 if (ctx == NULL) 664 { 665 ctx = new_ctx = BN_CTX_new(); 666 if (ctx == NULL) 667 return 0; 668 } 669 670 BN_CTX_start(ctx); 671 n0 = BN_CTX_get(ctx); 672 n1 = BN_CTX_get(ctx); 673 n2 = BN_CTX_get(ctx); 674 n3 = BN_CTX_get(ctx); 675 n4 = BN_CTX_get(ctx); 676 n5 = BN_CTX_get(ctx); 677 n6 = BN_CTX_get(ctx); 678 if (n6 == NULL) goto end; 679 680 /* Note that in this function we must not read components of 'a' or 'b' 681 * once we have written the corresponding components of 'r'. 682 * ('r' might be one of 'a' or 'b'.) 683 */ 684 685 /* n1, n2 */ 686 if (b->Z_is_one) 687 { 688 if (!BN_copy(n1, &a->X)) goto end; 689 if (!BN_copy(n2, &a->Y)) goto end; 690 /* n1 = X_a */ 691 /* n2 = Y_a */ 692 } 693 else 694 { 695 if (!field_sqr(group, n0, &b->Z, ctx)) goto end; 696 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end; 697 /* n1 = X_a * Z_b^2 */ 698 699 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end; 700 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end; 701 /* n2 = Y_a * Z_b^3 */ 702 } 703 704 /* n3, n4 */ 705 if (a->Z_is_one) 706 { 707 if (!BN_copy(n3, &b->X)) goto end; 708 if (!BN_copy(n4, &b->Y)) goto end; 709 /* n3 = X_b */ 710 /* n4 = Y_b */ 711 } 712 else 713 { 714 if (!field_sqr(group, n0, &a->Z, ctx)) goto end; 715 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end; 716 /* n3 = X_b * Z_a^2 */ 717 718 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end; 719 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end; 720 /* n4 = Y_b * Z_a^3 */ 721 } 722 723 /* n5, n6 */ 724 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; 725 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; 726 /* n5 = n1 - n3 */ 727 /* n6 = n2 - n4 */ 728 729 if (BN_is_zero(n5)) 730 { 731 if (BN_is_zero(n6)) 732 { 733 /* a is the same point as b */ 734 BN_CTX_end(ctx); 735 ret = EC_POINT_dbl(group, r, a, ctx); 736 ctx = NULL; 737 goto end; 738 } 739 else 740 { 741 /* a is the inverse of b */ 742 BN_zero(&r->Z); 743 r->Z_is_one = 0; 744 ret = 1; 745 goto end; 746 } 747 } 748 749 /* 'n7', 'n8' */ 750 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; 751 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; 752 /* 'n7' = n1 + n3 */ 753 /* 'n8' = n2 + n4 */ 754 755 /* Z_r */ 756 if (a->Z_is_one && b->Z_is_one) 757 { 758 if (!BN_copy(&r->Z, n5)) goto end; 759 } 760 else 761 { 762 if (a->Z_is_one) 763 { if (!BN_copy(n0, &b->Z)) goto end; } 764 else if (b->Z_is_one) 765 { if (!BN_copy(n0, &a->Z)) goto end; } 766 else 767 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; } 768 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end; 769 } 770 r->Z_is_one = 0; 771 /* Z_r = Z_a * Z_b * n5 */ 772 773 /* X_r */ 774 if (!field_sqr(group, n0, n6, ctx)) goto end; 775 if (!field_sqr(group, n4, n5, ctx)) goto end; 776 if (!field_mul(group, n3, n1, n4, ctx)) goto end; 777 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end; 778 /* X_r = n6^2 - n5^2 * 'n7' */ 779 780 /* 'n9' */ 781 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end; 782 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; 783 /* n9 = n5^2 * 'n7' - 2 * X_r */ 784 785 /* Y_r */ 786 if (!field_mul(group, n0, n0, n6, ctx)) goto end; 787 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ 788 if (!field_mul(group, n1, n2, n5, ctx)) goto end; 789 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; 790 if (BN_is_odd(n0)) 791 if (!BN_add(n0, n0, p)) goto end; 792 /* now 0 <= n0 < 2*p, and n0 is even */ 793 if (!BN_rshift1(&r->Y, n0)) goto end; 794 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ 795 796 ret = 1; 797 798 end: 799 if (ctx) /* otherwise we already called BN_CTX_end */ 800 BN_CTX_end(ctx); 801 if (new_ctx != NULL) 802 BN_CTX_free(new_ctx); 803 return ret; 804 } 805 806 807 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) 808 { 809 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 810 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 811 const BIGNUM *p; 812 BN_CTX *new_ctx = NULL; 813 BIGNUM *n0, *n1, *n2, *n3; 814 int ret = 0; 815 816 if (EC_POINT_is_at_infinity(group, a)) 817 { 818 BN_zero(&r->Z); 819 r->Z_is_one = 0; 820 return 1; 821 } 822 823 field_mul = group->meth->field_mul; 824 field_sqr = group->meth->field_sqr; 825 p = &group->field; 826 827 if (ctx == NULL) 828 { 829 ctx = new_ctx = BN_CTX_new(); 830 if (ctx == NULL) 831 return 0; 832 } 833 834 BN_CTX_start(ctx); 835 n0 = BN_CTX_get(ctx); 836 n1 = BN_CTX_get(ctx); 837 n2 = BN_CTX_get(ctx); 838 n3 = BN_CTX_get(ctx); 839 if (n3 == NULL) goto err; 840 841 /* Note that in this function we must not read components of 'a' 842 * once we have written the corresponding components of 'r'. 843 * ('r' might the same as 'a'.) 844 */ 845 846 /* n1 */ 847 if (a->Z_is_one) 848 { 849 if (!field_sqr(group, n0, &a->X, ctx)) goto err; 850 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; 851 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; 852 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err; 853 /* n1 = 3 * X_a^2 + a_curve */ 854 } 855 else if (group->a_is_minus3) 856 { 857 if (!field_sqr(group, n1, &a->Z, ctx)) goto err; 858 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err; 859 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err; 860 if (!field_mul(group, n1, n0, n2, ctx)) goto err; 861 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; 862 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; 863 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) 864 * = 3 * X_a^2 - 3 * Z_a^4 */ 865 } 866 else 867 { 868 if (!field_sqr(group, n0, &a->X, ctx)) goto err; 869 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; 870 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; 871 if (!field_sqr(group, n1, &a->Z, ctx)) goto err; 872 if (!field_sqr(group, n1, n1, ctx)) goto err; 873 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err; 874 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; 875 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ 876 } 877 878 /* Z_r */ 879 if (a->Z_is_one) 880 { 881 if (!BN_copy(n0, &a->Y)) goto err; 882 } 883 else 884 { 885 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err; 886 } 887 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err; 888 r->Z_is_one = 0; 889 /* Z_r = 2 * Y_a * Z_a */ 890 891 /* n2 */ 892 if (!field_sqr(group, n3, &a->Y, ctx)) goto err; 893 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err; 894 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; 895 /* n2 = 4 * X_a * Y_a^2 */ 896 897 /* X_r */ 898 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; 899 if (!field_sqr(group, &r->X, n1, ctx)) goto err; 900 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err; 901 /* X_r = n1^2 - 2 * n2 */ 902 903 /* n3 */ 904 if (!field_sqr(group, n0, n3, ctx)) goto err; 905 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; 906 /* n3 = 8 * Y_a^4 */ 907 908 /* Y_r */ 909 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err; 910 if (!field_mul(group, n0, n1, n0, ctx)) goto err; 911 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err; 912 /* Y_r = n1 * (n2 - X_r) - n3 */ 913 914 ret = 1; 915 916 err: 917 BN_CTX_end(ctx); 918 if (new_ctx != NULL) 919 BN_CTX_free(new_ctx); 920 return ret; 921 } 922 923 924 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 925 { 926 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) 927 /* point is its own inverse */ 928 return 1; 929 930 return BN_usub(&point->Y, &group->field, &point->Y); 931 } 932 933 934 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 935 { 936 return BN_is_zero(&point->Z); 937 } 938 939 940 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 941 { 942 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 943 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 944 const BIGNUM *p; 945 BN_CTX *new_ctx = NULL; 946 BIGNUM *rh, *tmp, *Z4, *Z6; 947 int ret = -1; 948 949 if (EC_POINT_is_at_infinity(group, point)) 950 return 1; 951 952 field_mul = group->meth->field_mul; 953 field_sqr = group->meth->field_sqr; 954 p = &group->field; 955 956 if (ctx == NULL) 957 { 958 ctx = new_ctx = BN_CTX_new(); 959 if (ctx == NULL) 960 return -1; 961 } 962 963 BN_CTX_start(ctx); 964 rh = BN_CTX_get(ctx); 965 tmp = BN_CTX_get(ctx); 966 Z4 = BN_CTX_get(ctx); 967 Z6 = BN_CTX_get(ctx); 968 if (Z6 == NULL) goto err; 969 970 /* We have a curve defined by a Weierstrass equation 971 * y^2 = x^3 + a*x + b. 972 * The point to consider is given in Jacobian projective coordinates 973 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). 974 * Substituting this and multiplying by Z^6 transforms the above equation into 975 * Y^2 = X^3 + a*X*Z^4 + b*Z^6. 976 * To test this, we add up the right-hand side in 'rh'. 977 */ 978 979 /* rh := X^2 */ 980 if (!field_sqr(group, rh, &point->X, ctx)) goto err; 981 982 if (!point->Z_is_one) 983 { 984 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err; 985 if (!field_sqr(group, Z4, tmp, ctx)) goto err; 986 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; 987 988 /* rh := (rh + a*Z^4)*X */ 989 if (group->a_is_minus3) 990 { 991 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; 992 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; 993 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; 994 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; 995 } 996 else 997 { 998 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err; 999 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; 1000 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; 1001 } 1002 1003 /* rh := rh + b*Z^6 */ 1004 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err; 1005 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; 1006 } 1007 else 1008 { 1009 /* point->Z_is_one */ 1010 1011 /* rh := (rh + a)*X */ 1012 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err; 1013 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; 1014 /* rh := rh + b */ 1015 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; 1016 } 1017 1018 /* 'lh' := Y^2 */ 1019 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err; 1020 1021 ret = (0 == BN_ucmp(tmp, rh)); 1022 1023 err: 1024 BN_CTX_end(ctx); 1025 if (new_ctx != NULL) 1026 BN_CTX_free(new_ctx); 1027 return ret; 1028 } 1029 1030 1031 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 1032 { 1033 /* return values: 1034 * -1 error 1035 * 0 equal (in affine coordinates) 1036 * 1 not equal 1037 */ 1038 1039 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 1040 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 1041 BN_CTX *new_ctx = NULL; 1042 BIGNUM *tmp1, *tmp2, *Za23, *Zb23; 1043 const BIGNUM *tmp1_, *tmp2_; 1044 int ret = -1; 1045 1046 if (EC_POINT_is_at_infinity(group, a)) 1047 { 1048 return EC_POINT_is_at_infinity(group, b) ? 0 : 1; 1049 } 1050 1051 if (EC_POINT_is_at_infinity(group, b)) 1052 return 1; 1053 1054 if (a->Z_is_one && b->Z_is_one) 1055 { 1056 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 1057 } 1058 1059 field_mul = group->meth->field_mul; 1060 field_sqr = group->meth->field_sqr; 1061 1062 if (ctx == NULL) 1063 { 1064 ctx = new_ctx = BN_CTX_new(); 1065 if (ctx == NULL) 1066 return -1; 1067 } 1068 1069 BN_CTX_start(ctx); 1070 tmp1 = BN_CTX_get(ctx); 1071 tmp2 = BN_CTX_get(ctx); 1072 Za23 = BN_CTX_get(ctx); 1073 Zb23 = BN_CTX_get(ctx); 1074 if (Zb23 == NULL) goto end; 1075 1076 /* We have to decide whether 1077 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), 1078 * or equivalently, whether 1079 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). 1080 */ 1081 1082 if (!b->Z_is_one) 1083 { 1084 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end; 1085 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end; 1086 tmp1_ = tmp1; 1087 } 1088 else 1089 tmp1_ = &a->X; 1090 if (!a->Z_is_one) 1091 { 1092 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end; 1093 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end; 1094 tmp2_ = tmp2; 1095 } 1096 else 1097 tmp2_ = &b->X; 1098 1099 /* compare X_a*Z_b^2 with X_b*Z_a^2 */ 1100 if (BN_cmp(tmp1_, tmp2_) != 0) 1101 { 1102 ret = 1; /* points differ */ 1103 goto end; 1104 } 1105 1106 1107 if (!b->Z_is_one) 1108 { 1109 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end; 1110 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end; 1111 /* tmp1_ = tmp1 */ 1112 } 1113 else 1114 tmp1_ = &a->Y; 1115 if (!a->Z_is_one) 1116 { 1117 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end; 1118 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end; 1119 /* tmp2_ = tmp2 */ 1120 } 1121 else 1122 tmp2_ = &b->Y; 1123 1124 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ 1125 if (BN_cmp(tmp1_, tmp2_) != 0) 1126 { 1127 ret = 1; /* points differ */ 1128 goto end; 1129 } 1130 1131 /* points are equal */ 1132 ret = 0; 1133 1134 end: 1135 BN_CTX_end(ctx); 1136 if (new_ctx != NULL) 1137 BN_CTX_free(new_ctx); 1138 return ret; 1139 } 1140 1141 1142 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 1143 { 1144 BN_CTX *new_ctx = NULL; 1145 BIGNUM *x, *y; 1146 int ret = 0; 1147 1148 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) 1149 return 1; 1150 1151 if (ctx == NULL) 1152 { 1153 ctx = new_ctx = BN_CTX_new(); 1154 if (ctx == NULL) 1155 return 0; 1156 } 1157 1158 BN_CTX_start(ctx); 1159 x = BN_CTX_get(ctx); 1160 y = BN_CTX_get(ctx); 1161 if (y == NULL) goto err; 1162 1163 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; 1164 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; 1165 if (!point->Z_is_one) 1166 { 1167 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); 1168 goto err; 1169 } 1170 1171 ret = 1; 1172 1173 err: 1174 BN_CTX_end(ctx); 1175 if (new_ctx != NULL) 1176 BN_CTX_free(new_ctx); 1177 return ret; 1178 } 1179 1180 1181 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) 1182 { 1183 BN_CTX *new_ctx = NULL; 1184 BIGNUM *tmp0, *tmp1; 1185 size_t pow2 = 0; 1186 BIGNUM **heap = NULL; 1187 size_t i; 1188 int ret = 0; 1189 1190 if (num == 0) 1191 return 1; 1192 1193 if (ctx == NULL) 1194 { 1195 ctx = new_ctx = BN_CTX_new(); 1196 if (ctx == NULL) 1197 return 0; 1198 } 1199 1200 BN_CTX_start(ctx); 1201 tmp0 = BN_CTX_get(ctx); 1202 tmp1 = BN_CTX_get(ctx); 1203 if (tmp0 == NULL || tmp1 == NULL) goto err; 1204 1205 /* Before converting the individual points, compute inverses of all Z values. 1206 * Modular inversion is rather slow, but luckily we can do with a single 1207 * explicit inversion, plus about 3 multiplications per input value. 1208 */ 1209 1210 pow2 = 1; 1211 while (num > pow2) 1212 pow2 <<= 1; 1213 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num. 1214 * We need twice that. */ 1215 pow2 <<= 1; 1216 1217 heap = OPENSSL_malloc(pow2 * sizeof heap[0]); 1218 if (heap == NULL) goto err; 1219 1220 /* The array is used as a binary tree, exactly as in heapsort: 1221 * 1222 * heap[1] 1223 * heap[2] heap[3] 1224 * heap[4] heap[5] heap[6] heap[7] 1225 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15] 1226 * 1227 * We put the Z's in the last line; 1228 * then we set each other node to the product of its two child-nodes (where 1229 * empty or 0 entries are treated as ones); 1230 * then we invert heap[1]; 1231 * then we invert each other node by replacing it by the product of its 1232 * parent (after inversion) and its sibling (before inversion). 1233 */ 1234 heap[0] = NULL; 1235 for (i = pow2/2 - 1; i > 0; i--) 1236 heap[i] = NULL; 1237 for (i = 0; i < num; i++) 1238 heap[pow2/2 + i] = &points[i]->Z; 1239 for (i = pow2/2 + num; i < pow2; i++) 1240 heap[i] = NULL; 1241 1242 /* set each node to the product of its children */ 1243 for (i = pow2/2 - 1; i > 0; i--) 1244 { 1245 heap[i] = BN_new(); 1246 if (heap[i] == NULL) goto err; 1247 1248 if (heap[2*i] != NULL) 1249 { 1250 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1])) 1251 { 1252 if (!BN_copy(heap[i], heap[2*i])) goto err; 1253 } 1254 else 1255 { 1256 if (BN_is_zero(heap[2*i])) 1257 { 1258 if (!BN_copy(heap[i], heap[2*i + 1])) goto err; 1259 } 1260 else 1261 { 1262 if (!group->meth->field_mul(group, heap[i], 1263 heap[2*i], heap[2*i + 1], ctx)) goto err; 1264 } 1265 } 1266 } 1267 } 1268 1269 /* invert heap[1] */ 1270 if (!BN_is_zero(heap[1])) 1271 { 1272 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) 1273 { 1274 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); 1275 goto err; 1276 } 1277 } 1278 if (group->meth->field_encode != 0) 1279 { 1280 /* in the Montgomery case, we just turned R*H (representing H) 1281 * into 1/(R*H), but we need R*(1/H) (representing 1/H); 1282 * i.e. we have need to multiply by the Montgomery factor twice */ 1283 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; 1284 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; 1285 } 1286 1287 /* set other heap[i]'s to their inverses */ 1288 for (i = 2; i < pow2/2 + num; i += 2) 1289 { 1290 /* i is even */ 1291 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) 1292 { 1293 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err; 1294 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err; 1295 if (!BN_copy(heap[i], tmp0)) goto err; 1296 if (!BN_copy(heap[i + 1], tmp1)) goto err; 1297 } 1298 else 1299 { 1300 if (!BN_copy(heap[i], heap[i/2])) goto err; 1301 } 1302 } 1303 1304 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */ 1305 for (i = 0; i < num; i++) 1306 { 1307 EC_POINT *p = points[i]; 1308 1309 if (!BN_is_zero(&p->Z)) 1310 { 1311 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ 1312 1313 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err; 1314 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err; 1315 1316 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err; 1317 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err; 1318 1319 if (group->meth->field_set_to_one != 0) 1320 { 1321 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err; 1322 } 1323 else 1324 { 1325 if (!BN_one(&p->Z)) goto err; 1326 } 1327 p->Z_is_one = 1; 1328 } 1329 } 1330 1331 ret = 1; 1332 1333 err: 1334 BN_CTX_end(ctx); 1335 if (new_ctx != NULL) 1336 BN_CTX_free(new_ctx); 1337 if (heap != NULL) 1338 { 1339 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */ 1340 for (i = pow2/2 - 1; i > 0; i--) 1341 { 1342 if (heap[i] != NULL) 1343 BN_clear_free(heap[i]); 1344 } 1345 OPENSSL_free(heap); 1346 } 1347 return ret; 1348 } 1349 1350 1351 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1352 { 1353 return BN_mod_mul(r, a, b, &group->field, ctx); 1354 } 1355 1356 1357 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) 1358 { 1359 return BN_mod_sqr(r, a, &group->field, ctx); 1360 } 1361
