1 /* $OpenBSD: ec2_smpl.c,v 1.23 2021/09/08 17:29:21 tb Exp $ */ 2 /* ==================================================================== 3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 4 * 5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included 6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed 7 * to the OpenSSL project. 8 * 9 * The ECC Code is licensed pursuant to the OpenSSL open source 10 * license provided below. 11 * 12 * The software is originally written by Sheueling Chang Shantz and 13 * Douglas Stebila of Sun Microsystems Laboratories. 14 * 15 */ 16 /* ==================================================================== 17 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. 18 * 19 * Redistribution and use in source and binary forms, with or without 20 * modification, are permitted provided that the following conditions 21 * are met: 22 * 23 * 1. Redistributions of source code must retain the above copyright 24 * notice, this list of conditions and the following disclaimer. 25 * 26 * 2. Redistributions in binary form must reproduce the above copyright 27 * notice, this list of conditions and the following disclaimer in 28 * the documentation and/or other materials provided with the 29 * distribution. 30 * 31 * 3. All advertising materials mentioning features or use of this 32 * software must display the following acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 35 * 36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 37 * endorse or promote products derived from this software without 38 * prior written permission. For written permission, please contact 39 * openssl-core@openssl.org. 40 * 41 * 5. Products derived from this software may not be called "OpenSSL" 42 * nor may "OpenSSL" appear in their names without prior written 43 * permission of the OpenSSL Project. 44 * 45 * 6. Redistributions of any form whatsoever must retain the following 46 * acknowledgment: 47 * "This product includes software developed by the OpenSSL Project 48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 49 * 50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 61 * OF THE POSSIBILITY OF SUCH DAMAGE. 62 * ==================================================================== 63 * 64 * This product includes cryptographic software written by Eric Young 65 * (eay@cryptsoft.com). This product includes software written by Tim 66 * Hudson (tjh@cryptsoft.com). 67 * 68 */ 69 70 #include <openssl/opensslconf.h> 71 72 #include <openssl/err.h> 73 74 #include "ec_lcl.h" 75 76 #ifndef OPENSSL_NO_EC2M 77 78 const EC_METHOD * 79 EC_GF2m_simple_method(void) 80 { 81 static const EC_METHOD ret = { 82 .flags = EC_FLAGS_DEFAULT_OCT, 83 .field_type = NID_X9_62_characteristic_two_field, 84 .group_init = ec_GF2m_simple_group_init, 85 .group_finish = ec_GF2m_simple_group_finish, 86 .group_clear_finish = ec_GF2m_simple_group_clear_finish, 87 .group_copy = ec_GF2m_simple_group_copy, 88 .group_set_curve = ec_GF2m_simple_group_set_curve, 89 .group_get_curve = ec_GF2m_simple_group_get_curve, 90 .group_get_degree = ec_GF2m_simple_group_get_degree, 91 .group_order_bits = ec_group_simple_order_bits, 92 .group_check_discriminant = 93 ec_GF2m_simple_group_check_discriminant, 94 .point_init = ec_GF2m_simple_point_init, 95 .point_finish = ec_GF2m_simple_point_finish, 96 .point_clear_finish = ec_GF2m_simple_point_clear_finish, 97 .point_copy = ec_GF2m_simple_point_copy, 98 .point_set_to_infinity = ec_GF2m_simple_point_set_to_infinity, 99 .point_set_affine_coordinates = 100 ec_GF2m_simple_point_set_affine_coordinates, 101 .point_get_affine_coordinates = 102 ec_GF2m_simple_point_get_affine_coordinates, 103 .add = ec_GF2m_simple_add, 104 .dbl = ec_GF2m_simple_dbl, 105 .invert = ec_GF2m_simple_invert, 106 .is_at_infinity = ec_GF2m_simple_is_at_infinity, 107 .is_on_curve = ec_GF2m_simple_is_on_curve, 108 .point_cmp = ec_GF2m_simple_cmp, 109 .make_affine = ec_GF2m_simple_make_affine, 110 .points_make_affine = ec_GF2m_simple_points_make_affine, 111 .mul_generator_ct = ec_GFp_simple_mul_generator_ct, 112 .mul_single_ct = ec_GFp_simple_mul_single_ct, 113 .mul_double_nonct = ec_GFp_simple_mul_double_nonct, 114 .precompute_mult = ec_GF2m_precompute_mult, 115 .have_precompute_mult = ec_GF2m_have_precompute_mult, 116 .field_mul = ec_GF2m_simple_field_mul, 117 .field_sqr = ec_GF2m_simple_field_sqr, 118 .field_div = ec_GF2m_simple_field_div, 119 .blind_coordinates = NULL, 120 }; 121 122 return &ret; 123 } 124 125 126 /* Initialize a GF(2^m)-based EC_GROUP structure. 127 * Note that all other members are handled by EC_GROUP_new. 128 */ 129 int 130 ec_GF2m_simple_group_init(EC_GROUP * group) 131 { 132 BN_init(&group->field); 133 BN_init(&group->a); 134 BN_init(&group->b); 135 return 1; 136 } 137 138 139 /* Free a GF(2^m)-based EC_GROUP structure. 140 * Note that all other members are handled by EC_GROUP_free. 141 */ 142 void 143 ec_GF2m_simple_group_finish(EC_GROUP * group) 144 { 145 BN_free(&group->field); 146 BN_free(&group->a); 147 BN_free(&group->b); 148 } 149 150 151 /* Clear and free a GF(2^m)-based EC_GROUP structure. 152 * Note that all other members are handled by EC_GROUP_clear_free. 153 */ 154 void 155 ec_GF2m_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 group->poly[0] = 0; 161 group->poly[1] = 0; 162 group->poly[2] = 0; 163 group->poly[3] = 0; 164 group->poly[4] = 0; 165 group->poly[5] = -1; 166 } 167 168 169 /* Copy a GF(2^m)-based EC_GROUP structure. 170 * Note that all other members are handled by EC_GROUP_copy. 171 */ 172 int 173 ec_GF2m_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) 174 { 175 int i; 176 177 if (!BN_copy(&dest->field, &src->field)) 178 return 0; 179 if (!BN_copy(&dest->a, &src->a)) 180 return 0; 181 if (!BN_copy(&dest->b, &src->b)) 182 return 0; 183 dest->poly[0] = src->poly[0]; 184 dest->poly[1] = src->poly[1]; 185 dest->poly[2] = src->poly[2]; 186 dest->poly[3] = src->poly[3]; 187 dest->poly[4] = src->poly[4]; 188 dest->poly[5] = src->poly[5]; 189 if (bn_wexpand(&dest->a, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 190 return 0; 191 if (bn_wexpand(&dest->b, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 192 return 0; 193 for (i = dest->a.top; i < dest->a.dmax; i++) 194 dest->a.d[i] = 0; 195 for (i = dest->b.top; i < dest->b.dmax; i++) 196 dest->b.d[i] = 0; 197 return 1; 198 } 199 200 201 /* Set the curve parameters of an EC_GROUP structure. */ 202 int 203 ec_GF2m_simple_group_set_curve(EC_GROUP * group, 204 const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) 205 { 206 int ret = 0, i; 207 208 /* group->field */ 209 if (!BN_copy(&group->field, p)) 210 goto err; 211 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; 212 if ((i != 5) && (i != 3)) { 213 ECerror(EC_R_UNSUPPORTED_FIELD); 214 goto err; 215 } 216 /* group->a */ 217 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) 218 goto err; 219 if (bn_wexpand(&group->a, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 220 goto err; 221 for (i = group->a.top; i < group->a.dmax; i++) 222 group->a.d[i] = 0; 223 224 /* group->b */ 225 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) 226 goto err; 227 if (bn_wexpand(&group->b, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 228 goto err; 229 for (i = group->b.top; i < group->b.dmax; i++) 230 group->b.d[i] = 0; 231 232 ret = 1; 233 err: 234 return ret; 235 } 236 237 238 /* Get the curve parameters of an EC_GROUP structure. 239 * If p, a, or b are NULL then there values will not be set but the method will return with success. 240 */ 241 int 242 ec_GF2m_simple_group_get_curve(const EC_GROUP *group, 243 BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 244 { 245 int ret = 0; 246 247 if (p != NULL) { 248 if (!BN_copy(p, &group->field)) 249 return 0; 250 } 251 if (a != NULL) { 252 if (!BN_copy(a, &group->a)) 253 goto err; 254 } 255 if (b != NULL) { 256 if (!BN_copy(b, &group->b)) 257 goto err; 258 } 259 ret = 1; 260 261 err: 262 return ret; 263 } 264 265 266 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ 267 int 268 ec_GF2m_simple_group_get_degree(const EC_GROUP * group) 269 { 270 return BN_num_bits(&group->field) - 1; 271 } 272 273 274 /* Checks the discriminant of the curve. 275 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 276 */ 277 int 278 ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) 279 { 280 int ret = 0; 281 BIGNUM *b; 282 BN_CTX *new_ctx = NULL; 283 284 if (ctx == NULL) { 285 ctx = new_ctx = BN_CTX_new(); 286 if (ctx == NULL) { 287 ECerror(ERR_R_MALLOC_FAILURE); 288 goto err; 289 } 290 } 291 BN_CTX_start(ctx); 292 if ((b = BN_CTX_get(ctx)) == NULL) 293 goto err; 294 295 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) 296 goto err; 297 298 /* 299 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic 300 * curve <=> b != 0 (mod p) 301 */ 302 if (BN_is_zero(b)) 303 goto err; 304 305 ret = 1; 306 307 err: 308 if (ctx != NULL) 309 BN_CTX_end(ctx); 310 BN_CTX_free(new_ctx); 311 return ret; 312 } 313 314 315 /* Initializes an EC_POINT. */ 316 int 317 ec_GF2m_simple_point_init(EC_POINT * point) 318 { 319 BN_init(&point->X); 320 BN_init(&point->Y); 321 BN_init(&point->Z); 322 return 1; 323 } 324 325 326 /* Frees an EC_POINT. */ 327 void 328 ec_GF2m_simple_point_finish(EC_POINT * point) 329 { 330 BN_free(&point->X); 331 BN_free(&point->Y); 332 BN_free(&point->Z); 333 } 334 335 336 /* Clears and frees an EC_POINT. */ 337 void 338 ec_GF2m_simple_point_clear_finish(EC_POINT * point) 339 { 340 BN_clear_free(&point->X); 341 BN_clear_free(&point->Y); 342 BN_clear_free(&point->Z); 343 point->Z_is_one = 0; 344 } 345 346 347 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ 348 int 349 ec_GF2m_simple_point_copy(EC_POINT * dest, const EC_POINT * src) 350 { 351 if (!BN_copy(&dest->X, &src->X)) 352 return 0; 353 if (!BN_copy(&dest->Y, &src->Y)) 354 return 0; 355 if (!BN_copy(&dest->Z, &src->Z)) 356 return 0; 357 dest->Z_is_one = src->Z_is_one; 358 359 return 1; 360 } 361 362 363 /* Set an EC_POINT to the point at infinity. 364 * A point at infinity is represented by having Z=0. 365 */ 366 int 367 ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) 368 { 369 point->Z_is_one = 0; 370 BN_zero(&point->Z); 371 return 1; 372 } 373 374 375 /* Set the coordinates of an EC_POINT using affine coordinates. 376 * Note that the simple implementation only uses affine coordinates. 377 */ 378 int 379 ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, 380 const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) 381 { 382 int ret = 0; 383 if (x == NULL || y == NULL) { 384 ECerror(ERR_R_PASSED_NULL_PARAMETER); 385 return 0; 386 } 387 if (!BN_copy(&point->X, x)) 388 goto err; 389 BN_set_negative(&point->X, 0); 390 if (!BN_copy(&point->Y, y)) 391 goto err; 392 BN_set_negative(&point->Y, 0); 393 if (!BN_copy(&point->Z, BN_value_one())) 394 goto err; 395 BN_set_negative(&point->Z, 0); 396 point->Z_is_one = 1; 397 ret = 1; 398 399 err: 400 return ret; 401 } 402 403 404 /* Gets the affine coordinates of an EC_POINT. 405 * Note that the simple implementation only uses affine coordinates. 406 */ 407 int 408 ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, 409 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 410 { 411 int ret = 0; 412 413 if (EC_POINT_is_at_infinity(group, point) > 0) { 414 ECerror(EC_R_POINT_AT_INFINITY); 415 return 0; 416 } 417 if (BN_cmp(&point->Z, BN_value_one())) { 418 ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 419 return 0; 420 } 421 if (x != NULL) { 422 if (!BN_copy(x, &point->X)) 423 goto err; 424 BN_set_negative(x, 0); 425 } 426 if (y != NULL) { 427 if (!BN_copy(y, &point->Y)) 428 goto err; 429 BN_set_negative(y, 0); 430 } 431 ret = 1; 432 433 err: 434 return ret; 435 } 436 437 /* Computes a + b and stores the result in r. r could be a or b, a could be b. 438 * Uses algorithm A.10.2 of IEEE P1363. 439 */ 440 int 441 ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 442 const EC_POINT *b, BN_CTX *ctx) 443 { 444 BN_CTX *new_ctx = NULL; 445 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; 446 int ret = 0; 447 448 if (EC_POINT_is_at_infinity(group, a) > 0) { 449 if (!EC_POINT_copy(r, b)) 450 return 0; 451 return 1; 452 } 453 if (EC_POINT_is_at_infinity(group, b) > 0) { 454 if (!EC_POINT_copy(r, a)) 455 return 0; 456 return 1; 457 } 458 if (ctx == NULL) { 459 ctx = new_ctx = BN_CTX_new(); 460 if (ctx == NULL) 461 return 0; 462 } 463 BN_CTX_start(ctx); 464 if ((x0 = BN_CTX_get(ctx)) == NULL) 465 goto err; 466 if ((y0 = BN_CTX_get(ctx)) == NULL) 467 goto err; 468 if ((x1 = BN_CTX_get(ctx)) == NULL) 469 goto err; 470 if ((y1 = BN_CTX_get(ctx)) == NULL) 471 goto err; 472 if ((x2 = BN_CTX_get(ctx)) == NULL) 473 goto err; 474 if ((y2 = BN_CTX_get(ctx)) == NULL) 475 goto err; 476 if ((s = BN_CTX_get(ctx)) == NULL) 477 goto err; 478 if ((t = BN_CTX_get(ctx)) == NULL) 479 goto err; 480 481 if (a->Z_is_one) { 482 if (!BN_copy(x0, &a->X)) 483 goto err; 484 if (!BN_copy(y0, &a->Y)) 485 goto err; 486 } else { 487 if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx)) 488 goto err; 489 } 490 if (b->Z_is_one) { 491 if (!BN_copy(x1, &b->X)) 492 goto err; 493 if (!BN_copy(y1, &b->Y)) 494 goto err; 495 } else { 496 if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx)) 497 goto err; 498 } 499 500 501 if (BN_GF2m_cmp(x0, x1)) { 502 if (!BN_GF2m_add(t, x0, x1)) 503 goto err; 504 if (!BN_GF2m_add(s, y0, y1)) 505 goto err; 506 if (!group->meth->field_div(group, s, s, t, ctx)) 507 goto err; 508 if (!group->meth->field_sqr(group, x2, s, ctx)) 509 goto err; 510 if (!BN_GF2m_add(x2, x2, &group->a)) 511 goto err; 512 if (!BN_GF2m_add(x2, x2, s)) 513 goto err; 514 if (!BN_GF2m_add(x2, x2, t)) 515 goto err; 516 } else { 517 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { 518 if (!EC_POINT_set_to_infinity(group, r)) 519 goto err; 520 ret = 1; 521 goto err; 522 } 523 if (!group->meth->field_div(group, s, y1, x1, ctx)) 524 goto err; 525 if (!BN_GF2m_add(s, s, x1)) 526 goto err; 527 528 if (!group->meth->field_sqr(group, x2, s, ctx)) 529 goto err; 530 if (!BN_GF2m_add(x2, x2, s)) 531 goto err; 532 if (!BN_GF2m_add(x2, x2, &group->a)) 533 goto err; 534 } 535 536 if (!BN_GF2m_add(y2, x1, x2)) 537 goto err; 538 if (!group->meth->field_mul(group, y2, y2, s, ctx)) 539 goto err; 540 if (!BN_GF2m_add(y2, y2, x2)) 541 goto err; 542 if (!BN_GF2m_add(y2, y2, y1)) 543 goto err; 544 545 if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx)) 546 goto err; 547 548 ret = 1; 549 550 err: 551 BN_CTX_end(ctx); 552 BN_CTX_free(new_ctx); 553 return ret; 554 } 555 556 557 /* Computes 2 * a and stores the result in r. r could be a. 558 * Uses algorithm A.10.2 of IEEE P1363. 559 */ 560 int 561 ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 562 BN_CTX *ctx) 563 { 564 return ec_GF2m_simple_add(group, r, a, a, ctx); 565 } 566 567 int 568 ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 569 { 570 if (EC_POINT_is_at_infinity(group, point) > 0 || BN_is_zero(&point->Y)) 571 /* point is its own inverse */ 572 return 1; 573 574 if (!EC_POINT_make_affine(group, point, ctx)) 575 return 0; 576 return BN_GF2m_add(&point->Y, &point->X, &point->Y); 577 } 578 579 580 /* Indicates whether the given point is the point at infinity. */ 581 int 582 ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 583 { 584 return BN_is_zero(&point->Z); 585 } 586 587 588 /* Determines whether the given EC_POINT is an actual point on the curve defined 589 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: 590 * y^2 + x*y = x^3 + a*x^2 + b. 591 */ 592 int 593 ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 594 { 595 int ret = -1; 596 BN_CTX *new_ctx = NULL; 597 BIGNUM *lh, *y2; 598 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 599 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 600 601 if (EC_POINT_is_at_infinity(group, point) > 0) 602 return 1; 603 604 field_mul = group->meth->field_mul; 605 field_sqr = group->meth->field_sqr; 606 607 /* only support affine coordinates */ 608 if (!point->Z_is_one) 609 return -1; 610 611 if (ctx == NULL) { 612 ctx = new_ctx = BN_CTX_new(); 613 if (ctx == NULL) 614 return -1; 615 } 616 BN_CTX_start(ctx); 617 if ((y2 = BN_CTX_get(ctx)) == NULL) 618 goto err; 619 if ((lh = BN_CTX_get(ctx)) == NULL) 620 goto err; 621 622 /* 623 * We have a curve defined by a Weierstrass equation y^2 + x*y = x^3 624 * + a*x^2 + b. <=> x^3 + a*x^2 + x*y + b + y^2 = 0 <=> ((x + a) * x 625 * + y ) * x + b + y^2 = 0 626 */ 627 if (!BN_GF2m_add(lh, &point->X, &group->a)) 628 goto err; 629 if (!field_mul(group, lh, lh, &point->X, ctx)) 630 goto err; 631 if (!BN_GF2m_add(lh, lh, &point->Y)) 632 goto err; 633 if (!field_mul(group, lh, lh, &point->X, ctx)) 634 goto err; 635 if (!BN_GF2m_add(lh, lh, &group->b)) 636 goto err; 637 if (!field_sqr(group, y2, &point->Y, ctx)) 638 goto err; 639 if (!BN_GF2m_add(lh, lh, y2)) 640 goto err; 641 ret = BN_is_zero(lh); 642 err: 643 if (ctx) 644 BN_CTX_end(ctx); 645 BN_CTX_free(new_ctx); 646 return ret; 647 } 648 649 650 /* Indicates whether two points are equal. 651 * Return values: 652 * -1 error 653 * 0 equal (in affine coordinates) 654 * 1 not equal 655 */ 656 int 657 ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, 658 const EC_POINT *b, BN_CTX *ctx) 659 { 660 BIGNUM *aX, *aY, *bX, *bY; 661 BN_CTX *new_ctx = NULL; 662 int ret = -1; 663 664 if (EC_POINT_is_at_infinity(group, a) > 0) { 665 return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1; 666 } 667 if (EC_POINT_is_at_infinity(group, b) > 0) 668 return 1; 669 670 if (a->Z_is_one && b->Z_is_one) { 671 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 672 } 673 if (ctx == NULL) { 674 ctx = new_ctx = BN_CTX_new(); 675 if (ctx == NULL) 676 return -1; 677 } 678 BN_CTX_start(ctx); 679 if ((aX = BN_CTX_get(ctx)) == NULL) 680 goto err; 681 if ((aY = BN_CTX_get(ctx)) == NULL) 682 goto err; 683 if ((bX = BN_CTX_get(ctx)) == NULL) 684 goto err; 685 if ((bY = BN_CTX_get(ctx)) == NULL) 686 goto err; 687 688 if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx)) 689 goto err; 690 if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx)) 691 goto err; 692 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; 693 694 err: 695 if (ctx) 696 BN_CTX_end(ctx); 697 BN_CTX_free(new_ctx); 698 return ret; 699 } 700 701 702 /* Forces the given EC_POINT to internally use affine coordinates. */ 703 int 704 ec_GF2m_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) 705 { 706 BN_CTX *new_ctx = NULL; 707 BIGNUM *x, *y; 708 int ret = 0; 709 710 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point) > 0) 711 return 1; 712 713 if (ctx == NULL) { 714 ctx = new_ctx = BN_CTX_new(); 715 if (ctx == NULL) 716 return 0; 717 } 718 BN_CTX_start(ctx); 719 if ((x = BN_CTX_get(ctx)) == NULL) 720 goto err; 721 if ((y = BN_CTX_get(ctx)) == NULL) 722 goto err; 723 724 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) 725 goto err; 726 if (!BN_copy(&point->X, x)) 727 goto err; 728 if (!BN_copy(&point->Y, y)) 729 goto err; 730 if (!BN_one(&point->Z)) 731 goto err; 732 733 ret = 1; 734 735 err: 736 if (ctx) 737 BN_CTX_end(ctx); 738 BN_CTX_free(new_ctx); 739 return ret; 740 } 741 742 743 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ 744 int 745 ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, 746 EC_POINT *points[], BN_CTX *ctx) 747 { 748 size_t i; 749 750 for (i = 0; i < num; i++) { 751 if (!group->meth->make_affine(group, points[i], ctx)) 752 return 0; 753 } 754 755 return 1; 756 } 757 758 759 /* Wrapper to simple binary polynomial field multiplication implementation. */ 760 int 761 ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 762 const BIGNUM *b, BN_CTX *ctx) 763 { 764 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); 765 } 766 767 768 /* Wrapper to simple binary polynomial field squaring implementation. */ 769 int 770 ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 771 BN_CTX *ctx) 772 { 773 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); 774 } 775 776 777 /* Wrapper to simple binary polynomial field division implementation. */ 778 int 779 ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 780 const BIGNUM *b, BN_CTX *ctx) 781 { 782 return BN_GF2m_mod_div(r, a, b, &group->field, ctx); 783 } 784 785 #endif 786