1 /* $OpenBSD: ec2_smpl.c,v 1.21 2018/11/05 20:18:21 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_check_discriminant = 92 ec_GF2m_simple_group_check_discriminant, 93 .point_init = ec_GF2m_simple_point_init, 94 .point_finish = ec_GF2m_simple_point_finish, 95 .point_clear_finish = ec_GF2m_simple_point_clear_finish, 96 .point_copy = ec_GF2m_simple_point_copy, 97 .point_set_to_infinity = ec_GF2m_simple_point_set_to_infinity, 98 .point_set_affine_coordinates = 99 ec_GF2m_simple_point_set_affine_coordinates, 100 .point_get_affine_coordinates = 101 ec_GF2m_simple_point_get_affine_coordinates, 102 .add = ec_GF2m_simple_add, 103 .dbl = ec_GF2m_simple_dbl, 104 .invert = ec_GF2m_simple_invert, 105 .is_at_infinity = ec_GF2m_simple_is_at_infinity, 106 .is_on_curve = ec_GF2m_simple_is_on_curve, 107 .point_cmp = ec_GF2m_simple_cmp, 108 .make_affine = ec_GF2m_simple_make_affine, 109 .points_make_affine = ec_GF2m_simple_points_make_affine, 110 .mul_generator_ct = ec_GFp_simple_mul_generator_ct, 111 .mul_single_ct = ec_GFp_simple_mul_single_ct, 112 .mul_double_nonct = ec_GFp_simple_mul_double_nonct, 113 .precompute_mult = ec_GF2m_precompute_mult, 114 .have_precompute_mult = ec_GF2m_have_precompute_mult, 115 .field_mul = ec_GF2m_simple_field_mul, 116 .field_sqr = ec_GF2m_simple_field_sqr, 117 .field_div = ec_GF2m_simple_field_div, 118 .blind_coordinates = NULL, 119 }; 120 121 return &ret; 122 } 123 124 125 /* Initialize a GF(2^m)-based EC_GROUP structure. 126 * Note that all other members are handled by EC_GROUP_new. 127 */ 128 int 129 ec_GF2m_simple_group_init(EC_GROUP * group) 130 { 131 BN_init(&group->field); 132 BN_init(&group->a); 133 BN_init(&group->b); 134 return 1; 135 } 136 137 138 /* Free a GF(2^m)-based EC_GROUP structure. 139 * Note that all other members are handled by EC_GROUP_free. 140 */ 141 void 142 ec_GF2m_simple_group_finish(EC_GROUP * group) 143 { 144 BN_free(&group->field); 145 BN_free(&group->a); 146 BN_free(&group->b); 147 } 148 149 150 /* Clear and free a GF(2^m)-based EC_GROUP structure. 151 * Note that all other members are handled by EC_GROUP_clear_free. 152 */ 153 void 154 ec_GF2m_simple_group_clear_finish(EC_GROUP * group) 155 { 156 BN_clear_free(&group->field); 157 BN_clear_free(&group->a); 158 BN_clear_free(&group->b); 159 group->poly[0] = 0; 160 group->poly[1] = 0; 161 group->poly[2] = 0; 162 group->poly[3] = 0; 163 group->poly[4] = 0; 164 group->poly[5] = -1; 165 } 166 167 168 /* Copy a GF(2^m)-based EC_GROUP structure. 169 * Note that all other members are handled by EC_GROUP_copy. 170 */ 171 int 172 ec_GF2m_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) 173 { 174 int i; 175 176 if (!BN_copy(&dest->field, &src->field)) 177 return 0; 178 if (!BN_copy(&dest->a, &src->a)) 179 return 0; 180 if (!BN_copy(&dest->b, &src->b)) 181 return 0; 182 dest->poly[0] = src->poly[0]; 183 dest->poly[1] = src->poly[1]; 184 dest->poly[2] = src->poly[2]; 185 dest->poly[3] = src->poly[3]; 186 dest->poly[4] = src->poly[4]; 187 dest->poly[5] = src->poly[5]; 188 if (bn_wexpand(&dest->a, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 189 return 0; 190 if (bn_wexpand(&dest->b, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 191 return 0; 192 for (i = dest->a.top; i < dest->a.dmax; i++) 193 dest->a.d[i] = 0; 194 for (i = dest->b.top; i < dest->b.dmax; i++) 195 dest->b.d[i] = 0; 196 return 1; 197 } 198 199 200 /* Set the curve parameters of an EC_GROUP structure. */ 201 int 202 ec_GF2m_simple_group_set_curve(EC_GROUP * group, 203 const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) 204 { 205 int ret = 0, i; 206 207 /* group->field */ 208 if (!BN_copy(&group->field, p)) 209 goto err; 210 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; 211 if ((i != 5) && (i != 3)) { 212 ECerror(EC_R_UNSUPPORTED_FIELD); 213 goto err; 214 } 215 /* group->a */ 216 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) 217 goto err; 218 if (bn_wexpand(&group->a, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 219 goto err; 220 for (i = group->a.top; i < group->a.dmax; i++) 221 group->a.d[i] = 0; 222 223 /* group->b */ 224 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) 225 goto err; 226 if (bn_wexpand(&group->b, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 227 goto err; 228 for (i = group->b.top; i < group->b.dmax; i++) 229 group->b.d[i] = 0; 230 231 ret = 1; 232 err: 233 return ret; 234 } 235 236 237 /* Get the curve parameters of an EC_GROUP structure. 238 * If p, a, or b are NULL then there values will not be set but the method will return with success. 239 */ 240 int 241 ec_GF2m_simple_group_get_curve(const EC_GROUP *group, 242 BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 243 { 244 int ret = 0; 245 246 if (p != NULL) { 247 if (!BN_copy(p, &group->field)) 248 return 0; 249 } 250 if (a != NULL) { 251 if (!BN_copy(a, &group->a)) 252 goto err; 253 } 254 if (b != NULL) { 255 if (!BN_copy(b, &group->b)) 256 goto err; 257 } 258 ret = 1; 259 260 err: 261 return ret; 262 } 263 264 265 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ 266 int 267 ec_GF2m_simple_group_get_degree(const EC_GROUP * group) 268 { 269 return BN_num_bits(&group->field) - 1; 270 } 271 272 273 /* Checks the discriminant of the curve. 274 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 275 */ 276 int 277 ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) 278 { 279 int ret = 0; 280 BIGNUM *b; 281 BN_CTX *new_ctx = NULL; 282 283 if (ctx == NULL) { 284 ctx = new_ctx = BN_CTX_new(); 285 if (ctx == NULL) { 286 ECerror(ERR_R_MALLOC_FAILURE); 287 goto err; 288 } 289 } 290 BN_CTX_start(ctx); 291 if ((b = BN_CTX_get(ctx)) == NULL) 292 goto err; 293 294 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) 295 goto err; 296 297 /* 298 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic 299 * curve <=> b != 0 (mod p) 300 */ 301 if (BN_is_zero(b)) 302 goto err; 303 304 ret = 1; 305 306 err: 307 if (ctx != NULL) 308 BN_CTX_end(ctx); 309 BN_CTX_free(new_ctx); 310 return ret; 311 } 312 313 314 /* Initializes an EC_POINT. */ 315 int 316 ec_GF2m_simple_point_init(EC_POINT * point) 317 { 318 BN_init(&point->X); 319 BN_init(&point->Y); 320 BN_init(&point->Z); 321 return 1; 322 } 323 324 325 /* Frees an EC_POINT. */ 326 void 327 ec_GF2m_simple_point_finish(EC_POINT * point) 328 { 329 BN_free(&point->X); 330 BN_free(&point->Y); 331 BN_free(&point->Z); 332 } 333 334 335 /* Clears and frees an EC_POINT. */ 336 void 337 ec_GF2m_simple_point_clear_finish(EC_POINT * point) 338 { 339 BN_clear_free(&point->X); 340 BN_clear_free(&point->Y); 341 BN_clear_free(&point->Z); 342 point->Z_is_one = 0; 343 } 344 345 346 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ 347 int 348 ec_GF2m_simple_point_copy(EC_POINT * dest, const EC_POINT * src) 349 { 350 if (!BN_copy(&dest->X, &src->X)) 351 return 0; 352 if (!BN_copy(&dest->Y, &src->Y)) 353 return 0; 354 if (!BN_copy(&dest->Z, &src->Z)) 355 return 0; 356 dest->Z_is_one = src->Z_is_one; 357 358 return 1; 359 } 360 361 362 /* Set an EC_POINT to the point at infinity. 363 * A point at infinity is represented by having Z=0. 364 */ 365 int 366 ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) 367 { 368 point->Z_is_one = 0; 369 BN_zero(&point->Z); 370 return 1; 371 } 372 373 374 /* Set the coordinates of an EC_POINT using affine coordinates. 375 * Note that the simple implementation only uses affine coordinates. 376 */ 377 int 378 ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, 379 const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) 380 { 381 int ret = 0; 382 if (x == NULL || y == NULL) { 383 ECerror(ERR_R_PASSED_NULL_PARAMETER); 384 return 0; 385 } 386 if (!BN_copy(&point->X, x)) 387 goto err; 388 BN_set_negative(&point->X, 0); 389 if (!BN_copy(&point->Y, y)) 390 goto err; 391 BN_set_negative(&point->Y, 0); 392 if (!BN_copy(&point->Z, BN_value_one())) 393 goto err; 394 BN_set_negative(&point->Z, 0); 395 point->Z_is_one = 1; 396 ret = 1; 397 398 err: 399 return ret; 400 } 401 402 403 /* Gets the affine coordinates of an EC_POINT. 404 * Note that the simple implementation only uses affine coordinates. 405 */ 406 int 407 ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, 408 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 409 { 410 int ret = 0; 411 412 if (EC_POINT_is_at_infinity(group, point) > 0) { 413 ECerror(EC_R_POINT_AT_INFINITY); 414 return 0; 415 } 416 if (BN_cmp(&point->Z, BN_value_one())) { 417 ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 418 return 0; 419 } 420 if (x != NULL) { 421 if (!BN_copy(x, &point->X)) 422 goto err; 423 BN_set_negative(x, 0); 424 } 425 if (y != NULL) { 426 if (!BN_copy(y, &point->Y)) 427 goto err; 428 BN_set_negative(y, 0); 429 } 430 ret = 1; 431 432 err: 433 return ret; 434 } 435 436 /* Computes a + b and stores the result in r. r could be a or b, a could be b. 437 * Uses algorithm A.10.2 of IEEE P1363. 438 */ 439 int 440 ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 441 const EC_POINT *b, BN_CTX *ctx) 442 { 443 BN_CTX *new_ctx = NULL; 444 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; 445 int ret = 0; 446 447 if (EC_POINT_is_at_infinity(group, a) > 0) { 448 if (!EC_POINT_copy(r, b)) 449 return 0; 450 return 1; 451 } 452 if (EC_POINT_is_at_infinity(group, b) > 0) { 453 if (!EC_POINT_copy(r, a)) 454 return 0; 455 return 1; 456 } 457 if (ctx == NULL) { 458 ctx = new_ctx = BN_CTX_new(); 459 if (ctx == NULL) 460 return 0; 461 } 462 BN_CTX_start(ctx); 463 if ((x0 = BN_CTX_get(ctx)) == NULL) 464 goto err; 465 if ((y0 = BN_CTX_get(ctx)) == NULL) 466 goto err; 467 if ((x1 = BN_CTX_get(ctx)) == NULL) 468 goto err; 469 if ((y1 = BN_CTX_get(ctx)) == NULL) 470 goto err; 471 if ((x2 = BN_CTX_get(ctx)) == NULL) 472 goto err; 473 if ((y2 = BN_CTX_get(ctx)) == NULL) 474 goto err; 475 if ((s = BN_CTX_get(ctx)) == NULL) 476 goto err; 477 if ((t = BN_CTX_get(ctx)) == NULL) 478 goto err; 479 480 if (a->Z_is_one) { 481 if (!BN_copy(x0, &a->X)) 482 goto err; 483 if (!BN_copy(y0, &a->Y)) 484 goto err; 485 } else { 486 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) 487 goto err; 488 } 489 if (b->Z_is_one) { 490 if (!BN_copy(x1, &b->X)) 491 goto err; 492 if (!BN_copy(y1, &b->Y)) 493 goto err; 494 } else { 495 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) 496 goto err; 497 } 498 499 500 if (BN_GF2m_cmp(x0, x1)) { 501 if (!BN_GF2m_add(t, x0, x1)) 502 goto err; 503 if (!BN_GF2m_add(s, y0, y1)) 504 goto err; 505 if (!group->meth->field_div(group, s, s, t, ctx)) 506 goto err; 507 if (!group->meth->field_sqr(group, x2, s, ctx)) 508 goto err; 509 if (!BN_GF2m_add(x2, x2, &group->a)) 510 goto err; 511 if (!BN_GF2m_add(x2, x2, s)) 512 goto err; 513 if (!BN_GF2m_add(x2, x2, t)) 514 goto err; 515 } else { 516 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { 517 if (!EC_POINT_set_to_infinity(group, r)) 518 goto err; 519 ret = 1; 520 goto err; 521 } 522 if (!group->meth->field_div(group, s, y1, x1, ctx)) 523 goto err; 524 if (!BN_GF2m_add(s, s, x1)) 525 goto err; 526 527 if (!group->meth->field_sqr(group, x2, s, ctx)) 528 goto err; 529 if (!BN_GF2m_add(x2, x2, s)) 530 goto err; 531 if (!BN_GF2m_add(x2, x2, &group->a)) 532 goto err; 533 } 534 535 if (!BN_GF2m_add(y2, x1, x2)) 536 goto err; 537 if (!group->meth->field_mul(group, y2, y2, s, ctx)) 538 goto err; 539 if (!BN_GF2m_add(y2, y2, x2)) 540 goto err; 541 if (!BN_GF2m_add(y2, y2, y1)) 542 goto err; 543 544 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) 545 goto err; 546 547 ret = 1; 548 549 err: 550 BN_CTX_end(ctx); 551 BN_CTX_free(new_ctx); 552 return ret; 553 } 554 555 556 /* Computes 2 * a and stores the result in r. r could be a. 557 * Uses algorithm A.10.2 of IEEE P1363. 558 */ 559 int 560 ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 561 BN_CTX *ctx) 562 { 563 return ec_GF2m_simple_add(group, r, a, a, ctx); 564 } 565 566 int 567 ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 568 { 569 if (EC_POINT_is_at_infinity(group, point) > 0 || BN_is_zero(&point->Y)) 570 /* point is its own inverse */ 571 return 1; 572 573 if (!EC_POINT_make_affine(group, point, ctx)) 574 return 0; 575 return BN_GF2m_add(&point->Y, &point->X, &point->Y); 576 } 577 578 579 /* Indicates whether the given point is the point at infinity. */ 580 int 581 ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 582 { 583 return BN_is_zero(&point->Z); 584 } 585 586 587 /* Determines whether the given EC_POINT is an actual point on the curve defined 588 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: 589 * y^2 + x*y = x^3 + a*x^2 + b. 590 */ 591 int 592 ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 593 { 594 int ret = -1; 595 BN_CTX *new_ctx = NULL; 596 BIGNUM *lh, *y2; 597 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 598 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 599 600 if (EC_POINT_is_at_infinity(group, point) > 0) 601 return 1; 602 603 field_mul = group->meth->field_mul; 604 field_sqr = group->meth->field_sqr; 605 606 /* only support affine coordinates */ 607 if (!point->Z_is_one) 608 return -1; 609 610 if (ctx == NULL) { 611 ctx = new_ctx = BN_CTX_new(); 612 if (ctx == NULL) 613 return -1; 614 } 615 BN_CTX_start(ctx); 616 if ((y2 = BN_CTX_get(ctx)) == NULL) 617 goto err; 618 if ((lh = BN_CTX_get(ctx)) == NULL) 619 goto err; 620 621 /* 622 * We have a curve defined by a Weierstrass equation y^2 + x*y = x^3 623 * + a*x^2 + b. <=> x^3 + a*x^2 + x*y + b + y^2 = 0 <=> ((x + a) * x 624 * + y ) * x + b + y^2 = 0 625 */ 626 if (!BN_GF2m_add(lh, &point->X, &group->a)) 627 goto err; 628 if (!field_mul(group, lh, lh, &point->X, ctx)) 629 goto err; 630 if (!BN_GF2m_add(lh, lh, &point->Y)) 631 goto err; 632 if (!field_mul(group, lh, lh, &point->X, ctx)) 633 goto err; 634 if (!BN_GF2m_add(lh, lh, &group->b)) 635 goto err; 636 if (!field_sqr(group, y2, &point->Y, ctx)) 637 goto err; 638 if (!BN_GF2m_add(lh, lh, y2)) 639 goto err; 640 ret = BN_is_zero(lh); 641 err: 642 if (ctx) 643 BN_CTX_end(ctx); 644 BN_CTX_free(new_ctx); 645 return ret; 646 } 647 648 649 /* Indicates whether two points are equal. 650 * Return values: 651 * -1 error 652 * 0 equal (in affine coordinates) 653 * 1 not equal 654 */ 655 int 656 ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, 657 const EC_POINT *b, BN_CTX *ctx) 658 { 659 BIGNUM *aX, *aY, *bX, *bY; 660 BN_CTX *new_ctx = NULL; 661 int ret = -1; 662 663 if (EC_POINT_is_at_infinity(group, a) > 0) { 664 return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1; 665 } 666 if (EC_POINT_is_at_infinity(group, b) > 0) 667 return 1; 668 669 if (a->Z_is_one && b->Z_is_one) { 670 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 671 } 672 if (ctx == NULL) { 673 ctx = new_ctx = BN_CTX_new(); 674 if (ctx == NULL) 675 return -1; 676 } 677 BN_CTX_start(ctx); 678 if ((aX = BN_CTX_get(ctx)) == NULL) 679 goto err; 680 if ((aY = BN_CTX_get(ctx)) == NULL) 681 goto err; 682 if ((bX = BN_CTX_get(ctx)) == NULL) 683 goto err; 684 if ((bY = BN_CTX_get(ctx)) == NULL) 685 goto err; 686 687 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) 688 goto err; 689 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) 690 goto err; 691 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; 692 693 err: 694 if (ctx) 695 BN_CTX_end(ctx); 696 BN_CTX_free(new_ctx); 697 return ret; 698 } 699 700 701 /* Forces the given EC_POINT to internally use affine coordinates. */ 702 int 703 ec_GF2m_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) 704 { 705 BN_CTX *new_ctx = NULL; 706 BIGNUM *x, *y; 707 int ret = 0; 708 709 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point) > 0) 710 return 1; 711 712 if (ctx == NULL) { 713 ctx = new_ctx = BN_CTX_new(); 714 if (ctx == NULL) 715 return 0; 716 } 717 BN_CTX_start(ctx); 718 if ((x = BN_CTX_get(ctx)) == NULL) 719 goto err; 720 if ((y = BN_CTX_get(ctx)) == NULL) 721 goto err; 722 723 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) 724 goto err; 725 if (!BN_copy(&point->X, x)) 726 goto err; 727 if (!BN_copy(&point->Y, y)) 728 goto err; 729 if (!BN_one(&point->Z)) 730 goto err; 731 732 ret = 1; 733 734 err: 735 if (ctx) 736 BN_CTX_end(ctx); 737 BN_CTX_free(new_ctx); 738 return ret; 739 } 740 741 742 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ 743 int 744 ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, 745 EC_POINT *points[], BN_CTX *ctx) 746 { 747 size_t i; 748 749 for (i = 0; i < num; i++) { 750 if (!group->meth->make_affine(group, points[i], ctx)) 751 return 0; 752 } 753 754 return 1; 755 } 756 757 758 /* Wrapper to simple binary polynomial field multiplication implementation. */ 759 int 760 ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 761 const BIGNUM *b, BN_CTX *ctx) 762 { 763 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); 764 } 765 766 767 /* Wrapper to simple binary polynomial field squaring implementation. */ 768 int 769 ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 770 BN_CTX *ctx) 771 { 772 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); 773 } 774 775 776 /* Wrapper to simple binary polynomial field division implementation. */ 777 int 778 ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 779 const BIGNUM *b, BN_CTX *ctx) 780 { 781 return BN_GF2m_mod_div(r, a, b, &group->field, ctx); 782 } 783 784 #endif 785