1 /* crypto/ec/ec2_smpl.c */ 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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 66 * Hudson (tjh (at) cryptsoft.com). 67 * 68 */ 69 70 #include <openssl/err.h> 71 72 #include "ec_lcl.h" 73 74 75 const EC_METHOD *EC_GF2m_simple_method(void) 76 { 77 static const EC_METHOD ret = { 78 NID_X9_62_characteristic_two_field, 79 ec_GF2m_simple_group_init, 80 ec_GF2m_simple_group_finish, 81 ec_GF2m_simple_group_clear_finish, 82 ec_GF2m_simple_group_copy, 83 ec_GF2m_simple_group_set_curve, 84 ec_GF2m_simple_group_get_curve, 85 ec_GF2m_simple_group_get_degree, 86 ec_GF2m_simple_group_check_discriminant, 87 ec_GF2m_simple_point_init, 88 ec_GF2m_simple_point_finish, 89 ec_GF2m_simple_point_clear_finish, 90 ec_GF2m_simple_point_copy, 91 ec_GF2m_simple_point_set_to_infinity, 92 0 /* set_Jprojective_coordinates_GFp */, 93 0 /* get_Jprojective_coordinates_GFp */, 94 ec_GF2m_simple_point_set_affine_coordinates, 95 ec_GF2m_simple_point_get_affine_coordinates, 96 ec_GF2m_simple_set_compressed_coordinates, 97 ec_GF2m_simple_point2oct, 98 ec_GF2m_simple_oct2point, 99 ec_GF2m_simple_add, 100 ec_GF2m_simple_dbl, 101 ec_GF2m_simple_invert, 102 ec_GF2m_simple_is_at_infinity, 103 ec_GF2m_simple_is_on_curve, 104 ec_GF2m_simple_cmp, 105 ec_GF2m_simple_make_affine, 106 ec_GF2m_simple_points_make_affine, 107 108 /* the following three method functions are defined in ec2_mult.c */ 109 ec_GF2m_simple_mul, 110 ec_GF2m_precompute_mult, 111 ec_GF2m_have_precompute_mult, 112 113 ec_GF2m_simple_field_mul, 114 ec_GF2m_simple_field_sqr, 115 ec_GF2m_simple_field_div, 116 0 /* field_encode */, 117 0 /* field_decode */, 118 0 /* field_set_to_one */ }; 119 120 return &ret; 121 } 122 123 124 /* Initialize a GF(2^m)-based EC_GROUP structure. 125 * Note that all other members are handled by EC_GROUP_new. 126 */ 127 int ec_GF2m_simple_group_init(EC_GROUP *group) 128 { 129 BN_init(&group->field); 130 BN_init(&group->a); 131 BN_init(&group->b); 132 return 1; 133 } 134 135 136 /* Free a GF(2^m)-based EC_GROUP structure. 137 * Note that all other members are handled by EC_GROUP_free. 138 */ 139 void ec_GF2m_simple_group_finish(EC_GROUP *group) 140 { 141 BN_free(&group->field); 142 BN_free(&group->a); 143 BN_free(&group->b); 144 } 145 146 147 /* Clear and free a GF(2^m)-based EC_GROUP structure. 148 * Note that all other members are handled by EC_GROUP_clear_free. 149 */ 150 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) 151 { 152 BN_clear_free(&group->field); 153 BN_clear_free(&group->a); 154 BN_clear_free(&group->b); 155 group->poly[0] = 0; 156 group->poly[1] = 0; 157 group->poly[2] = 0; 158 group->poly[3] = 0; 159 group->poly[4] = 0; 160 group->poly[5] = -1; 161 } 162 163 164 /* Copy a GF(2^m)-based EC_GROUP structure. 165 * Note that all other members are handled by EC_GROUP_copy. 166 */ 167 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) 168 { 169 int i; 170 if (!BN_copy(&dest->field, &src->field)) return 0; 171 if (!BN_copy(&dest->a, &src->a)) return 0; 172 if (!BN_copy(&dest->b, &src->b)) return 0; 173 dest->poly[0] = src->poly[0]; 174 dest->poly[1] = src->poly[1]; 175 dest->poly[2] = src->poly[2]; 176 dest->poly[3] = src->poly[3]; 177 dest->poly[4] = src->poly[4]; 178 dest->poly[5] = src->poly[5]; 179 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; 180 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; 181 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; 182 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; 183 return 1; 184 } 185 186 187 /* Set the curve parameters of an EC_GROUP structure. */ 188 int ec_GF2m_simple_group_set_curve(EC_GROUP *group, 189 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 190 { 191 int ret = 0, i; 192 193 /* group->field */ 194 if (!BN_copy(&group->field, p)) goto err; 195 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; 196 if ((i != 5) && (i != 3)) 197 { 198 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); 199 goto err; 200 } 201 202 /* group->a */ 203 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; 204 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; 205 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; 206 207 /* group->b */ 208 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; 209 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; 210 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; 211 212 ret = 1; 213 err: 214 return ret; 215 } 216 217 218 /* Get the curve parameters of an EC_GROUP structure. 219 * If p, a, or b are NULL then there values will not be set but the method will return with success. 220 */ 221 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 222 { 223 int ret = 0; 224 225 if (p != NULL) 226 { 227 if (!BN_copy(p, &group->field)) return 0; 228 } 229 230 if (a != NULL) 231 { 232 if (!BN_copy(a, &group->a)) goto err; 233 } 234 235 if (b != NULL) 236 { 237 if (!BN_copy(b, &group->b)) goto err; 238 } 239 240 ret = 1; 241 242 err: 243 return ret; 244 } 245 246 247 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ 248 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) 249 { 250 return BN_num_bits(&group->field)-1; 251 } 252 253 254 /* Checks the discriminant of the curve. 255 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 256 */ 257 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) 258 { 259 int ret = 0; 260 BIGNUM *b; 261 BN_CTX *new_ctx = NULL; 262 263 if (ctx == NULL) 264 { 265 ctx = new_ctx = BN_CTX_new(); 266 if (ctx == NULL) 267 { 268 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); 269 goto err; 270 } 271 } 272 BN_CTX_start(ctx); 273 b = BN_CTX_get(ctx); 274 if (b == NULL) goto err; 275 276 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; 277 278 /* check the discriminant: 279 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 280 */ 281 if (BN_is_zero(b)) goto err; 282 283 ret = 1; 284 285 err: 286 if (ctx != NULL) 287 BN_CTX_end(ctx); 288 if (new_ctx != NULL) 289 BN_CTX_free(new_ctx); 290 return ret; 291 } 292 293 294 /* Initializes an EC_POINT. */ 295 int ec_GF2m_simple_point_init(EC_POINT *point) 296 { 297 BN_init(&point->X); 298 BN_init(&point->Y); 299 BN_init(&point->Z); 300 return 1; 301 } 302 303 304 /* Frees an EC_POINT. */ 305 void ec_GF2m_simple_point_finish(EC_POINT *point) 306 { 307 BN_free(&point->X); 308 BN_free(&point->Y); 309 BN_free(&point->Z); 310 } 311 312 313 /* Clears and frees an EC_POINT. */ 314 void ec_GF2m_simple_point_clear_finish(EC_POINT *point) 315 { 316 BN_clear_free(&point->X); 317 BN_clear_free(&point->Y); 318 BN_clear_free(&point->Z); 319 point->Z_is_one = 0; 320 } 321 322 323 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ 324 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) 325 { 326 if (!BN_copy(&dest->X, &src->X)) return 0; 327 if (!BN_copy(&dest->Y, &src->Y)) return 0; 328 if (!BN_copy(&dest->Z, &src->Z)) return 0; 329 dest->Z_is_one = src->Z_is_one; 330 331 return 1; 332 } 333 334 335 /* Set an EC_POINT to the point at infinity. 336 * A point at infinity is represented by having Z=0. 337 */ 338 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) 339 { 340 point->Z_is_one = 0; 341 BN_zero(&point->Z); 342 return 1; 343 } 344 345 346 /* Set the coordinates of an EC_POINT using affine coordinates. 347 * Note that the simple implementation only uses affine coordinates. 348 */ 349 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, 350 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) 351 { 352 int ret = 0; 353 if (x == NULL || y == NULL) 354 { 355 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); 356 return 0; 357 } 358 359 if (!BN_copy(&point->X, x)) goto err; 360 BN_set_negative(&point->X, 0); 361 if (!BN_copy(&point->Y, y)) goto err; 362 BN_set_negative(&point->Y, 0); 363 if (!BN_copy(&point->Z, BN_value_one())) goto err; 364 BN_set_negative(&point->Z, 0); 365 point->Z_is_one = 1; 366 ret = 1; 367 368 err: 369 return ret; 370 } 371 372 373 /* Gets the affine coordinates of an EC_POINT. 374 * Note that the simple implementation only uses affine coordinates. 375 */ 376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, 377 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 378 { 379 int ret = 0; 380 381 if (EC_POINT_is_at_infinity(group, point)) 382 { 383 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); 384 return 0; 385 } 386 387 if (BN_cmp(&point->Z, BN_value_one())) 388 { 389 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 390 return 0; 391 } 392 if (x != NULL) 393 { 394 if (!BN_copy(x, &point->X)) goto err; 395 BN_set_negative(x, 0); 396 } 397 if (y != NULL) 398 { 399 if (!BN_copy(y, &point->Y)) goto err; 400 BN_set_negative(y, 0); 401 } 402 ret = 1; 403 404 err: 405 return ret; 406 } 407 408 409 /* Calculates and sets the affine coordinates of an EC_POINT from the given 410 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. 411 * Note that the simple implementation only uses affine coordinates. 412 * 413 * The method is from the following publication: 414 * 415 * Harper, Menezes, Vanstone: 416 * "Public-Key Cryptosystems with Very Small Key Lengths", 417 * EUROCRYPT '92, Springer-Verlag LNCS 658, 418 * published February 1993 419 * 420 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe 421 * the same method, but claim no priority date earlier than July 29, 1994 422 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). 423 */ 424 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, 425 const BIGNUM *x_, int y_bit, BN_CTX *ctx) 426 { 427 BN_CTX *new_ctx = NULL; 428 BIGNUM *tmp, *x, *y, *z; 429 int ret = 0, z0; 430 431 /* clear error queue */ 432 ERR_clear_error(); 433 434 if (ctx == NULL) 435 { 436 ctx = new_ctx = BN_CTX_new(); 437 if (ctx == NULL) 438 return 0; 439 } 440 441 y_bit = (y_bit != 0) ? 1 : 0; 442 443 BN_CTX_start(ctx); 444 tmp = BN_CTX_get(ctx); 445 x = BN_CTX_get(ctx); 446 y = BN_CTX_get(ctx); 447 z = BN_CTX_get(ctx); 448 if (z == NULL) goto err; 449 450 if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; 451 if (BN_is_zero(x)) 452 { 453 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; 454 } 455 else 456 { 457 if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; 458 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; 459 if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; 460 if (!BN_GF2m_add(tmp, x, tmp)) goto err; 461 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) 462 { 463 unsigned long err = ERR_peek_last_error(); 464 465 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) 466 { 467 ERR_clear_error(); 468 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); 469 } 470 else 471 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); 472 goto err; 473 } 474 z0 = (BN_is_odd(z)) ? 1 : 0; 475 if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; 476 if (z0 != y_bit) 477 { 478 if (!BN_GF2m_add(y, y, x)) goto err; 479 } 480 } 481 482 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; 483 484 ret = 1; 485 486 err: 487 BN_CTX_end(ctx); 488 if (new_ctx != NULL) 489 BN_CTX_free(new_ctx); 490 return ret; 491 } 492 493 494 /* Converts an EC_POINT to an octet string. 495 * If buf is NULL, the encoded length will be returned. 496 * If the length len of buf is smaller than required an error will be returned. 497 */ 498 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, 499 unsigned char *buf, size_t len, BN_CTX *ctx) 500 { 501 size_t ret; 502 BN_CTX *new_ctx = NULL; 503 int used_ctx = 0; 504 BIGNUM *x, *y, *yxi; 505 size_t field_len, i, skip; 506 507 if ((form != POINT_CONVERSION_COMPRESSED) 508 && (form != POINT_CONVERSION_UNCOMPRESSED) 509 && (form != POINT_CONVERSION_HYBRID)) 510 { 511 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); 512 goto err; 513 } 514 515 if (EC_POINT_is_at_infinity(group, point)) 516 { 517 /* encodes to a single 0 octet */ 518 if (buf != NULL) 519 { 520 if (len < 1) 521 { 522 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); 523 return 0; 524 } 525 buf[0] = 0; 526 } 527 return 1; 528 } 529 530 531 /* ret := required output buffer length */ 532 field_len = (EC_GROUP_get_degree(group) + 7) / 8; 533 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; 534 535 /* if 'buf' is NULL, just return required length */ 536 if (buf != NULL) 537 { 538 if (len < ret) 539 { 540 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); 541 goto err; 542 } 543 544 if (ctx == NULL) 545 { 546 ctx = new_ctx = BN_CTX_new(); 547 if (ctx == NULL) 548 return 0; 549 } 550 551 BN_CTX_start(ctx); 552 used_ctx = 1; 553 x = BN_CTX_get(ctx); 554 y = BN_CTX_get(ctx); 555 yxi = BN_CTX_get(ctx); 556 if (yxi == NULL) goto err; 557 558 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; 559 560 buf[0] = form; 561 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) 562 { 563 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; 564 if (BN_is_odd(yxi)) buf[0]++; 565 } 566 567 i = 1; 568 569 skip = field_len - BN_num_bytes(x); 570 if (skip > field_len) 571 { 572 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); 573 goto err; 574 } 575 while (skip > 0) 576 { 577 buf[i++] = 0; 578 skip--; 579 } 580 skip = BN_bn2bin(x, buf + i); 581 i += skip; 582 if (i != 1 + field_len) 583 { 584 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); 585 goto err; 586 } 587 588 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) 589 { 590 skip = field_len - BN_num_bytes(y); 591 if (skip > field_len) 592 { 593 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); 594 goto err; 595 } 596 while (skip > 0) 597 { 598 buf[i++] = 0; 599 skip--; 600 } 601 skip = BN_bn2bin(y, buf + i); 602 i += skip; 603 } 604 605 if (i != ret) 606 { 607 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); 608 goto err; 609 } 610 } 611 612 if (used_ctx) 613 BN_CTX_end(ctx); 614 if (new_ctx != NULL) 615 BN_CTX_free(new_ctx); 616 return ret; 617 618 err: 619 if (used_ctx) 620 BN_CTX_end(ctx); 621 if (new_ctx != NULL) 622 BN_CTX_free(new_ctx); 623 return 0; 624 } 625 626 627 /* Converts an octet string representation to an EC_POINT. 628 * Note that the simple implementation only uses affine coordinates. 629 */ 630 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, 631 const unsigned char *buf, size_t len, BN_CTX *ctx) 632 { 633 point_conversion_form_t form; 634 int y_bit; 635 BN_CTX *new_ctx = NULL; 636 BIGNUM *x, *y, *yxi; 637 size_t field_len, enc_len; 638 int ret = 0; 639 640 if (len == 0) 641 { 642 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); 643 return 0; 644 } 645 form = buf[0]; 646 y_bit = form & 1; 647 form = form & ~1U; 648 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) 649 && (form != POINT_CONVERSION_UNCOMPRESSED) 650 && (form != POINT_CONVERSION_HYBRID)) 651 { 652 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 653 return 0; 654 } 655 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) 656 { 657 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 658 return 0; 659 } 660 661 if (form == 0) 662 { 663 if (len != 1) 664 { 665 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 666 return 0; 667 } 668 669 return EC_POINT_set_to_infinity(group, point); 670 } 671 672 field_len = (EC_GROUP_get_degree(group) + 7) / 8; 673 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; 674 675 if (len != enc_len) 676 { 677 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 678 return 0; 679 } 680 681 if (ctx == NULL) 682 { 683 ctx = new_ctx = BN_CTX_new(); 684 if (ctx == NULL) 685 return 0; 686 } 687 688 BN_CTX_start(ctx); 689 x = BN_CTX_get(ctx); 690 y = BN_CTX_get(ctx); 691 yxi = BN_CTX_get(ctx); 692 if (yxi == NULL) goto err; 693 694 if (!BN_bin2bn(buf + 1, field_len, x)) goto err; 695 if (BN_ucmp(x, &group->field) >= 0) 696 { 697 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 698 goto err; 699 } 700 701 if (form == POINT_CONVERSION_COMPRESSED) 702 { 703 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; 704 } 705 else 706 { 707 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; 708 if (BN_ucmp(y, &group->field) >= 0) 709 { 710 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 711 goto err; 712 } 713 if (form == POINT_CONVERSION_HYBRID) 714 { 715 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; 716 if (y_bit != BN_is_odd(yxi)) 717 { 718 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); 719 goto err; 720 } 721 } 722 723 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; 724 } 725 726 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ 727 { 728 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); 729 goto err; 730 } 731 732 ret = 1; 733 734 err: 735 BN_CTX_end(ctx); 736 if (new_ctx != NULL) 737 BN_CTX_free(new_ctx); 738 return ret; 739 } 740 741 742 /* Computes a + b and stores the result in r. r could be a or b, a could be b. 743 * Uses algorithm A.10.2 of IEEE P1363. 744 */ 745 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 746 { 747 BN_CTX *new_ctx = NULL; 748 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; 749 int ret = 0; 750 751 if (EC_POINT_is_at_infinity(group, a)) 752 { 753 if (!EC_POINT_copy(r, b)) return 0; 754 return 1; 755 } 756 757 if (EC_POINT_is_at_infinity(group, b)) 758 { 759 if (!EC_POINT_copy(r, a)) return 0; 760 return 1; 761 } 762 763 if (ctx == NULL) 764 { 765 ctx = new_ctx = BN_CTX_new(); 766 if (ctx == NULL) 767 return 0; 768 } 769 770 BN_CTX_start(ctx); 771 x0 = BN_CTX_get(ctx); 772 y0 = BN_CTX_get(ctx); 773 x1 = BN_CTX_get(ctx); 774 y1 = BN_CTX_get(ctx); 775 x2 = BN_CTX_get(ctx); 776 y2 = BN_CTX_get(ctx); 777 s = BN_CTX_get(ctx); 778 t = BN_CTX_get(ctx); 779 if (t == NULL) goto err; 780 781 if (a->Z_is_one) 782 { 783 if (!BN_copy(x0, &a->X)) goto err; 784 if (!BN_copy(y0, &a->Y)) goto err; 785 } 786 else 787 { 788 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; 789 } 790 if (b->Z_is_one) 791 { 792 if (!BN_copy(x1, &b->X)) goto err; 793 if (!BN_copy(y1, &b->Y)) goto err; 794 } 795 else 796 { 797 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; 798 } 799 800 801 if (BN_GF2m_cmp(x0, x1)) 802 { 803 if (!BN_GF2m_add(t, x0, x1)) goto err; 804 if (!BN_GF2m_add(s, y0, y1)) goto err; 805 if (!group->meth->field_div(group, s, s, t, ctx)) goto err; 806 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; 807 if (!BN_GF2m_add(x2, x2, &group->a)) goto err; 808 if (!BN_GF2m_add(x2, x2, s)) goto err; 809 if (!BN_GF2m_add(x2, x2, t)) goto err; 810 } 811 else 812 { 813 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) 814 { 815 if (!EC_POINT_set_to_infinity(group, r)) goto err; 816 ret = 1; 817 goto err; 818 } 819 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; 820 if (!BN_GF2m_add(s, s, x1)) goto err; 821 822 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; 823 if (!BN_GF2m_add(x2, x2, s)) goto err; 824 if (!BN_GF2m_add(x2, x2, &group->a)) goto err; 825 } 826 827 if (!BN_GF2m_add(y2, x1, x2)) goto err; 828 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; 829 if (!BN_GF2m_add(y2, y2, x2)) goto err; 830 if (!BN_GF2m_add(y2, y2, y1)) goto err; 831 832 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; 833 834 ret = 1; 835 836 err: 837 BN_CTX_end(ctx); 838 if (new_ctx != NULL) 839 BN_CTX_free(new_ctx); 840 return ret; 841 } 842 843 844 /* Computes 2 * a and stores the result in r. r could be a. 845 * Uses algorithm A.10.2 of IEEE P1363. 846 */ 847 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) 848 { 849 return ec_GF2m_simple_add(group, r, a, a, ctx); 850 } 851 852 853 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 854 { 855 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) 856 /* point is its own inverse */ 857 return 1; 858 859 if (!EC_POINT_make_affine(group, point, ctx)) return 0; 860 return BN_GF2m_add(&point->Y, &point->X, &point->Y); 861 } 862 863 864 /* Indicates whether the given point is the point at infinity. */ 865 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 866 { 867 return BN_is_zero(&point->Z); 868 } 869 870 871 /* Determines whether the given EC_POINT is an actual point on the curve defined 872 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: 873 * y^2 + x*y = x^3 + a*x^2 + b. 874 */ 875 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 876 { 877 int ret = -1; 878 BN_CTX *new_ctx = NULL; 879 BIGNUM *lh, *y2; 880 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 881 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 882 883 if (EC_POINT_is_at_infinity(group, point)) 884 return 1; 885 886 field_mul = group->meth->field_mul; 887 field_sqr = group->meth->field_sqr; 888 889 /* only support affine coordinates */ 890 if (!point->Z_is_one) goto err; 891 892 if (ctx == NULL) 893 { 894 ctx = new_ctx = BN_CTX_new(); 895 if (ctx == NULL) 896 return -1; 897 } 898 899 BN_CTX_start(ctx); 900 y2 = BN_CTX_get(ctx); 901 lh = BN_CTX_get(ctx); 902 if (lh == NULL) goto err; 903 904 /* We have a curve defined by a Weierstrass equation 905 * y^2 + x*y = x^3 + a*x^2 + b. 906 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 907 * <=> ((x + a) * x + y ) * x + b + y^2 = 0 908 */ 909 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; 910 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; 911 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; 912 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; 913 if (!BN_GF2m_add(lh, lh, &group->b)) goto err; 914 if (!field_sqr(group, y2, &point->Y, ctx)) goto err; 915 if (!BN_GF2m_add(lh, lh, y2)) goto err; 916 ret = BN_is_zero(lh); 917 err: 918 if (ctx) BN_CTX_end(ctx); 919 if (new_ctx) BN_CTX_free(new_ctx); 920 return ret; 921 } 922 923 924 /* Indicates whether two points are equal. 925 * Return values: 926 * -1 error 927 * 0 equal (in affine coordinates) 928 * 1 not equal 929 */ 930 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 931 { 932 BIGNUM *aX, *aY, *bX, *bY; 933 BN_CTX *new_ctx = NULL; 934 int ret = -1; 935 936 if (EC_POINT_is_at_infinity(group, a)) 937 { 938 return EC_POINT_is_at_infinity(group, b) ? 0 : 1; 939 } 940 941 if (EC_POINT_is_at_infinity(group, b)) 942 return 1; 943 944 if (a->Z_is_one && b->Z_is_one) 945 { 946 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 947 } 948 949 if (ctx == NULL) 950 { 951 ctx = new_ctx = BN_CTX_new(); 952 if (ctx == NULL) 953 return -1; 954 } 955 956 BN_CTX_start(ctx); 957 aX = BN_CTX_get(ctx); 958 aY = BN_CTX_get(ctx); 959 bX = BN_CTX_get(ctx); 960 bY = BN_CTX_get(ctx); 961 if (bY == NULL) goto err; 962 963 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; 964 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; 965 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; 966 967 err: 968 if (ctx) BN_CTX_end(ctx); 969 if (new_ctx) BN_CTX_free(new_ctx); 970 return ret; 971 } 972 973 974 /* Forces the given EC_POINT to internally use affine coordinates. */ 975 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 976 { 977 BN_CTX *new_ctx = NULL; 978 BIGNUM *x, *y; 979 int ret = 0; 980 981 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) 982 return 1; 983 984 if (ctx == NULL) 985 { 986 ctx = new_ctx = BN_CTX_new(); 987 if (ctx == NULL) 988 return 0; 989 } 990 991 BN_CTX_start(ctx); 992 x = BN_CTX_get(ctx); 993 y = BN_CTX_get(ctx); 994 if (y == NULL) goto err; 995 996 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; 997 if (!BN_copy(&point->X, x)) goto err; 998 if (!BN_copy(&point->Y, y)) goto err; 999 if (!BN_one(&point->Z)) goto err; 1000 1001 ret = 1; 1002 1003 err: 1004 if (ctx) BN_CTX_end(ctx); 1005 if (new_ctx) BN_CTX_free(new_ctx); 1006 return ret; 1007 } 1008 1009 1010 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ 1011 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) 1012 { 1013 size_t i; 1014 1015 for (i = 0; i < num; i++) 1016 { 1017 if (!group->meth->make_affine(group, points[i], ctx)) return 0; 1018 } 1019 1020 return 1; 1021 } 1022 1023 1024 /* Wrapper to simple binary polynomial field multiplication implementation. */ 1025 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1026 { 1027 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); 1028 } 1029 1030 1031 /* Wrapper to simple binary polynomial field squaring implementation. */ 1032 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) 1033 { 1034 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); 1035 } 1036 1037 1038 /* Wrapper to simple binary polynomial field division implementation. */ 1039 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 1040 { 1041 return BN_GF2m_mod_div(r, a, b, &group->field, ctx); 1042 } 1043
