crypto/ec/ecp_smpl.c

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