crypto/ec/ecp_smpl.c

   1 /*
   2  * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the OpenSSL license (the "License").  You may not use
   5  * this file except in compliance with the License.  You can obtain a copy
   6  * in the file LICENSE in the source distribution or at
   7  * https://www.openssl.org/source/license.html
   8  */
   9
  10 /* ====================================================================
  11  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  12  * Portions of this software developed by SUN MICROSYSTEMS, INC.,
  13  * and contributed to the OpenSSL project.
  14  */
  15
  16 #include <openssl/err.h>
  17 #include <openssl/symhacks.h>
  18
  19 #include "ec_lcl.h"
  20
  21 const EC_METHOD *EC_GFp_simple_method(void)
  22 {
  23     static const EC_METHOD ret = {
  24         EC_FLAGS_DEFAULT_OCT,
  25         NID_X9_62_prime_field,
  26         ec_GFp_simple_group_init,
  27         ec_GFp_simple_group_finish,
  28         ec_GFp_simple_group_clear_finish,
  29         ec_GFp_simple_group_copy,
  30         ec_GFp_simple_group_set_curve,
  31         ec_GFp_simple_group_get_curve,
  32         ec_GFp_simple_group_get_degree,
  33         ec_group_simple_order_bits,
  34         ec_GFp_simple_group_check_discriminant,
  35         ec_GFp_simple_point_init,
  36         ec_GFp_simple_point_finish,
  37         ec_GFp_simple_point_clear_finish,
  38         ec_GFp_simple_point_copy,
  39         ec_GFp_simple_point_set_to_infinity,
  40         ec_GFp_simple_set_Jprojective_coordinates_GFp,
  41         ec_GFp_simple_get_Jprojective_coordinates_GFp,
  42         ec_GFp_simple_point_set_affine_coordinates,
  43         ec_GFp_simple_point_get_affine_coordinates,
  44         0, 0, 0,
  45         ec_GFp_simple_add,
  46         ec_GFp_simple_dbl,
  47         ec_GFp_simple_invert,
  48         ec_GFp_simple_is_at_infinity,
  49         ec_GFp_simple_is_on_curve,
  50         ec_GFp_simple_cmp,
  51         ec_GFp_simple_make_affine,
  52         ec_GFp_simple_points_make_affine,
  53         0 /* mul */ ,
  54         0 /* precompute_mult */ ,
  55         0 /* have_precompute_mult */ ,
  56         ec_GFp_simple_field_mul,
  57         ec_GFp_simple_field_sqr,
  58         0 /* field_div */ ,
  59         0 /* field_encode */ ,
  60         0 /* field_decode */ ,
  61         0,                      /* field_set_to_one */
  62         ec_key_simple_priv2oct,
  63         ec_key_simple_oct2priv,
  64         0, /* set private */
  65         ec_key_simple_generate_key,
  66         ec_key_simple_check_key,
  67         ec_key_simple_generate_public_key,
  68         0, /* keycopy */
  69         0, /* keyfinish */
  70         ecdh_simple_compute_key
  71     };
  72
  73     return &ret;
  74 }
  75
  76 /*
  77  * Most method functions in this file are designed to work with
  78  * non-trivial representations of field elements if necessary
  79  * (see ecp_mont.c): while standard modular addition and subtraction
  80  * are used, the field_mul and field_sqr methods will be used for
  81  * multiplication, and field_encode and field_decode (if defined)
  82  * will be used for converting between representations.
  83  *
  84  * Functions ec_GFp_simple_points_make_affine() and
  85  * ec_GFp_simple_point_get_affine_coordinates() specifically assume
  86  * that if a non-trivial representation is used, it is a Montgomery
  87  * representation (i.e. 'encoding' means multiplying by some factor R).
  88  */
  89
  90 int ec_GFp_simple_group_init(EC_GROUP *group)
  91 {
  92     group->field = BN_new();
  93     group->a = BN_new();
  94     group->b = BN_new();
  95     if (group->field == NULL || group->a == NULL || group->b == NULL) {
  96         BN_free(group->field);
  97         BN_free(group->a);
  98         BN_free(group->b);
  99         return 0;
 100     }
 101     group->a_is_minus3 = 0;
 102     return 1;
 103 }
 104
 105 void ec_GFp_simple_group_finish(EC_GROUP *group)
 106 {
 107     BN_free(group->field);
 108     BN_free(group->a);
 109     BN_free(group->b);
 110 }
 111
 112 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
 113 {
 114     BN_clear_free(group->field);
 115     BN_clear_free(group->a);
 116     BN_clear_free(group->b);
 117 }
 118
 119 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
 120 {
 121     if (!BN_copy(dest->field, src->field))
 122         return 0;
 123     if (!BN_copy(dest->a, src->a))
 124         return 0;
 125     if (!BN_copy(dest->b, src->b))
 126         return 0;
 127
 128     dest->a_is_minus3 = src->a_is_minus3;
 129
 130     return 1;
 131 }
 132
 133 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
 134                                   const BIGNUM *p, const BIGNUM *a,
 135                                   const BIGNUM *b, BN_CTX *ctx)
 136 {
 137     int ret = 0;
 138     BN_CTX *new_ctx = NULL;
 139     BIGNUM *tmp_a;
 140
 141     /* p must be a prime > 3 */
 142     if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
 143         ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
 144         return 0;
 145     }
 146
 147     if (ctx == NULL) {
 148         ctx = new_ctx = BN_CTX_new();
 149         if (ctx == NULL)
 150             return 0;
 151     }
 152
 153     BN_CTX_start(ctx);
 154     tmp_a = BN_CTX_get(ctx);
 155     if (tmp_a == NULL)
 156         goto err;
 157
 158     /* group->field */
 159     if (!BN_copy(group->field, p))
 160         goto err;
 161     BN_set_negative(group->field, 0);
 162
 163     /* group->a */
 164     if (!BN_nnmod(tmp_a, a, p, ctx))
 165         goto err;
 166     if (group->meth->field_encode) {
 167         if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
 168             goto err;
 169     } else if (!BN_copy(group->a, tmp_a))
 170         goto err;
 171
 172     /* group->b */
 173     if (!BN_nnmod(group->b, b, p, ctx))
 174         goto err;
 175     if (group->meth->field_encode)
 176         if (!group->meth->field_encode(group, group->b, group->b, ctx))
 177             goto err;
 178
 179     /* group->a_is_minus3 */
 180     if (!BN_add_word(tmp_a, 3))
 181         goto err;
 182     group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
 183
 184     ret = 1;
 185
 186  err:
 187     BN_CTX_end(ctx);
 188     BN_CTX_free(new_ctx);
 189     return ret;
 190 }
 191
 192 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
 193                                   BIGNUM *b, BN_CTX *ctx)
 194 {
 195     int ret = 0;
 196     BN_CTX *new_ctx = NULL;
 197
 198     if (p != NULL) {
 199         if (!BN_copy(p, group->field))
 200             return 0;
 201     }
 202
 203     if (a != NULL || b != NULL) {
 204         if (group->meth->field_decode) {
 205             if (ctx == NULL) {
 206                 ctx = new_ctx = BN_CTX_new();
 207                 if (ctx == NULL)
 208                     return 0;
 209             }
 210             if (a != NULL) {
 211                 if (!group->meth->field_decode(group, a, group->a, ctx))
 212                     goto err;
 213             }
 214             if (b != NULL) {
 215                 if (!group->meth->field_decode(group, b, group->b, ctx))
 216                     goto err;
 217             }
 218         } else {
 219             if (a != NULL) {
 220                 if (!BN_copy(a, group->a))
 221                     goto err;
 222             }
 223             if (b != NULL) {
 224                 if (!BN_copy(b, group->b))
 225                     goto err;
 226             }
 227         }
 228     }
 229
 230     ret = 1;
 231
 232  err:
 233     BN_CTX_free(new_ctx);
 234     return ret;
 235 }
 236
 237 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
 238 {
 239     return BN_num_bits(group->field);
 240 }
 241
 242 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 243 {
 244     int ret = 0;
 245     BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
 246     const BIGNUM *p = group->field;
 247     BN_CTX *new_ctx = NULL;
 248
 249     if (ctx == NULL) {
 250         ctx = new_ctx = BN_CTX_new();
 251         if (ctx == NULL) {
 252             ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
 253                   ERR_R_MALLOC_FAILURE);
 254             goto err;
 255         }
 256     }
 257     BN_CTX_start(ctx);
 258     a = BN_CTX_get(ctx);
 259     b = BN_CTX_get(ctx);
 260     tmp_1 = BN_CTX_get(ctx);
 261     tmp_2 = BN_CTX_get(ctx);
 262     order = BN_CTX_get(ctx);
 263     if (order == NULL)
 264         goto err;
 265
 266     if (group->meth->field_decode) {
 267         if (!group->meth->field_decode(group, a, group->a, ctx))
 268             goto err;
 269         if (!group->meth->field_decode(group, b, group->b, ctx))
 270             goto err;
 271     } else {
 272         if (!BN_copy(a, group->a))
 273             goto err;
 274         if (!BN_copy(b, group->b))
 275             goto err;
 276     }
 277
 278     /*-
 279      * check the discriminant:
 280      * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
 281      * 0 =< a, b < p
 282      */
 283     if (BN_is_zero(a)) {
 284         if (BN_is_zero(b))
 285             goto err;
 286     } else if (!BN_is_zero(b)) {
 287         if (!BN_mod_sqr(tmp_1, a, p, ctx))
 288             goto err;
 289         if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
 290             goto err;
 291         if (!BN_lshift(tmp_1, tmp_2, 2))
 292             goto err;
 293         /* tmp_1 = 4*a^3 */
 294
 295         if (!BN_mod_sqr(tmp_2, b, p, ctx))
 296             goto err;
 297         if (!BN_mul_word(tmp_2, 27))
 298             goto err;
 299         /* tmp_2 = 27*b^2 */
 300
 301         if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
 302             goto err;
 303         if (BN_is_zero(a))
 304             goto err;
 305     }
 306     ret = 1;
 307
 308  err:
 309     if (ctx != NULL)
 310         BN_CTX_end(ctx);
 311     BN_CTX_free(new_ctx);
 312     return ret;
 313 }
 314
 315 int ec_GFp_simple_point_init(EC_POINT *point)
 316 {
 317     point->X = BN_new();
 318     point->Y = BN_new();
 319     point->Z = BN_new();
 320     point->Z_is_one = 0;
 321
 322     if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
 323         BN_free(point->X);
 324         BN_free(point->Y);
 325         BN_free(point->Z);
 326         return 0;
 327     }
 328     return 1;
 329 }
 330
 331 void ec_GFp_simple_point_finish(EC_POINT *point)
 332 {
 333     BN_free(point->X);
 334     BN_free(point->Y);
 335     BN_free(point->Z);
 336 }
 337
 338 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
 339 {
 340     BN_clear_free(point->X);
 341     BN_clear_free(point->Y);
 342     BN_clear_free(point->Z);
 343     point->Z_is_one = 0;
 344 }
 345
 346 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
 347 {
 348     if (!BN_copy(dest->X, src->X))
 349         return 0;
 350     if (!BN_copy(dest->Y, src->Y))
 351         return 0;
 352     if (!BN_copy(dest->Z, src->Z))
 353         return 0;
 354     dest->Z_is_one = src->Z_is_one;
 355
 356     return 1;
 357 }
 358
 359 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
 360                                         EC_POINT *point)
 361 {
 362     point->Z_is_one = 0;
 363     BN_zero(point->Z);
 364     return 1;
 365 }
 366
 367 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
 368                                                   EC_POINT *point,
 369                                                   const BIGNUM *x,
 370                                                   const BIGNUM *y,
 371                                                   const BIGNUM *z,
 372                                                   BN_CTX *ctx)
 373 {
 374     BN_CTX *new_ctx = NULL;
 375     int ret = 0;
 376
 377     if (ctx == NULL) {
 378         ctx = new_ctx = BN_CTX_new();
 379         if (ctx == NULL)
 380             return 0;
 381     }
 382
 383     if (x != NULL) {
 384         if (!BN_nnmod(point->X, x, group->field, ctx))
 385             goto err;
 386         if (group->meth->field_encode) {
 387             if (!group->meth->field_encode(group, point->X, point->X, ctx))
 388                 goto err;
 389         }
 390     }
 391
 392     if (y != NULL) {
 393         if (!BN_nnmod(point->Y, y, group->field, ctx))
 394             goto err;
 395         if (group->meth->field_encode) {
 396             if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
 397                 goto err;
 398         }
 399     }
 400
 401     if (z != NULL) {
 402         int Z_is_one;
 403
 404         if (!BN_nnmod(point->Z, z, group->field, ctx))
 405             goto err;
 406         Z_is_one = BN_is_one(point->Z);
 407         if (group->meth->field_encode) {
 408             if (Z_is_one && (group->meth->field_set_to_one != 0)) {
 409                 if (!group->meth->field_set_to_one(group, point->Z, ctx))
 410                     goto err;
 411             } else {
 412                 if (!group->
 413                     meth->field_encode(group, point->Z, point->Z, ctx))
 414                     goto err;
 415             }
 416         }
 417         point->Z_is_one = Z_is_one;
 418     }
 419
 420     ret = 1;
 421
 422  err:
 423     BN_CTX_free(new_ctx);
 424     return ret;
 425 }
 426
 427 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
 428                                                   const EC_POINT *point,
 429                                                   BIGNUM *x, BIGNUM *y,
 430                                                   BIGNUM *z, BN_CTX *ctx)
 431 {
 432     BN_CTX *new_ctx = NULL;
 433     int ret = 0;
 434
 435     if (group->meth->field_decode != 0) {
 436         if (ctx == NULL) {
 437             ctx = new_ctx = BN_CTX_new();
 438             if (ctx == NULL)
 439                 return 0;
 440         }
 441
 442         if (x != NULL) {
 443             if (!group->meth->field_decode(group, x, point->X, ctx))
 444                 goto err;
 445         }
 446         if (y != NULL) {
 447             if (!group->meth->field_decode(group, y, point->Y, ctx))
 448                 goto err;
 449         }
 450         if (z != NULL) {
 451             if (!group->meth->field_decode(group, z, point->Z, ctx))
 452                 goto err;
 453         }
 454     } else {
 455         if (x != NULL) {
 456             if (!BN_copy(x, point->X))
 457                 goto err;
 458         }
 459         if (y != NULL) {
 460             if (!BN_copy(y, point->Y))
 461                 goto err;
 462         }
 463         if (z != NULL) {
 464             if (!BN_copy(z, point->Z))
 465                 goto err;
 466         }
 467     }
 468
 469     ret = 1;
 470
 471  err:
 472     BN_CTX_free(new_ctx);
 473     return ret;
 474 }
 475
 476 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
 477                                                EC_POINT *point,
 478                                                const BIGNUM *x,
 479                                                const BIGNUM *y, BN_CTX *ctx)
 480 {
 481     if (x == NULL || y == NULL) {
 482         /*
 483          * unlike for projective coordinates, we do not tolerate this
 484          */
 485         ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
 486               ERR_R_PASSED_NULL_PARAMETER);
 487         return 0;
 488     }
 489
 490     return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
 491                                                     BN_value_one(), ctx);
 492 }
 493
 494 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
 495                                                const EC_POINT *point,
 496                                                BIGNUM *x, BIGNUM *y,
 497                                                BN_CTX *ctx)
 498 {
 499     BN_CTX *new_ctx = NULL;
 500     BIGNUM *Z, *Z_1, *Z_2, *Z_3;
 501     const BIGNUM *Z_;
 502     int ret = 0;
 503
 504     if (EC_POINT_is_at_infinity(group, point)) {
 505         ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
 506               EC_R_POINT_AT_INFINITY);
 507         return 0;
 508     }
 509
 510     if (ctx == NULL) {
 511         ctx = new_ctx = BN_CTX_new();
 512         if (ctx == NULL)
 513             return 0;
 514     }
 515
 516     BN_CTX_start(ctx);
 517     Z = BN_CTX_get(ctx);
 518     Z_1 = BN_CTX_get(ctx);
 519     Z_2 = BN_CTX_get(ctx);
 520     Z_3 = BN_CTX_get(ctx);
 521     if (Z_3 == NULL)
 522         goto err;
 523
 524     /* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */
 525
 526     if (group->meth->field_decode) {
 527         if (!group->meth->field_decode(group, Z, point->Z, ctx))
 528             goto err;
 529         Z_ = Z;
 530     } else {
 531         Z_ = point->Z;
 532     }
 533
 534     if (BN_is_one(Z_)) {
 535         if (group->meth->field_decode) {
 536             if (x != NULL) {
 537                 if (!group->meth->field_decode(group, x, point->X, ctx))
 538                     goto err;
 539             }
 540             if (y != NULL) {
 541                 if (!group->meth->field_decode(group, y, point->Y, ctx))
 542                     goto err;
 543             }
 544         } else {
 545             if (x != NULL) {
 546                 if (!BN_copy(x, point->X))
 547                     goto err;
 548             }
 549             if (y != NULL) {
 550                 if (!BN_copy(y, point->Y))
 551                     goto err;
 552             }
 553         }
 554     } else {
 555         if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
 556             ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
 557                   ERR_R_BN_LIB);
 558             goto err;
 559         }
 560
 561         if (group->meth->field_encode == 0) {
 562             /* field_sqr works on standard representation */
 563             if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
 564                 goto err;
 565         } else {
 566             if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
 567                 goto err;
 568         }
 569
 570         if (x != NULL) {
 571             /*
 572              * in the Montgomery case, field_mul will cancel out Montgomery
 573              * factor in X:
 574              */
 575             if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
 576                 goto err;
 577         }
 578
 579         if (y != NULL) {
 580             if (group->meth->field_encode == 0) {
 581                 /*
 582                  * field_mul works on standard representation
 583                  */
 584                 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
 585                     goto err;
 586             } else {
 587                 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
 588                     goto err;
 589             }
 590
 591             /*
 592              * in the Montgomery case, field_mul will cancel out Montgomery
 593              * factor in Y:
 594              */
 595             if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
 596                 goto err;
 597         }
 598     }
 599
 600     ret = 1;
 601
 602  err:
 603     BN_CTX_end(ctx);
 604     BN_CTX_free(new_ctx);
 605     return ret;
 606 }
 607
 608 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 609                       const EC_POINT *b, BN_CTX *ctx)
 610 {
 611     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 612                       const BIGNUM *, BN_CTX *);
 613     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 614     const BIGNUM *p;
 615     BN_CTX *new_ctx = NULL;
 616     BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
 617     int ret = 0;
 618
 619     if (a == b)
 620         return EC_POINT_dbl(group, r, a, ctx);
 621     if (EC_POINT_is_at_infinity(group, a))
 622         return EC_POINT_copy(r, b);
 623     if (EC_POINT_is_at_infinity(group, b))
 624         return EC_POINT_copy(r, a);
 625
 626     field_mul = group->meth->field_mul;
 627     field_sqr = group->meth->field_sqr;
 628     p = group->field;
 629
 630     if (ctx == NULL) {
 631         ctx = new_ctx = BN_CTX_new();
 632         if (ctx == NULL)
 633             return 0;
 634     }
 635
 636     BN_CTX_start(ctx);
 637     n0 = BN_CTX_get(ctx);
 638     n1 = BN_CTX_get(ctx);
 639     n2 = BN_CTX_get(ctx);
 640     n3 = BN_CTX_get(ctx);
 641     n4 = BN_CTX_get(ctx);
 642     n5 = BN_CTX_get(ctx);
 643     n6 = BN_CTX_get(ctx);
 644     if (n6 == NULL)
 645         goto end;
 646
 647     /*
 648      * Note that in this function we must not read components of 'a' or 'b'
 649      * once we have written the corresponding components of 'r'. ('r' might
 650      * be one of 'a' or 'b'.)
 651      */
 652
 653     /* n1, n2 */
 654     if (b->Z_is_one) {
 655         if (!BN_copy(n1, a->X))
 656             goto end;
 657         if (!BN_copy(n2, a->Y))
 658             goto end;
 659         /* n1 = X_a */
 660         /* n2 = Y_a */
 661     } else {
 662         if (!field_sqr(group, n0, b->Z, ctx))
 663             goto end;
 664         if (!field_mul(group, n1, a->X, n0, ctx))
 665             goto end;
 666         /* n1 = X_a * Z_b^2 */
 667
 668         if (!field_mul(group, n0, n0, b->Z, ctx))
 669             goto end;
 670         if (!field_mul(group, n2, a->Y, n0, ctx))
 671             goto end;
 672         /* n2 = Y_a * Z_b^3 */
 673     }
 674
 675     /* n3, n4 */
 676     if (a->Z_is_one) {
 677         if (!BN_copy(n3, b->X))
 678             goto end;
 679         if (!BN_copy(n4, b->Y))
 680             goto end;
 681         /* n3 = X_b */
 682         /* n4 = Y_b */
 683     } else {
 684         if (!field_sqr(group, n0, a->Z, ctx))
 685             goto end;
 686         if (!field_mul(group, n3, b->X, n0, ctx))
 687             goto end;
 688         /* n3 = X_b * Z_a^2 */
 689
 690         if (!field_mul(group, n0, n0, a->Z, ctx))
 691             goto end;
 692         if (!field_mul(group, n4, b->Y, n0, ctx))
 693             goto end;
 694         /* n4 = Y_b * Z_a^3 */
 695     }
 696
 697     /* n5, n6 */
 698     if (!BN_mod_sub_quick(n5, n1, n3, p))
 699         goto end;
 700     if (!BN_mod_sub_quick(n6, n2, n4, p))
 701         goto end;
 702     /* n5 = n1 - n3 */
 703     /* n6 = n2 - n4 */
 704
 705     if (BN_is_zero(n5)) {
 706         if (BN_is_zero(n6)) {
 707             /* a is the same point as b */
 708             BN_CTX_end(ctx);
 709             ret = EC_POINT_dbl(group, r, a, ctx);
 710             ctx = NULL;
 711             goto end;
 712         } else {
 713             /* a is the inverse of b */
 714             BN_zero(r->Z);
 715             r->Z_is_one = 0;
 716             ret = 1;
 717             goto end;
 718         }
 719     }
 720
 721     /* 'n7', 'n8' */
 722     if (!BN_mod_add_quick(n1, n1, n3, p))
 723         goto end;
 724     if (!BN_mod_add_quick(n2, n2, n4, p))
 725         goto end;
 726     /* 'n7' = n1 + n3 */
 727     /* 'n8' = n2 + n4 */
 728
 729     /* Z_r */
 730     if (a->Z_is_one && b->Z_is_one) {
 731         if (!BN_copy(r->Z, n5))
 732             goto end;
 733     } else {
 734         if (a->Z_is_one) {
 735             if (!BN_copy(n0, b->Z))
 736                 goto end;
 737         } else if (b->Z_is_one) {
 738             if (!BN_copy(n0, a->Z))
 739                 goto end;
 740         } else {
 741             if (!field_mul(group, n0, a->Z, b->Z, ctx))
 742                 goto end;
 743         }
 744         if (!field_mul(group, r->Z, n0, n5, ctx))
 745             goto end;
 746     }
 747     r->Z_is_one = 0;
 748     /* Z_r = Z_a * Z_b * n5 */
 749
 750     /* X_r */
 751     if (!field_sqr(group, n0, n6, ctx))
 752         goto end;
 753     if (!field_sqr(group, n4, n5, ctx))
 754         goto end;
 755     if (!field_mul(group, n3, n1, n4, ctx))
 756         goto end;
 757     if (!BN_mod_sub_quick(r->X, n0, n3, p))
 758         goto end;
 759     /* X_r = n6^2 - n5^2 * 'n7' */
 760
 761     /* 'n9' */
 762     if (!BN_mod_lshift1_quick(n0, r->X, p))
 763         goto end;
 764     if (!BN_mod_sub_quick(n0, n3, n0, p))
 765         goto end;
 766     /* n9 = n5^2 * 'n7' - 2 * X_r */
 767
 768     /* Y_r */
 769     if (!field_mul(group, n0, n0, n6, ctx))
 770         goto end;
 771     if (!field_mul(group, n5, n4, n5, ctx))
 772         goto end;               /* now n5 is n5^3 */
 773     if (!field_mul(group, n1, n2, n5, ctx))
 774         goto end;
 775     if (!BN_mod_sub_quick(n0, n0, n1, p))
 776         goto end;
 777     if (BN_is_odd(n0))
 778         if (!BN_add(n0, n0, p))
 779             goto end;
 780     /* now  0 <= n0 < 2*p,  and n0 is even */
 781     if (!BN_rshift1(r->Y, n0))
 782         goto end;
 783     /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
 784
 785     ret = 1;
 786
 787  end:
 788     if (ctx)                    /* otherwise we already called BN_CTX_end */
 789         BN_CTX_end(ctx);
 790     BN_CTX_free(new_ctx);
 791     return ret;
 792 }
 793
 794 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 795                       BN_CTX *ctx)
 796 {
 797     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 798                       const BIGNUM *, BN_CTX *);
 799     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 800     const BIGNUM *p;
 801     BN_CTX *new_ctx = NULL;
 802     BIGNUM *n0, *n1, *n2, *n3;
 803     int ret = 0;
 804
 805     if (EC_POINT_is_at_infinity(group, a)) {
 806         BN_zero(r->Z);
 807         r->Z_is_one = 0;
 808         return 1;
 809     }
 810
 811     field_mul = group->meth->field_mul;
 812     field_sqr = group->meth->field_sqr;
 813     p = group->field;
 814
 815     if (ctx == NULL) {
 816         ctx = new_ctx = BN_CTX_new();
 817         if (ctx == NULL)
 818             return 0;
 819     }
 820
 821     BN_CTX_start(ctx);
 822     n0 = BN_CTX_get(ctx);
 823     n1 = BN_CTX_get(ctx);
 824     n2 = BN_CTX_get(ctx);
 825     n3 = BN_CTX_get(ctx);
 826     if (n3 == NULL)
 827         goto err;
 828
 829     /*
 830      * Note that in this function we must not read components of 'a' once we
 831      * have written the corresponding components of 'r'. ('r' might the same
 832      * as 'a'.)
 833      */
 834
 835     /* n1 */
 836     if (a->Z_is_one) {
 837         if (!field_sqr(group, n0, a->X, ctx))
 838             goto err;
 839         if (!BN_mod_lshift1_quick(n1, n0, p))
 840             goto err;
 841         if (!BN_mod_add_quick(n0, n0, n1, p))
 842             goto err;
 843         if (!BN_mod_add_quick(n1, n0, group->a, p))
 844             goto err;
 845         /* n1 = 3 * X_a^2 + a_curve */
 846     } else if (group->a_is_minus3) {
 847         if (!field_sqr(group, n1, a->Z, ctx))
 848             goto err;
 849         if (!BN_mod_add_quick(n0, a->X, n1, p))
 850             goto err;
 851         if (!BN_mod_sub_quick(n2, a->X, n1, p))
 852             goto err;
 853         if (!field_mul(group, n1, n0, n2, ctx))
 854             goto err;
 855         if (!BN_mod_lshift1_quick(n0, n1, p))
 856             goto err;
 857         if (!BN_mod_add_quick(n1, n0, n1, p))
 858             goto err;
 859         /*-
 860          * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
 861          *    = 3 * X_a^2 - 3 * Z_a^4
 862          */
 863     } else {
 864         if (!field_sqr(group, n0, a->X, ctx))
 865             goto err;
 866         if (!BN_mod_lshift1_quick(n1, n0, p))
 867             goto err;
 868         if (!BN_mod_add_quick(n0, n0, n1, p))
 869             goto err;
 870         if (!field_sqr(group, n1, a->Z, ctx))
 871             goto err;
 872         if (!field_sqr(group, n1, n1, ctx))
 873             goto err;
 874         if (!field_mul(group, n1, n1, group->a, ctx))
 875             goto err;
 876         if (!BN_mod_add_quick(n1, n1, n0, p))
 877             goto err;
 878         /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
 879     }
 880
 881     /* Z_r */
 882     if (a->Z_is_one) {
 883         if (!BN_copy(n0, a->Y))
 884             goto err;
 885     } else {
 886         if (!field_mul(group, n0, a->Y, a->Z, ctx))
 887             goto err;
 888     }
 889     if (!BN_mod_lshift1_quick(r->Z, n0, p))
 890         goto err;
 891     r->Z_is_one = 0;
 892     /* Z_r = 2 * Y_a * Z_a */
 893
 894     /* n2 */
 895     if (!field_sqr(group, n3, a->Y, ctx))
 896         goto err;
 897     if (!field_mul(group, n2, a->X, n3, ctx))
 898         goto err;
 899     if (!BN_mod_lshift_quick(n2, n2, 2, p))
 900         goto err;
 901     /* n2 = 4 * X_a * Y_a^2 */
 902
 903     /* X_r */
 904     if (!BN_mod_lshift1_quick(n0, n2, p))
 905         goto err;
 906     if (!field_sqr(group, r->X, n1, ctx))
 907         goto err;
 908     if (!BN_mod_sub_quick(r->X, r->X, n0, p))
 909         goto err;
 910     /* X_r = n1^2 - 2 * n2 */
 911
 912     /* n3 */
 913     if (!field_sqr(group, n0, n3, ctx))
 914         goto err;
 915     if (!BN_mod_lshift_quick(n3, n0, 3, p))
 916         goto err;
 917     /* n3 = 8 * Y_a^4 */
 918
 919     /* Y_r */
 920     if (!BN_mod_sub_quick(n0, n2, r->X, p))
 921         goto err;
 922     if (!field_mul(group, n0, n1, n0, ctx))
 923         goto err;
 924     if (!BN_mod_sub_quick(r->Y, n0, n3, p))
 925         goto err;
 926     /* Y_r = n1 * (n2 - X_r) - n3 */
 927
 928     ret = 1;
 929
 930  err:
 931     BN_CTX_end(ctx);
 932     BN_CTX_free(new_ctx);
 933     return ret;
 934 }
 935
 936 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
 937 {
 938     if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
 939         /* point is its own inverse */
 940         return 1;
 941
 942     return BN_usub(point->Y, group->field, point->Y);
 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 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
 951                               BN_CTX *ctx)
 952 {
 953     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 954                       const BIGNUM *, BN_CTX *);
 955     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 956     const BIGNUM *p;
 957     BN_CTX *new_ctx = NULL;
 958     BIGNUM *rh, *tmp, *Z4, *Z6;
 959     int ret = -1;
 960
 961     if (EC_POINT_is_at_infinity(group, point))
 962         return 1;
 963
 964     field_mul = group->meth->field_mul;
 965     field_sqr = group->meth->field_sqr;
 966     p = group->field;
 967
 968     if (ctx == NULL) {
 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)
 980         goto err;
 981
 982     /*-
 983      * We have a curve defined by a Weierstrass equation
 984      *      y^2 = x^3 + a*x + b.
 985      * The point to consider is given in Jacobian projective coordinates
 986      * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).
 987      * Substituting this and multiplying by  Z^6  transforms the above equation into
 988      *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.
 989      * To test this, we add up the right-hand side in 'rh'.
 990      */
 991
 992     /* rh := X^2 */
 993     if (!field_sqr(group, rh, point->X, ctx))
 994         goto err;
 995
 996     if (!point->Z_is_one) {
 997         if (!field_sqr(group, tmp, point->Z, ctx))
 998             goto err;
 999         if (!field_sqr(group, Z4, tmp, ctx))
1000             goto err;
1001         if (!field_mul(group, Z6, Z4, tmp, ctx))
1002             goto err;
1003
1004         /* rh := (rh + a*Z^4)*X */
1005         if (group->a_is_minus3) {
1006             if (!BN_mod_lshift1_quick(tmp, Z4, p))
1007                 goto err;
1008             if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1009                 goto err;
1010             if (!BN_mod_sub_quick(rh, rh, tmp, p))
1011                 goto err;
1012             if (!field_mul(group, rh, rh, point->X, ctx))
1013                 goto err;
1014         } else {
1015             if (!field_mul(group, tmp, Z4, group->a, ctx))
1016                 goto err;
1017             if (!BN_mod_add_quick(rh, rh, tmp, p))
1018                 goto err;
1019             if (!field_mul(group, rh, rh, point->X, ctx))
1020                 goto err;
1021         }
1022
1023         /* rh := rh + b*Z^6 */
1024         if (!field_mul(group, tmp, group->b, Z6, ctx))
1025             goto err;
1026         if (!BN_mod_add_quick(rh, rh, tmp, p))
1027             goto err;
1028     } else {
1029         /* point->Z_is_one */
1030
1031         /* rh := (rh + a)*X */
1032         if (!BN_mod_add_quick(rh, rh, group->a, p))
1033             goto err;
1034         if (!field_mul(group, rh, rh, point->X, ctx))
1035             goto err;
1036         /* rh := rh + b */
1037         if (!BN_mod_add_quick(rh, rh, group->b, p))
1038             goto err;
1039     }
1040
1041     /* 'lh' := Y^2 */
1042     if (!field_sqr(group, tmp, point->Y, ctx))
1043         goto err;
1044
1045     ret = (0 == BN_ucmp(tmp, rh));
1046
1047  err:
1048     BN_CTX_end(ctx);
1049     BN_CTX_free(new_ctx);
1050     return ret;
1051 }
1052
1053 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1054                       const EC_POINT *b, BN_CTX *ctx)
1055 {
1056     /*-
1057      * return values:
1058      *  -1   error
1059      *   0   equal (in affine coordinates)
1060      *   1   not equal
1061      */
1062
1063     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1064                       const BIGNUM *, BN_CTX *);
1065     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1066     BN_CTX *new_ctx = NULL;
1067     BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1068     const BIGNUM *tmp1_, *tmp2_;
1069     int ret = -1;
1070
1071     if (EC_POINT_is_at_infinity(group, a)) {
1072         return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1073     }
1074
1075     if (EC_POINT_is_at_infinity(group, b))
1076         return 1;
1077
1078     if (a->Z_is_one && b->Z_is_one) {
1079         return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1080     }
1081
1082     field_mul = group->meth->field_mul;
1083     field_sqr = group->meth->field_sqr;
1084
1085     if (ctx == NULL) {
1086         ctx = new_ctx = BN_CTX_new();
1087         if (ctx == NULL)
1088             return -1;
1089     }
1090
1091     BN_CTX_start(ctx);
1092     tmp1 = BN_CTX_get(ctx);
1093     tmp2 = BN_CTX_get(ctx);
1094     Za23 = BN_CTX_get(ctx);
1095     Zb23 = BN_CTX_get(ctx);
1096     if (Zb23 == NULL)
1097         goto end;
1098
1099     /*-
1100      * We have to decide whether
1101      *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1102      * or equivalently, whether
1103      *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1104      */
1105
1106     if (!b->Z_is_one) {
1107         if (!field_sqr(group, Zb23, b->Z, ctx))
1108             goto end;
1109         if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1110             goto end;
1111         tmp1_ = tmp1;
1112     } else
1113         tmp1_ = a->X;
1114     if (!a->Z_is_one) {
1115         if (!field_sqr(group, Za23, a->Z, ctx))
1116             goto end;
1117         if (!field_mul(group, tmp2, b->X, Za23, ctx))
1118             goto end;
1119         tmp2_ = tmp2;
1120     } else
1121         tmp2_ = b->X;
1122
1123     /* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
1124     if (BN_cmp(tmp1_, tmp2_) != 0) {
1125         ret = 1;                /* points differ */
1126         goto end;
1127     }
1128
1129     if (!b->Z_is_one) {
1130         if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1131             goto end;
1132         if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1133             goto end;
1134         /* tmp1_ = tmp1 */
1135     } else
1136         tmp1_ = a->Y;
1137     if (!a->Z_is_one) {
1138         if (!field_mul(group, Za23, Za23, a->Z, ctx))
1139             goto end;
1140         if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1141             goto end;
1142         /* tmp2_ = tmp2 */
1143     } else
1144         tmp2_ = b->Y;
1145
1146     /* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
1147     if (BN_cmp(tmp1_, tmp2_) != 0) {
1148         ret = 1;                /* points differ */
1149         goto end;
1150     }
1151
1152     /* points are equal */
1153     ret = 0;
1154
1155  end:
1156     BN_CTX_end(ctx);
1157     BN_CTX_free(new_ctx);
1158     return ret;
1159 }
1160
1161 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1162                               BN_CTX *ctx)
1163 {
1164     BN_CTX *new_ctx = NULL;
1165     BIGNUM *x, *y;
1166     int ret = 0;
1167
1168     if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1169         return 1;
1170
1171     if (ctx == NULL) {
1172         ctx = new_ctx = BN_CTX_new();
1173         if (ctx == NULL)
1174             return 0;
1175     }
1176
1177     BN_CTX_start(ctx);
1178     x = BN_CTX_get(ctx);
1179     y = BN_CTX_get(ctx);
1180     if (y == NULL)
1181         goto err;
1182
1183     if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1184         goto err;
1185     if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1186         goto err;
1187     if (!point->Z_is_one) {
1188         ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1189         goto err;
1190     }
1191
1192     ret = 1;
1193
1194  err:
1195     BN_CTX_end(ctx);
1196     BN_CTX_free(new_ctx);
1197     return ret;
1198 }
1199
1200 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1201                                      EC_POINT *points[], BN_CTX *ctx)
1202 {
1203     BN_CTX *new_ctx = NULL;
1204     BIGNUM *tmp, *tmp_Z;
1205     BIGNUM **prod_Z = NULL;
1206     size_t i;
1207     int ret = 0;
1208
1209     if (num == 0)
1210         return 1;
1211
1212     if (ctx == NULL) {
1213         ctx = new_ctx = BN_CTX_new();
1214         if (ctx == NULL)
1215             return 0;
1216     }
1217
1218     BN_CTX_start(ctx);
1219     tmp = BN_CTX_get(ctx);
1220     tmp_Z = BN_CTX_get(ctx);
1221     if (tmp == NULL || tmp_Z == NULL)
1222         goto err;
1223
1224     prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1225     if (prod_Z == NULL)
1226         goto err;
1227     for (i = 0; i < num; i++) {
1228         prod_Z[i] = BN_new();
1229         if (prod_Z[i] == NULL)
1230             goto err;
1231     }
1232
1233     /*
1234      * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1235      * skipping any zero-valued inputs (pretend that they're 1).
1236      */
1237
1238     if (!BN_is_zero(points[0]->Z)) {
1239         if (!BN_copy(prod_Z[0], points[0]->Z))
1240             goto err;
1241     } else {
1242         if (group->meth->field_set_to_one != 0) {
1243             if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1244                 goto err;
1245         } else {
1246             if (!BN_one(prod_Z[0]))
1247                 goto err;
1248         }
1249     }
1250
1251     for (i = 1; i < num; i++) {
1252         if (!BN_is_zero(points[i]->Z)) {
1253             if (!group->
1254                 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1255                                 ctx))
1256                 goto err;
1257         } else {
1258             if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1259                 goto err;
1260         }
1261     }
1262
1263     /*
1264      * Now use a single explicit inversion to replace every non-zero
1265      * points[i]->Z by its inverse.
1266      */
1267
1268     if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1269         ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1270         goto err;
1271     }
1272     if (group->meth->field_encode != 0) {
1273         /*
1274          * In the Montgomery case, we just turned R*H (representing H) into
1275          * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1276          * multiply by the Montgomery factor twice.
1277          */
1278         if (!group->meth->field_encode(group, tmp, tmp, ctx))
1279             goto err;
1280         if (!group->meth->field_encode(group, tmp, tmp, ctx))
1281             goto err;
1282     }
1283
1284     for (i = num - 1; i > 0; --i) {
1285         /*
1286          * Loop invariant: tmp is the product of the inverses of points[0]->Z
1287          * .. points[i]->Z (zero-valued inputs skipped).
1288          */
1289         if (!BN_is_zero(points[i]->Z)) {
1290             /*
1291              * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1292              * inverses 0 .. i, Z values 0 .. i - 1).
1293              */
1294             if (!group->
1295                 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1296                 goto err;
1297             /*
1298              * Update tmp to satisfy the loop invariant for i - 1.
1299              */
1300             if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1301                 goto err;
1302             /* Replace points[i]->Z by its inverse. */
1303             if (!BN_copy(points[i]->Z, tmp_Z))
1304                 goto err;
1305         }
1306     }
1307
1308     if (!BN_is_zero(points[0]->Z)) {
1309         /* Replace points[0]->Z by its inverse. */
1310         if (!BN_copy(points[0]->Z, tmp))
1311             goto err;
1312     }
1313
1314     /* Finally, fix up the X and Y coordinates for all points. */
1315
1316     for (i = 0; i < num; i++) {
1317         EC_POINT *p = points[i];
1318
1319         if (!BN_is_zero(p->Z)) {
1320             /* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */
1321
1322             if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1323                 goto err;
1324             if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1325                 goto err;
1326
1327             if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1328                 goto err;
1329             if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1330                 goto err;
1331
1332             if (group->meth->field_set_to_one != 0) {
1333                 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1334                     goto err;
1335             } else {
1336                 if (!BN_one(p->Z))
1337                     goto err;
1338             }
1339             p->Z_is_one = 1;
1340         }
1341     }
1342
1343     ret = 1;
1344
1345  err:
1346     BN_CTX_end(ctx);
1347     BN_CTX_free(new_ctx);
1348     if (prod_Z != NULL) {
1349         for (i = 0; i < num; i++) {
1350             if (prod_Z[i] == NULL)
1351                 break;
1352             BN_clear_free(prod_Z[i]);
1353         }
1354         OPENSSL_free(prod_Z);
1355     }
1356     return ret;
1357 }
1358
1359 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1360                             const BIGNUM *b, BN_CTX *ctx)
1361 {
1362     return BN_mod_mul(r, a, b, group->field, ctx);
1363 }
1364
1365 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1366                             BN_CTX *ctx)
1367 {
1368     return BN_mod_sqr(r, a, group->field, ctx);
1369 }