crypto/ec/ec_lib.c

   1 /*
   2  * Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
   4  *
   5  * Licensed under the Apache License 2.0 (the "License").  You may not use
   6  * this file except in compliance with the License.  You can obtain a copy
   7  * in the file LICENSE in the source distribution or at
   8  * https://www.openssl.org/source/license.html
   9  */
  10
  11 /*
  12  * ECDSA low level APIs are deprecated for public use, but still ok for
  13  * internal use.
  14  */
  15 #include "internal/deprecated.h"
  16
  17 #include <string.h>
  18 #include <openssl/params.h>
  19 #include <openssl/core_names.h>
  20 #include <openssl/err.h>
  21 #include <openssl/opensslv.h>
  22 #include "crypto/ec.h"
  23 #include "internal/nelem.h"
  24 #include "ec_local.h"
  25 #include "e_os.h" /* strcasecmp */
  26
  27 /* functions for EC_GROUP objects */
  28
  29 EC_GROUP *ec_group_new_with_libctx(OPENSSL_CTX *libctx, const char *propq,
  30                                    const EC_METHOD *meth)
  31 {
  32     EC_GROUP *ret;
  33
  34     if (meth == NULL) {
  35         ECerr(0, EC_R_SLOT_FULL);
  36         return NULL;
  37     }
  38     if (meth->group_init == 0) {
  39         ECerr(0, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
  40         return NULL;
  41     }
  42
  43     ret = OPENSSL_zalloc(sizeof(*ret));
  44     if (ret == NULL) {
  45         ECerr(0, ERR_R_MALLOC_FAILURE);
  46         return NULL;
  47     }
  48
  49     ret->libctx = libctx;
  50     if (propq != NULL) {
  51         ret->propq = OPENSSL_strdup(propq);
  52         if (ret->propq == NULL) {
  53             ECerr(0, ERR_R_MALLOC_FAILURE);
  54             goto err;
  55         }
  56     }
  57     ret->meth = meth;
  58     if ((ret->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) {
  59         ret->order = BN_new();
  60         if (ret->order == NULL)
  61             goto err;
  62         ret->cofactor = BN_new();
  63         if (ret->cofactor == NULL)
  64             goto err;
  65     }
  66     ret->asn1_flag = OPENSSL_EC_NAMED_CURVE;
  67     ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED;
  68     if (!meth->group_init(ret))
  69         goto err;
  70     return ret;
  71
  72  err:
  73     BN_free(ret->order);
  74     BN_free(ret->cofactor);
  75     OPENSSL_free(ret->propq);
  76     OPENSSL_free(ret);
  77     return NULL;
  78 }
  79
  80 #ifndef OPENSSL_NO_DEPRECATED_3_0
  81 # ifndef FIPS_MODULE
  82 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth)
  83 {
  84     return ec_group_new_with_libctx(NULL, NULL, meth);
  85 }
  86 # endif
  87 #endif
  88
  89 void EC_pre_comp_free(EC_GROUP *group)
  90 {
  91     switch (group->pre_comp_type) {
  92     case PCT_none:
  93         break;
  94     case PCT_nistz256:
  95 #ifdef ECP_NISTZ256_ASM
  96         EC_nistz256_pre_comp_free(group->pre_comp.nistz256);
  97 #endif
  98         break;
  99 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 100     case PCT_nistp224:
 101         EC_nistp224_pre_comp_free(group->pre_comp.nistp224);
 102         break;
 103     case PCT_nistp256:
 104         EC_nistp256_pre_comp_free(group->pre_comp.nistp256);
 105         break;
 106     case PCT_nistp521:
 107         EC_nistp521_pre_comp_free(group->pre_comp.nistp521);
 108         break;
 109 #else
 110     case PCT_nistp224:
 111     case PCT_nistp256:
 112     case PCT_nistp521:
 113         break;
 114 #endif
 115     case PCT_ec:
 116         EC_ec_pre_comp_free(group->pre_comp.ec);
 117         break;
 118     }
 119     group->pre_comp.ec = NULL;
 120 }
 121
 122 void EC_GROUP_free(EC_GROUP *group)
 123 {
 124     if (!group)
 125         return;
 126
 127     if (group->meth->group_finish != 0)
 128         group->meth->group_finish(group);
 129
 130     EC_pre_comp_free(group);
 131     BN_MONT_CTX_free(group->mont_data);
 132     EC_POINT_free(group->generator);
 133     BN_free(group->order);
 134     BN_free(group->cofactor);
 135     OPENSSL_free(group->seed);
 136     OPENSSL_free(group->propq);
 137     OPENSSL_free(group);
 138 }
 139
 140 #ifndef OPENSSL_NO_DEPRECATED_3_0
 141 void EC_GROUP_clear_free(EC_GROUP *group)
 142 {
 143     if (!group)
 144         return;
 145
 146     if (group->meth->group_clear_finish != 0)
 147         group->meth->group_clear_finish(group);
 148     else if (group->meth->group_finish != 0)
 149         group->meth->group_finish(group);
 150
 151     EC_pre_comp_free(group);
 152     BN_MONT_CTX_free(group->mont_data);
 153     EC_POINT_clear_free(group->generator);
 154     BN_clear_free(group->order);
 155     BN_clear_free(group->cofactor);
 156     OPENSSL_clear_free(group->seed, group->seed_len);
 157     OPENSSL_clear_free(group, sizeof(*group));
 158 }
 159 #endif
 160
 161 int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src)
 162 {
 163     if (dest->meth->group_copy == 0) {
 164         ECerr(EC_F_EC_GROUP_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 165         return 0;
 166     }
 167     if (dest->meth != src->meth) {
 168         ECerr(EC_F_EC_GROUP_COPY, EC_R_INCOMPATIBLE_OBJECTS);
 169         return 0;
 170     }
 171     if (dest == src)
 172         return 1;
 173
 174     dest->libctx = src->libctx;
 175     dest->curve_name = src->curve_name;
 176
 177     /* Copy precomputed */
 178     dest->pre_comp_type = src->pre_comp_type;
 179     switch (src->pre_comp_type) {
 180     case PCT_none:
 181         dest->pre_comp.ec = NULL;
 182         break;
 183     case PCT_nistz256:
 184 #ifdef ECP_NISTZ256_ASM
 185         dest->pre_comp.nistz256 = EC_nistz256_pre_comp_dup(src->pre_comp.nistz256);
 186 #endif
 187         break;
 188 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 189     case PCT_nistp224:
 190         dest->pre_comp.nistp224 = EC_nistp224_pre_comp_dup(src->pre_comp.nistp224);
 191         break;
 192     case PCT_nistp256:
 193         dest->pre_comp.nistp256 = EC_nistp256_pre_comp_dup(src->pre_comp.nistp256);
 194         break;
 195     case PCT_nistp521:
 196         dest->pre_comp.nistp521 = EC_nistp521_pre_comp_dup(src->pre_comp.nistp521);
 197         break;
 198 #else
 199     case PCT_nistp224:
 200     case PCT_nistp256:
 201     case PCT_nistp521:
 202         break;
 203 #endif
 204     case PCT_ec:
 205         dest->pre_comp.ec = EC_ec_pre_comp_dup(src->pre_comp.ec);
 206         break;
 207     }
 208
 209     if (src->mont_data != NULL) {
 210         if (dest->mont_data == NULL) {
 211             dest->mont_data = BN_MONT_CTX_new();
 212             if (dest->mont_data == NULL)
 213                 return 0;
 214         }
 215         if (!BN_MONT_CTX_copy(dest->mont_data, src->mont_data))
 216             return 0;
 217     } else {
 218         /* src->generator == NULL */
 219         BN_MONT_CTX_free(dest->mont_data);
 220         dest->mont_data = NULL;
 221     }
 222
 223     if (src->generator != NULL) {
 224         if (dest->generator == NULL) {
 225             dest->generator = EC_POINT_new(dest);
 226             if (dest->generator == NULL)
 227                 return 0;
 228         }
 229         if (!EC_POINT_copy(dest->generator, src->generator))
 230             return 0;
 231     } else {
 232         /* src->generator == NULL */
 233         EC_POINT_clear_free(dest->generator);
 234         dest->generator = NULL;
 235     }
 236
 237     if ((src->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) {
 238         if (!BN_copy(dest->order, src->order))
 239             return 0;
 240         if (!BN_copy(dest->cofactor, src->cofactor))
 241             return 0;
 242     }
 243
 244     dest->asn1_flag = src->asn1_flag;
 245     dest->asn1_form = src->asn1_form;
 246     dest->decoded_from_explicit_params = src->decoded_from_explicit_params;
 247
 248     if (src->seed) {
 249         OPENSSL_free(dest->seed);
 250         if ((dest->seed = OPENSSL_malloc(src->seed_len)) == NULL) {
 251             ECerr(EC_F_EC_GROUP_COPY, ERR_R_MALLOC_FAILURE);
 252             return 0;
 253         }
 254         if (!memcpy(dest->seed, src->seed, src->seed_len))
 255             return 0;
 256         dest->seed_len = src->seed_len;
 257     } else {
 258         OPENSSL_free(dest->seed);
 259         dest->seed = NULL;
 260         dest->seed_len = 0;
 261     }
 262
 263     return dest->meth->group_copy(dest, src);
 264 }
 265
 266 EC_GROUP *EC_GROUP_dup(const EC_GROUP *a)
 267 {
 268     EC_GROUP *t = NULL;
 269     int ok = 0;
 270
 271     if (a == NULL)
 272         return NULL;
 273
 274     if ((t = ec_group_new_with_libctx(a->libctx, a->propq, a->meth)) == NULL)
 275         return NULL;
 276     if (!EC_GROUP_copy(t, a))
 277         goto err;
 278
 279     ok = 1;
 280
 281  err:
 282     if (!ok) {
 283         EC_GROUP_free(t);
 284         return NULL;
 285     }
 286         return t;
 287 }
 288
 289 #ifndef OPENSSL_NO_DEPRECATED_3_0
 290 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group)
 291 {
 292     return group->meth;
 293 }
 294
 295 int EC_METHOD_get_field_type(const EC_METHOD *meth)
 296 {
 297     return meth->field_type;
 298 }
 299 #endif
 300
 301 static int ec_precompute_mont_data(EC_GROUP *);
 302
 303 /*-
 304  * Try computing cofactor from the generator order (n) and field cardinality (q).
 305  * This works for all curves of cryptographic interest.
 306  *
 307  * Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
 308  * h_min = (q + 1 - 2*sqrt(q))/n
 309  * h_max = (q + 1 + 2*sqrt(q))/n
 310  * h_max - h_min = 4*sqrt(q)/n
 311  * So if n > 4*sqrt(q) holds, there is only one possible value for h:
 312  * h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
 313  *
 314  * Otherwise, zero cofactor and return success.
 315  */
 316 static int ec_guess_cofactor(EC_GROUP *group) {
 317     int ret = 0;
 318     BN_CTX *ctx = NULL;
 319     BIGNUM *q = NULL;
 320
 321     /*-
 322      * If the cofactor is too large, we cannot guess it.
 323      * The RHS of below is a strict overestimate of lg(4 * sqrt(q))
 324      */
 325     if (BN_num_bits(group->order) <= (BN_num_bits(group->field) + 1) / 2 + 3) {
 326         /* default to 0 */
 327         BN_zero(group->cofactor);
 328         /* return success */
 329         return 1;
 330     }
 331
 332     if ((ctx = BN_CTX_new_ex(group->libctx)) == NULL)
 333         return 0;
 334
 335     BN_CTX_start(ctx);
 336     if ((q = BN_CTX_get(ctx)) == NULL)
 337         goto err;
 338
 339     /* set q = 2**m for binary fields; q = p otherwise */
 340     if (group->meth->field_type == NID_X9_62_characteristic_two_field) {
 341         BN_zero(q);
 342         if (!BN_set_bit(q, BN_num_bits(group->field) - 1))
 343             goto err;
 344     } else {
 345         if (!BN_copy(q, group->field))
 346             goto err;
 347     }
 348
 349     /* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
 350     if (!BN_rshift1(group->cofactor, group->order) /* n/2 */
 351         || !BN_add(group->cofactor, group->cofactor, q) /* q + n/2 */
 352         /* q + 1 + n/2 */
 353         || !BN_add(group->cofactor, group->cofactor, BN_value_one())
 354         /* (q + 1 + n/2)/n */
 355         || !BN_div(group->cofactor, NULL, group->cofactor, group->order, ctx))
 356         goto err;
 357     ret = 1;
 358  err:
 359     BN_CTX_end(ctx);
 360     BN_CTX_free(ctx);
 361     return ret;
 362 }
 363
 364 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
 365                            const BIGNUM *order, const BIGNUM *cofactor)
 366 {
 367     if (generator == NULL) {
 368         ECerr(EC_F_EC_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
 369         return 0;
 370     }
 371
 372     /* require group->field >= 1 */
 373     if (group->field == NULL || BN_is_zero(group->field)
 374         || BN_is_negative(group->field)) {
 375         ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_FIELD);
 376         return 0;
 377     }
 378
 379     /*-
 380      * - require order >= 1
 381      * - enforce upper bound due to Hasse thm: order can be no more than one bit
 382      *   longer than field cardinality
 383      */
 384     if (order == NULL || BN_is_zero(order) || BN_is_negative(order)
 385         || BN_num_bits(order) > BN_num_bits(group->field) + 1) {
 386         ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_GROUP_ORDER);
 387         return 0;
 388     }
 389
 390     /*-
 391      * Unfortunately the cofactor is an optional field in many standards.
 392      * Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
 393      * So accept cofactor == NULL or cofactor >= 0.
 394      */
 395     if (cofactor != NULL && BN_is_negative(cofactor)) {
 396         ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_UNKNOWN_COFACTOR);
 397         return 0;
 398     }
 399
 400     if (group->generator == NULL) {
 401         group->generator = EC_POINT_new(group);
 402         if (group->generator == NULL)
 403             return 0;
 404     }
 405     if (!EC_POINT_copy(group->generator, generator))
 406         return 0;
 407
 408     if (!BN_copy(group->order, order))
 409         return 0;
 410
 411     /* Either take the provided positive cofactor, or try to compute it */
 412     if (cofactor != NULL && !BN_is_zero(cofactor)) {
 413         if (!BN_copy(group->cofactor, cofactor))
 414             return 0;
 415     } else if (!ec_guess_cofactor(group)) {
 416         BN_zero(group->cofactor);
 417         return 0;
 418     }
 419
 420     /*
 421      * Some groups have an order with
 422      * factors of two, which makes the Montgomery setup fail.
 423      * |group->mont_data| will be NULL in this case.
 424      */
 425     if (BN_is_odd(group->order)) {
 426         return ec_precompute_mont_data(group);
 427     }
 428
 429     BN_MONT_CTX_free(group->mont_data);
 430     group->mont_data = NULL;
 431     return 1;
 432 }
 433
 434 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group)
 435 {
 436     return group->generator;
 437 }
 438
 439 BN_MONT_CTX *EC_GROUP_get_mont_data(const EC_GROUP *group)
 440 {
 441     return group->mont_data;
 442 }
 443
 444 int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
 445 {
 446     if (group->order == NULL)
 447         return 0;
 448     if (!BN_copy(order, group->order))
 449         return 0;
 450
 451     return !BN_is_zero(order);
 452 }
 453
 454 const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group)
 455 {
 456     return group->order;
 457 }
 458
 459 int EC_GROUP_order_bits(const EC_GROUP *group)
 460 {
 461     return group->meth->group_order_bits(group);
 462 }
 463
 464 int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor,
 465                           BN_CTX *ctx)
 466 {
 467
 468     if (group->cofactor == NULL)
 469         return 0;
 470     if (!BN_copy(cofactor, group->cofactor))
 471         return 0;
 472
 473     return !BN_is_zero(group->cofactor);
 474 }
 475
 476 const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group)
 477 {
 478     return group->cofactor;
 479 }
 480
 481 void EC_GROUP_set_curve_name(EC_GROUP *group, int nid)
 482 {
 483     group->curve_name = nid;
 484 }
 485
 486 int EC_GROUP_get_curve_name(const EC_GROUP *group)
 487 {
 488     return group->curve_name;
 489 }
 490
 491 const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group)
 492 {
 493     return group->field;
 494 }
 495
 496 int EC_GROUP_get_field_type(const EC_GROUP *group)
 497 {
 498     return group->meth->field_type;
 499 }
 500
 501 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag)
 502 {
 503     group->asn1_flag = flag;
 504 }
 505
 506 int EC_GROUP_get_asn1_flag(const EC_GROUP *group)
 507 {
 508     return group->asn1_flag;
 509 }
 510
 511 void EC_GROUP_set_point_conversion_form(EC_GROUP *group,
 512                                         point_conversion_form_t form)
 513 {
 514     group->asn1_form = form;
 515 }
 516
 517 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP
 518                                                            *group)
 519 {
 520     return group->asn1_form;
 521 }
 522
 523 size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len)
 524 {
 525     OPENSSL_free(group->seed);
 526     group->seed = NULL;
 527     group->seed_len = 0;
 528
 529     if (!len || !p)
 530         return 1;
 531
 532     if ((group->seed = OPENSSL_malloc(len)) == NULL) {
 533         ECerr(EC_F_EC_GROUP_SET_SEED, ERR_R_MALLOC_FAILURE);
 534         return 0;
 535     }
 536     memcpy(group->seed, p, len);
 537     group->seed_len = len;
 538
 539     return len;
 540 }
 541
 542 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group)
 543 {
 544     return group->seed;
 545 }
 546
 547 size_t EC_GROUP_get_seed_len(const EC_GROUP *group)
 548 {
 549     return group->seed_len;
 550 }
 551
 552 int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
 553                        const BIGNUM *b, BN_CTX *ctx)
 554 {
 555     if (group->meth->group_set_curve == 0) {
 556         ECerr(EC_F_EC_GROUP_SET_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 557         return 0;
 558     }
 559     return group->meth->group_set_curve(group, p, a, b, ctx);
 560 }
 561
 562 int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
 563                        BN_CTX *ctx)
 564 {
 565     if (group->meth->group_get_curve == NULL) {
 566         ECerr(EC_F_EC_GROUP_GET_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 567         return 0;
 568     }
 569     return group->meth->group_get_curve(group, p, a, b, ctx);
 570 }
 571
 572 #ifndef OPENSSL_NO_DEPRECATED_3_0
 573 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
 574                            const BIGNUM *b, BN_CTX *ctx)
 575 {
 576     return EC_GROUP_set_curve(group, p, a, b, ctx);
 577 }
 578
 579 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
 580                            BIGNUM *b, BN_CTX *ctx)
 581 {
 582     return EC_GROUP_get_curve(group, p, a, b, ctx);
 583 }
 584
 585 # ifndef OPENSSL_NO_EC2M
 586 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
 587                             const BIGNUM *b, BN_CTX *ctx)
 588 {
 589     return EC_GROUP_set_curve(group, p, a, b, ctx);
 590 }
 591
 592 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
 593                             BIGNUM *b, BN_CTX *ctx)
 594 {
 595     return EC_GROUP_get_curve(group, p, a, b, ctx);
 596 }
 597 # endif
 598 #endif
 599
 600 int EC_GROUP_get_degree(const EC_GROUP *group)
 601 {
 602     if (group->meth->group_get_degree == 0) {
 603         ECerr(EC_F_EC_GROUP_GET_DEGREE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 604         return 0;
 605     }
 606     return group->meth->group_get_degree(group);
 607 }
 608
 609 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 610 {
 611     if (group->meth->group_check_discriminant == 0) {
 612         ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT,
 613               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 614         return 0;
 615     }
 616     return group->meth->group_check_discriminant(group, ctx);
 617 }
 618
 619 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx)
 620 {
 621     int r = 0;
 622     BIGNUM *a1, *a2, *a3, *b1, *b2, *b3;
 623 #ifndef FIPS_MODULE
 624     BN_CTX *ctx_new = NULL;
 625 #endif
 626
 627     /* compare the field types */
 628     if (EC_GROUP_get_field_type(a) != EC_GROUP_get_field_type(b))
 629         return 1;
 630     /* compare the curve name (if present in both) */
 631     if (EC_GROUP_get_curve_name(a) && EC_GROUP_get_curve_name(b) &&
 632         EC_GROUP_get_curve_name(a) != EC_GROUP_get_curve_name(b))
 633         return 1;
 634     if (a->meth->flags & EC_FLAGS_CUSTOM_CURVE)
 635         return 0;
 636
 637 #ifndef FIPS_MODULE
 638     if (ctx == NULL)
 639         ctx_new = ctx = BN_CTX_new();
 640 #endif
 641     if (ctx == NULL)
 642         return -1;
 643
 644     BN_CTX_start(ctx);
 645     a1 = BN_CTX_get(ctx);
 646     a2 = BN_CTX_get(ctx);
 647     a3 = BN_CTX_get(ctx);
 648     b1 = BN_CTX_get(ctx);
 649     b2 = BN_CTX_get(ctx);
 650     b3 = BN_CTX_get(ctx);
 651     if (b3 == NULL) {
 652         BN_CTX_end(ctx);
 653 #ifndef FIPS_MODULE
 654         BN_CTX_free(ctx_new);
 655 #endif
 656         return -1;
 657     }
 658
 659     /*
 660      * XXX This approach assumes that the external representation of curves
 661      * over the same field type is the same.
 662      */
 663     if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) ||
 664         !b->meth->group_get_curve(b, b1, b2, b3, ctx))
 665         r = 1;
 666
 667     /* return 1 if the curve parameters are different */
 668     if (r || BN_cmp(a1, b1) != 0 || BN_cmp(a2, b2) != 0 || BN_cmp(a3, b3) != 0)
 669         r = 1;
 670
 671     /* XXX EC_POINT_cmp() assumes that the methods are equal */
 672     /* return 1 if the generators are different */
 673     if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a),
 674                           EC_GROUP_get0_generator(b), ctx) != 0)
 675         r = 1;
 676
 677     if (!r) {
 678         const BIGNUM *ao, *bo, *ac, *bc;
 679         /* compare the orders */
 680         ao = EC_GROUP_get0_order(a);
 681         bo = EC_GROUP_get0_order(b);
 682         if (ao == NULL || bo == NULL) {
 683             /* return an error if either order is NULL */
 684             r = -1;
 685             goto end;
 686         }
 687         if (BN_cmp(ao, bo) != 0) {
 688             /* return 1 if orders are different */
 689             r = 1;
 690             goto end;
 691         }
 692         /*
 693          * It gets here if the curve parameters and generator matched.
 694          * Now check the optional cofactors (if both are present).
 695          */
 696         ac = EC_GROUP_get0_cofactor(a);
 697         bc = EC_GROUP_get0_cofactor(b);
 698         /* Returns 1 (mismatch) if both cofactors are specified and different */
 699         if (!BN_is_zero(ac) && !BN_is_zero(bc) && BN_cmp(ac, bc) != 0)
 700             r = 1;
 701         /* Returns 0 if the parameters matched */
 702     }
 703 end:
 704     BN_CTX_end(ctx);
 705 #ifndef FIPS_MODULE
 706     BN_CTX_free(ctx_new);
 707 #endif
 708     return r;
 709 }
 710
 711 /* functions for EC_POINT objects */
 712
 713 EC_POINT *EC_POINT_new(const EC_GROUP *group)
 714 {
 715     EC_POINT *ret;
 716
 717     if (group == NULL) {
 718         ECerr(EC_F_EC_POINT_NEW, ERR_R_PASSED_NULL_PARAMETER);
 719         return NULL;
 720     }
 721     if (group->meth->point_init == NULL) {
 722         ECerr(EC_F_EC_POINT_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 723         return NULL;
 724     }
 725
 726     ret = OPENSSL_zalloc(sizeof(*ret));
 727     if (ret == NULL) {
 728         ECerr(EC_F_EC_POINT_NEW, ERR_R_MALLOC_FAILURE);
 729         return NULL;
 730     }
 731
 732     ret->meth = group->meth;
 733     ret->curve_name = group->curve_name;
 734
 735     if (!ret->meth->point_init(ret)) {
 736         OPENSSL_free(ret);
 737         return NULL;
 738     }
 739
 740     return ret;
 741 }
 742
 743 void EC_POINT_free(EC_POINT *point)
 744 {
 745     if (point == NULL)
 746         return;
 747
 748     if (point->meth->point_finish != 0)
 749         point->meth->point_finish(point);
 750     OPENSSL_free(point);
 751 }
 752
 753 void EC_POINT_clear_free(EC_POINT *point)
 754 {
 755     if (point == NULL)
 756         return;
 757
 758     if (point->meth->point_clear_finish != 0)
 759         point->meth->point_clear_finish(point);
 760     else if (point->meth->point_finish != 0)
 761         point->meth->point_finish(point);
 762     OPENSSL_clear_free(point, sizeof(*point));
 763 }
 764
 765 int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src)
 766 {
 767     if (dest->meth->point_copy == 0) {
 768         ECerr(EC_F_EC_POINT_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 769         return 0;
 770     }
 771     if (dest->meth != src->meth
 772             || (dest->curve_name != src->curve_name
 773                  && dest->curve_name != 0
 774                  && src->curve_name != 0)) {
 775         ECerr(EC_F_EC_POINT_COPY, EC_R_INCOMPATIBLE_OBJECTS);
 776         return 0;
 777     }
 778     if (dest == src)
 779         return 1;
 780     return dest->meth->point_copy(dest, src);
 781 }
 782
 783 EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group)
 784 {
 785     EC_POINT *t;
 786     int r;
 787
 788     if (a == NULL)
 789         return NULL;
 790
 791     t = EC_POINT_new(group);
 792     if (t == NULL)
 793         return NULL;
 794     r = EC_POINT_copy(t, a);
 795     if (!r) {
 796         EC_POINT_free(t);
 797         return NULL;
 798     }
 799     return t;
 800 }
 801
 802 #ifndef OPENSSL_NO_DEPRECATED_3_0
 803 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point)
 804 {
 805     return point->meth;
 806 }
 807 #endif
 808
 809 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
 810 {
 811     if (group->meth->point_set_to_infinity == 0) {
 812         ECerr(EC_F_EC_POINT_SET_TO_INFINITY,
 813               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 814         return 0;
 815     }
 816     if (group->meth != point->meth) {
 817         ECerr(EC_F_EC_POINT_SET_TO_INFINITY, EC_R_INCOMPATIBLE_OBJECTS);
 818         return 0;
 819     }
 820     return group->meth->point_set_to_infinity(group, point);
 821 }
 822
 823 #ifndef OPENSSL_NO_DEPRECATED_3_0
 824 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
 825                                              EC_POINT *point, const BIGNUM *x,
 826                                              const BIGNUM *y, const BIGNUM *z,
 827                                              BN_CTX *ctx)
 828 {
 829     if (group->meth->field_type != NID_X9_62_prime_field) {
 830         ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP,
 831               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 832         return 0;
 833     }
 834     if (!ec_point_is_compat(point, group)) {
 835         ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP,
 836               EC_R_INCOMPATIBLE_OBJECTS);
 837         return 0;
 838     }
 839     return ec_GFp_simple_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx);
 840 }
 841
 842 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
 843                                              const EC_POINT *point, BIGNUM *x,
 844                                              BIGNUM *y, BIGNUM *z,
 845                                              BN_CTX *ctx)
 846 {
 847     if (group->meth->field_type != NID_X9_62_prime_field) {
 848         ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP,
 849               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 850         return 0;
 851     }
 852     if (!ec_point_is_compat(point, group)) {
 853         ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP,
 854               EC_R_INCOMPATIBLE_OBJECTS);
 855         return 0;
 856     }
 857     return ec_GFp_simple_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx);
 858 }
 859 #endif
 860
 861 int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
 862                                     const BIGNUM *x, const BIGNUM *y,
 863                                     BN_CTX *ctx)
 864 {
 865     if (group->meth->point_set_affine_coordinates == NULL) {
 866         ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES,
 867               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 868         return 0;
 869     }
 870     if (!ec_point_is_compat(point, group)) {
 871         ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_INCOMPATIBLE_OBJECTS);
 872         return 0;
 873     }
 874     if (!group->meth->point_set_affine_coordinates(group, point, x, y, ctx))
 875         return 0;
 876
 877     if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
 878         ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_POINT_IS_NOT_ON_CURVE);
 879         return 0;
 880     }
 881     return 1;
 882 }
 883
 884 #ifndef OPENSSL_NO_DEPRECATED_3_0
 885 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
 886                                         EC_POINT *point, const BIGNUM *x,
 887                                         const BIGNUM *y, BN_CTX *ctx)
 888 {
 889     return EC_POINT_set_affine_coordinates(group, point, x, y, ctx);
 890 }
 891
 892 # ifndef OPENSSL_NO_EC2M
 893 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group,
 894                                          EC_POINT *point, const BIGNUM *x,
 895                                          const BIGNUM *y, BN_CTX *ctx)
 896 {
 897     return EC_POINT_set_affine_coordinates(group, point, x, y, ctx);
 898 }
 899 # endif
 900 #endif
 901
 902 int EC_POINT_get_affine_coordinates(const EC_GROUP *group,
 903                                     const EC_POINT *point, BIGNUM *x, BIGNUM *y,
 904                                     BN_CTX *ctx)
 905 {
 906     if (group->meth->point_get_affine_coordinates == NULL) {
 907         ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES,
 908               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 909         return 0;
 910     }
 911     if (!ec_point_is_compat(point, group)) {
 912         ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES, EC_R_INCOMPATIBLE_OBJECTS);
 913         return 0;
 914     }
 915     if (EC_POINT_is_at_infinity(group, point)) {
 916         ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
 917         return 0;
 918     }
 919     return group->meth->point_get_affine_coordinates(group, point, x, y, ctx);
 920 }
 921
 922 #ifndef OPENSSL_NO_DEPRECATED_3_0
 923 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
 924                                         const EC_POINT *point, BIGNUM *x,
 925                                         BIGNUM *y, BN_CTX *ctx)
 926 {
 927     return EC_POINT_get_affine_coordinates(group, point, x, y, ctx);
 928 }
 929
 930 # ifndef OPENSSL_NO_EC2M
 931 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
 932                                          const EC_POINT *point, BIGNUM *x,
 933                                          BIGNUM *y, BN_CTX *ctx)
 934 {
 935     return EC_POINT_get_affine_coordinates(group, point, x, y, ctx);
 936 }
 937 # endif
 938 #endif
 939
 940 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 941                  const EC_POINT *b, BN_CTX *ctx)
 942 {
 943     if (group->meth->add == 0) {
 944         ECerr(EC_F_EC_POINT_ADD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 945         return 0;
 946     }
 947     if (!ec_point_is_compat(r, group) || !ec_point_is_compat(a, group)
 948         || !ec_point_is_compat(b, group)) {
 949         ECerr(EC_F_EC_POINT_ADD, EC_R_INCOMPATIBLE_OBJECTS);
 950         return 0;
 951     }
 952     return group->meth->add(group, r, a, b, ctx);
 953 }
 954
 955 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 956                  BN_CTX *ctx)
 957 {
 958     if (group->meth->dbl == 0) {
 959         ECerr(EC_F_EC_POINT_DBL, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 960         return 0;
 961     }
 962     if (!ec_point_is_compat(r, group) || !ec_point_is_compat(a, group)) {
 963         ECerr(EC_F_EC_POINT_DBL, EC_R_INCOMPATIBLE_OBJECTS);
 964         return 0;
 965     }
 966     return group->meth->dbl(group, r, a, ctx);
 967 }
 968
 969 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx)
 970 {
 971     if (group->meth->invert == 0) {
 972         ECerr(EC_F_EC_POINT_INVERT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 973         return 0;
 974     }
 975     if (!ec_point_is_compat(a, group)) {
 976         ECerr(EC_F_EC_POINT_INVERT, EC_R_INCOMPATIBLE_OBJECTS);
 977         return 0;
 978     }
 979     return group->meth->invert(group, a, ctx);
 980 }
 981
 982 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
 983 {
 984     if (group->meth->is_at_infinity == 0) {
 985         ECerr(EC_F_EC_POINT_IS_AT_INFINITY,
 986               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 987         return 0;
 988     }
 989     if (!ec_point_is_compat(point, group)) {
 990         ECerr(EC_F_EC_POINT_IS_AT_INFINITY, EC_R_INCOMPATIBLE_OBJECTS);
 991         return 0;
 992     }
 993     return group->meth->is_at_infinity(group, point);
 994 }
 995
 996 /*
 997  * Check whether an EC_POINT is on the curve or not. Note that the return
 998  * value for this function should NOT be treated as a boolean. Return values:
 999  *  1: The point is on the curve
1000  *  0: The point is not on the curve
1001  * -1: An error occurred
1002  */
1003 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
1004                          BN_CTX *ctx)
1005 {
1006     if (group->meth->is_on_curve == 0) {
1007         ECerr(EC_F_EC_POINT_IS_ON_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1008         return 0;
1009     }
1010     if (!ec_point_is_compat(point, group)) {
1011         ECerr(EC_F_EC_POINT_IS_ON_CURVE, EC_R_INCOMPATIBLE_OBJECTS);
1012         return 0;
1013     }
1014     return group->meth->is_on_curve(group, point, ctx);
1015 }
1016
1017 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b,
1018                  BN_CTX *ctx)
1019 {
1020     if (group->meth->point_cmp == 0) {
1021         ECerr(EC_F_EC_POINT_CMP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1022         return -1;
1023     }
1024     if (!ec_point_is_compat(a, group) || !ec_point_is_compat(b, group)) {
1025         ECerr(EC_F_EC_POINT_CMP, EC_R_INCOMPATIBLE_OBJECTS);
1026         return -1;
1027     }
1028     return group->meth->point_cmp(group, a, b, ctx);
1029 }
1030
1031 #ifndef OPENSSL_NO_DEPRECATED_3_0
1032 int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1033 {
1034     if (group->meth->make_affine == 0) {
1035         ECerr(EC_F_EC_POINT_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1036         return 0;
1037     }
1038     if (!ec_point_is_compat(point, group)) {
1039         ECerr(EC_F_EC_POINT_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS);
1040         return 0;
1041     }
1042     return group->meth->make_affine(group, point, ctx);
1043 }
1044
1045 int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
1046                           EC_POINT *points[], BN_CTX *ctx)
1047 {
1048     size_t i;
1049
1050     if (group->meth->points_make_affine == 0) {
1051         ECerr(EC_F_EC_POINTS_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1052         return 0;
1053     }
1054     for (i = 0; i < num; i++) {
1055         if (!ec_point_is_compat(points[i], group)) {
1056             ECerr(EC_F_EC_POINTS_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS);
1057             return 0;
1058         }
1059     }
1060     return group->meth->points_make_affine(group, num, points, ctx);
1061 }
1062 #endif
1063
1064 /*
1065  * Functions for point multiplication. If group->meth->mul is 0, we use the
1066  * wNAF-based implementations in ec_mult.c; otherwise we dispatch through
1067  * methods.
1068  */
1069
1070 #ifndef OPENSSL_NO_DEPRECATED_3_0
1071 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
1072                   size_t num, const EC_POINT *points[],
1073                   const BIGNUM *scalars[], BN_CTX *ctx)
1074 {
1075     int ret = 0;
1076     size_t i = 0;
1077 #ifndef FIPS_MODULE
1078     BN_CTX *new_ctx = NULL;
1079 #endif
1080
1081     if (!ec_point_is_compat(r, group)) {
1082         ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1083         return 0;
1084     }
1085
1086     if (scalar == NULL && num == 0)
1087         return EC_POINT_set_to_infinity(group, r);
1088
1089     for (i = 0; i < num; i++) {
1090         if (!ec_point_is_compat(points[i], group)) {
1091             ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1092             return 0;
1093         }
1094     }
1095
1096 #ifndef FIPS_MODULE
1097     if (ctx == NULL)
1098         ctx = new_ctx = BN_CTX_secure_new();
1099 #endif
1100     if (ctx == NULL) {
1101         ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
1102         return 0;
1103     }
1104
1105     if (group->meth->mul != NULL)
1106         ret = group->meth->mul(group, r, scalar, num, points, scalars, ctx);
1107     else
1108         /* use default */
1109         ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
1110
1111 #ifndef FIPS_MODULE
1112     BN_CTX_free(new_ctx);
1113 #endif
1114     return ret;
1115 }
1116 #endif
1117
1118 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
1119                  const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
1120 {
1121     int ret = 0;
1122     size_t num;
1123 #ifndef FIPS_MODULE
1124     BN_CTX *new_ctx = NULL;
1125 #endif
1126
1127     if (!ec_point_is_compat(r, group)
1128         || (point != NULL && !ec_point_is_compat(point, group))) {
1129         ECerr(EC_F_EC_POINT_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1130         return 0;
1131     }
1132
1133     if (g_scalar == NULL && p_scalar == NULL)
1134         return EC_POINT_set_to_infinity(group, r);
1135
1136 #ifndef FIPS_MODULE
1137     if (ctx == NULL)
1138         ctx = new_ctx = BN_CTX_secure_new();
1139 #endif
1140     if (ctx == NULL) {
1141         ECerr(EC_F_EC_POINT_MUL, ERR_R_INTERNAL_ERROR);
1142         return 0;
1143     }
1144
1145     num = (point != NULL && p_scalar != NULL) ? 1 : 0;
1146     if (group->meth->mul != NULL)
1147         ret = group->meth->mul(group, r, g_scalar, num, &point, &p_scalar, ctx);
1148     else
1149         /* use default */
1150         ret = ec_wNAF_mul(group, r, g_scalar, num, &point, &p_scalar, ctx);
1151
1152 #ifndef FIPS_MODULE
1153     BN_CTX_free(new_ctx);
1154 #endif
1155     return ret;
1156 }
1157
1158 #ifndef OPENSSL_NO_DEPRECATED_3_0
1159 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1160 {
1161     if (group->meth->mul == 0)
1162         /* use default */
1163         return ec_wNAF_precompute_mult(group, ctx);
1164
1165     if (group->meth->precompute_mult != 0)
1166         return group->meth->precompute_mult(group, ctx);
1167     else
1168         return 1;               /* nothing to do, so report success */
1169 }
1170
1171 int EC_GROUP_have_precompute_mult(const EC_GROUP *group)
1172 {
1173     if (group->meth->mul == 0)
1174         /* use default */
1175         return ec_wNAF_have_precompute_mult(group);
1176
1177     if (group->meth->have_precompute_mult != 0)
1178         return group->meth->have_precompute_mult(group);
1179     else
1180         return 0;               /* cannot tell whether precomputation has
1181                                  * been performed */
1182 }
1183 #endif
1184
1185 /*
1186  * ec_precompute_mont_data sets |group->mont_data| from |group->order| and
1187  * returns one on success. On error it returns zero.
1188  */
1189 static int ec_precompute_mont_data(EC_GROUP *group)
1190 {
1191     BN_CTX *ctx = BN_CTX_new_ex(group->libctx);
1192     int ret = 0;
1193
1194     BN_MONT_CTX_free(group->mont_data);
1195     group->mont_data = NULL;
1196
1197     if (ctx == NULL)
1198         goto err;
1199
1200     group->mont_data = BN_MONT_CTX_new();
1201     if (group->mont_data == NULL)
1202         goto err;
1203
1204     if (!BN_MONT_CTX_set(group->mont_data, group->order, ctx)) {
1205         BN_MONT_CTX_free(group->mont_data);
1206         group->mont_data = NULL;
1207         goto err;
1208     }
1209
1210     ret = 1;
1211
1212  err:
1213
1214     BN_CTX_free(ctx);
1215     return ret;
1216 }
1217
1218 #ifndef FIPS_MODULE
1219 int EC_KEY_set_ex_data(EC_KEY *key, int idx, void *arg)
1220 {
1221     return CRYPTO_set_ex_data(&key->ex_data, idx, arg);
1222 }
1223
1224 void *EC_KEY_get_ex_data(const EC_KEY *key, int idx)
1225 {
1226     return CRYPTO_get_ex_data(&key->ex_data, idx);
1227 }
1228 #endif
1229
1230 int ec_group_simple_order_bits(const EC_GROUP *group)
1231 {
1232     if (group->order == NULL)
1233         return 0;
1234     return BN_num_bits(group->order);
1235 }
1236
1237 static int ec_field_inverse_mod_ord(const EC_GROUP *group, BIGNUM *r,
1238                                     const BIGNUM *x, BN_CTX *ctx)
1239 {
1240     BIGNUM *e = NULL;
1241     int ret = 0;
1242 #ifndef FIPS_MODULE
1243     BN_CTX *new_ctx = NULL;
1244 #endif
1245
1246     if (group->mont_data == NULL)
1247         return 0;
1248
1249 #ifndef FIPS_MODULE
1250     if (ctx == NULL)
1251         ctx = new_ctx = BN_CTX_secure_new();
1252 #endif
1253     if (ctx == NULL)
1254         return 0;
1255
1256     BN_CTX_start(ctx);
1257     if ((e = BN_CTX_get(ctx)) == NULL)
1258         goto err;
1259
1260     /*-
1261      * We want inverse in constant time, therefore we utilize the fact
1262      * order must be prime and use Fermats Little Theorem instead.
1263      */
1264     if (!BN_set_word(e, 2))
1265         goto err;
1266     if (!BN_sub(e, group->order, e))
1267         goto err;
1268     /*-
1269      * Exponent e is public.
1270      * No need for scatter-gather or BN_FLG_CONSTTIME.
1271      */
1272     if (!BN_mod_exp_mont(r, x, e, group->order, ctx, group->mont_data))
1273         goto err;
1274
1275     ret = 1;
1276
1277  err:
1278     BN_CTX_end(ctx);
1279 #ifndef FIPS_MODULE
1280     BN_CTX_free(new_ctx);
1281 #endif
1282     return ret;
1283 }
1284
1285 /*-
1286  * Default behavior, if group->meth->field_inverse_mod_ord is NULL:
1287  * - When group->order is even, this function returns an error.
1288  * - When group->order is otherwise composite, the correctness
1289  *   of the output is not guaranteed.
1290  * - When x is outside the range [1, group->order), the correctness
1291  *   of the output is not guaranteed.
1292  * - Otherwise, this function returns the multiplicative inverse in the
1293  *   range [1, group->order).
1294  *
1295  * EC_METHODs must implement their own field_inverse_mod_ord for
1296  * other functionality.
1297  */
1298 int ec_group_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
1299                             const BIGNUM *x, BN_CTX *ctx)
1300 {
1301     if (group->meth->field_inverse_mod_ord != NULL)
1302         return group->meth->field_inverse_mod_ord(group, res, x, ctx);
1303     else
1304         return ec_field_inverse_mod_ord(group, res, x, ctx);
1305 }
1306
1307 /*-
1308  * Coordinate blinding for EC_POINT.
1309  *
1310  * The underlying EC_METHOD can optionally implement this function:
1311  * underlying implementations should return 0 on errors, or 1 on
1312  * success.
1313  *
1314  * This wrapper returns 1 in case the underlying EC_METHOD does not
1315  * support coordinate blinding.
1316  */
1317 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx)
1318 {
1319     if (group->meth->blind_coordinates == NULL)
1320         return 1; /* ignore if not implemented */
1321
1322     return group->meth->blind_coordinates(group, p, ctx);
1323 }
1324
1325 int EC_GROUP_get_basis_type(const EC_GROUP *group)
1326 {
1327     int i;
1328
1329     if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field)
1330         /* everything else is currently not supported */
1331         return 0;
1332
1333     /* Find the last non-zero element of group->poly[] */
1334     for (i = 0;
1335          i < (int)OSSL_NELEM(group->poly) && group->poly[i] != 0;
1336          i++)
1337         continue;
1338
1339     if (i == 4)
1340         return NID_X9_62_ppBasis;
1341     else if (i == 2)
1342         return NID_X9_62_tpBasis;
1343     else
1344         /* everything else is currently not supported */
1345         return 0;
1346 }
1347
1348 #ifndef OPENSSL_NO_EC2M
1349 int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k)
1350 {
1351     if (group == NULL)
1352         return 0;
1353
1354     if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field
1355         || !((group->poly[0] != 0) && (group->poly[1] != 0)
1356              && (group->poly[2] == 0))) {
1357         ECerr(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS,
1358               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1359         return 0;
1360     }
1361
1362     if (k)
1363         *k = group->poly[1];
1364
1365     return 1;
1366 }
1367
1368 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1,
1369                                    unsigned int *k2, unsigned int *k3)
1370 {
1371     if (group == NULL)
1372         return 0;
1373
1374     if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field
1375         || !((group->poly[0] != 0) && (group->poly[1] != 0)
1376              && (group->poly[2] != 0) && (group->poly[3] != 0)
1377              && (group->poly[4] == 0))) {
1378         ECerr(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS,
1379               ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1380         return 0;
1381     }
1382
1383     if (k1)
1384         *k1 = group->poly[3];
1385     if (k2)
1386         *k2 = group->poly[2];
1387     if (k3)
1388         *k3 = group->poly[1];
1389
1390     return 1;
1391 }
1392 #endif
1393
1394 /*
1395  * Check if the explicit parameters group matches any built-in curves.
1396  *
1397  * We create a copy of the group just built, so that we can remove optional
1398  * fields for the lookup: we do this to avoid the possibility that one of
1399  * the optional parameters is used to force the library into using a less
1400  * performant and less secure EC_METHOD instead of the specialized one.
1401  * In any case, `seed` is not really used in any computation, while a
1402  * cofactor different from the one in the built-in table is just
1403  * mathematically wrong anyway and should not be used.
1404  */
1405 static EC_GROUP *ec_group_explicit_to_named(const EC_GROUP *group,
1406                                             OPENSSL_CTX *libctx,
1407                                             const char *propq,
1408                                             BN_CTX *ctx)
1409 {
1410     EC_GROUP *ret_group = NULL, *dup = NULL;
1411     int curve_name_nid;
1412
1413     const EC_POINT *point = EC_GROUP_get0_generator(group);
1414     const BIGNUM *order = EC_GROUP_get0_order(group);
1415     int no_seed = (EC_GROUP_get0_seed(group) == NULL);
1416
1417     if ((dup = EC_GROUP_dup(group)) == NULL
1418             || EC_GROUP_set_seed(dup, NULL, 0) != 1
1419             || !EC_GROUP_set_generator(dup, point, order, NULL))
1420         goto err;
1421     if ((curve_name_nid = ec_curve_nid_from_params(dup, ctx)) != NID_undef) {
1422         /*
1423          * The input explicit parameters successfully matched one of the
1424          * built-in curves: often for built-in curves we have specialized
1425          * methods with better performance and hardening.
1426          *
1427          * In this case we replace the `EC_GROUP` created through explicit
1428          * parameters with one created from a named group.
1429          */
1430
1431 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1432         /*
1433          * NID_wap_wsg_idm_ecid_wtls12 and NID_secp224r1 are both aliases for
1434          * the same curve, we prefer the SECP nid when matching explicit
1435          * parameters as that is associated with a specialized EC_METHOD.
1436          */
1437         if (curve_name_nid == NID_wap_wsg_idm_ecid_wtls12)
1438             curve_name_nid = NID_secp224r1;
1439 #endif /* !def(OPENSSL_NO_EC_NISTP_64_GCC_128) */
1440
1441         ret_group = EC_GROUP_new_by_curve_name_with_libctx(libctx, propq,
1442                                                            curve_name_nid);
1443         if (ret_group == NULL)
1444             goto err;
1445
1446         /*
1447          * Set the flag so that EC_GROUPs created from explicit parameters are
1448          * serialized using explicit parameters by default.
1449          */
1450         EC_GROUP_set_asn1_flag(ret_group, OPENSSL_EC_EXPLICIT_CURVE);
1451
1452         /*
1453          * If the input params do not contain the optional seed field we make
1454          * sure it is not added to the returned group.
1455          *
1456          * The seed field is not really used inside libcrypto anyway, and
1457          * adding it to parsed explicit parameter keys would alter their DER
1458          * encoding output (because of the extra field) which could impact
1459          * applications fingerprinting keys by their DER encoding.
1460          */
1461         if (no_seed) {
1462             if (EC_GROUP_set_seed(ret_group, NULL, 0) != 1)
1463                 goto err;
1464         }
1465     } else {
1466         ret_group = (EC_GROUP *)group;
1467     }
1468     EC_GROUP_free(dup);
1469     return ret_group;
1470 err:
1471     EC_GROUP_free(dup);
1472     EC_GROUP_free(ret_group);
1473     return NULL;
1474 }
1475
1476 static int ec_encoding_param2id(const OSSL_PARAM *p, int *id)
1477 {
1478     const char *name = NULL;
1479     int status = 0;
1480
1481     switch (p->data_type) {
1482     case OSSL_PARAM_UTF8_STRING:
1483         /* The OSSL_PARAM functions have no support for this */
1484         name = p->data;
1485         status = (name != NULL);
1486         break;
1487     case OSSL_PARAM_UTF8_PTR:
1488         status = OSSL_PARAM_get_utf8_ptr(p, &name);
1489         break;
1490     }
1491     if (status) {
1492         int i = ec_encoding_name2id(name);
1493
1494         if (i >= 0) {
1495             *id = i;
1496             return 1;
1497         }
1498     }
1499     return 0;
1500 }
1501
1502 static EC_GROUP *group_new_from_name(const OSSL_PARAM *p,
1503                                      OPENSSL_CTX *libctx, const char *propq)
1504 {
1505     int ok = 0, nid;
1506     const char *curve_name = NULL;
1507
1508     switch (p->data_type) {
1509     case OSSL_PARAM_UTF8_STRING:
1510         /* The OSSL_PARAM functions have no support for this */
1511         curve_name = p->data;
1512         ok = (curve_name != NULL);
1513         break;
1514     case OSSL_PARAM_UTF8_PTR:
1515         ok = OSSL_PARAM_get_utf8_ptr(p, &curve_name);
1516         break;
1517     }
1518
1519     if (ok) {
1520         nid = ec_curve_name2nid(curve_name);
1521         if (nid == NID_undef) {
1522             ECerr(0, EC_R_INVALID_CURVE);
1523             return NULL;
1524         } else {
1525             return EC_GROUP_new_by_curve_name_with_libctx(libctx, propq, nid);
1526         }
1527     }
1528     return NULL;
1529 }
1530
1531 EC_GROUP *EC_GROUP_new_from_params(const OSSL_PARAM params[],
1532                                    OPENSSL_CTX *libctx, const char *propq)
1533 {
1534     const OSSL_PARAM *ptmp, *pa, *pb;
1535     int ok = 0;
1536     EC_GROUP *group = NULL, *named_group = NULL;
1537     BIGNUM *p = NULL, *a = NULL, *b = NULL, *order = NULL, *cofactor = NULL;
1538     EC_POINT *point = NULL;
1539     int field_bits = 0;
1540     int is_prime_field = 1;
1541     BN_CTX *bnctx = NULL;
1542     const unsigned char *buf = NULL;
1543     int encoding_flag = -1;
1544
1545     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_ENCODING);
1546     if (ptmp != NULL && !ec_encoding_param2id(ptmp, &encoding_flag)) {
1547         ECerr(0, EC_R_INVALID_ENCODING);
1548         return 0;
1549     }
1550
1551     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_GROUP_NAME);
1552     if (ptmp != NULL) {
1553         group = group_new_from_name(ptmp, libctx, propq);
1554         if (group != NULL)
1555             EC_GROUP_set_asn1_flag(group, encoding_flag);
1556         return group;
1557     }
1558     bnctx = BN_CTX_new_ex(libctx);
1559     if (bnctx == NULL) {
1560         ECerr(0, ERR_R_MALLOC_FAILURE);
1561         return 0;
1562     }
1563     BN_CTX_start(bnctx);
1564
1565     p = BN_CTX_get(bnctx);
1566     a = BN_CTX_get(bnctx);
1567     b = BN_CTX_get(bnctx);
1568     order = BN_CTX_get(bnctx);
1569     if (order == NULL) {
1570         ECerr(0, ERR_R_MALLOC_FAILURE);
1571         goto err;
1572     }
1573
1574     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_FIELD_TYPE);
1575     if (ptmp == NULL || ptmp->data_type != OSSL_PARAM_UTF8_STRING) {
1576         ECerr(0, EC_R_INVALID_FIELD);
1577         goto err;
1578     }
1579     if (strcasecmp(ptmp->data, SN_X9_62_prime_field) == 0) {
1580         is_prime_field = 1;
1581     } else if (strcasecmp(ptmp->data, SN_X9_62_characteristic_two_field) == 0) {
1582         is_prime_field = 0;
1583     } else {
1584         /* Invalid field */
1585         ECerr(0, EC_R_UNSUPPORTED_FIELD);
1586         goto err;
1587     }
1588
1589     pa = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_A);
1590     if (!OSSL_PARAM_get_BN(pa, &a)) {
1591         ECerr(0, EC_R_INVALID_A);
1592         goto err;
1593     }
1594     pb = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_B);
1595     if (!OSSL_PARAM_get_BN(pb, &b)) {
1596         ECerr(0, EC_R_INVALID_B);
1597         goto err;
1598     }
1599
1600     /* extract the prime number or irreducible polynomial */
1601     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_P);
1602     if (!OSSL_PARAM_get_BN(ptmp, &p)) {
1603         ECerr(0, EC_R_INVALID_P);
1604         goto err;
1605     }
1606
1607     if (is_prime_field) {
1608         if (BN_is_negative(p) || BN_is_zero(p)) {
1609             ECerr(0, EC_R_INVALID_P);
1610             goto err;
1611         }
1612         field_bits = BN_num_bits(p);
1613         if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) {
1614             ECerr(0, EC_R_FIELD_TOO_LARGE);
1615             goto err;
1616         }
1617
1618         /* create the EC_GROUP structure */
1619         group = EC_GROUP_new_curve_GFp(p, a, b, bnctx);
1620     } else {
1621 #ifdef OPENSSL_NO_EC2M
1622         ECerr(0, EC_R_GF2M_NOT_SUPPORTED);
1623         goto err;
1624 #else
1625         /* create the EC_GROUP structure */
1626         group = EC_GROUP_new_curve_GF2m(p, a, b, NULL);
1627         if (group != NULL) {
1628             field_bits = EC_GROUP_get_degree(group);
1629             if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) {
1630                 ECerr(0, EC_R_FIELD_TOO_LARGE);
1631                 goto err;
1632             }
1633         }
1634 #endif /* OPENSSL_NO_EC2M */
1635     }
1636
1637     if (group == NULL) {
1638         ECerr(0, ERR_R_EC_LIB);
1639         goto err;
1640     }
1641
1642     /* Optional seed */
1643     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_SEED);
1644     if (ptmp != NULL) {
1645         if (ptmp->data_type != OSSL_PARAM_OCTET_STRING) {
1646             ECerr(0, EC_R_INVALID_SEED);
1647             goto err;
1648         }
1649         if (!EC_GROUP_set_seed(group, ptmp->data, ptmp->data_size))
1650             goto err;
1651     }
1652
1653     /* generator base point */
1654     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_GENERATOR);
1655     if (ptmp == NULL
1656         || ptmp->data_type != OSSL_PARAM_OCTET_STRING) {
1657         ECerr(0, EC_R_INVALID_GENERATOR);
1658         goto err;
1659     }
1660     buf = (const unsigned char *)(ptmp->data);
1661     if ((point = EC_POINT_new(group)) == NULL)
1662         goto err;
1663     EC_GROUP_set_point_conversion_form(group,
1664                                        (point_conversion_form_t)buf[0] & ~0x01);
1665     if (!EC_POINT_oct2point(group, point, buf, ptmp->data_size, bnctx)) {
1666         ECerr(0, EC_R_INVALID_GENERATOR);
1667         goto err;
1668     }
1669
1670     /* order */
1671     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_ORDER);
1672     if (!OSSL_PARAM_get_BN(ptmp, &order)
1673         || (BN_is_negative(order) || BN_is_zero(order))
1674         || (BN_num_bits(order) > (int)field_bits + 1)) { /* Hasse bound */
1675         ECerr(0, EC_R_INVALID_GROUP_ORDER);
1676         goto err;
1677     }
1678
1679     /* Optional cofactor */
1680     ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_COFACTOR);
1681     if (ptmp != NULL) {
1682         cofactor = BN_CTX_get(bnctx);
1683         if (cofactor == NULL || !OSSL_PARAM_get_BN(ptmp, &cofactor)) {
1684             ECerr(0, EC_R_INVALID_COFACTOR);
1685             goto err;
1686         }
1687     }
1688
1689     /* set the generator, order and cofactor (if present) */
1690     if (!EC_GROUP_set_generator(group, point, order, cofactor)) {
1691         ECerr(0, EC_R_INVALID_GENERATOR);
1692         goto err;
1693     }
1694
1695     named_group = ec_group_explicit_to_named(group, libctx, propq, bnctx);
1696     if (named_group == NULL) {
1697         ECerr(0, EC_R_INVALID_NAMED_GROUP_CONVERSION);
1698         goto err;
1699     }
1700     if (named_group == group) {
1701         /*
1702          * If we did not find a named group then the encoding should be explicit
1703          * if it was specified
1704          */
1705         if (encoding_flag == OPENSSL_EC_NAMED_CURVE) {
1706             ECerr(0, EC_R_INVALID_ENCODING);
1707             goto err;
1708         }
1709         EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE);
1710     } else {
1711         EC_GROUP_free(group);
1712         group = named_group;
1713     }
1714     ok = 1;
1715  err:
1716     if (!ok) {
1717         EC_GROUP_free(group);
1718         group = NULL;
1719     }
1720     EC_POINT_free(point);
1721     BN_CTX_end(bnctx);
1722     BN_CTX_free(bnctx);
1723
1724     return group;
1725 }