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