crypto/ec/ecp_smpl.c

   1 /*
   2  * Copyright 2001-2021 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 <openssl/err.h>
  18 #include <openssl/symhacks.h>
  19
  20 #include "ec_local.h"
  21
  22 const EC_METHOD *EC_GFp_simple_method(void)
  23 {
  24     static const EC_METHOD ret = {
  25         EC_FLAGS_DEFAULT_OCT,
  26         NID_X9_62_prime_field,
  27         ossl_ec_GFp_simple_group_init,
  28         ossl_ec_GFp_simple_group_finish,
  29         ossl_ec_GFp_simple_group_clear_finish,
  30         ossl_ec_GFp_simple_group_copy,
  31         ossl_ec_GFp_simple_group_set_curve,
  32         ossl_ec_GFp_simple_group_get_curve,
  33         ossl_ec_GFp_simple_group_get_degree,
  34         ossl_ec_group_simple_order_bits,
  35         ossl_ec_GFp_simple_group_check_discriminant,
  36         ossl_ec_GFp_simple_point_init,
  37         ossl_ec_GFp_simple_point_finish,
  38         ossl_ec_GFp_simple_point_clear_finish,
  39         ossl_ec_GFp_simple_point_copy,
  40         ossl_ec_GFp_simple_point_set_to_infinity,
  41         ossl_ec_GFp_simple_point_set_affine_coordinates,
  42         ossl_ec_GFp_simple_point_get_affine_coordinates,
  43         0, 0, 0,
  44         ossl_ec_GFp_simple_add,
  45         ossl_ec_GFp_simple_dbl,
  46         ossl_ec_GFp_simple_invert,
  47         ossl_ec_GFp_simple_is_at_infinity,
  48         ossl_ec_GFp_simple_is_on_curve,
  49         ossl_ec_GFp_simple_cmp,
  50         ossl_ec_GFp_simple_make_affine,
  51         ossl_ec_GFp_simple_points_make_affine,
  52         0 /* mul */ ,
  53         0 /* precompute_mult */ ,
  54         0 /* have_precompute_mult */ ,
  55         ossl_ec_GFp_simple_field_mul,
  56         ossl_ec_GFp_simple_field_sqr,
  57         0 /* field_div */ ,
  58         ossl_ec_GFp_simple_field_inv,
  59         0 /* field_encode */ ,
  60         0 /* field_decode */ ,
  61         0,                      /* field_set_to_one */
  62         ossl_ec_key_simple_priv2oct,
  63         ossl_ec_key_simple_oct2priv,
  64         0, /* set private */
  65         ossl_ec_key_simple_generate_key,
  66         ossl_ec_key_simple_check_key,
  67         ossl_ec_key_simple_generate_public_key,
  68         0, /* keycopy */
  69         0, /* keyfinish */
  70         ossl_ecdh_simple_compute_key,
  71         ossl_ecdsa_simple_sign_setup,
  72         ossl_ecdsa_simple_sign_sig,
  73         ossl_ecdsa_simple_verify_sig,
  74         0, /* field_inverse_mod_ord */
  75         ossl_ec_GFp_simple_blind_coordinates,
  76         ossl_ec_GFp_simple_ladder_pre,
  77         ossl_ec_GFp_simple_ladder_step,
  78         ossl_ec_GFp_simple_ladder_post
  79     };
  80
  81     return &ret;
  82 }
  83
  84 /*
  85  * Most method functions in this file are designed to work with
  86  * non-trivial representations of field elements if necessary
  87  * (see ecp_mont.c): while standard modular addition and subtraction
  88  * are used, the field_mul and field_sqr methods will be used for
  89  * multiplication, and field_encode and field_decode (if defined)
  90  * will be used for converting between representations.
  91  *
  92  * Functions ec_GFp_simple_points_make_affine() and
  93  * ec_GFp_simple_point_get_affine_coordinates() specifically assume
  94  * that if a non-trivial representation is used, it is a Montgomery
  95  * representation (i.e. 'encoding' means multiplying by some factor R).
  96  */
  97
  98 int ossl_ec_GFp_simple_group_init(EC_GROUP *group)
  99 {
 100     group->field = BN_new();
 101     group->a = BN_new();
 102     group->b = BN_new();
 103     if (group->field == NULL || group->a == NULL || group->b == NULL) {
 104         BN_free(group->field);
 105         BN_free(group->a);
 106         BN_free(group->b);
 107         return 0;
 108     }
 109     group->a_is_minus3 = 0;
 110     return 1;
 111 }
 112
 113 void ossl_ec_GFp_simple_group_finish(EC_GROUP *group)
 114 {
 115     BN_free(group->field);
 116     BN_free(group->a);
 117     BN_free(group->b);
 118 }
 119
 120 void ossl_ec_GFp_simple_group_clear_finish(EC_GROUP *group)
 121 {
 122     BN_clear_free(group->field);
 123     BN_clear_free(group->a);
 124     BN_clear_free(group->b);
 125 }
 126
 127 int ossl_ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
 128 {
 129     if (!BN_copy(dest->field, src->field))
 130         return 0;
 131     if (!BN_copy(dest->a, src->a))
 132         return 0;
 133     if (!BN_copy(dest->b, src->b))
 134         return 0;
 135
 136     dest->a_is_minus3 = src->a_is_minus3;
 137
 138     return 1;
 139 }
 140
 141 int ossl_ec_GFp_simple_group_set_curve(EC_GROUP *group,
 142                                        const BIGNUM *p, const BIGNUM *a,
 143                                        const BIGNUM *b, BN_CTX *ctx)
 144 {
 145     int ret = 0;
 146     BN_CTX *new_ctx = NULL;
 147     BIGNUM *tmp_a;
 148
 149     /* p must be a prime > 3 */
 150     if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
 151         ERR_raise(ERR_LIB_EC, EC_R_INVALID_FIELD);
 152         return 0;
 153     }
 154
 155     if (ctx == NULL) {
 156         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 157         if (ctx == NULL)
 158             return 0;
 159     }
 160
 161     BN_CTX_start(ctx);
 162     tmp_a = BN_CTX_get(ctx);
 163     if (tmp_a == NULL)
 164         goto err;
 165
 166     /* group->field */
 167     if (!BN_copy(group->field, p))
 168         goto err;
 169     BN_set_negative(group->field, 0);
 170
 171     /* group->a */
 172     if (!BN_nnmod(tmp_a, a, p, ctx))
 173         goto err;
 174     if (group->meth->field_encode) {
 175         if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
 176             goto err;
 177     } else if (!BN_copy(group->a, tmp_a))
 178         goto err;
 179
 180     /* group->b */
 181     if (!BN_nnmod(group->b, b, p, ctx))
 182         goto err;
 183     if (group->meth->field_encode)
 184         if (!group->meth->field_encode(group, group->b, group->b, ctx))
 185             goto err;
 186
 187     /* group->a_is_minus3 */
 188     if (!BN_add_word(tmp_a, 3))
 189         goto err;
 190     group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
 191
 192     ret = 1;
 193
 194  err:
 195     BN_CTX_end(ctx);
 196     BN_CTX_free(new_ctx);
 197     return ret;
 198 }
 199
 200 int ossl_ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
 201                                        BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 202 {
 203     int ret = 0;
 204     BN_CTX *new_ctx = NULL;
 205
 206     if (p != NULL) {
 207         if (!BN_copy(p, group->field))
 208             return 0;
 209     }
 210
 211     if (a != NULL || b != NULL) {
 212         if (group->meth->field_decode) {
 213             if (ctx == NULL) {
 214                 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 215                 if (ctx == NULL)
 216                     return 0;
 217             }
 218             if (a != NULL) {
 219                 if (!group->meth->field_decode(group, a, group->a, ctx))
 220                     goto err;
 221             }
 222             if (b != NULL) {
 223                 if (!group->meth->field_decode(group, b, group->b, ctx))
 224                     goto err;
 225             }
 226         } else {
 227             if (a != NULL) {
 228                 if (!BN_copy(a, group->a))
 229                     goto err;
 230             }
 231             if (b != NULL) {
 232                 if (!BN_copy(b, group->b))
 233                     goto err;
 234             }
 235         }
 236     }
 237
 238     ret = 1;
 239
 240  err:
 241     BN_CTX_free(new_ctx);
 242     return ret;
 243 }
 244
 245 int ossl_ec_GFp_simple_group_get_degree(const EC_GROUP *group)
 246 {
 247     return BN_num_bits(group->field);
 248 }
 249
 250 int ossl_ec_GFp_simple_group_check_discriminant(const EC_GROUP *group,
 251                                                 BN_CTX *ctx)
 252 {
 253     int ret = 0;
 254     BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
 255     const BIGNUM *p = group->field;
 256     BN_CTX *new_ctx = NULL;
 257
 258     if (ctx == NULL) {
 259         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 260         if (ctx == NULL) {
 261             ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 262             goto err;
 263         }
 264     }
 265     BN_CTX_start(ctx);
 266     a = BN_CTX_get(ctx);
 267     b = BN_CTX_get(ctx);
 268     tmp_1 = BN_CTX_get(ctx);
 269     tmp_2 = BN_CTX_get(ctx);
 270     order = BN_CTX_get(ctx);
 271     if (order == NULL)
 272         goto err;
 273
 274     if (group->meth->field_decode) {
 275         if (!group->meth->field_decode(group, a, group->a, ctx))
 276             goto err;
 277         if (!group->meth->field_decode(group, b, group->b, ctx))
 278             goto err;
 279     } else {
 280         if (!BN_copy(a, group->a))
 281             goto err;
 282         if (!BN_copy(b, group->b))
 283             goto err;
 284     }
 285
 286     /*-
 287      * check the discriminant:
 288      * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
 289      * 0 =< a, b < p
 290      */
 291     if (BN_is_zero(a)) {
 292         if (BN_is_zero(b))
 293             goto err;
 294     } else if (!BN_is_zero(b)) {
 295         if (!BN_mod_sqr(tmp_1, a, p, ctx))
 296             goto err;
 297         if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
 298             goto err;
 299         if (!BN_lshift(tmp_1, tmp_2, 2))
 300             goto err;
 301         /* tmp_1 = 4*a^3 */
 302
 303         if (!BN_mod_sqr(tmp_2, b, p, ctx))
 304             goto err;
 305         if (!BN_mul_word(tmp_2, 27))
 306             goto err;
 307         /* tmp_2 = 27*b^2 */
 308
 309         if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
 310             goto err;
 311         if (BN_is_zero(a))
 312             goto err;
 313     }
 314     ret = 1;
 315
 316  err:
 317     BN_CTX_end(ctx);
 318     BN_CTX_free(new_ctx);
 319     return ret;
 320 }
 321
 322 int ossl_ec_GFp_simple_point_init(EC_POINT *point)
 323 {
 324     point->X = BN_new();
 325     point->Y = BN_new();
 326     point->Z = BN_new();
 327     point->Z_is_one = 0;
 328
 329     if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
 330         BN_free(point->X);
 331         BN_free(point->Y);
 332         BN_free(point->Z);
 333         return 0;
 334     }
 335     return 1;
 336 }
 337
 338 void ossl_ec_GFp_simple_point_finish(EC_POINT *point)
 339 {
 340     BN_free(point->X);
 341     BN_free(point->Y);
 342     BN_free(point->Z);
 343 }
 344
 345 void ossl_ec_GFp_simple_point_clear_finish(EC_POINT *point)
 346 {
 347     BN_clear_free(point->X);
 348     BN_clear_free(point->Y);
 349     BN_clear_free(point->Z);
 350     point->Z_is_one = 0;
 351 }
 352
 353 int ossl_ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
 354 {
 355     if (!BN_copy(dest->X, src->X))
 356         return 0;
 357     if (!BN_copy(dest->Y, src->Y))
 358         return 0;
 359     if (!BN_copy(dest->Z, src->Z))
 360         return 0;
 361     dest->Z_is_one = src->Z_is_one;
 362     dest->curve_name = src->curve_name;
 363
 364     return 1;
 365 }
 366
 367 int ossl_ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
 368                                              EC_POINT *point)
 369 {
 370     point->Z_is_one = 0;
 371     BN_zero(point->Z);
 372     return 1;
 373 }
 374
 375 int ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
 376                                                        EC_POINT *point,
 377                                                        const BIGNUM *x,
 378                                                        const BIGNUM *y,
 379                                                        const BIGNUM *z,
 380                                                        BN_CTX *ctx)
 381 {
 382     BN_CTX *new_ctx = NULL;
 383     int ret = 0;
 384
 385     if (ctx == NULL) {
 386         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 387         if (ctx == NULL)
 388             return 0;
 389     }
 390
 391     if (x != NULL) {
 392         if (!BN_nnmod(point->X, x, group->field, ctx))
 393             goto err;
 394         if (group->meth->field_encode) {
 395             if (!group->meth->field_encode(group, point->X, point->X, ctx))
 396                 goto err;
 397         }
 398     }
 399
 400     if (y != NULL) {
 401         if (!BN_nnmod(point->Y, y, group->field, ctx))
 402             goto err;
 403         if (group->meth->field_encode) {
 404             if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
 405                 goto err;
 406         }
 407     }
 408
 409     if (z != NULL) {
 410         int Z_is_one;
 411
 412         if (!BN_nnmod(point->Z, z, group->field, ctx))
 413             goto err;
 414         Z_is_one = BN_is_one(point->Z);
 415         if (group->meth->field_encode) {
 416             if (Z_is_one && (group->meth->field_set_to_one != 0)) {
 417                 if (!group->meth->field_set_to_one(group, point->Z, ctx))
 418                     goto err;
 419             } else {
 420                 if (!group->
 421                     meth->field_encode(group, point->Z, point->Z, ctx))
 422                     goto err;
 423             }
 424         }
 425         point->Z_is_one = Z_is_one;
 426     }
 427
 428     ret = 1;
 429
 430  err:
 431     BN_CTX_free(new_ctx);
 432     return ret;
 433 }
 434
 435 int ossl_ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
 436                                                        const EC_POINT *point,
 437                                                        BIGNUM *x, BIGNUM *y,
 438                                                        BIGNUM *z, BN_CTX *ctx)
 439 {
 440     BN_CTX *new_ctx = NULL;
 441     int ret = 0;
 442
 443     if (group->meth->field_decode != 0) {
 444         if (ctx == NULL) {
 445             ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 446             if (ctx == NULL)
 447                 return 0;
 448         }
 449
 450         if (x != NULL) {
 451             if (!group->meth->field_decode(group, x, point->X, ctx))
 452                 goto err;
 453         }
 454         if (y != NULL) {
 455             if (!group->meth->field_decode(group, y, point->Y, ctx))
 456                 goto err;
 457         }
 458         if (z != NULL) {
 459             if (!group->meth->field_decode(group, z, point->Z, ctx))
 460                 goto err;
 461         }
 462     } else {
 463         if (x != NULL) {
 464             if (!BN_copy(x, point->X))
 465                 goto err;
 466         }
 467         if (y != NULL) {
 468             if (!BN_copy(y, point->Y))
 469                 goto err;
 470         }
 471         if (z != NULL) {
 472             if (!BN_copy(z, point->Z))
 473                 goto err;
 474         }
 475     }
 476
 477     ret = 1;
 478
 479  err:
 480     BN_CTX_free(new_ctx);
 481     return ret;
 482 }
 483
 484 int ossl_ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
 485                                                     EC_POINT *point,
 486                                                     const BIGNUM *x,
 487                                                     const BIGNUM *y, BN_CTX *ctx)
 488 {
 489     if (x == NULL || y == NULL) {
 490         /*
 491          * unlike for projective coordinates, we do not tolerate this
 492          */
 493         ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER);
 494         return 0;
 495     }
 496
 497     return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
 498                                                     BN_value_one(), ctx);
 499 }
 500
 501 int ossl_ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
 502                                                     const EC_POINT *point,
 503                                                     BIGNUM *x, BIGNUM *y,
 504                                                     BN_CTX *ctx)
 505 {
 506     BN_CTX *new_ctx = NULL;
 507     BIGNUM *Z, *Z_1, *Z_2, *Z_3;
 508     const BIGNUM *Z_;
 509     int ret = 0;
 510
 511     if (EC_POINT_is_at_infinity(group, point)) {
 512         ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
 513         return 0;
 514     }
 515
 516     if (ctx == NULL) {
 517         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 518         if (ctx == NULL)
 519             return 0;
 520     }
 521
 522     BN_CTX_start(ctx);
 523     Z = BN_CTX_get(ctx);
 524     Z_1 = BN_CTX_get(ctx);
 525     Z_2 = BN_CTX_get(ctx);
 526     Z_3 = BN_CTX_get(ctx);
 527     if (Z_3 == NULL)
 528         goto err;
 529
 530     /* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */
 531
 532     if (group->meth->field_decode) {
 533         if (!group->meth->field_decode(group, Z, point->Z, ctx))
 534             goto err;
 535         Z_ = Z;
 536     } else {
 537         Z_ = point->Z;
 538     }
 539
 540     if (BN_is_one(Z_)) {
 541         if (group->meth->field_decode) {
 542             if (x != NULL) {
 543                 if (!group->meth->field_decode(group, x, point->X, ctx))
 544                     goto err;
 545             }
 546             if (y != NULL) {
 547                 if (!group->meth->field_decode(group, y, point->Y, ctx))
 548                     goto err;
 549             }
 550         } else {
 551             if (x != NULL) {
 552                 if (!BN_copy(x, point->X))
 553                     goto err;
 554             }
 555             if (y != NULL) {
 556                 if (!BN_copy(y, point->Y))
 557                     goto err;
 558             }
 559         }
 560     } else {
 561         if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
 562             ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 563             goto err;
 564         }
 565
 566         if (group->meth->field_encode == 0) {
 567             /* field_sqr works on standard representation */
 568             if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
 569                 goto err;
 570         } else {
 571             if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
 572                 goto err;
 573         }
 574
 575         if (x != NULL) {
 576             /*
 577              * in the Montgomery case, field_mul will cancel out Montgomery
 578              * factor in X:
 579              */
 580             if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
 581                 goto err;
 582         }
 583
 584         if (y != NULL) {
 585             if (group->meth->field_encode == 0) {
 586                 /*
 587                  * field_mul works on standard representation
 588                  */
 589                 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
 590                     goto err;
 591             } else {
 592                 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
 593                     goto err;
 594             }
 595
 596             /*
 597              * in the Montgomery case, field_mul will cancel out Montgomery
 598              * factor in Y:
 599              */
 600             if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
 601                 goto err;
 602         }
 603     }
 604
 605     ret = 1;
 606
 607  err:
 608     BN_CTX_end(ctx);
 609     BN_CTX_free(new_ctx);
 610     return ret;
 611 }
 612
 613 int ossl_ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 614                            const EC_POINT *b, BN_CTX *ctx)
 615 {
 616     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 617                       const BIGNUM *, BN_CTX *);
 618     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 619     const BIGNUM *p;
 620     BN_CTX *new_ctx = NULL;
 621     BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
 622     int ret = 0;
 623
 624     if (a == b)
 625         return EC_POINT_dbl(group, r, a, ctx);
 626     if (EC_POINT_is_at_infinity(group, a))
 627         return EC_POINT_copy(r, b);
 628     if (EC_POINT_is_at_infinity(group, b))
 629         return EC_POINT_copy(r, a);
 630
 631     field_mul = group->meth->field_mul;
 632     field_sqr = group->meth->field_sqr;
 633     p = group->field;
 634
 635     if (ctx == NULL) {
 636         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 637         if (ctx == NULL)
 638             return 0;
 639     }
 640
 641     BN_CTX_start(ctx);
 642     n0 = BN_CTX_get(ctx);
 643     n1 = BN_CTX_get(ctx);
 644     n2 = BN_CTX_get(ctx);
 645     n3 = BN_CTX_get(ctx);
 646     n4 = BN_CTX_get(ctx);
 647     n5 = BN_CTX_get(ctx);
 648     n6 = BN_CTX_get(ctx);
 649     if (n6 == NULL)
 650         goto end;
 651
 652     /*
 653      * Note that in this function we must not read components of 'a' or 'b'
 654      * once we have written the corresponding components of 'r'. ('r' might
 655      * be one of 'a' or 'b'.)
 656      */
 657
 658     /* n1, n2 */
 659     if (b->Z_is_one) {
 660         if (!BN_copy(n1, a->X))
 661             goto end;
 662         if (!BN_copy(n2, a->Y))
 663             goto end;
 664         /* n1 = X_a */
 665         /* n2 = Y_a */
 666     } else {
 667         if (!field_sqr(group, n0, b->Z, ctx))
 668             goto end;
 669         if (!field_mul(group, n1, a->X, n0, ctx))
 670             goto end;
 671         /* n1 = X_a * Z_b^2 */
 672
 673         if (!field_mul(group, n0, n0, b->Z, ctx))
 674             goto end;
 675         if (!field_mul(group, n2, a->Y, n0, ctx))
 676             goto end;
 677         /* n2 = Y_a * Z_b^3 */
 678     }
 679
 680     /* n3, n4 */
 681     if (a->Z_is_one) {
 682         if (!BN_copy(n3, b->X))
 683             goto end;
 684         if (!BN_copy(n4, b->Y))
 685             goto end;
 686         /* n3 = X_b */
 687         /* n4 = Y_b */
 688     } else {
 689         if (!field_sqr(group, n0, a->Z, ctx))
 690             goto end;
 691         if (!field_mul(group, n3, b->X, n0, ctx))
 692             goto end;
 693         /* n3 = X_b * Z_a^2 */
 694
 695         if (!field_mul(group, n0, n0, a->Z, ctx))
 696             goto end;
 697         if (!field_mul(group, n4, b->Y, n0, ctx))
 698             goto end;
 699         /* n4 = Y_b * Z_a^3 */
 700     }
 701
 702     /* n5, n6 */
 703     if (!BN_mod_sub_quick(n5, n1, n3, p))
 704         goto end;
 705     if (!BN_mod_sub_quick(n6, n2, n4, p))
 706         goto end;
 707     /* n5 = n1 - n3 */
 708     /* n6 = n2 - n4 */
 709
 710     if (BN_is_zero(n5)) {
 711         if (BN_is_zero(n6)) {
 712             /* a is the same point as b */
 713             BN_CTX_end(ctx);
 714             ret = EC_POINT_dbl(group, r, a, ctx);
 715             ctx = NULL;
 716             goto end;
 717         } else {
 718             /* a is the inverse of b */
 719             BN_zero(r->Z);
 720             r->Z_is_one = 0;
 721             ret = 1;
 722             goto end;
 723         }
 724     }
 725
 726     /* 'n7', 'n8' */
 727     if (!BN_mod_add_quick(n1, n1, n3, p))
 728         goto end;
 729     if (!BN_mod_add_quick(n2, n2, n4, p))
 730         goto end;
 731     /* 'n7' = n1 + n3 */
 732     /* 'n8' = n2 + n4 */
 733
 734     /* Z_r */
 735     if (a->Z_is_one && b->Z_is_one) {
 736         if (!BN_copy(r->Z, n5))
 737             goto end;
 738     } else {
 739         if (a->Z_is_one) {
 740             if (!BN_copy(n0, b->Z))
 741                 goto end;
 742         } else if (b->Z_is_one) {
 743             if (!BN_copy(n0, a->Z))
 744                 goto end;
 745         } else {
 746             if (!field_mul(group, n0, a->Z, b->Z, ctx))
 747                 goto end;
 748         }
 749         if (!field_mul(group, r->Z, n0, n5, ctx))
 750             goto end;
 751     }
 752     r->Z_is_one = 0;
 753     /* Z_r = Z_a * Z_b * n5 */
 754
 755     /* X_r */
 756     if (!field_sqr(group, n0, n6, ctx))
 757         goto end;
 758     if (!field_sqr(group, n4, n5, ctx))
 759         goto end;
 760     if (!field_mul(group, n3, n1, n4, ctx))
 761         goto end;
 762     if (!BN_mod_sub_quick(r->X, n0, n3, p))
 763         goto end;
 764     /* X_r = n6^2 - n5^2 * 'n7' */
 765
 766     /* 'n9' */
 767     if (!BN_mod_lshift1_quick(n0, r->X, p))
 768         goto end;
 769     if (!BN_mod_sub_quick(n0, n3, n0, p))
 770         goto end;
 771     /* n9 = n5^2 * 'n7' - 2 * X_r */
 772
 773     /* Y_r */
 774     if (!field_mul(group, n0, n0, n6, ctx))
 775         goto end;
 776     if (!field_mul(group, n5, n4, n5, ctx))
 777         goto end;               /* now n5 is n5^3 */
 778     if (!field_mul(group, n1, n2, n5, ctx))
 779         goto end;
 780     if (!BN_mod_sub_quick(n0, n0, n1, p))
 781         goto end;
 782     if (BN_is_odd(n0))
 783         if (!BN_add(n0, n0, p))
 784             goto end;
 785     /* now  0 <= n0 < 2*p,  and n0 is even */
 786     if (!BN_rshift1(r->Y, n0))
 787         goto end;
 788     /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
 789
 790     ret = 1;
 791
 792  end:
 793     BN_CTX_end(ctx);
 794     BN_CTX_free(new_ctx);
 795     return ret;
 796 }
 797
 798 int ossl_ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
 799                            BN_CTX *ctx)
 800 {
 801     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 802                       const BIGNUM *, BN_CTX *);
 803     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 804     const BIGNUM *p;
 805     BN_CTX *new_ctx = NULL;
 806     BIGNUM *n0, *n1, *n2, *n3;
 807     int ret = 0;
 808
 809     if (EC_POINT_is_at_infinity(group, a)) {
 810         BN_zero(r->Z);
 811         r->Z_is_one = 0;
 812         return 1;
 813     }
 814
 815     field_mul = group->meth->field_mul;
 816     field_sqr = group->meth->field_sqr;
 817     p = group->field;
 818
 819     if (ctx == NULL) {
 820         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 821         if (ctx == NULL)
 822             return 0;
 823     }
 824
 825     BN_CTX_start(ctx);
 826     n0 = BN_CTX_get(ctx);
 827     n1 = BN_CTX_get(ctx);
 828     n2 = BN_CTX_get(ctx);
 829     n3 = BN_CTX_get(ctx);
 830     if (n3 == NULL)
 831         goto err;
 832
 833     /*
 834      * Note that in this function we must not read components of 'a' once we
 835      * have written the corresponding components of 'r'. ('r' might the same
 836      * as 'a'.)
 837      */
 838
 839     /* n1 */
 840     if (a->Z_is_one) {
 841         if (!field_sqr(group, n0, a->X, ctx))
 842             goto err;
 843         if (!BN_mod_lshift1_quick(n1, n0, p))
 844             goto err;
 845         if (!BN_mod_add_quick(n0, n0, n1, p))
 846             goto err;
 847         if (!BN_mod_add_quick(n1, n0, group->a, p))
 848             goto err;
 849         /* n1 = 3 * X_a^2 + a_curve */
 850     } else if (group->a_is_minus3) {
 851         if (!field_sqr(group, n1, a->Z, ctx))
 852             goto err;
 853         if (!BN_mod_add_quick(n0, a->X, n1, p))
 854             goto err;
 855         if (!BN_mod_sub_quick(n2, a->X, n1, p))
 856             goto err;
 857         if (!field_mul(group, n1, n0, n2, ctx))
 858             goto err;
 859         if (!BN_mod_lshift1_quick(n0, n1, p))
 860             goto err;
 861         if (!BN_mod_add_quick(n1, n0, n1, p))
 862             goto err;
 863         /*-
 864          * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
 865          *    = 3 * X_a^2 - 3 * Z_a^4
 866          */
 867     } else {
 868         if (!field_sqr(group, n0, a->X, ctx))
 869             goto err;
 870         if (!BN_mod_lshift1_quick(n1, n0, p))
 871             goto err;
 872         if (!BN_mod_add_quick(n0, n0, n1, p))
 873             goto err;
 874         if (!field_sqr(group, n1, a->Z, ctx))
 875             goto err;
 876         if (!field_sqr(group, n1, n1, ctx))
 877             goto err;
 878         if (!field_mul(group, n1, n1, group->a, ctx))
 879             goto err;
 880         if (!BN_mod_add_quick(n1, n1, n0, p))
 881             goto err;
 882         /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
 883     }
 884
 885     /* Z_r */
 886     if (a->Z_is_one) {
 887         if (!BN_copy(n0, a->Y))
 888             goto err;
 889     } else {
 890         if (!field_mul(group, n0, a->Y, a->Z, ctx))
 891             goto err;
 892     }
 893     if (!BN_mod_lshift1_quick(r->Z, n0, p))
 894         goto err;
 895     r->Z_is_one = 0;
 896     /* Z_r = 2 * Y_a * Z_a */
 897
 898     /* n2 */
 899     if (!field_sqr(group, n3, a->Y, ctx))
 900         goto err;
 901     if (!field_mul(group, n2, a->X, n3, ctx))
 902         goto err;
 903     if (!BN_mod_lshift_quick(n2, n2, 2, p))
 904         goto err;
 905     /* n2 = 4 * X_a * Y_a^2 */
 906
 907     /* X_r */
 908     if (!BN_mod_lshift1_quick(n0, n2, p))
 909         goto err;
 910     if (!field_sqr(group, r->X, n1, ctx))
 911         goto err;
 912     if (!BN_mod_sub_quick(r->X, r->X, n0, p))
 913         goto err;
 914     /* X_r = n1^2 - 2 * n2 */
 915
 916     /* n3 */
 917     if (!field_sqr(group, n0, n3, ctx))
 918         goto err;
 919     if (!BN_mod_lshift_quick(n3, n0, 3, p))
 920         goto err;
 921     /* n3 = 8 * Y_a^4 */
 922
 923     /* Y_r */
 924     if (!BN_mod_sub_quick(n0, n2, r->X, p))
 925         goto err;
 926     if (!field_mul(group, n0, n1, n0, ctx))
 927         goto err;
 928     if (!BN_mod_sub_quick(r->Y, n0, n3, p))
 929         goto err;
 930     /* Y_r = n1 * (n2 - X_r) - n3 */
 931
 932     ret = 1;
 933
 934  err:
 935     BN_CTX_end(ctx);
 936     BN_CTX_free(new_ctx);
 937     return ret;
 938 }
 939
 940 int ossl_ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point,
 941                               BN_CTX *ctx)
 942 {
 943     if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
 944         /* point is its own inverse */
 945         return 1;
 946
 947     return BN_usub(point->Y, group->field, point->Y);
 948 }
 949
 950 int ossl_ec_GFp_simple_is_at_infinity(const EC_GROUP *group,
 951                                       const EC_POINT *point)
 952 {
 953     return BN_is_zero(point->Z);
 954 }
 955
 956 int ossl_ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
 957                                    BN_CTX *ctx)
 958 {
 959     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
 960                       const BIGNUM *, BN_CTX *);
 961     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 962     const BIGNUM *p;
 963     BN_CTX *new_ctx = NULL;
 964     BIGNUM *rh, *tmp, *Z4, *Z6;
 965     int ret = -1;
 966
 967     if (EC_POINT_is_at_infinity(group, point))
 968         return 1;
 969
 970     field_mul = group->meth->field_mul;
 971     field_sqr = group->meth->field_sqr;
 972     p = group->field;
 973
 974     if (ctx == NULL) {
 975         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
 976         if (ctx == NULL)
 977             return -1;
 978     }
 979
 980     BN_CTX_start(ctx);
 981     rh = BN_CTX_get(ctx);
 982     tmp = BN_CTX_get(ctx);
 983     Z4 = BN_CTX_get(ctx);
 984     Z6 = BN_CTX_get(ctx);
 985     if (Z6 == NULL)
 986         goto err;
 987
 988     /*-
 989      * We have a curve defined by a Weierstrass equation
 990      *      y^2 = x^3 + a*x + b.
 991      * The point to consider is given in Jacobian projective coordinates
 992      * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).
 993      * Substituting this and multiplying by  Z^6  transforms the above equation into
 994      *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.
 995      * To test this, we add up the right-hand side in 'rh'.
 996      */
 997
 998     /* rh := X^2 */
 999     if (!field_sqr(group, rh, point->X, ctx))
1000         goto err;
1001
1002     if (!point->Z_is_one) {
1003         if (!field_sqr(group, tmp, point->Z, ctx))
1004             goto err;
1005         if (!field_sqr(group, Z4, tmp, ctx))
1006             goto err;
1007         if (!field_mul(group, Z6, Z4, tmp, ctx))
1008             goto err;
1009
1010         /* rh := (rh + a*Z^4)*X */
1011         if (group->a_is_minus3) {
1012             if (!BN_mod_lshift1_quick(tmp, Z4, p))
1013                 goto err;
1014             if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1015                 goto err;
1016             if (!BN_mod_sub_quick(rh, rh, tmp, p))
1017                 goto err;
1018             if (!field_mul(group, rh, rh, point->X, ctx))
1019                 goto err;
1020         } else {
1021             if (!field_mul(group, tmp, Z4, group->a, ctx))
1022                 goto err;
1023             if (!BN_mod_add_quick(rh, rh, tmp, p))
1024                 goto err;
1025             if (!field_mul(group, rh, rh, point->X, ctx))
1026                 goto err;
1027         }
1028
1029         /* rh := rh + b*Z^6 */
1030         if (!field_mul(group, tmp, group->b, Z6, ctx))
1031             goto err;
1032         if (!BN_mod_add_quick(rh, rh, tmp, p))
1033             goto err;
1034     } else {
1035         /* point->Z_is_one */
1036
1037         /* rh := (rh + a)*X */
1038         if (!BN_mod_add_quick(rh, rh, group->a, p))
1039             goto err;
1040         if (!field_mul(group, rh, rh, point->X, ctx))
1041             goto err;
1042         /* rh := rh + b */
1043         if (!BN_mod_add_quick(rh, rh, group->b, p))
1044             goto err;
1045     }
1046
1047     /* 'lh' := Y^2 */
1048     if (!field_sqr(group, tmp, point->Y, ctx))
1049         goto err;
1050
1051     ret = (0 == BN_ucmp(tmp, rh));
1052
1053  err:
1054     BN_CTX_end(ctx);
1055     BN_CTX_free(new_ctx);
1056     return ret;
1057 }
1058
1059 int ossl_ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1060                            const EC_POINT *b, BN_CTX *ctx)
1061 {
1062     /*-
1063      * return values:
1064      *  -1   error
1065      *   0   equal (in affine coordinates)
1066      *   1   not equal
1067      */
1068
1069     int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1070                       const BIGNUM *, BN_CTX *);
1071     int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1072     BN_CTX *new_ctx = NULL;
1073     BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1074     const BIGNUM *tmp1_, *tmp2_;
1075     int ret = -1;
1076
1077     if (EC_POINT_is_at_infinity(group, a)) {
1078         return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1079     }
1080
1081     if (EC_POINT_is_at_infinity(group, b))
1082         return 1;
1083
1084     if (a->Z_is_one && b->Z_is_one) {
1085         return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1086     }
1087
1088     field_mul = group->meth->field_mul;
1089     field_sqr = group->meth->field_sqr;
1090
1091     if (ctx == NULL) {
1092         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1093         if (ctx == NULL)
1094             return -1;
1095     }
1096
1097     BN_CTX_start(ctx);
1098     tmp1 = BN_CTX_get(ctx);
1099     tmp2 = BN_CTX_get(ctx);
1100     Za23 = BN_CTX_get(ctx);
1101     Zb23 = BN_CTX_get(ctx);
1102     if (Zb23 == NULL)
1103         goto end;
1104
1105     /*-
1106      * We have to decide whether
1107      *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1108      * or equivalently, whether
1109      *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1110      */
1111
1112     if (!b->Z_is_one) {
1113         if (!field_sqr(group, Zb23, b->Z, ctx))
1114             goto end;
1115         if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1116             goto end;
1117         tmp1_ = tmp1;
1118     } else
1119         tmp1_ = a->X;
1120     if (!a->Z_is_one) {
1121         if (!field_sqr(group, Za23, a->Z, ctx))
1122             goto end;
1123         if (!field_mul(group, tmp2, b->X, Za23, ctx))
1124             goto end;
1125         tmp2_ = tmp2;
1126     } else
1127         tmp2_ = b->X;
1128
1129     /* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
1130     if (BN_cmp(tmp1_, tmp2_) != 0) {
1131         ret = 1;                /* points differ */
1132         goto end;
1133     }
1134
1135     if (!b->Z_is_one) {
1136         if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1137             goto end;
1138         if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1139             goto end;
1140         /* tmp1_ = tmp1 */
1141     } else
1142         tmp1_ = a->Y;
1143     if (!a->Z_is_one) {
1144         if (!field_mul(group, Za23, Za23, a->Z, ctx))
1145             goto end;
1146         if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1147             goto end;
1148         /* tmp2_ = tmp2 */
1149     } else
1150         tmp2_ = b->Y;
1151
1152     /* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
1153     if (BN_cmp(tmp1_, tmp2_) != 0) {
1154         ret = 1;                /* points differ */
1155         goto end;
1156     }
1157
1158     /* points are equal */
1159     ret = 0;
1160
1161  end:
1162     BN_CTX_end(ctx);
1163     BN_CTX_free(new_ctx);
1164     return ret;
1165 }
1166
1167 int ossl_ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1168                                    BN_CTX *ctx)
1169 {
1170     BN_CTX *new_ctx = NULL;
1171     BIGNUM *x, *y;
1172     int ret = 0;
1173
1174     if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1175         return 1;
1176
1177     if (ctx == NULL) {
1178         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1179         if (ctx == NULL)
1180             return 0;
1181     }
1182
1183     BN_CTX_start(ctx);
1184     x = BN_CTX_get(ctx);
1185     y = BN_CTX_get(ctx);
1186     if (y == NULL)
1187         goto err;
1188
1189     if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
1190         goto err;
1191     if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
1192         goto err;
1193     if (!point->Z_is_one) {
1194         ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
1195         goto err;
1196     }
1197
1198     ret = 1;
1199
1200  err:
1201     BN_CTX_end(ctx);
1202     BN_CTX_free(new_ctx);
1203     return ret;
1204 }
1205
1206 int ossl_ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1207                                           EC_POINT *points[], BN_CTX *ctx)
1208 {
1209     BN_CTX *new_ctx = NULL;
1210     BIGNUM *tmp, *tmp_Z;
1211     BIGNUM **prod_Z = NULL;
1212     size_t i;
1213     int ret = 0;
1214
1215     if (num == 0)
1216         return 1;
1217
1218     if (ctx == NULL) {
1219         ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1220         if (ctx == NULL)
1221             return 0;
1222     }
1223
1224     BN_CTX_start(ctx);
1225     tmp = BN_CTX_get(ctx);
1226     tmp_Z = BN_CTX_get(ctx);
1227     if (tmp_Z == NULL)
1228         goto err;
1229
1230     prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
1231     if (prod_Z == NULL)
1232         goto err;
1233     for (i = 0; i < num; i++) {
1234         prod_Z[i] = BN_new();
1235         if (prod_Z[i] == NULL)
1236             goto err;
1237     }
1238
1239     /*
1240      * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1241      * skipping any zero-valued inputs (pretend that they're 1).
1242      */
1243
1244     if (!BN_is_zero(points[0]->Z)) {
1245         if (!BN_copy(prod_Z[0], points[0]->Z))
1246             goto err;
1247     } else {
1248         if (group->meth->field_set_to_one != 0) {
1249             if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1250                 goto err;
1251         } else {
1252             if (!BN_one(prod_Z[0]))
1253                 goto err;
1254         }
1255     }
1256
1257     for (i = 1; i < num; i++) {
1258         if (!BN_is_zero(points[i]->Z)) {
1259             if (!group->
1260                 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1261                                 ctx))
1262                 goto err;
1263         } else {
1264             if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1265                 goto err;
1266         }
1267     }
1268
1269     /*
1270      * Now use a single explicit inversion to replace every non-zero
1271      * points[i]->Z by its inverse.
1272      */
1273
1274     if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) {
1275         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1276         goto err;
1277     }
1278     if (group->meth->field_encode != 0) {
1279         /*
1280          * In the Montgomery case, we just turned R*H (representing H) into
1281          * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1282          * multiply by the Montgomery factor twice.
1283          */
1284         if (!group->meth->field_encode(group, tmp, tmp, ctx))
1285             goto err;
1286         if (!group->meth->field_encode(group, tmp, tmp, ctx))
1287             goto err;
1288     }
1289
1290     for (i = num - 1; i > 0; --i) {
1291         /*
1292          * Loop invariant: tmp is the product of the inverses of points[0]->Z
1293          * .. points[i]->Z (zero-valued inputs skipped).
1294          */
1295         if (!BN_is_zero(points[i]->Z)) {
1296             /*
1297              * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1298              * inverses 0 .. i, Z values 0 .. i - 1).
1299              */
1300             if (!group->
1301                 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1302                 goto err;
1303             /*
1304              * Update tmp to satisfy the loop invariant for i - 1.
1305              */
1306             if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1307                 goto err;
1308             /* Replace points[i]->Z by its inverse. */
1309             if (!BN_copy(points[i]->Z, tmp_Z))
1310                 goto err;
1311         }
1312     }
1313
1314     if (!BN_is_zero(points[0]->Z)) {
1315         /* Replace points[0]->Z by its inverse. */
1316         if (!BN_copy(points[0]->Z, tmp))
1317             goto err;
1318     }
1319
1320     /* Finally, fix up the X and Y coordinates for all points. */
1321
1322     for (i = 0; i < num; i++) {
1323         EC_POINT *p = points[i];
1324
1325         if (!BN_is_zero(p->Z)) {
1326             /* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */
1327
1328             if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1329                 goto err;
1330             if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1331                 goto err;
1332
1333             if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1334                 goto err;
1335             if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1336                 goto err;
1337
1338             if (group->meth->field_set_to_one != 0) {
1339                 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1340                     goto err;
1341             } else {
1342                 if (!BN_one(p->Z))
1343                     goto err;
1344             }
1345             p->Z_is_one = 1;
1346         }
1347     }
1348
1349     ret = 1;
1350
1351  err:
1352     BN_CTX_end(ctx);
1353     BN_CTX_free(new_ctx);
1354     if (prod_Z != NULL) {
1355         for (i = 0; i < num; i++) {
1356             if (prod_Z[i] == NULL)
1357                 break;
1358             BN_clear_free(prod_Z[i]);
1359         }
1360         OPENSSL_free(prod_Z);
1361     }
1362     return ret;
1363 }
1364
1365 int ossl_ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1366                                  const BIGNUM *b, BN_CTX *ctx)
1367 {
1368     return BN_mod_mul(r, a, b, group->field, ctx);
1369 }
1370
1371 int ossl_ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1372                                  BN_CTX *ctx)
1373 {
1374     return BN_mod_sqr(r, a, group->field, ctx);
1375 }
1376
1377 /*-
1378  * Computes the multiplicative inverse of a in GF(p), storing the result in r.
1379  * If a is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error.
1380  * Since we don't have a Mont structure here, SCA hardening is with blinding.
1381  * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.)
1382  */
1383 int ossl_ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
1384                                  const BIGNUM *a, BN_CTX *ctx)
1385 {
1386     BIGNUM *e = NULL;
1387     BN_CTX *new_ctx = NULL;
1388     int ret = 0;
1389
1390     if (ctx == NULL
1391             && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL)
1392         return 0;
1393
1394     BN_CTX_start(ctx);
1395     if ((e = BN_CTX_get(ctx)) == NULL)
1396         goto err;
1397
1398     do {
1399         if (!BN_priv_rand_range_ex(e, group->field, 0, ctx))
1400         goto err;
1401     } while (BN_is_zero(e));
1402
1403     /* r := a * e */
1404     if (!group->meth->field_mul(group, r, a, e, ctx))
1405         goto err;
1406     /* r := 1/(a * e) */
1407     if (!BN_mod_inverse(r, r, group->field, ctx)) {
1408         ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT);
1409         goto err;
1410     }
1411     /* r := e/(a * e) = 1/a */
1412     if (!group->meth->field_mul(group, r, r, e, ctx))
1413         goto err;
1414
1415     ret = 1;
1416
1417  err:
1418     BN_CTX_end(ctx);
1419     BN_CTX_free(new_ctx);
1420     return ret;
1421 }
1422
1423 /*-
1424  * Apply randomization of EC point projective coordinates:
1425  *
1426  *   (X, Y, Z) = (lambda^2*X, lambda^3*Y, lambda*Z)
1427  *   lambda = [1, group->field)
1428  *
1429  */
1430 int ossl_ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
1431                                          BN_CTX *ctx)
1432 {
1433     int ret = 0;
1434     BIGNUM *lambda = NULL;
1435     BIGNUM *temp = NULL;
1436
1437     BN_CTX_start(ctx);
1438     lambda = BN_CTX_get(ctx);
1439     temp = BN_CTX_get(ctx);
1440     if (temp == NULL) {
1441         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1442         goto end;
1443     }
1444
1445     /*-
1446      * Make sure lambda is not zero.
1447      * If the RNG fails, we cannot blind but nevertheless want
1448      * code to continue smoothly and not clobber the error stack.
1449      */
1450     do {
1451         ERR_set_mark();
1452         ret = BN_priv_rand_range_ex(lambda, group->field, 0, ctx);
1453         ERR_pop_to_mark();
1454         if (ret == 0) {
1455             ret = 1;
1456             goto end;
1457         }
1458     } while (BN_is_zero(lambda));
1459
1460     /* if field_encode defined convert between representations */
1461     if ((group->meth->field_encode != NULL
1462          && !group->meth->field_encode(group, lambda, lambda, ctx))
1463         || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)
1464         || !group->meth->field_sqr(group, temp, lambda, ctx)
1465         || !group->meth->field_mul(group, p->X, p->X, temp, ctx)
1466         || !group->meth->field_mul(group, temp, temp, lambda, ctx)
1467         || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
1468         goto end;
1469
1470     p->Z_is_one = 0;
1471     ret = 1;
1472
1473  end:
1474     BN_CTX_end(ctx);
1475     return ret;
1476 }
1477
1478 /*-
1479  * Input:
1480  * - p: affine coordinates
1481  *
1482  * Output:
1483  * - s := p, r := 2p: blinded projective (homogeneous) coordinates
1484  *
1485  * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
1486  * multiplication resistant against side channel attacks" appendix, described at
1487  * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
1488  * simplified for Z1=1.
1489  *
1490  * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z)
1491  * for any non-zero \lambda that holds for projective (homogeneous) coords.
1492  */
1493 int ossl_ec_GFp_simple_ladder_pre(const EC_GROUP *group,
1494                                   EC_POINT *r, EC_POINT *s,
1495                                   EC_POINT *p, BN_CTX *ctx)
1496 {
1497     BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL;
1498
1499     t1 = s->Z;
1500     t2 = r->Z;
1501     t3 = s->X;
1502     t4 = r->X;
1503     t5 = s->Y;
1504
1505     if (!p->Z_is_one /* r := 2p */
1506         || !group->meth->field_sqr(group, t3, p->X, ctx)
1507         || !BN_mod_sub_quick(t4, t3, group->a, group->field)
1508         || !group->meth->field_sqr(group, t4, t4, ctx)
1509         || !group->meth->field_mul(group, t5, p->X, group->b, ctx)
1510         || !BN_mod_lshift_quick(t5, t5, 3, group->field)
1511         /* r->X coord output */
1512         || !BN_mod_sub_quick(r->X, t4, t5, group->field)
1513         || !BN_mod_add_quick(t1, t3, group->a, group->field)
1514         || !group->meth->field_mul(group, t2, p->X, t1, ctx)
1515         || !BN_mod_add_quick(t2, group->b, t2, group->field)
1516         /* r->Z coord output */
1517         || !BN_mod_lshift_quick(r->Z, t2, 2, group->field))
1518         return 0;
1519
1520     /* make sure lambda (r->Y here for storage) is not zero */
1521     do {
1522         if (!BN_priv_rand_range_ex(r->Y, group->field, 0, ctx))
1523             return 0;
1524     } while (BN_is_zero(r->Y));
1525
1526     /* make sure lambda (s->Z here for storage) is not zero */
1527     do {
1528         if (!BN_priv_rand_range_ex(s->Z, group->field, 0, ctx))
1529             return 0;
1530     } while (BN_is_zero(s->Z));
1531
1532     /* if field_encode defined convert between representations */
1533     if (group->meth->field_encode != NULL
1534         && (!group->meth->field_encode(group, r->Y, r->Y, ctx)
1535             || !group->meth->field_encode(group, s->Z, s->Z, ctx)))
1536         return 0;
1537
1538     /* blind r and s independently */
1539     if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
1540         || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)
1541         || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */
1542         return 0;
1543
1544     r->Z_is_one = 0;
1545     s->Z_is_one = 0;
1546
1547     return 1;
1548 }
1549
1550 /*-
1551  * Input:
1552  * - s, r: projective (homogeneous) coordinates
1553  * - p: affine coordinates
1554  *
1555  * Output:
1556  * - s := r + s, r := 2r: projective (homogeneous) coordinates
1557  *
1558  * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
1559  * "A fast parallel elliptic curve multiplication resistant against side channel
1560  * attacks", as described at
1561  * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4
1562  */
1563 int ossl_ec_GFp_simple_ladder_step(const EC_GROUP *group,
1564                                    EC_POINT *r, EC_POINT *s,
1565                                    EC_POINT *p, BN_CTX *ctx)
1566 {
1567     int ret = 0;
1568     BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1569
1570     BN_CTX_start(ctx);
1571     t0 = BN_CTX_get(ctx);
1572     t1 = BN_CTX_get(ctx);
1573     t2 = BN_CTX_get(ctx);
1574     t3 = BN_CTX_get(ctx);
1575     t4 = BN_CTX_get(ctx);
1576     t5 = BN_CTX_get(ctx);
1577     t6 = BN_CTX_get(ctx);
1578
1579     if (t6 == NULL
1580         || !group->meth->field_mul(group, t6, r->X, s->X, ctx)
1581         || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
1582         || !group->meth->field_mul(group, t4, r->X, s->Z, ctx)
1583         || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
1584         || !group->meth->field_mul(group, t5, group->a, t0, ctx)
1585         || !BN_mod_add_quick(t5, t6, t5, group->field)
1586         || !BN_mod_add_quick(t6, t3, t4, group->field)
1587         || !group->meth->field_mul(group, t5, t6, t5, ctx)
1588         || !group->meth->field_sqr(group, t0, t0, ctx)
1589         || !BN_mod_lshift_quick(t2, group->b, 2, group->field)
1590         || !group->meth->field_mul(group, t0, t2, t0, ctx)
1591         || !BN_mod_lshift1_quick(t5, t5, group->field)
1592         || !BN_mod_sub_quick(t3, t4, t3, group->field)
1593         /* s->Z coord output */
1594         || !group->meth->field_sqr(group, s->Z, t3, ctx)
1595         || !group->meth->field_mul(group, t4, s->Z, p->X, ctx)
1596         || !BN_mod_add_quick(t0, t0, t5, group->field)
1597         /* s->X coord output */
1598         || !BN_mod_sub_quick(s->X, t0, t4, group->field)
1599         || !group->meth->field_sqr(group, t4, r->X, ctx)
1600         || !group->meth->field_sqr(group, t5, r->Z, ctx)
1601         || !group->meth->field_mul(group, t6, t5, group->a, ctx)
1602         || !BN_mod_add_quick(t1, r->X, r->Z, group->field)
1603         || !group->meth->field_sqr(group, t1, t1, ctx)
1604         || !BN_mod_sub_quick(t1, t1, t4, group->field)
1605         || !BN_mod_sub_quick(t1, t1, t5, group->field)
1606         || !BN_mod_sub_quick(t3, t4, t6, group->field)
1607         || !group->meth->field_sqr(group, t3, t3, ctx)
1608         || !group->meth->field_mul(group, t0, t5, t1, ctx)
1609         || !group->meth->field_mul(group, t0, t2, t0, ctx)
1610         /* r->X coord output */
1611         || !BN_mod_sub_quick(r->X, t3, t0, group->field)
1612         || !BN_mod_add_quick(t3, t4, t6, group->field)
1613         || !group->meth->field_sqr(group, t4, t5, ctx)
1614         || !group->meth->field_mul(group, t4, t4, t2, ctx)
1615         || !group->meth->field_mul(group, t1, t1, t3, ctx)
1616         || !BN_mod_lshift1_quick(t1, t1, group->field)
1617         /* r->Z coord output */
1618         || !BN_mod_add_quick(r->Z, t4, t1, group->field))
1619         goto err;
1620
1621     ret = 1;
1622
1623  err:
1624     BN_CTX_end(ctx);
1625     return ret;
1626 }
1627
1628 /*-
1629  * Input:
1630  * - s, r: projective (homogeneous) coordinates
1631  * - p: affine coordinates
1632  *
1633  * Output:
1634  * - r := (x,y): affine coordinates
1635  *
1636  * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
1637  * Elliptic Curves and Side-Channel Attacks", modified to work in mixed
1638  * projective coords, i.e. p is affine and (r,s) in projective (homogeneous)
1639  * coords, and return r in affine coordinates.
1640  *
1641  * X4 = two*Y1*X2*Z3*Z2;
1642  * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2);
1643  * Z4 = two*Y1*Z3*SQR(Z2);
1644  *
1645  * Z4 != 0 because:
1646  *  - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
1647  *  - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
1648  *  - Y1==0 implies p has order 2, so either r or s are infinity and handled by
1649  *    one of the BN_is_zero(...) branches.
1650  */
1651 int ossl_ec_GFp_simple_ladder_post(const EC_GROUP *group,
1652                                    EC_POINT *r, EC_POINT *s,
1653                                    EC_POINT *p, BN_CTX *ctx)
1654 {
1655     int ret = 0;
1656     BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1657
1658     if (BN_is_zero(r->Z))
1659         return EC_POINT_set_to_infinity(group, r);
1660
1661     if (BN_is_zero(s->Z)) {
1662         if (!EC_POINT_copy(r, p)
1663             || !EC_POINT_invert(group, r, ctx))
1664             return 0;
1665         return 1;
1666     }
1667
1668     BN_CTX_start(ctx);
1669     t0 = BN_CTX_get(ctx);
1670     t1 = BN_CTX_get(ctx);
1671     t2 = BN_CTX_get(ctx);
1672     t3 = BN_CTX_get(ctx);
1673     t4 = BN_CTX_get(ctx);
1674     t5 = BN_CTX_get(ctx);
1675     t6 = BN_CTX_get(ctx);
1676
1677     if (t6 == NULL
1678         || !BN_mod_lshift1_quick(t4, p->Y, group->field)
1679         || !group->meth->field_mul(group, t6, r->X, t4, ctx)
1680         || !group->meth->field_mul(group, t6, s->Z, t6, ctx)
1681         || !group->meth->field_mul(group, t5, r->Z, t6, ctx)
1682         || !BN_mod_lshift1_quick(t1, group->b, group->field)
1683         || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
1684         || !group->meth->field_sqr(group, t3, r->Z, ctx)
1685         || !group->meth->field_mul(group, t2, t3, t1, ctx)
1686         || !group->meth->field_mul(group, t6, r->Z, group->a, ctx)
1687         || !group->meth->field_mul(group, t1, p->X, r->X, ctx)
1688         || !BN_mod_add_quick(t1, t1, t6, group->field)
1689         || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
1690         || !group->meth->field_mul(group, t0, p->X, r->Z, ctx)
1691         || !BN_mod_add_quick(t6, r->X, t0, group->field)
1692         || !group->meth->field_mul(group, t6, t6, t1, ctx)
1693         || !BN_mod_add_quick(t6, t6, t2, group->field)
1694         || !BN_mod_sub_quick(t0, t0, r->X, group->field)
1695         || !group->meth->field_sqr(group, t0, t0, ctx)
1696         || !group->meth->field_mul(group, t0, t0, s->X, ctx)
1697         || !BN_mod_sub_quick(t0, t6, t0, group->field)
1698         || !group->meth->field_mul(group, t1, s->Z, t4, ctx)
1699         || !group->meth->field_mul(group, t1, t3, t1, ctx)
1700         || (group->meth->field_decode != NULL
1701             && !group->meth->field_decode(group, t1, t1, ctx))
1702         || !group->meth->field_inv(group, t1, t1, ctx)
1703         || (group->meth->field_encode != NULL
1704             && !group->meth->field_encode(group, t1, t1, ctx))
1705         || !group->meth->field_mul(group, r->X, t5, t1, ctx)
1706         || !group->meth->field_mul(group, r->Y, t0, t1, ctx))
1707         goto err;
1708
1709     if (group->meth->field_set_to_one != NULL) {
1710         if (!group->meth->field_set_to_one(group, r->Z, ctx))
1711             goto err;
1712     } else {
1713         if (!BN_one(r->Z))
1714             goto err;
1715     }
1716
1717     r->Z_is_one = 1;
1718     ret = 1;
1719
1720  err:
1721     BN_CTX_end(ctx);
1722     return ret;
1723 }