2 * Copyright 2001-2017 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (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
11 #include <openssl/err.h>
12 #include <openssl/symhacks.h>
16 const EC_METHOD *EC_GFp_simple_method(void)
18 static const EC_METHOD ret = {
20 NID_X9_62_prime_field,
21 ec_GFp_simple_group_init,
22 ec_GFp_simple_group_finish,
23 ec_GFp_simple_group_clear_finish,
24 ec_GFp_simple_group_copy,
25 ec_GFp_simple_group_set_curve,
26 ec_GFp_simple_group_get_curve,
27 ec_GFp_simple_group_get_degree,
28 ec_group_simple_order_bits,
29 ec_GFp_simple_group_check_discriminant,
30 ec_GFp_simple_point_init,
31 ec_GFp_simple_point_finish,
32 ec_GFp_simple_point_clear_finish,
33 ec_GFp_simple_point_copy,
34 ec_GFp_simple_point_set_to_infinity,
35 ec_GFp_simple_set_Jprojective_coordinates_GFp,
36 ec_GFp_simple_get_Jprojective_coordinates_GFp,
37 ec_GFp_simple_point_set_affine_coordinates,
38 ec_GFp_simple_point_get_affine_coordinates,
43 ec_GFp_simple_is_at_infinity,
44 ec_GFp_simple_is_on_curve,
46 ec_GFp_simple_make_affine,
47 ec_GFp_simple_points_make_affine,
49 0 /* precompute_mult */ ,
50 0 /* have_precompute_mult */ ,
51 ec_GFp_simple_field_mul,
52 ec_GFp_simple_field_sqr,
54 0 /* field_encode */ ,
55 0 /* field_decode */ ,
56 0, /* field_set_to_one */
57 ec_key_simple_priv2oct,
58 ec_key_simple_oct2priv,
60 ec_key_simple_generate_key,
61 ec_key_simple_check_key,
62 ec_key_simple_generate_public_key,
65 ecdh_simple_compute_key
72 * Most method functions in this file are designed to work with
73 * non-trivial representations of field elements if necessary
74 * (see ecp_mont.c): while standard modular addition and subtraction
75 * are used, the field_mul and field_sqr methods will be used for
76 * multiplication, and field_encode and field_decode (if defined)
77 * will be used for converting between representations.
79 * Functions ec_GFp_simple_points_make_affine() and
80 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
81 * that if a non-trivial representation is used, it is a Montgomery
82 * representation (i.e. 'encoding' means multiplying by some factor R).
85 int ec_GFp_simple_group_init(EC_GROUP *group)
87 group->field = BN_new();
90 if (group->field == NULL || group->a == NULL || group->b == NULL) {
91 BN_free(group->field);
96 group->a_is_minus3 = 0;
100 void ec_GFp_simple_group_finish(EC_GROUP *group)
102 BN_free(group->field);
107 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
109 BN_clear_free(group->field);
110 BN_clear_free(group->a);
111 BN_clear_free(group->b);
114 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
116 if (!BN_copy(dest->field, src->field))
118 if (!BN_copy(dest->a, src->a))
120 if (!BN_copy(dest->b, src->b))
123 dest->a_is_minus3 = src->a_is_minus3;
128 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
129 const BIGNUM *p, const BIGNUM *a,
130 const BIGNUM *b, BN_CTX *ctx)
133 BN_CTX *new_ctx = NULL;
136 /* p must be a prime > 3 */
137 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
138 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
143 ctx = new_ctx = BN_CTX_new();
149 tmp_a = BN_CTX_get(ctx);
154 if (!BN_copy(group->field, p))
156 BN_set_negative(group->field, 0);
159 if (!BN_nnmod(tmp_a, a, p, ctx))
161 if (group->meth->field_encode) {
162 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
164 } else if (!BN_copy(group->a, tmp_a))
168 if (!BN_nnmod(group->b, b, p, ctx))
170 if (group->meth->field_encode)
171 if (!group->meth->field_encode(group, group->b, group->b, ctx))
174 /* group->a_is_minus3 */
175 if (!BN_add_word(tmp_a, 3))
177 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
183 BN_CTX_free(new_ctx);
187 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
188 BIGNUM *b, BN_CTX *ctx)
191 BN_CTX *new_ctx = NULL;
194 if (!BN_copy(p, group->field))
198 if (a != NULL || b != NULL) {
199 if (group->meth->field_decode) {
201 ctx = new_ctx = BN_CTX_new();
206 if (!group->meth->field_decode(group, a, group->a, ctx))
210 if (!group->meth->field_decode(group, b, group->b, ctx))
215 if (!BN_copy(a, group->a))
219 if (!BN_copy(b, group->b))
228 BN_CTX_free(new_ctx);
232 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
234 return BN_num_bits(group->field);
237 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
240 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
241 const BIGNUM *p = group->field;
242 BN_CTX *new_ctx = NULL;
245 ctx = new_ctx = BN_CTX_new();
247 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
248 ERR_R_MALLOC_FAILURE);
255 tmp_1 = BN_CTX_get(ctx);
256 tmp_2 = BN_CTX_get(ctx);
257 order = BN_CTX_get(ctx);
261 if (group->meth->field_decode) {
262 if (!group->meth->field_decode(group, a, group->a, ctx))
264 if (!group->meth->field_decode(group, b, group->b, ctx))
267 if (!BN_copy(a, group->a))
269 if (!BN_copy(b, group->b))
274 * check the discriminant:
275 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
281 } else if (!BN_is_zero(b)) {
282 if (!BN_mod_sqr(tmp_1, a, p, ctx))
284 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
286 if (!BN_lshift(tmp_1, tmp_2, 2))
290 if (!BN_mod_sqr(tmp_2, b, p, ctx))
292 if (!BN_mul_word(tmp_2, 27))
296 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
306 BN_CTX_free(new_ctx);
310 int ec_GFp_simple_point_init(EC_POINT *point)
317 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
326 void ec_GFp_simple_point_finish(EC_POINT *point)
333 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
335 BN_clear_free(point->X);
336 BN_clear_free(point->Y);
337 BN_clear_free(point->Z);
341 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
343 if (!BN_copy(dest->X, src->X))
345 if (!BN_copy(dest->Y, src->Y))
347 if (!BN_copy(dest->Z, src->Z))
349 dest->Z_is_one = src->Z_is_one;
354 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
362 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
369 BN_CTX *new_ctx = NULL;
373 ctx = new_ctx = BN_CTX_new();
379 if (!BN_nnmod(point->X, x, group->field, ctx))
381 if (group->meth->field_encode) {
382 if (!group->meth->field_encode(group, point->X, point->X, ctx))
388 if (!BN_nnmod(point->Y, y, group->field, ctx))
390 if (group->meth->field_encode) {
391 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
399 if (!BN_nnmod(point->Z, z, group->field, ctx))
401 Z_is_one = BN_is_one(point->Z);
402 if (group->meth->field_encode) {
403 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
404 if (!group->meth->field_set_to_one(group, point->Z, ctx))
408 meth->field_encode(group, point->Z, point->Z, ctx))
412 point->Z_is_one = Z_is_one;
418 BN_CTX_free(new_ctx);
422 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
423 const EC_POINT *point,
424 BIGNUM *x, BIGNUM *y,
425 BIGNUM *z, BN_CTX *ctx)
427 BN_CTX *new_ctx = NULL;
430 if (group->meth->field_decode != 0) {
432 ctx = new_ctx = BN_CTX_new();
438 if (!group->meth->field_decode(group, x, point->X, ctx))
442 if (!group->meth->field_decode(group, y, point->Y, ctx))
446 if (!group->meth->field_decode(group, z, point->Z, ctx))
451 if (!BN_copy(x, point->X))
455 if (!BN_copy(y, point->Y))
459 if (!BN_copy(z, point->Z))
467 BN_CTX_free(new_ctx);
471 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
474 const BIGNUM *y, BN_CTX *ctx)
476 if (x == NULL || y == NULL) {
478 * unlike for projective coordinates, we do not tolerate this
480 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
481 ERR_R_PASSED_NULL_PARAMETER);
485 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
486 BN_value_one(), ctx);
489 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
490 const EC_POINT *point,
491 BIGNUM *x, BIGNUM *y,
494 BN_CTX *new_ctx = NULL;
495 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
499 if (EC_POINT_is_at_infinity(group, point)) {
500 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
501 EC_R_POINT_AT_INFINITY);
506 ctx = new_ctx = BN_CTX_new();
513 Z_1 = BN_CTX_get(ctx);
514 Z_2 = BN_CTX_get(ctx);
515 Z_3 = BN_CTX_get(ctx);
519 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
521 if (group->meth->field_decode) {
522 if (!group->meth->field_decode(group, Z, point->Z, ctx))
530 if (group->meth->field_decode) {
532 if (!group->meth->field_decode(group, x, point->X, ctx))
536 if (!group->meth->field_decode(group, y, point->Y, ctx))
541 if (!BN_copy(x, point->X))
545 if (!BN_copy(y, point->Y))
550 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
551 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
556 if (group->meth->field_encode == 0) {
557 /* field_sqr works on standard representation */
558 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
561 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
567 * in the Montgomery case, field_mul will cancel out Montgomery
570 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
575 if (group->meth->field_encode == 0) {
577 * field_mul works on standard representation
579 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
582 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
587 * in the Montgomery case, field_mul will cancel out Montgomery
590 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
599 BN_CTX_free(new_ctx);
603 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
604 const EC_POINT *b, BN_CTX *ctx)
606 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
607 const BIGNUM *, BN_CTX *);
608 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
610 BN_CTX *new_ctx = NULL;
611 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
615 return EC_POINT_dbl(group, r, a, ctx);
616 if (EC_POINT_is_at_infinity(group, a))
617 return EC_POINT_copy(r, b);
618 if (EC_POINT_is_at_infinity(group, b))
619 return EC_POINT_copy(r, a);
621 field_mul = group->meth->field_mul;
622 field_sqr = group->meth->field_sqr;
626 ctx = new_ctx = BN_CTX_new();
632 n0 = BN_CTX_get(ctx);
633 n1 = BN_CTX_get(ctx);
634 n2 = BN_CTX_get(ctx);
635 n3 = BN_CTX_get(ctx);
636 n4 = BN_CTX_get(ctx);
637 n5 = BN_CTX_get(ctx);
638 n6 = BN_CTX_get(ctx);
643 * Note that in this function we must not read components of 'a' or 'b'
644 * once we have written the corresponding components of 'r'. ('r' might
645 * be one of 'a' or 'b'.)
650 if (!BN_copy(n1, a->X))
652 if (!BN_copy(n2, a->Y))
657 if (!field_sqr(group, n0, b->Z, ctx))
659 if (!field_mul(group, n1, a->X, n0, ctx))
661 /* n1 = X_a * Z_b^2 */
663 if (!field_mul(group, n0, n0, b->Z, ctx))
665 if (!field_mul(group, n2, a->Y, n0, ctx))
667 /* n2 = Y_a * Z_b^3 */
672 if (!BN_copy(n3, b->X))
674 if (!BN_copy(n4, b->Y))
679 if (!field_sqr(group, n0, a->Z, ctx))
681 if (!field_mul(group, n3, b->X, n0, ctx))
683 /* n3 = X_b * Z_a^2 */
685 if (!field_mul(group, n0, n0, a->Z, ctx))
687 if (!field_mul(group, n4, b->Y, n0, ctx))
689 /* n4 = Y_b * Z_a^3 */
693 if (!BN_mod_sub_quick(n5, n1, n3, p))
695 if (!BN_mod_sub_quick(n6, n2, n4, p))
700 if (BN_is_zero(n5)) {
701 if (BN_is_zero(n6)) {
702 /* a is the same point as b */
704 ret = EC_POINT_dbl(group, r, a, ctx);
708 /* a is the inverse of b */
717 if (!BN_mod_add_quick(n1, n1, n3, p))
719 if (!BN_mod_add_quick(n2, n2, n4, p))
725 if (a->Z_is_one && b->Z_is_one) {
726 if (!BN_copy(r->Z, n5))
730 if (!BN_copy(n0, b->Z))
732 } else if (b->Z_is_one) {
733 if (!BN_copy(n0, a->Z))
736 if (!field_mul(group, n0, a->Z, b->Z, ctx))
739 if (!field_mul(group, r->Z, n0, n5, ctx))
743 /* Z_r = Z_a * Z_b * n5 */
746 if (!field_sqr(group, n0, n6, ctx))
748 if (!field_sqr(group, n4, n5, ctx))
750 if (!field_mul(group, n3, n1, n4, ctx))
752 if (!BN_mod_sub_quick(r->X, n0, n3, p))
754 /* X_r = n6^2 - n5^2 * 'n7' */
757 if (!BN_mod_lshift1_quick(n0, r->X, p))
759 if (!BN_mod_sub_quick(n0, n3, n0, p))
761 /* n9 = n5^2 * 'n7' - 2 * X_r */
764 if (!field_mul(group, n0, n0, n6, ctx))
766 if (!field_mul(group, n5, n4, n5, ctx))
767 goto end; /* now n5 is n5^3 */
768 if (!field_mul(group, n1, n2, n5, ctx))
770 if (!BN_mod_sub_quick(n0, n0, n1, p))
773 if (!BN_add(n0, n0, p))
775 /* now 0 <= n0 < 2*p, and n0 is even */
776 if (!BN_rshift1(r->Y, n0))
778 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
783 if (ctx) /* otherwise we already called BN_CTX_end */
785 BN_CTX_free(new_ctx);
789 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
792 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
793 const BIGNUM *, BN_CTX *);
794 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
796 BN_CTX *new_ctx = NULL;
797 BIGNUM *n0, *n1, *n2, *n3;
800 if (EC_POINT_is_at_infinity(group, a)) {
806 field_mul = group->meth->field_mul;
807 field_sqr = group->meth->field_sqr;
811 ctx = new_ctx = BN_CTX_new();
817 n0 = BN_CTX_get(ctx);
818 n1 = BN_CTX_get(ctx);
819 n2 = BN_CTX_get(ctx);
820 n3 = BN_CTX_get(ctx);
825 * Note that in this function we must not read components of 'a' once we
826 * have written the corresponding components of 'r'. ('r' might the same
832 if (!field_sqr(group, n0, a->X, ctx))
834 if (!BN_mod_lshift1_quick(n1, n0, p))
836 if (!BN_mod_add_quick(n0, n0, n1, p))
838 if (!BN_mod_add_quick(n1, n0, group->a, p))
840 /* n1 = 3 * X_a^2 + a_curve */
841 } else if (group->a_is_minus3) {
842 if (!field_sqr(group, n1, a->Z, ctx))
844 if (!BN_mod_add_quick(n0, a->X, n1, p))
846 if (!BN_mod_sub_quick(n2, a->X, n1, p))
848 if (!field_mul(group, n1, n0, n2, ctx))
850 if (!BN_mod_lshift1_quick(n0, n1, p))
852 if (!BN_mod_add_quick(n1, n0, n1, p))
855 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
856 * = 3 * X_a^2 - 3 * Z_a^4
859 if (!field_sqr(group, n0, a->X, ctx))
861 if (!BN_mod_lshift1_quick(n1, n0, p))
863 if (!BN_mod_add_quick(n0, n0, n1, p))
865 if (!field_sqr(group, n1, a->Z, ctx))
867 if (!field_sqr(group, n1, n1, ctx))
869 if (!field_mul(group, n1, n1, group->a, ctx))
871 if (!BN_mod_add_quick(n1, n1, n0, p))
873 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
878 if (!BN_copy(n0, a->Y))
881 if (!field_mul(group, n0, a->Y, a->Z, ctx))
884 if (!BN_mod_lshift1_quick(r->Z, n0, p))
887 /* Z_r = 2 * Y_a * Z_a */
890 if (!field_sqr(group, n3, a->Y, ctx))
892 if (!field_mul(group, n2, a->X, n3, ctx))
894 if (!BN_mod_lshift_quick(n2, n2, 2, p))
896 /* n2 = 4 * X_a * Y_a^2 */
899 if (!BN_mod_lshift1_quick(n0, n2, p))
901 if (!field_sqr(group, r->X, n1, ctx))
903 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
905 /* X_r = n1^2 - 2 * n2 */
908 if (!field_sqr(group, n0, n3, ctx))
910 if (!BN_mod_lshift_quick(n3, n0, 3, p))
915 if (!BN_mod_sub_quick(n0, n2, r->X, p))
917 if (!field_mul(group, n0, n1, n0, ctx))
919 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
921 /* Y_r = n1 * (n2 - X_r) - n3 */
927 BN_CTX_free(new_ctx);
931 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
933 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
934 /* point is its own inverse */
937 return BN_usub(point->Y, group->field, point->Y);
940 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
942 return BN_is_zero(point->Z);
945 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
948 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
949 const BIGNUM *, BN_CTX *);
950 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
952 BN_CTX *new_ctx = NULL;
953 BIGNUM *rh, *tmp, *Z4, *Z6;
956 if (EC_POINT_is_at_infinity(group, point))
959 field_mul = group->meth->field_mul;
960 field_sqr = group->meth->field_sqr;
964 ctx = new_ctx = BN_CTX_new();
970 rh = BN_CTX_get(ctx);
971 tmp = BN_CTX_get(ctx);
972 Z4 = BN_CTX_get(ctx);
973 Z6 = BN_CTX_get(ctx);
978 * We have a curve defined by a Weierstrass equation
979 * y^2 = x^3 + a*x + b.
980 * The point to consider is given in Jacobian projective coordinates
981 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
982 * Substituting this and multiplying by Z^6 transforms the above equation into
983 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
984 * To test this, we add up the right-hand side in 'rh'.
988 if (!field_sqr(group, rh, point->X, ctx))
991 if (!point->Z_is_one) {
992 if (!field_sqr(group, tmp, point->Z, ctx))
994 if (!field_sqr(group, Z4, tmp, ctx))
996 if (!field_mul(group, Z6, Z4, tmp, ctx))
999 /* rh := (rh + a*Z^4)*X */
1000 if (group->a_is_minus3) {
1001 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1003 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1005 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1007 if (!field_mul(group, rh, rh, point->X, ctx))
1010 if (!field_mul(group, tmp, Z4, group->a, ctx))
1012 if (!BN_mod_add_quick(rh, rh, tmp, p))
1014 if (!field_mul(group, rh, rh, point->X, ctx))
1018 /* rh := rh + b*Z^6 */
1019 if (!field_mul(group, tmp, group->b, Z6, ctx))
1021 if (!BN_mod_add_quick(rh, rh, tmp, p))
1024 /* point->Z_is_one */
1026 /* rh := (rh + a)*X */
1027 if (!BN_mod_add_quick(rh, rh, group->a, p))
1029 if (!field_mul(group, rh, rh, point->X, ctx))
1032 if (!BN_mod_add_quick(rh, rh, group->b, p))
1037 if (!field_sqr(group, tmp, point->Y, ctx))
1040 ret = (0 == BN_ucmp(tmp, rh));
1044 BN_CTX_free(new_ctx);
1048 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1049 const EC_POINT *b, BN_CTX *ctx)
1054 * 0 equal (in affine coordinates)
1058 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1059 const BIGNUM *, BN_CTX *);
1060 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1061 BN_CTX *new_ctx = NULL;
1062 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1063 const BIGNUM *tmp1_, *tmp2_;
1066 if (EC_POINT_is_at_infinity(group, a)) {
1067 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1070 if (EC_POINT_is_at_infinity(group, b))
1073 if (a->Z_is_one && b->Z_is_one) {
1074 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1077 field_mul = group->meth->field_mul;
1078 field_sqr = group->meth->field_sqr;
1081 ctx = new_ctx = BN_CTX_new();
1087 tmp1 = BN_CTX_get(ctx);
1088 tmp2 = BN_CTX_get(ctx);
1089 Za23 = BN_CTX_get(ctx);
1090 Zb23 = BN_CTX_get(ctx);
1095 * We have to decide whether
1096 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1097 * or equivalently, whether
1098 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1102 if (!field_sqr(group, Zb23, b->Z, ctx))
1104 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1110 if (!field_sqr(group, Za23, a->Z, ctx))
1112 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1118 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1119 if (BN_cmp(tmp1_, tmp2_) != 0) {
1120 ret = 1; /* points differ */
1125 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1127 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1133 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1135 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1141 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1142 if (BN_cmp(tmp1_, tmp2_) != 0) {
1143 ret = 1; /* points differ */
1147 /* points are equal */
1152 BN_CTX_free(new_ctx);
1156 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1159 BN_CTX *new_ctx = NULL;
1163 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1167 ctx = new_ctx = BN_CTX_new();
1173 x = BN_CTX_get(ctx);
1174 y = BN_CTX_get(ctx);
1178 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1180 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1182 if (!point->Z_is_one) {
1183 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1191 BN_CTX_free(new_ctx);
1195 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1196 EC_POINT *points[], BN_CTX *ctx)
1198 BN_CTX *new_ctx = NULL;
1199 BIGNUM *tmp, *tmp_Z;
1200 BIGNUM **prod_Z = NULL;
1208 ctx = new_ctx = BN_CTX_new();
1214 tmp = BN_CTX_get(ctx);
1215 tmp_Z = BN_CTX_get(ctx);
1219 prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
1222 for (i = 0; i < num; i++) {
1223 prod_Z[i] = BN_new();
1224 if (prod_Z[i] == NULL)
1229 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1230 * skipping any zero-valued inputs (pretend that they're 1).
1233 if (!BN_is_zero(points[0]->Z)) {
1234 if (!BN_copy(prod_Z[0], points[0]->Z))
1237 if (group->meth->field_set_to_one != 0) {
1238 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1241 if (!BN_one(prod_Z[0]))
1246 for (i = 1; i < num; i++) {
1247 if (!BN_is_zero(points[i]->Z)) {
1249 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1253 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1259 * Now use a single explicit inversion to replace every non-zero
1260 * points[i]->Z by its inverse.
1263 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1264 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1267 if (group->meth->field_encode != 0) {
1269 * In the Montgomery case, we just turned R*H (representing H) into
1270 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1271 * multiply by the Montgomery factor twice.
1273 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1275 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1279 for (i = num - 1; i > 0; --i) {
1281 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1282 * .. points[i]->Z (zero-valued inputs skipped).
1284 if (!BN_is_zero(points[i]->Z)) {
1286 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1287 * inverses 0 .. i, Z values 0 .. i - 1).
1290 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1293 * Update tmp to satisfy the loop invariant for i - 1.
1295 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1297 /* Replace points[i]->Z by its inverse. */
1298 if (!BN_copy(points[i]->Z, tmp_Z))
1303 if (!BN_is_zero(points[0]->Z)) {
1304 /* Replace points[0]->Z by its inverse. */
1305 if (!BN_copy(points[0]->Z, tmp))
1309 /* Finally, fix up the X and Y coordinates for all points. */
1311 for (i = 0; i < num; i++) {
1312 EC_POINT *p = points[i];
1314 if (!BN_is_zero(p->Z)) {
1315 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1317 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1319 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1322 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1324 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1327 if (group->meth->field_set_to_one != 0) {
1328 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1342 BN_CTX_free(new_ctx);
1343 if (prod_Z != NULL) {
1344 for (i = 0; i < num; i++) {
1345 if (prod_Z[i] == NULL)
1347 BN_clear_free(prod_Z[i]);
1349 OPENSSL_free(prod_Z);
1354 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1355 const BIGNUM *b, BN_CTX *ctx)
1357 return BN_mod_mul(r, a, b, group->field, ctx);
1360 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1363 return BN_mod_sqr(r, a, group->field, ctx);