2 * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 /* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
12 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
13 * and contributed to the OpenSSL project.
16 #include <openssl/err.h>
17 #include <openssl/symhacks.h>
21 const EC_METHOD *EC_GFp_simple_method(void)
23 static const EC_METHOD ret = {
25 NID_X9_62_prime_field,
26 ec_GFp_simple_group_init,
27 ec_GFp_simple_group_finish,
28 ec_GFp_simple_group_clear_finish,
29 ec_GFp_simple_group_copy,
30 ec_GFp_simple_group_set_curve,
31 ec_GFp_simple_group_get_curve,
32 ec_GFp_simple_group_get_degree,
33 ec_group_simple_order_bits,
34 ec_GFp_simple_group_check_discriminant,
35 ec_GFp_simple_point_init,
36 ec_GFp_simple_point_finish,
37 ec_GFp_simple_point_clear_finish,
38 ec_GFp_simple_point_copy,
39 ec_GFp_simple_point_set_to_infinity,
40 ec_GFp_simple_set_Jprojective_coordinates_GFp,
41 ec_GFp_simple_get_Jprojective_coordinates_GFp,
42 ec_GFp_simple_point_set_affine_coordinates,
43 ec_GFp_simple_point_get_affine_coordinates,
48 ec_GFp_simple_is_at_infinity,
49 ec_GFp_simple_is_on_curve,
51 ec_GFp_simple_make_affine,
52 ec_GFp_simple_points_make_affine,
54 0 /* precompute_mult */ ,
55 0 /* have_precompute_mult */ ,
56 ec_GFp_simple_field_mul,
57 ec_GFp_simple_field_sqr,
59 0 /* field_encode */ ,
60 0 /* field_decode */ ,
61 0, /* field_set_to_one */
62 ec_key_simple_priv2oct,
63 ec_key_simple_oct2priv,
65 ec_key_simple_generate_key,
66 ec_key_simple_check_key,
67 ec_key_simple_generate_public_key,
70 ecdh_simple_compute_key
77 * Most method functions in this file are designed to work with
78 * non-trivial representations of field elements if necessary
79 * (see ecp_mont.c): while standard modular addition and subtraction
80 * are used, the field_mul and field_sqr methods will be used for
81 * multiplication, and field_encode and field_decode (if defined)
82 * will be used for converting between representations.
84 * Functions ec_GFp_simple_points_make_affine() and
85 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
86 * that if a non-trivial representation is used, it is a Montgomery
87 * representation (i.e. 'encoding' means multiplying by some factor R).
90 int ec_GFp_simple_group_init(EC_GROUP *group)
92 group->field = BN_new();
95 if (group->field == NULL || group->a == NULL || group->b == NULL) {
96 BN_free(group->field);
101 group->a_is_minus3 = 0;
105 void ec_GFp_simple_group_finish(EC_GROUP *group)
107 BN_free(group->field);
112 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
114 BN_clear_free(group->field);
115 BN_clear_free(group->a);
116 BN_clear_free(group->b);
119 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
121 if (!BN_copy(dest->field, src->field))
123 if (!BN_copy(dest->a, src->a))
125 if (!BN_copy(dest->b, src->b))
128 dest->a_is_minus3 = src->a_is_minus3;
133 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
134 const BIGNUM *p, const BIGNUM *a,
135 const BIGNUM *b, BN_CTX *ctx)
138 BN_CTX *new_ctx = NULL;
141 /* p must be a prime > 3 */
142 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
143 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
148 ctx = new_ctx = BN_CTX_new();
154 tmp_a = BN_CTX_get(ctx);
159 if (!BN_copy(group->field, p))
161 BN_set_negative(group->field, 0);
164 if (!BN_nnmod(tmp_a, a, p, ctx))
166 if (group->meth->field_encode) {
167 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
169 } else if (!BN_copy(group->a, tmp_a))
173 if (!BN_nnmod(group->b, b, p, ctx))
175 if (group->meth->field_encode)
176 if (!group->meth->field_encode(group, group->b, group->b, ctx))
179 /* group->a_is_minus3 */
180 if (!BN_add_word(tmp_a, 3))
182 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
188 BN_CTX_free(new_ctx);
192 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
193 BIGNUM *b, BN_CTX *ctx)
196 BN_CTX *new_ctx = NULL;
199 if (!BN_copy(p, group->field))
203 if (a != NULL || b != NULL) {
204 if (group->meth->field_decode) {
206 ctx = new_ctx = BN_CTX_new();
211 if (!group->meth->field_decode(group, a, group->a, ctx))
215 if (!group->meth->field_decode(group, b, group->b, ctx))
220 if (!BN_copy(a, group->a))
224 if (!BN_copy(b, group->b))
233 BN_CTX_free(new_ctx);
237 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
239 return BN_num_bits(group->field);
242 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
245 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
246 const BIGNUM *p = group->field;
247 BN_CTX *new_ctx = NULL;
250 ctx = new_ctx = BN_CTX_new();
252 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
253 ERR_R_MALLOC_FAILURE);
260 tmp_1 = BN_CTX_get(ctx);
261 tmp_2 = BN_CTX_get(ctx);
262 order = BN_CTX_get(ctx);
266 if (group->meth->field_decode) {
267 if (!group->meth->field_decode(group, a, group->a, ctx))
269 if (!group->meth->field_decode(group, b, group->b, ctx))
272 if (!BN_copy(a, group->a))
274 if (!BN_copy(b, group->b))
279 * check the discriminant:
280 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
286 } else if (!BN_is_zero(b)) {
287 if (!BN_mod_sqr(tmp_1, a, p, ctx))
289 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
291 if (!BN_lshift(tmp_1, tmp_2, 2))
295 if (!BN_mod_sqr(tmp_2, b, p, ctx))
297 if (!BN_mul_word(tmp_2, 27))
301 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
311 BN_CTX_free(new_ctx);
315 int ec_GFp_simple_point_init(EC_POINT *point)
322 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
331 void ec_GFp_simple_point_finish(EC_POINT *point)
338 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
340 BN_clear_free(point->X);
341 BN_clear_free(point->Y);
342 BN_clear_free(point->Z);
346 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
348 if (!BN_copy(dest->X, src->X))
350 if (!BN_copy(dest->Y, src->Y))
352 if (!BN_copy(dest->Z, src->Z))
354 dest->Z_is_one = src->Z_is_one;
359 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
367 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
374 BN_CTX *new_ctx = NULL;
378 ctx = new_ctx = BN_CTX_new();
384 if (!BN_nnmod(point->X, x, group->field, ctx))
386 if (group->meth->field_encode) {
387 if (!group->meth->field_encode(group, point->X, point->X, ctx))
393 if (!BN_nnmod(point->Y, y, group->field, ctx))
395 if (group->meth->field_encode) {
396 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
404 if (!BN_nnmod(point->Z, z, group->field, ctx))
406 Z_is_one = BN_is_one(point->Z);
407 if (group->meth->field_encode) {
408 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
409 if (!group->meth->field_set_to_one(group, point->Z, ctx))
413 meth->field_encode(group, point->Z, point->Z, ctx))
417 point->Z_is_one = Z_is_one;
423 BN_CTX_free(new_ctx);
427 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
428 const EC_POINT *point,
429 BIGNUM *x, BIGNUM *y,
430 BIGNUM *z, BN_CTX *ctx)
432 BN_CTX *new_ctx = NULL;
435 if (group->meth->field_decode != 0) {
437 ctx = new_ctx = BN_CTX_new();
443 if (!group->meth->field_decode(group, x, point->X, ctx))
447 if (!group->meth->field_decode(group, y, point->Y, ctx))
451 if (!group->meth->field_decode(group, z, point->Z, ctx))
456 if (!BN_copy(x, point->X))
460 if (!BN_copy(y, point->Y))
464 if (!BN_copy(z, point->Z))
472 BN_CTX_free(new_ctx);
476 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
479 const BIGNUM *y, BN_CTX *ctx)
481 if (x == NULL || y == NULL) {
483 * unlike for projective coordinates, we do not tolerate this
485 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
486 ERR_R_PASSED_NULL_PARAMETER);
490 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
491 BN_value_one(), ctx);
494 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
495 const EC_POINT *point,
496 BIGNUM *x, BIGNUM *y,
499 BN_CTX *new_ctx = NULL;
500 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
504 if (EC_POINT_is_at_infinity(group, point)) {
505 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
506 EC_R_POINT_AT_INFINITY);
511 ctx = new_ctx = BN_CTX_new();
518 Z_1 = BN_CTX_get(ctx);
519 Z_2 = BN_CTX_get(ctx);
520 Z_3 = BN_CTX_get(ctx);
524 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
526 if (group->meth->field_decode) {
527 if (!group->meth->field_decode(group, Z, point->Z, ctx))
535 if (group->meth->field_decode) {
537 if (!group->meth->field_decode(group, x, point->X, ctx))
541 if (!group->meth->field_decode(group, y, point->Y, ctx))
546 if (!BN_copy(x, point->X))
550 if (!BN_copy(y, point->Y))
555 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
556 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
561 if (group->meth->field_encode == 0) {
562 /* field_sqr works on standard representation */
563 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
566 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
572 * in the Montgomery case, field_mul will cancel out Montgomery
575 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
580 if (group->meth->field_encode == 0) {
582 * field_mul works on standard representation
584 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
587 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
592 * in the Montgomery case, field_mul will cancel out Montgomery
595 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
604 BN_CTX_free(new_ctx);
608 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
609 const EC_POINT *b, BN_CTX *ctx)
611 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
612 const BIGNUM *, BN_CTX *);
613 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
615 BN_CTX *new_ctx = NULL;
616 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
620 return EC_POINT_dbl(group, r, a, ctx);
621 if (EC_POINT_is_at_infinity(group, a))
622 return EC_POINT_copy(r, b);
623 if (EC_POINT_is_at_infinity(group, b))
624 return EC_POINT_copy(r, a);
626 field_mul = group->meth->field_mul;
627 field_sqr = group->meth->field_sqr;
631 ctx = new_ctx = BN_CTX_new();
637 n0 = BN_CTX_get(ctx);
638 n1 = BN_CTX_get(ctx);
639 n2 = BN_CTX_get(ctx);
640 n3 = BN_CTX_get(ctx);
641 n4 = BN_CTX_get(ctx);
642 n5 = BN_CTX_get(ctx);
643 n6 = BN_CTX_get(ctx);
648 * Note that in this function we must not read components of 'a' or 'b'
649 * once we have written the corresponding components of 'r'. ('r' might
650 * be one of 'a' or 'b'.)
655 if (!BN_copy(n1, a->X))
657 if (!BN_copy(n2, a->Y))
662 if (!field_sqr(group, n0, b->Z, ctx))
664 if (!field_mul(group, n1, a->X, n0, ctx))
666 /* n1 = X_a * Z_b^2 */
668 if (!field_mul(group, n0, n0, b->Z, ctx))
670 if (!field_mul(group, n2, a->Y, n0, ctx))
672 /* n2 = Y_a * Z_b^3 */
677 if (!BN_copy(n3, b->X))
679 if (!BN_copy(n4, b->Y))
684 if (!field_sqr(group, n0, a->Z, ctx))
686 if (!field_mul(group, n3, b->X, n0, ctx))
688 /* n3 = X_b * Z_a^2 */
690 if (!field_mul(group, n0, n0, a->Z, ctx))
692 if (!field_mul(group, n4, b->Y, n0, ctx))
694 /* n4 = Y_b * Z_a^3 */
698 if (!BN_mod_sub_quick(n5, n1, n3, p))
700 if (!BN_mod_sub_quick(n6, n2, n4, p))
705 if (BN_is_zero(n5)) {
706 if (BN_is_zero(n6)) {
707 /* a is the same point as b */
709 ret = EC_POINT_dbl(group, r, a, ctx);
713 /* a is the inverse of b */
722 if (!BN_mod_add_quick(n1, n1, n3, p))
724 if (!BN_mod_add_quick(n2, n2, n4, p))
730 if (a->Z_is_one && b->Z_is_one) {
731 if (!BN_copy(r->Z, n5))
735 if (!BN_copy(n0, b->Z))
737 } else if (b->Z_is_one) {
738 if (!BN_copy(n0, a->Z))
741 if (!field_mul(group, n0, a->Z, b->Z, ctx))
744 if (!field_mul(group, r->Z, n0, n5, ctx))
748 /* Z_r = Z_a * Z_b * n5 */
751 if (!field_sqr(group, n0, n6, ctx))
753 if (!field_sqr(group, n4, n5, ctx))
755 if (!field_mul(group, n3, n1, n4, ctx))
757 if (!BN_mod_sub_quick(r->X, n0, n3, p))
759 /* X_r = n6^2 - n5^2 * 'n7' */
762 if (!BN_mod_lshift1_quick(n0, r->X, p))
764 if (!BN_mod_sub_quick(n0, n3, n0, p))
766 /* n9 = n5^2 * 'n7' - 2 * X_r */
769 if (!field_mul(group, n0, n0, n6, ctx))
771 if (!field_mul(group, n5, n4, n5, ctx))
772 goto end; /* now n5 is n5^3 */
773 if (!field_mul(group, n1, n2, n5, ctx))
775 if (!BN_mod_sub_quick(n0, n0, n1, p))
778 if (!BN_add(n0, n0, p))
780 /* now 0 <= n0 < 2*p, and n0 is even */
781 if (!BN_rshift1(r->Y, n0))
783 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
788 if (ctx) /* otherwise we already called BN_CTX_end */
790 BN_CTX_free(new_ctx);
794 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
797 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
798 const BIGNUM *, BN_CTX *);
799 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
801 BN_CTX *new_ctx = NULL;
802 BIGNUM *n0, *n1, *n2, *n3;
805 if (EC_POINT_is_at_infinity(group, a)) {
811 field_mul = group->meth->field_mul;
812 field_sqr = group->meth->field_sqr;
816 ctx = new_ctx = BN_CTX_new();
822 n0 = BN_CTX_get(ctx);
823 n1 = BN_CTX_get(ctx);
824 n2 = BN_CTX_get(ctx);
825 n3 = BN_CTX_get(ctx);
830 * Note that in this function we must not read components of 'a' once we
831 * have written the corresponding components of 'r'. ('r' might the same
837 if (!field_sqr(group, n0, a->X, ctx))
839 if (!BN_mod_lshift1_quick(n1, n0, p))
841 if (!BN_mod_add_quick(n0, n0, n1, p))
843 if (!BN_mod_add_quick(n1, n0, group->a, p))
845 /* n1 = 3 * X_a^2 + a_curve */
846 } else if (group->a_is_minus3) {
847 if (!field_sqr(group, n1, a->Z, ctx))
849 if (!BN_mod_add_quick(n0, a->X, n1, p))
851 if (!BN_mod_sub_quick(n2, a->X, n1, p))
853 if (!field_mul(group, n1, n0, n2, ctx))
855 if (!BN_mod_lshift1_quick(n0, n1, p))
857 if (!BN_mod_add_quick(n1, n0, n1, p))
860 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
861 * = 3 * X_a^2 - 3 * Z_a^4
864 if (!field_sqr(group, n0, a->X, ctx))
866 if (!BN_mod_lshift1_quick(n1, n0, p))
868 if (!BN_mod_add_quick(n0, n0, n1, p))
870 if (!field_sqr(group, n1, a->Z, ctx))
872 if (!field_sqr(group, n1, n1, ctx))
874 if (!field_mul(group, n1, n1, group->a, ctx))
876 if (!BN_mod_add_quick(n1, n1, n0, p))
878 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
883 if (!BN_copy(n0, a->Y))
886 if (!field_mul(group, n0, a->Y, a->Z, ctx))
889 if (!BN_mod_lshift1_quick(r->Z, n0, p))
892 /* Z_r = 2 * Y_a * Z_a */
895 if (!field_sqr(group, n3, a->Y, ctx))
897 if (!field_mul(group, n2, a->X, n3, ctx))
899 if (!BN_mod_lshift_quick(n2, n2, 2, p))
901 /* n2 = 4 * X_a * Y_a^2 */
904 if (!BN_mod_lshift1_quick(n0, n2, p))
906 if (!field_sqr(group, r->X, n1, ctx))
908 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
910 /* X_r = n1^2 - 2 * n2 */
913 if (!field_sqr(group, n0, n3, ctx))
915 if (!BN_mod_lshift_quick(n3, n0, 3, p))
920 if (!BN_mod_sub_quick(n0, n2, r->X, p))
922 if (!field_mul(group, n0, n1, n0, ctx))
924 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
926 /* Y_r = n1 * (n2 - X_r) - n3 */
932 BN_CTX_free(new_ctx);
936 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
938 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
939 /* point is its own inverse */
942 return BN_usub(point->Y, group->field, point->Y);
945 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
947 return BN_is_zero(point->Z);
950 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
953 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
954 const BIGNUM *, BN_CTX *);
955 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
957 BN_CTX *new_ctx = NULL;
958 BIGNUM *rh, *tmp, *Z4, *Z6;
961 if (EC_POINT_is_at_infinity(group, point))
964 field_mul = group->meth->field_mul;
965 field_sqr = group->meth->field_sqr;
969 ctx = new_ctx = BN_CTX_new();
975 rh = BN_CTX_get(ctx);
976 tmp = BN_CTX_get(ctx);
977 Z4 = BN_CTX_get(ctx);
978 Z6 = BN_CTX_get(ctx);
983 * We have a curve defined by a Weierstrass equation
984 * y^2 = x^3 + a*x + b.
985 * The point to consider is given in Jacobian projective coordinates
986 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
987 * Substituting this and multiplying by Z^6 transforms the above equation into
988 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
989 * To test this, we add up the right-hand side in 'rh'.
993 if (!field_sqr(group, rh, point->X, ctx))
996 if (!point->Z_is_one) {
997 if (!field_sqr(group, tmp, point->Z, ctx))
999 if (!field_sqr(group, Z4, tmp, ctx))
1001 if (!field_mul(group, Z6, Z4, tmp, ctx))
1004 /* rh := (rh + a*Z^4)*X */
1005 if (group->a_is_minus3) {
1006 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1008 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1010 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1012 if (!field_mul(group, rh, rh, point->X, ctx))
1015 if (!field_mul(group, tmp, Z4, group->a, ctx))
1017 if (!BN_mod_add_quick(rh, rh, tmp, p))
1019 if (!field_mul(group, rh, rh, point->X, ctx))
1023 /* rh := rh + b*Z^6 */
1024 if (!field_mul(group, tmp, group->b, Z6, ctx))
1026 if (!BN_mod_add_quick(rh, rh, tmp, p))
1029 /* point->Z_is_one */
1031 /* rh := (rh + a)*X */
1032 if (!BN_mod_add_quick(rh, rh, group->a, p))
1034 if (!field_mul(group, rh, rh, point->X, ctx))
1037 if (!BN_mod_add_quick(rh, rh, group->b, p))
1042 if (!field_sqr(group, tmp, point->Y, ctx))
1045 ret = (0 == BN_ucmp(tmp, rh));
1049 BN_CTX_free(new_ctx);
1053 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1054 const EC_POINT *b, BN_CTX *ctx)
1059 * 0 equal (in affine coordinates)
1063 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1064 const BIGNUM *, BN_CTX *);
1065 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1066 BN_CTX *new_ctx = NULL;
1067 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1068 const BIGNUM *tmp1_, *tmp2_;
1071 if (EC_POINT_is_at_infinity(group, a)) {
1072 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1075 if (EC_POINT_is_at_infinity(group, b))
1078 if (a->Z_is_one && b->Z_is_one) {
1079 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1082 field_mul = group->meth->field_mul;
1083 field_sqr = group->meth->field_sqr;
1086 ctx = new_ctx = BN_CTX_new();
1092 tmp1 = BN_CTX_get(ctx);
1093 tmp2 = BN_CTX_get(ctx);
1094 Za23 = BN_CTX_get(ctx);
1095 Zb23 = BN_CTX_get(ctx);
1100 * We have to decide whether
1101 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1102 * or equivalently, whether
1103 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1107 if (!field_sqr(group, Zb23, b->Z, ctx))
1109 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1115 if (!field_sqr(group, Za23, a->Z, ctx))
1117 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1123 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1124 if (BN_cmp(tmp1_, tmp2_) != 0) {
1125 ret = 1; /* points differ */
1130 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1132 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1138 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1140 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1146 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1147 if (BN_cmp(tmp1_, tmp2_) != 0) {
1148 ret = 1; /* points differ */
1152 /* points are equal */
1157 BN_CTX_free(new_ctx);
1161 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1164 BN_CTX *new_ctx = NULL;
1168 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1172 ctx = new_ctx = BN_CTX_new();
1178 x = BN_CTX_get(ctx);
1179 y = BN_CTX_get(ctx);
1183 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1185 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1187 if (!point->Z_is_one) {
1188 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1196 BN_CTX_free(new_ctx);
1200 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1201 EC_POINT *points[], BN_CTX *ctx)
1203 BN_CTX *new_ctx = NULL;
1204 BIGNUM *tmp, *tmp_Z;
1205 BIGNUM **prod_Z = NULL;
1213 ctx = new_ctx = BN_CTX_new();
1219 tmp = BN_CTX_get(ctx);
1220 tmp_Z = BN_CTX_get(ctx);
1221 if (tmp == NULL || tmp_Z == NULL)
1224 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1227 for (i = 0; i < num; i++) {
1228 prod_Z[i] = BN_new();
1229 if (prod_Z[i] == NULL)
1234 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1235 * skipping any zero-valued inputs (pretend that they're 1).
1238 if (!BN_is_zero(points[0]->Z)) {
1239 if (!BN_copy(prod_Z[0], points[0]->Z))
1242 if (group->meth->field_set_to_one != 0) {
1243 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1246 if (!BN_one(prod_Z[0]))
1251 for (i = 1; i < num; i++) {
1252 if (!BN_is_zero(points[i]->Z)) {
1254 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1258 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1264 * Now use a single explicit inversion to replace every non-zero
1265 * points[i]->Z by its inverse.
1268 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1269 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1272 if (group->meth->field_encode != 0) {
1274 * In the Montgomery case, we just turned R*H (representing H) into
1275 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1276 * multiply by the Montgomery factor twice.
1278 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1280 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1284 for (i = num - 1; i > 0; --i) {
1286 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1287 * .. points[i]->Z (zero-valued inputs skipped).
1289 if (!BN_is_zero(points[i]->Z)) {
1291 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1292 * inverses 0 .. i, Z values 0 .. i - 1).
1295 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1298 * Update tmp to satisfy the loop invariant for i - 1.
1300 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1302 /* Replace points[i]->Z by its inverse. */
1303 if (!BN_copy(points[i]->Z, tmp_Z))
1308 if (!BN_is_zero(points[0]->Z)) {
1309 /* Replace points[0]->Z by its inverse. */
1310 if (!BN_copy(points[0]->Z, tmp))
1314 /* Finally, fix up the X and Y coordinates for all points. */
1316 for (i = 0; i < num; i++) {
1317 EC_POINT *p = points[i];
1319 if (!BN_is_zero(p->Z)) {
1320 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1322 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1324 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1327 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1329 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1332 if (group->meth->field_set_to_one != 0) {
1333 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1347 BN_CTX_free(new_ctx);
1348 if (prod_Z != NULL) {
1349 for (i = 0; i < num; i++) {
1350 if (prod_Z[i] == NULL)
1352 BN_clear_free(prod_Z[i]);
1354 OPENSSL_free(prod_Z);
1359 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1360 const BIGNUM *b, BN_CTX *ctx)
1362 return BN_mod_mul(r, a, b, group->field, ctx);
1365 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1368 return BN_mod_sqr(r, a, group->field, ctx);