1 /* crypto/ec/ecp_smpl.c */
3 * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
4 * for the OpenSSL project. Includes code written by Bodo Moeller for the
7 /* ====================================================================
8 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
14 * 1. Redistributions of source code must retain the above copyright
15 * notice, this list of conditions and the following disclaimer.
17 * 2. Redistributions in binary form must reproduce the above copyright
18 * notice, this list of conditions and the following disclaimer in
19 * the documentation and/or other materials provided with the
22 * 3. All advertising materials mentioning features or use of this
23 * software must display the following acknowledgment:
24 * "This product includes software developed by the OpenSSL Project
25 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
27 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
28 * endorse or promote products derived from this software without
29 * prior written permission. For written permission, please contact
30 * openssl-core@openssl.org.
32 * 5. Products derived from this software may not be called "OpenSSL"
33 * nor may "OpenSSL" appear in their names without prior written
34 * permission of the OpenSSL Project.
36 * 6. Redistributions of any form whatsoever must retain the following
38 * "This product includes software developed by the OpenSSL Project
39 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
41 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
42 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
44 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
45 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
46 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
47 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
48 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
49 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
50 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
51 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
52 * OF THE POSSIBILITY OF SUCH DAMAGE.
53 * ====================================================================
55 * This product includes cryptographic software written by Eric Young
56 * (eay@cryptsoft.com). This product includes software written by Tim
57 * Hudson (tjh@cryptsoft.com).
60 /* ====================================================================
61 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
62 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
63 * and contributed to the OpenSSL project.
66 #include <openssl/err.h>
67 #include <openssl/symhacks.h>
70 # include <openssl/fips.h>
75 const EC_METHOD *EC_GFp_simple_method(void)
77 static const EC_METHOD ret = {
79 NID_X9_62_prime_field,
80 ec_GFp_simple_group_init,
81 ec_GFp_simple_group_finish,
82 ec_GFp_simple_group_clear_finish,
83 ec_GFp_simple_group_copy,
84 ec_GFp_simple_group_set_curve,
85 ec_GFp_simple_group_get_curve,
86 ec_GFp_simple_group_get_degree,
87 ec_GFp_simple_group_check_discriminant,
88 ec_GFp_simple_point_init,
89 ec_GFp_simple_point_finish,
90 ec_GFp_simple_point_clear_finish,
91 ec_GFp_simple_point_copy,
92 ec_GFp_simple_point_set_to_infinity,
93 ec_GFp_simple_set_Jprojective_coordinates_GFp,
94 ec_GFp_simple_get_Jprojective_coordinates_GFp,
95 ec_GFp_simple_point_set_affine_coordinates,
96 ec_GFp_simple_point_get_affine_coordinates,
100 ec_GFp_simple_invert,
101 ec_GFp_simple_is_at_infinity,
102 ec_GFp_simple_is_on_curve,
104 ec_GFp_simple_make_affine,
105 ec_GFp_simple_points_make_affine,
107 0 /* precompute_mult */ ,
108 0 /* have_precompute_mult */ ,
109 ec_GFp_simple_field_mul,
110 ec_GFp_simple_field_sqr,
112 0 /* field_encode */ ,
113 0 /* field_decode */ ,
114 0 /* field_set_to_one */
119 return fips_ec_gfp_simple_method();
126 * Most method functions in this file are designed to work with
127 * non-trivial representations of field elements if necessary
128 * (see ecp_mont.c): while standard modular addition and subtraction
129 * are used, the field_mul and field_sqr methods will be used for
130 * multiplication, and field_encode and field_decode (if defined)
131 * will be used for converting between representations.
133 * Functions ec_GFp_simple_points_make_affine() and
134 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
135 * that if a non-trivial representation is used, it is a Montgomery
136 * representation (i.e. 'encoding' means multiplying by some factor R).
139 int ec_GFp_simple_group_init(EC_GROUP *group)
141 BN_init(&group->field);
144 group->a_is_minus3 = 0;
148 void ec_GFp_simple_group_finish(EC_GROUP *group)
150 BN_free(&group->field);
155 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
157 BN_clear_free(&group->field);
158 BN_clear_free(&group->a);
159 BN_clear_free(&group->b);
162 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
164 if (!BN_copy(&dest->field, &src->field))
166 if (!BN_copy(&dest->a, &src->a))
168 if (!BN_copy(&dest->b, &src->b))
171 dest->a_is_minus3 = src->a_is_minus3;
176 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
177 const BIGNUM *p, const BIGNUM *a,
178 const BIGNUM *b, BN_CTX *ctx)
181 BN_CTX *new_ctx = NULL;
184 /* p must be a prime > 3 */
185 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
186 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
191 ctx = new_ctx = BN_CTX_new();
197 tmp_a = BN_CTX_get(ctx);
202 if (!BN_copy(&group->field, p))
204 BN_set_negative(&group->field, 0);
207 if (!BN_nnmod(tmp_a, a, p, ctx))
209 if (group->meth->field_encode) {
210 if (!group->meth->field_encode(group, &group->a, tmp_a, ctx))
212 } else if (!BN_copy(&group->a, tmp_a))
216 if (!BN_nnmod(&group->b, b, p, ctx))
218 if (group->meth->field_encode)
219 if (!group->meth->field_encode(group, &group->b, &group->b, ctx))
222 /* group->a_is_minus3 */
223 if (!BN_add_word(tmp_a, 3))
225 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
232 BN_CTX_free(new_ctx);
236 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
237 BIGNUM *b, BN_CTX *ctx)
240 BN_CTX *new_ctx = NULL;
243 if (!BN_copy(p, &group->field))
247 if (a != NULL || b != NULL) {
248 if (group->meth->field_decode) {
250 ctx = new_ctx = BN_CTX_new();
255 if (!group->meth->field_decode(group, a, &group->a, ctx))
259 if (!group->meth->field_decode(group, b, &group->b, ctx))
264 if (!BN_copy(a, &group->a))
268 if (!BN_copy(b, &group->b))
278 BN_CTX_free(new_ctx);
282 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
284 return BN_num_bits(&group->field);
287 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
290 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
291 const BIGNUM *p = &group->field;
292 BN_CTX *new_ctx = NULL;
295 ctx = new_ctx = BN_CTX_new();
297 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
298 ERR_R_MALLOC_FAILURE);
305 tmp_1 = BN_CTX_get(ctx);
306 tmp_2 = BN_CTX_get(ctx);
307 order = BN_CTX_get(ctx);
311 if (group->meth->field_decode) {
312 if (!group->meth->field_decode(group, a, &group->a, ctx))
314 if (!group->meth->field_decode(group, b, &group->b, ctx))
317 if (!BN_copy(a, &group->a))
319 if (!BN_copy(b, &group->b))
324 * check the discriminant:
325 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
331 } else if (!BN_is_zero(b)) {
332 if (!BN_mod_sqr(tmp_1, a, p, ctx))
334 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
336 if (!BN_lshift(tmp_1, tmp_2, 2))
340 if (!BN_mod_sqr(tmp_2, b, p, ctx))
342 if (!BN_mul_word(tmp_2, 27))
346 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
357 BN_CTX_free(new_ctx);
361 int ec_GFp_simple_point_init(EC_POINT *point)
371 void ec_GFp_simple_point_finish(EC_POINT *point)
378 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
380 BN_clear_free(&point->X);
381 BN_clear_free(&point->Y);
382 BN_clear_free(&point->Z);
386 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
388 if (!BN_copy(&dest->X, &src->X))
390 if (!BN_copy(&dest->Y, &src->Y))
392 if (!BN_copy(&dest->Z, &src->Z))
394 dest->Z_is_one = src->Z_is_one;
399 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
407 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
414 BN_CTX *new_ctx = NULL;
418 ctx = new_ctx = BN_CTX_new();
424 if (!BN_nnmod(&point->X, x, &group->field, ctx))
426 if (group->meth->field_encode) {
427 if (!group->meth->field_encode(group, &point->X, &point->X, ctx))
433 if (!BN_nnmod(&point->Y, y, &group->field, ctx))
435 if (group->meth->field_encode) {
436 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx))
444 if (!BN_nnmod(&point->Z, z, &group->field, ctx))
446 Z_is_one = BN_is_one(&point->Z);
447 if (group->meth->field_encode) {
448 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
449 if (!group->meth->field_set_to_one(group, &point->Z, ctx))
453 meth->field_encode(group, &point->Z, &point->Z, ctx))
457 point->Z_is_one = Z_is_one;
464 BN_CTX_free(new_ctx);
468 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
469 const EC_POINT *point,
470 BIGNUM *x, BIGNUM *y,
471 BIGNUM *z, BN_CTX *ctx)
473 BN_CTX *new_ctx = NULL;
476 if (group->meth->field_decode != 0) {
478 ctx = new_ctx = BN_CTX_new();
484 if (!group->meth->field_decode(group, x, &point->X, ctx))
488 if (!group->meth->field_decode(group, y, &point->Y, ctx))
492 if (!group->meth->field_decode(group, z, &point->Z, ctx))
497 if (!BN_copy(x, &point->X))
501 if (!BN_copy(y, &point->Y))
505 if (!BN_copy(z, &point->Z))
514 BN_CTX_free(new_ctx);
518 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
521 const BIGNUM *y, BN_CTX *ctx)
523 if (x == NULL || y == NULL) {
525 * unlike for projective coordinates, we do not tolerate this
527 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
528 ERR_R_PASSED_NULL_PARAMETER);
532 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
533 BN_value_one(), ctx);
536 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
537 const EC_POINT *point,
538 BIGNUM *x, BIGNUM *y,
541 BN_CTX *new_ctx = NULL;
542 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
546 if (EC_POINT_is_at_infinity(group, point)) {
547 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
548 EC_R_POINT_AT_INFINITY);
553 ctx = new_ctx = BN_CTX_new();
560 Z_1 = BN_CTX_get(ctx);
561 Z_2 = BN_CTX_get(ctx);
562 Z_3 = BN_CTX_get(ctx);
566 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
568 if (group->meth->field_decode) {
569 if (!group->meth->field_decode(group, Z, &point->Z, ctx))
577 if (group->meth->field_decode) {
579 if (!group->meth->field_decode(group, x, &point->X, ctx))
583 if (!group->meth->field_decode(group, y, &point->Y, ctx))
588 if (!BN_copy(x, &point->X))
592 if (!BN_copy(y, &point->Y))
597 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) {
598 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
603 if (group->meth->field_encode == 0) {
604 /* field_sqr works on standard representation */
605 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
608 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx))
614 * in the Montgomery case, field_mul will cancel out Montgomery
617 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx))
622 if (group->meth->field_encode == 0) {
624 * field_mul works on standard representation
626 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
629 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx))
634 * in the Montgomery case, field_mul will cancel out Montgomery
637 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx))
647 BN_CTX_free(new_ctx);
651 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
652 const EC_POINT *b, BN_CTX *ctx)
654 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
655 const BIGNUM *, BN_CTX *);
656 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
658 BN_CTX *new_ctx = NULL;
659 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
663 return EC_POINT_dbl(group, r, a, ctx);
664 if (EC_POINT_is_at_infinity(group, a))
665 return EC_POINT_copy(r, b);
666 if (EC_POINT_is_at_infinity(group, b))
667 return EC_POINT_copy(r, a);
669 field_mul = group->meth->field_mul;
670 field_sqr = group->meth->field_sqr;
674 ctx = new_ctx = BN_CTX_new();
680 n0 = BN_CTX_get(ctx);
681 n1 = BN_CTX_get(ctx);
682 n2 = BN_CTX_get(ctx);
683 n3 = BN_CTX_get(ctx);
684 n4 = BN_CTX_get(ctx);
685 n5 = BN_CTX_get(ctx);
686 n6 = BN_CTX_get(ctx);
691 * Note that in this function we must not read components of 'a' or 'b'
692 * once we have written the corresponding components of 'r'. ('r' might
693 * be one of 'a' or 'b'.)
698 if (!BN_copy(n1, &a->X))
700 if (!BN_copy(n2, &a->Y))
705 if (!field_sqr(group, n0, &b->Z, ctx))
707 if (!field_mul(group, n1, &a->X, n0, ctx))
709 /* n1 = X_a * Z_b^2 */
711 if (!field_mul(group, n0, n0, &b->Z, ctx))
713 if (!field_mul(group, n2, &a->Y, n0, ctx))
715 /* n2 = Y_a * Z_b^3 */
720 if (!BN_copy(n3, &b->X))
722 if (!BN_copy(n4, &b->Y))
727 if (!field_sqr(group, n0, &a->Z, ctx))
729 if (!field_mul(group, n3, &b->X, n0, ctx))
731 /* n3 = X_b * Z_a^2 */
733 if (!field_mul(group, n0, n0, &a->Z, ctx))
735 if (!field_mul(group, n4, &b->Y, n0, ctx))
737 /* n4 = Y_b * Z_a^3 */
741 if (!BN_mod_sub_quick(n5, n1, n3, p))
743 if (!BN_mod_sub_quick(n6, n2, n4, p))
748 if (BN_is_zero(n5)) {
749 if (BN_is_zero(n6)) {
750 /* a is the same point as b */
752 ret = EC_POINT_dbl(group, r, a, ctx);
756 /* a is the inverse of b */
765 if (!BN_mod_add_quick(n1, n1, n3, p))
767 if (!BN_mod_add_quick(n2, n2, n4, p))
773 if (a->Z_is_one && b->Z_is_one) {
774 if (!BN_copy(&r->Z, n5))
778 if (!BN_copy(n0, &b->Z))
780 } else if (b->Z_is_one) {
781 if (!BN_copy(n0, &a->Z))
784 if (!field_mul(group, n0, &a->Z, &b->Z, ctx))
787 if (!field_mul(group, &r->Z, n0, n5, ctx))
791 /* Z_r = Z_a * Z_b * n5 */
794 if (!field_sqr(group, n0, n6, ctx))
796 if (!field_sqr(group, n4, n5, ctx))
798 if (!field_mul(group, n3, n1, n4, ctx))
800 if (!BN_mod_sub_quick(&r->X, n0, n3, p))
802 /* X_r = n6^2 - n5^2 * 'n7' */
805 if (!BN_mod_lshift1_quick(n0, &r->X, p))
807 if (!BN_mod_sub_quick(n0, n3, n0, p))
809 /* n9 = n5^2 * 'n7' - 2 * X_r */
812 if (!field_mul(group, n0, n0, n6, ctx))
814 if (!field_mul(group, n5, n4, n5, ctx))
815 goto end; /* now n5 is n5^3 */
816 if (!field_mul(group, n1, n2, n5, ctx))
818 if (!BN_mod_sub_quick(n0, n0, n1, p))
821 if (!BN_add(n0, n0, p))
823 /* now 0 <= n0 < 2*p, and n0 is even */
824 if (!BN_rshift1(&r->Y, n0))
826 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
831 if (ctx) /* otherwise we already called BN_CTX_end */
834 BN_CTX_free(new_ctx);
838 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
841 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
842 const BIGNUM *, BN_CTX *);
843 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
845 BN_CTX *new_ctx = NULL;
846 BIGNUM *n0, *n1, *n2, *n3;
849 if (EC_POINT_is_at_infinity(group, a)) {
855 field_mul = group->meth->field_mul;
856 field_sqr = group->meth->field_sqr;
860 ctx = new_ctx = BN_CTX_new();
866 n0 = BN_CTX_get(ctx);
867 n1 = BN_CTX_get(ctx);
868 n2 = BN_CTX_get(ctx);
869 n3 = BN_CTX_get(ctx);
874 * Note that in this function we must not read components of 'a' once we
875 * have written the corresponding components of 'r'. ('r' might the same
881 if (!field_sqr(group, n0, &a->X, ctx))
883 if (!BN_mod_lshift1_quick(n1, n0, p))
885 if (!BN_mod_add_quick(n0, n0, n1, p))
887 if (!BN_mod_add_quick(n1, n0, &group->a, p))
889 /* n1 = 3 * X_a^2 + a_curve */
890 } else if (group->a_is_minus3) {
891 if (!field_sqr(group, n1, &a->Z, ctx))
893 if (!BN_mod_add_quick(n0, &a->X, n1, p))
895 if (!BN_mod_sub_quick(n2, &a->X, n1, p))
897 if (!field_mul(group, n1, n0, n2, ctx))
899 if (!BN_mod_lshift1_quick(n0, n1, p))
901 if (!BN_mod_add_quick(n1, n0, n1, p))
904 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
905 * = 3 * X_a^2 - 3 * Z_a^4
908 if (!field_sqr(group, n0, &a->X, ctx))
910 if (!BN_mod_lshift1_quick(n1, n0, p))
912 if (!BN_mod_add_quick(n0, n0, n1, p))
914 if (!field_sqr(group, n1, &a->Z, ctx))
916 if (!field_sqr(group, n1, n1, ctx))
918 if (!field_mul(group, n1, n1, &group->a, ctx))
920 if (!BN_mod_add_quick(n1, n1, n0, p))
922 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
927 if (!BN_copy(n0, &a->Y))
930 if (!field_mul(group, n0, &a->Y, &a->Z, ctx))
933 if (!BN_mod_lshift1_quick(&r->Z, n0, p))
936 /* Z_r = 2 * Y_a * Z_a */
939 if (!field_sqr(group, n3, &a->Y, ctx))
941 if (!field_mul(group, n2, &a->X, n3, ctx))
943 if (!BN_mod_lshift_quick(n2, n2, 2, p))
945 /* n2 = 4 * X_a * Y_a^2 */
948 if (!BN_mod_lshift1_quick(n0, n2, p))
950 if (!field_sqr(group, &r->X, n1, ctx))
952 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p))
954 /* X_r = n1^2 - 2 * n2 */
957 if (!field_sqr(group, n0, n3, ctx))
959 if (!BN_mod_lshift_quick(n3, n0, 3, p))
964 if (!BN_mod_sub_quick(n0, n2, &r->X, p))
966 if (!field_mul(group, n0, n1, n0, ctx))
968 if (!BN_mod_sub_quick(&r->Y, n0, n3, p))
970 /* Y_r = n1 * (n2 - X_r) - n3 */
977 BN_CTX_free(new_ctx);
981 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
983 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
984 /* point is its own inverse */
987 return BN_usub(&point->Y, &group->field, &point->Y);
990 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
992 return BN_is_zero(&point->Z);
995 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
998 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
999 const BIGNUM *, BN_CTX *);
1000 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1002 BN_CTX *new_ctx = NULL;
1003 BIGNUM *rh, *tmp, *Z4, *Z6;
1006 if (EC_POINT_is_at_infinity(group, point))
1009 field_mul = group->meth->field_mul;
1010 field_sqr = group->meth->field_sqr;
1014 ctx = new_ctx = BN_CTX_new();
1020 rh = BN_CTX_get(ctx);
1021 tmp = BN_CTX_get(ctx);
1022 Z4 = BN_CTX_get(ctx);
1023 Z6 = BN_CTX_get(ctx);
1028 * We have a curve defined by a Weierstrass equation
1029 * y^2 = x^3 + a*x + b.
1030 * The point to consider is given in Jacobian projective coordinates
1031 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1032 * Substituting this and multiplying by Z^6 transforms the above equation into
1033 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1034 * To test this, we add up the right-hand side in 'rh'.
1038 if (!field_sqr(group, rh, &point->X, ctx))
1041 if (!point->Z_is_one) {
1042 if (!field_sqr(group, tmp, &point->Z, ctx))
1044 if (!field_sqr(group, Z4, tmp, ctx))
1046 if (!field_mul(group, Z6, Z4, tmp, ctx))
1049 /* rh := (rh + a*Z^4)*X */
1050 if (group->a_is_minus3) {
1051 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1053 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1055 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1057 if (!field_mul(group, rh, rh, &point->X, ctx))
1060 if (!field_mul(group, tmp, Z4, &group->a, ctx))
1062 if (!BN_mod_add_quick(rh, rh, tmp, p))
1064 if (!field_mul(group, rh, rh, &point->X, ctx))
1068 /* rh := rh + b*Z^6 */
1069 if (!field_mul(group, tmp, &group->b, Z6, ctx))
1071 if (!BN_mod_add_quick(rh, rh, tmp, p))
1074 /* point->Z_is_one */
1076 /* rh := (rh + a)*X */
1077 if (!BN_mod_add_quick(rh, rh, &group->a, p))
1079 if (!field_mul(group, rh, rh, &point->X, ctx))
1082 if (!BN_mod_add_quick(rh, rh, &group->b, p))
1087 if (!field_sqr(group, tmp, &point->Y, ctx))
1090 ret = (0 == BN_ucmp(tmp, rh));
1094 if (new_ctx != NULL)
1095 BN_CTX_free(new_ctx);
1099 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1100 const EC_POINT *b, BN_CTX *ctx)
1105 * 0 equal (in affine coordinates)
1109 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1110 const BIGNUM *, BN_CTX *);
1111 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1112 BN_CTX *new_ctx = NULL;
1113 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1114 const BIGNUM *tmp1_, *tmp2_;
1117 if (EC_POINT_is_at_infinity(group, a)) {
1118 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1121 if (EC_POINT_is_at_infinity(group, b))
1124 if (a->Z_is_one && b->Z_is_one) {
1125 return ((BN_cmp(&a->X, &b->X) == 0)
1126 && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1129 field_mul = group->meth->field_mul;
1130 field_sqr = group->meth->field_sqr;
1133 ctx = new_ctx = BN_CTX_new();
1139 tmp1 = BN_CTX_get(ctx);
1140 tmp2 = BN_CTX_get(ctx);
1141 Za23 = BN_CTX_get(ctx);
1142 Zb23 = BN_CTX_get(ctx);
1147 * We have to decide whether
1148 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1149 * or equivalently, whether
1150 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1154 if (!field_sqr(group, Zb23, &b->Z, ctx))
1156 if (!field_mul(group, tmp1, &a->X, Zb23, ctx))
1162 if (!field_sqr(group, Za23, &a->Z, ctx))
1164 if (!field_mul(group, tmp2, &b->X, Za23, ctx))
1170 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1171 if (BN_cmp(tmp1_, tmp2_) != 0) {
1172 ret = 1; /* points differ */
1177 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx))
1179 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx))
1185 if (!field_mul(group, Za23, Za23, &a->Z, ctx))
1187 if (!field_mul(group, tmp2, &b->Y, Za23, ctx))
1193 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1194 if (BN_cmp(tmp1_, tmp2_) != 0) {
1195 ret = 1; /* points differ */
1199 /* points are equal */
1204 if (new_ctx != NULL)
1205 BN_CTX_free(new_ctx);
1209 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1212 BN_CTX *new_ctx = NULL;
1216 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1220 ctx = new_ctx = BN_CTX_new();
1226 x = BN_CTX_get(ctx);
1227 y = BN_CTX_get(ctx);
1231 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1233 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1235 if (!point->Z_is_one) {
1236 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1244 if (new_ctx != NULL)
1245 BN_CTX_free(new_ctx);
1249 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1250 EC_POINT *points[], BN_CTX *ctx)
1252 BN_CTX *new_ctx = NULL;
1253 BIGNUM *tmp, *tmp_Z;
1254 BIGNUM **prod_Z = NULL;
1262 ctx = new_ctx = BN_CTX_new();
1268 tmp = BN_CTX_get(ctx);
1269 tmp_Z = BN_CTX_get(ctx);
1270 if (tmp == NULL || tmp_Z == NULL)
1273 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1276 for (i = 0; i < num; i++) {
1277 prod_Z[i] = BN_new();
1278 if (prod_Z[i] == NULL)
1283 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1284 * skipping any zero-valued inputs (pretend that they're 1).
1287 if (!BN_is_zero(&points[0]->Z)) {
1288 if (!BN_copy(prod_Z[0], &points[0]->Z))
1291 if (group->meth->field_set_to_one != 0) {
1292 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1295 if (!BN_one(prod_Z[0]))
1300 for (i = 1; i < num; i++) {
1301 if (!BN_is_zero(&points[i]->Z)) {
1302 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1],
1303 &points[i]->Z, ctx))
1306 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1312 * Now use a single explicit inversion to replace every non-zero
1313 * points[i]->Z by its inverse.
1316 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) {
1317 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1320 if (group->meth->field_encode != 0) {
1322 * In the Montgomery case, we just turned R*H (representing H) into
1323 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1324 * multiply by the Montgomery factor twice.
1326 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1328 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1332 for (i = num - 1; i > 0; --i) {
1334 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1335 * .. points[i]->Z (zero-valued inputs skipped).
1337 if (!BN_is_zero(&points[i]->Z)) {
1339 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1340 * inverses 0 .. i, Z values 0 .. i - 1).
1343 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1346 * Update tmp to satisfy the loop invariant for i - 1.
1348 if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx))
1350 /* Replace points[i]->Z by its inverse. */
1351 if (!BN_copy(&points[i]->Z, tmp_Z))
1356 if (!BN_is_zero(&points[0]->Z)) {
1357 /* Replace points[0]->Z by its inverse. */
1358 if (!BN_copy(&points[0]->Z, tmp))
1362 /* Finally, fix up the X and Y coordinates for all points. */
1364 for (i = 0; i < num; i++) {
1365 EC_POINT *p = points[i];
1367 if (!BN_is_zero(&p->Z)) {
1368 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1370 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx))
1372 if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx))
1375 if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx))
1377 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx))
1380 if (group->meth->field_set_to_one != 0) {
1381 if (!group->meth->field_set_to_one(group, &p->Z, ctx))
1395 if (new_ctx != NULL)
1396 BN_CTX_free(new_ctx);
1397 if (prod_Z != NULL) {
1398 for (i = 0; i < num; i++) {
1399 if (prod_Z[i] == NULL)
1401 BN_clear_free(prod_Z[i]);
1403 OPENSSL_free(prod_Z);
1408 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1409 const BIGNUM *b, BN_CTX *ctx)
1411 return BN_mod_mul(r, a, b, &group->field, ctx);
1414 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1417 return BN_mod_sqr(r, a, &group->field, ctx);