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>
71 const EC_METHOD *EC_GFp_simple_method(void)
73 static const EC_METHOD ret = {
75 NID_X9_62_prime_field,
76 ec_GFp_simple_group_init,
77 ec_GFp_simple_group_finish,
78 ec_GFp_simple_group_clear_finish,
79 ec_GFp_simple_group_copy,
80 ec_GFp_simple_group_set_curve,
81 ec_GFp_simple_group_get_curve,
82 ec_GFp_simple_group_get_degree,
83 ec_GFp_simple_group_check_discriminant,
84 ec_GFp_simple_point_init,
85 ec_GFp_simple_point_finish,
86 ec_GFp_simple_point_clear_finish,
87 ec_GFp_simple_point_copy,
88 ec_GFp_simple_point_set_to_infinity,
89 ec_GFp_simple_set_Jprojective_coordinates_GFp,
90 ec_GFp_simple_get_Jprojective_coordinates_GFp,
91 ec_GFp_simple_point_set_affine_coordinates,
92 ec_GFp_simple_point_get_affine_coordinates,
97 ec_GFp_simple_is_at_infinity,
98 ec_GFp_simple_is_on_curve,
100 ec_GFp_simple_make_affine,
101 ec_GFp_simple_points_make_affine,
103 0 /* precompute_mult */ ,
104 0 /* have_precompute_mult */ ,
105 ec_GFp_simple_field_mul,
106 ec_GFp_simple_field_sqr,
108 0 /* field_encode */ ,
109 0 /* field_decode */ ,
110 0 /* field_set_to_one */
117 * Most method functions in this file are designed to work with
118 * non-trivial representations of field elements if necessary
119 * (see ecp_mont.c): while standard modular addition and subtraction
120 * are used, the field_mul and field_sqr methods will be used for
121 * multiplication, and field_encode and field_decode (if defined)
122 * will be used for converting between representations.
124 * Functions ec_GFp_simple_points_make_affine() and
125 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
126 * that if a non-trivial representation is used, it is a Montgomery
127 * representation (i.e. 'encoding' means multiplying by some factor R).
130 int ec_GFp_simple_group_init(EC_GROUP *group)
132 group->field = BN_new();
135 if (!group->field || !group->a || !group->b) {
137 BN_free(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)
368 if (!point->X || !point->Y || !point->Z) {
380 void ec_GFp_simple_point_finish(EC_POINT *point)
387 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
389 BN_clear_free(point->X);
390 BN_clear_free(point->Y);
391 BN_clear_free(point->Z);
395 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
397 if (!BN_copy(dest->X, src->X))
399 if (!BN_copy(dest->Y, src->Y))
401 if (!BN_copy(dest->Z, src->Z))
403 dest->Z_is_one = src->Z_is_one;
408 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
416 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
423 BN_CTX *new_ctx = NULL;
427 ctx = new_ctx = BN_CTX_new();
433 if (!BN_nnmod(point->X, x, group->field, ctx))
435 if (group->meth->field_encode) {
436 if (!group->meth->field_encode(group, point->X, point->X, ctx))
442 if (!BN_nnmod(point->Y, y, group->field, ctx))
444 if (group->meth->field_encode) {
445 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
453 if (!BN_nnmod(point->Z, z, group->field, ctx))
455 Z_is_one = BN_is_one(point->Z);
456 if (group->meth->field_encode) {
457 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
458 if (!group->meth->field_set_to_one(group, point->Z, ctx))
462 meth->field_encode(group, point->Z, point->Z, ctx))
466 point->Z_is_one = Z_is_one;
473 BN_CTX_free(new_ctx);
477 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
478 const EC_POINT *point,
479 BIGNUM *x, BIGNUM *y,
480 BIGNUM *z, BN_CTX *ctx)
482 BN_CTX *new_ctx = NULL;
485 if (group->meth->field_decode != 0) {
487 ctx = new_ctx = BN_CTX_new();
493 if (!group->meth->field_decode(group, x, point->X, ctx))
497 if (!group->meth->field_decode(group, y, point->Y, ctx))
501 if (!group->meth->field_decode(group, z, point->Z, ctx))
506 if (!BN_copy(x, point->X))
510 if (!BN_copy(y, point->Y))
514 if (!BN_copy(z, point->Z))
523 BN_CTX_free(new_ctx);
527 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
530 const BIGNUM *y, BN_CTX *ctx)
532 if (x == NULL || y == NULL) {
534 * unlike for projective coordinates, we do not tolerate this
536 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
537 ERR_R_PASSED_NULL_PARAMETER);
541 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
542 BN_value_one(), ctx);
545 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
546 const EC_POINT *point,
547 BIGNUM *x, BIGNUM *y,
550 BN_CTX *new_ctx = NULL;
551 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
555 if (EC_POINT_is_at_infinity(group, point)) {
556 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
557 EC_R_POINT_AT_INFINITY);
562 ctx = new_ctx = BN_CTX_new();
569 Z_1 = BN_CTX_get(ctx);
570 Z_2 = BN_CTX_get(ctx);
571 Z_3 = BN_CTX_get(ctx);
575 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
577 if (group->meth->field_decode) {
578 if (!group->meth->field_decode(group, Z, point->Z, ctx))
586 if (group->meth->field_decode) {
588 if (!group->meth->field_decode(group, x, point->X, ctx))
592 if (!group->meth->field_decode(group, y, point->Y, ctx))
597 if (!BN_copy(x, point->X))
601 if (!BN_copy(y, point->Y))
606 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
607 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
612 if (group->meth->field_encode == 0) {
613 /* field_sqr works on standard representation */
614 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
617 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
623 * in the Montgomery case, field_mul will cancel out Montgomery
626 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
631 if (group->meth->field_encode == 0) {
633 * field_mul works on standard representation
635 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
638 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
643 * in the Montgomery case, field_mul will cancel out Montgomery
646 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
656 BN_CTX_free(new_ctx);
660 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
661 const EC_POINT *b, BN_CTX *ctx)
663 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
664 const BIGNUM *, BN_CTX *);
665 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
667 BN_CTX *new_ctx = NULL;
668 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
672 return EC_POINT_dbl(group, r, a, ctx);
673 if (EC_POINT_is_at_infinity(group, a))
674 return EC_POINT_copy(r, b);
675 if (EC_POINT_is_at_infinity(group, b))
676 return EC_POINT_copy(r, a);
678 field_mul = group->meth->field_mul;
679 field_sqr = group->meth->field_sqr;
683 ctx = new_ctx = BN_CTX_new();
689 n0 = BN_CTX_get(ctx);
690 n1 = BN_CTX_get(ctx);
691 n2 = BN_CTX_get(ctx);
692 n3 = BN_CTX_get(ctx);
693 n4 = BN_CTX_get(ctx);
694 n5 = BN_CTX_get(ctx);
695 n6 = BN_CTX_get(ctx);
700 * Note that in this function we must not read components of 'a' or 'b'
701 * once we have written the corresponding components of 'r'. ('r' might
702 * be one of 'a' or 'b'.)
707 if (!BN_copy(n1, a->X))
709 if (!BN_copy(n2, a->Y))
714 if (!field_sqr(group, n0, b->Z, ctx))
716 if (!field_mul(group, n1, a->X, n0, ctx))
718 /* n1 = X_a * Z_b^2 */
720 if (!field_mul(group, n0, n0, b->Z, ctx))
722 if (!field_mul(group, n2, a->Y, n0, ctx))
724 /* n2 = Y_a * Z_b^3 */
729 if (!BN_copy(n3, b->X))
731 if (!BN_copy(n4, b->Y))
736 if (!field_sqr(group, n0, a->Z, ctx))
738 if (!field_mul(group, n3, b->X, n0, ctx))
740 /* n3 = X_b * Z_a^2 */
742 if (!field_mul(group, n0, n0, a->Z, ctx))
744 if (!field_mul(group, n4, b->Y, n0, ctx))
746 /* n4 = Y_b * Z_a^3 */
750 if (!BN_mod_sub_quick(n5, n1, n3, p))
752 if (!BN_mod_sub_quick(n6, n2, n4, p))
757 if (BN_is_zero(n5)) {
758 if (BN_is_zero(n6)) {
759 /* a is the same point as b */
761 ret = EC_POINT_dbl(group, r, a, ctx);
765 /* a is the inverse of b */
774 if (!BN_mod_add_quick(n1, n1, n3, p))
776 if (!BN_mod_add_quick(n2, n2, n4, p))
782 if (a->Z_is_one && b->Z_is_one) {
783 if (!BN_copy(r->Z, n5))
787 if (!BN_copy(n0, b->Z))
789 } else if (b->Z_is_one) {
790 if (!BN_copy(n0, a->Z))
793 if (!field_mul(group, n0, a->Z, b->Z, ctx))
796 if (!field_mul(group, r->Z, n0, n5, ctx))
800 /* Z_r = Z_a * Z_b * n5 */
803 if (!field_sqr(group, n0, n6, ctx))
805 if (!field_sqr(group, n4, n5, ctx))
807 if (!field_mul(group, n3, n1, n4, ctx))
809 if (!BN_mod_sub_quick(r->X, n0, n3, p))
811 /* X_r = n6^2 - n5^2 * 'n7' */
814 if (!BN_mod_lshift1_quick(n0, r->X, p))
816 if (!BN_mod_sub_quick(n0, n3, n0, p))
818 /* n9 = n5^2 * 'n7' - 2 * X_r */
821 if (!field_mul(group, n0, n0, n6, ctx))
823 if (!field_mul(group, n5, n4, n5, ctx))
824 goto end; /* now n5 is n5^3 */
825 if (!field_mul(group, n1, n2, n5, ctx))
827 if (!BN_mod_sub_quick(n0, n0, n1, p))
830 if (!BN_add(n0, n0, p))
832 /* now 0 <= n0 < 2*p, and n0 is even */
833 if (!BN_rshift1(r->Y, n0))
835 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
840 if (ctx) /* otherwise we already called BN_CTX_end */
843 BN_CTX_free(new_ctx);
847 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
850 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
851 const BIGNUM *, BN_CTX *);
852 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
854 BN_CTX *new_ctx = NULL;
855 BIGNUM *n0, *n1, *n2, *n3;
858 if (EC_POINT_is_at_infinity(group, a)) {
864 field_mul = group->meth->field_mul;
865 field_sqr = group->meth->field_sqr;
869 ctx = new_ctx = BN_CTX_new();
875 n0 = BN_CTX_get(ctx);
876 n1 = BN_CTX_get(ctx);
877 n2 = BN_CTX_get(ctx);
878 n3 = BN_CTX_get(ctx);
883 * Note that in this function we must not read components of 'a' once we
884 * have written the corresponding components of 'r'. ('r' might the same
890 if (!field_sqr(group, n0, a->X, ctx))
892 if (!BN_mod_lshift1_quick(n1, n0, p))
894 if (!BN_mod_add_quick(n0, n0, n1, p))
896 if (!BN_mod_add_quick(n1, n0, group->a, p))
898 /* n1 = 3 * X_a^2 + a_curve */
899 } else if (group->a_is_minus3) {
900 if (!field_sqr(group, n1, a->Z, ctx))
902 if (!BN_mod_add_quick(n0, a->X, n1, p))
904 if (!BN_mod_sub_quick(n2, a->X, n1, p))
906 if (!field_mul(group, n1, n0, n2, ctx))
908 if (!BN_mod_lshift1_quick(n0, n1, p))
910 if (!BN_mod_add_quick(n1, n0, n1, p))
913 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
914 * = 3 * X_a^2 - 3 * Z_a^4
917 if (!field_sqr(group, n0, a->X, ctx))
919 if (!BN_mod_lshift1_quick(n1, n0, p))
921 if (!BN_mod_add_quick(n0, n0, n1, p))
923 if (!field_sqr(group, n1, a->Z, ctx))
925 if (!field_sqr(group, n1, n1, ctx))
927 if (!field_mul(group, n1, n1, group->a, ctx))
929 if (!BN_mod_add_quick(n1, n1, n0, p))
931 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
936 if (!BN_copy(n0, a->Y))
939 if (!field_mul(group, n0, a->Y, a->Z, ctx))
942 if (!BN_mod_lshift1_quick(r->Z, n0, p))
945 /* Z_r = 2 * Y_a * Z_a */
948 if (!field_sqr(group, n3, a->Y, ctx))
950 if (!field_mul(group, n2, a->X, n3, ctx))
952 if (!BN_mod_lshift_quick(n2, n2, 2, p))
954 /* n2 = 4 * X_a * Y_a^2 */
957 if (!BN_mod_lshift1_quick(n0, n2, p))
959 if (!field_sqr(group, r->X, n1, ctx))
961 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
963 /* X_r = n1^2 - 2 * n2 */
966 if (!field_sqr(group, n0, n3, ctx))
968 if (!BN_mod_lshift_quick(n3, n0, 3, p))
973 if (!BN_mod_sub_quick(n0, n2, r->X, p))
975 if (!field_mul(group, n0, n1, n0, ctx))
977 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
979 /* Y_r = n1 * (n2 - X_r) - n3 */
986 BN_CTX_free(new_ctx);
990 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
992 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
993 /* point is its own inverse */
996 return BN_usub(point->Y, group->field, point->Y);
999 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1001 return BN_is_zero(point->Z);
1004 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
1007 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1008 const BIGNUM *, BN_CTX *);
1009 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1011 BN_CTX *new_ctx = NULL;
1012 BIGNUM *rh, *tmp, *Z4, *Z6;
1015 if (EC_POINT_is_at_infinity(group, point))
1018 field_mul = group->meth->field_mul;
1019 field_sqr = group->meth->field_sqr;
1023 ctx = new_ctx = BN_CTX_new();
1029 rh = BN_CTX_get(ctx);
1030 tmp = BN_CTX_get(ctx);
1031 Z4 = BN_CTX_get(ctx);
1032 Z6 = BN_CTX_get(ctx);
1037 * We have a curve defined by a Weierstrass equation
1038 * y^2 = x^3 + a*x + b.
1039 * The point to consider is given in Jacobian projective coordinates
1040 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1041 * Substituting this and multiplying by Z^6 transforms the above equation into
1042 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1043 * To test this, we add up the right-hand side in 'rh'.
1047 if (!field_sqr(group, rh, point->X, ctx))
1050 if (!point->Z_is_one) {
1051 if (!field_sqr(group, tmp, point->Z, ctx))
1053 if (!field_sqr(group, Z4, tmp, ctx))
1055 if (!field_mul(group, Z6, Z4, tmp, ctx))
1058 /* rh := (rh + a*Z^4)*X */
1059 if (group->a_is_minus3) {
1060 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1062 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1064 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1066 if (!field_mul(group, rh, rh, point->X, ctx))
1069 if (!field_mul(group, tmp, Z4, group->a, ctx))
1071 if (!BN_mod_add_quick(rh, rh, tmp, p))
1073 if (!field_mul(group, rh, rh, point->X, ctx))
1077 /* rh := rh + b*Z^6 */
1078 if (!field_mul(group, tmp, group->b, Z6, ctx))
1080 if (!BN_mod_add_quick(rh, rh, tmp, p))
1083 /* point->Z_is_one */
1085 /* rh := (rh + a)*X */
1086 if (!BN_mod_add_quick(rh, rh, group->a, p))
1088 if (!field_mul(group, rh, rh, point->X, ctx))
1091 if (!BN_mod_add_quick(rh, rh, group->b, p))
1096 if (!field_sqr(group, tmp, point->Y, ctx))
1099 ret = (0 == BN_ucmp(tmp, rh));
1103 if (new_ctx != NULL)
1104 BN_CTX_free(new_ctx);
1108 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1109 const EC_POINT *b, BN_CTX *ctx)
1114 * 0 equal (in affine coordinates)
1118 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1119 const BIGNUM *, BN_CTX *);
1120 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1121 BN_CTX *new_ctx = NULL;
1122 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1123 const BIGNUM *tmp1_, *tmp2_;
1126 if (EC_POINT_is_at_infinity(group, a)) {
1127 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1130 if (EC_POINT_is_at_infinity(group, b))
1133 if (a->Z_is_one && b->Z_is_one) {
1134 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1137 field_mul = group->meth->field_mul;
1138 field_sqr = group->meth->field_sqr;
1141 ctx = new_ctx = BN_CTX_new();
1147 tmp1 = BN_CTX_get(ctx);
1148 tmp2 = BN_CTX_get(ctx);
1149 Za23 = BN_CTX_get(ctx);
1150 Zb23 = BN_CTX_get(ctx);
1155 * We have to decide whether
1156 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1157 * or equivalently, whether
1158 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1162 if (!field_sqr(group, Zb23, b->Z, ctx))
1164 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1170 if (!field_sqr(group, Za23, a->Z, ctx))
1172 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1178 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1179 if (BN_cmp(tmp1_, tmp2_) != 0) {
1180 ret = 1; /* points differ */
1185 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1187 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1193 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1195 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1201 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1202 if (BN_cmp(tmp1_, tmp2_) != 0) {
1203 ret = 1; /* points differ */
1207 /* points are equal */
1212 if (new_ctx != NULL)
1213 BN_CTX_free(new_ctx);
1217 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1220 BN_CTX *new_ctx = NULL;
1224 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1228 ctx = new_ctx = BN_CTX_new();
1234 x = BN_CTX_get(ctx);
1235 y = BN_CTX_get(ctx);
1239 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1241 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1243 if (!point->Z_is_one) {
1244 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1252 if (new_ctx != NULL)
1253 BN_CTX_free(new_ctx);
1257 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1258 EC_POINT *points[], BN_CTX *ctx)
1260 BN_CTX *new_ctx = NULL;
1261 BIGNUM *tmp, *tmp_Z;
1262 BIGNUM **prod_Z = NULL;
1270 ctx = new_ctx = BN_CTX_new();
1276 tmp = BN_CTX_get(ctx);
1277 tmp_Z = BN_CTX_get(ctx);
1278 if (tmp == NULL || tmp_Z == NULL)
1281 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1284 for (i = 0; i < num; i++) {
1285 prod_Z[i] = BN_new();
1286 if (prod_Z[i] == NULL)
1291 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1292 * skipping any zero-valued inputs (pretend that they're 1).
1295 if (!BN_is_zero(points[0]->Z)) {
1296 if (!BN_copy(prod_Z[0], points[0]->Z))
1299 if (group->meth->field_set_to_one != 0) {
1300 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1303 if (!BN_one(prod_Z[0]))
1308 for (i = 1; i < num; i++) {
1309 if (!BN_is_zero(points[i]->Z)) {
1311 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1315 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1321 * Now use a single explicit inversion to replace every non-zero
1322 * points[i]->Z by its inverse.
1325 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1326 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1329 if (group->meth->field_encode != 0) {
1331 * In the Montgomery case, we just turned R*H (representing H) into
1332 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1333 * multiply by the Montgomery factor twice.
1335 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1337 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1341 for (i = num - 1; i > 0; --i) {
1343 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1344 * .. points[i]->Z (zero-valued inputs skipped).
1346 if (!BN_is_zero(points[i]->Z)) {
1348 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1349 * inverses 0 .. i, Z values 0 .. i - 1).
1352 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1355 * Update tmp to satisfy the loop invariant for i - 1.
1357 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1359 /* Replace points[i]->Z by its inverse. */
1360 if (!BN_copy(points[i]->Z, tmp_Z))
1365 if (!BN_is_zero(points[0]->Z)) {
1366 /* Replace points[0]->Z by its inverse. */
1367 if (!BN_copy(points[0]->Z, tmp))
1371 /* Finally, fix up the X and Y coordinates for all points. */
1373 for (i = 0; i < num; i++) {
1374 EC_POINT *p = points[i];
1376 if (!BN_is_zero(p->Z)) {
1377 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1379 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1381 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1384 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1386 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1389 if (group->meth->field_set_to_one != 0) {
1390 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1404 if (new_ctx != NULL)
1405 BN_CTX_free(new_ctx);
1406 if (prod_Z != NULL) {
1407 for (i = 0; i < num; i++) {
1408 if (prod_Z[i] == NULL)
1410 BN_clear_free(prod_Z[i]);
1412 OPENSSL_free(prod_Z);
1417 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1418 const BIGNUM *b, BN_CTX *ctx)
1420 return BN_mod_mul(r, a, b, group->field, ctx);
1423 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1426 return BN_mod_sqr(r, a, group->field, ctx);