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) {
136 BN_free(group->field);
141 group->a_is_minus3 = 0;
145 void ec_GFp_simple_group_finish(EC_GROUP *group)
147 BN_free(group->field);
152 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
154 BN_clear_free(group->field);
155 BN_clear_free(group->a);
156 BN_clear_free(group->b);
159 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
161 if (!BN_copy(dest->field, src->field))
163 if (!BN_copy(dest->a, src->a))
165 if (!BN_copy(dest->b, src->b))
168 dest->a_is_minus3 = src->a_is_minus3;
173 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
174 const BIGNUM *p, const BIGNUM *a,
175 const BIGNUM *b, BN_CTX *ctx)
178 BN_CTX *new_ctx = NULL;
181 /* p must be a prime > 3 */
182 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
183 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
188 ctx = new_ctx = BN_CTX_new();
194 tmp_a = BN_CTX_get(ctx);
199 if (!BN_copy(group->field, p))
201 BN_set_negative(group->field, 0);
204 if (!BN_nnmod(tmp_a, a, p, ctx))
206 if (group->meth->field_encode) {
207 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
209 } else if (!BN_copy(group->a, tmp_a))
213 if (!BN_nnmod(group->b, b, p, ctx))
215 if (group->meth->field_encode)
216 if (!group->meth->field_encode(group, group->b, group->b, ctx))
219 /* group->a_is_minus3 */
220 if (!BN_add_word(tmp_a, 3))
222 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
229 BN_CTX_free(new_ctx);
233 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
234 BIGNUM *b, BN_CTX *ctx)
237 BN_CTX *new_ctx = NULL;
240 if (!BN_copy(p, group->field))
244 if (a != NULL || b != NULL) {
245 if (group->meth->field_decode) {
247 ctx = new_ctx = BN_CTX_new();
252 if (!group->meth->field_decode(group, a, group->a, ctx))
256 if (!group->meth->field_decode(group, b, group->b, ctx))
261 if (!BN_copy(a, group->a))
265 if (!BN_copy(b, group->b))
275 BN_CTX_free(new_ctx);
279 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
281 return BN_num_bits(group->field);
284 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
287 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
288 const BIGNUM *p = group->field;
289 BN_CTX *new_ctx = NULL;
292 ctx = new_ctx = BN_CTX_new();
294 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
295 ERR_R_MALLOC_FAILURE);
302 tmp_1 = BN_CTX_get(ctx);
303 tmp_2 = BN_CTX_get(ctx);
304 order = BN_CTX_get(ctx);
308 if (group->meth->field_decode) {
309 if (!group->meth->field_decode(group, a, group->a, ctx))
311 if (!group->meth->field_decode(group, b, group->b, ctx))
314 if (!BN_copy(a, group->a))
316 if (!BN_copy(b, group->b))
321 * check the discriminant:
322 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
328 } else if (!BN_is_zero(b)) {
329 if (!BN_mod_sqr(tmp_1, a, p, ctx))
331 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
333 if (!BN_lshift(tmp_1, tmp_2, 2))
337 if (!BN_mod_sqr(tmp_2, b, p, ctx))
339 if (!BN_mul_word(tmp_2, 27))
343 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
354 BN_CTX_free(new_ctx);
358 int ec_GFp_simple_point_init(EC_POINT *point)
365 if (!point->X || !point->Y || !point->Z) {
377 void ec_GFp_simple_point_finish(EC_POINT *point)
384 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
386 BN_clear_free(point->X);
387 BN_clear_free(point->Y);
388 BN_clear_free(point->Z);
392 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
394 if (!BN_copy(dest->X, src->X))
396 if (!BN_copy(dest->Y, src->Y))
398 if (!BN_copy(dest->Z, src->Z))
400 dest->Z_is_one = src->Z_is_one;
405 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
413 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
420 BN_CTX *new_ctx = NULL;
424 ctx = new_ctx = BN_CTX_new();
430 if (!BN_nnmod(point->X, x, group->field, ctx))
432 if (group->meth->field_encode) {
433 if (!group->meth->field_encode(group, point->X, point->X, ctx))
439 if (!BN_nnmod(point->Y, y, group->field, ctx))
441 if (group->meth->field_encode) {
442 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
450 if (!BN_nnmod(point->Z, z, group->field, ctx))
452 Z_is_one = BN_is_one(point->Z);
453 if (group->meth->field_encode) {
454 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
455 if (!group->meth->field_set_to_one(group, point->Z, ctx))
459 meth->field_encode(group, point->Z, point->Z, ctx))
463 point->Z_is_one = Z_is_one;
470 BN_CTX_free(new_ctx);
474 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
475 const EC_POINT *point,
476 BIGNUM *x, BIGNUM *y,
477 BIGNUM *z, BN_CTX *ctx)
479 BN_CTX *new_ctx = NULL;
482 if (group->meth->field_decode != 0) {
484 ctx = new_ctx = BN_CTX_new();
490 if (!group->meth->field_decode(group, x, point->X, ctx))
494 if (!group->meth->field_decode(group, y, point->Y, ctx))
498 if (!group->meth->field_decode(group, z, point->Z, ctx))
503 if (!BN_copy(x, point->X))
507 if (!BN_copy(y, point->Y))
511 if (!BN_copy(z, point->Z))
520 BN_CTX_free(new_ctx);
524 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
527 const BIGNUM *y, BN_CTX *ctx)
529 if (x == NULL || y == NULL) {
531 * unlike for projective coordinates, we do not tolerate this
533 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
534 ERR_R_PASSED_NULL_PARAMETER);
538 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
539 BN_value_one(), ctx);
542 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
543 const EC_POINT *point,
544 BIGNUM *x, BIGNUM *y,
547 BN_CTX *new_ctx = NULL;
548 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
552 if (EC_POINT_is_at_infinity(group, point)) {
553 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
554 EC_R_POINT_AT_INFINITY);
559 ctx = new_ctx = BN_CTX_new();
566 Z_1 = BN_CTX_get(ctx);
567 Z_2 = BN_CTX_get(ctx);
568 Z_3 = BN_CTX_get(ctx);
572 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
574 if (group->meth->field_decode) {
575 if (!group->meth->field_decode(group, Z, point->Z, ctx))
583 if (group->meth->field_decode) {
585 if (!group->meth->field_decode(group, x, point->X, ctx))
589 if (!group->meth->field_decode(group, y, point->Y, ctx))
594 if (!BN_copy(x, point->X))
598 if (!BN_copy(y, point->Y))
603 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
604 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
609 if (group->meth->field_encode == 0) {
610 /* field_sqr works on standard representation */
611 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
614 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
620 * in the Montgomery case, field_mul will cancel out Montgomery
623 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
628 if (group->meth->field_encode == 0) {
630 * field_mul works on standard representation
632 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
635 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
640 * in the Montgomery case, field_mul will cancel out Montgomery
643 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
653 BN_CTX_free(new_ctx);
657 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
658 const EC_POINT *b, BN_CTX *ctx)
660 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
661 const BIGNUM *, BN_CTX *);
662 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
664 BN_CTX *new_ctx = NULL;
665 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
669 return EC_POINT_dbl(group, r, a, ctx);
670 if (EC_POINT_is_at_infinity(group, a))
671 return EC_POINT_copy(r, b);
672 if (EC_POINT_is_at_infinity(group, b))
673 return EC_POINT_copy(r, a);
675 field_mul = group->meth->field_mul;
676 field_sqr = group->meth->field_sqr;
680 ctx = new_ctx = BN_CTX_new();
686 n0 = BN_CTX_get(ctx);
687 n1 = BN_CTX_get(ctx);
688 n2 = BN_CTX_get(ctx);
689 n3 = BN_CTX_get(ctx);
690 n4 = BN_CTX_get(ctx);
691 n5 = BN_CTX_get(ctx);
692 n6 = BN_CTX_get(ctx);
697 * Note that in this function we must not read components of 'a' or 'b'
698 * once we have written the corresponding components of 'r'. ('r' might
699 * be one of 'a' or 'b'.)
704 if (!BN_copy(n1, a->X))
706 if (!BN_copy(n2, a->Y))
711 if (!field_sqr(group, n0, b->Z, ctx))
713 if (!field_mul(group, n1, a->X, n0, ctx))
715 /* n1 = X_a * Z_b^2 */
717 if (!field_mul(group, n0, n0, b->Z, ctx))
719 if (!field_mul(group, n2, a->Y, n0, ctx))
721 /* n2 = Y_a * Z_b^3 */
726 if (!BN_copy(n3, b->X))
728 if (!BN_copy(n4, b->Y))
733 if (!field_sqr(group, n0, a->Z, ctx))
735 if (!field_mul(group, n3, b->X, n0, ctx))
737 /* n3 = X_b * Z_a^2 */
739 if (!field_mul(group, n0, n0, a->Z, ctx))
741 if (!field_mul(group, n4, b->Y, n0, ctx))
743 /* n4 = Y_b * Z_a^3 */
747 if (!BN_mod_sub_quick(n5, n1, n3, p))
749 if (!BN_mod_sub_quick(n6, n2, n4, p))
754 if (BN_is_zero(n5)) {
755 if (BN_is_zero(n6)) {
756 /* a is the same point as b */
758 ret = EC_POINT_dbl(group, r, a, ctx);
762 /* a is the inverse of b */
771 if (!BN_mod_add_quick(n1, n1, n3, p))
773 if (!BN_mod_add_quick(n2, n2, n4, p))
779 if (a->Z_is_one && b->Z_is_one) {
780 if (!BN_copy(r->Z, n5))
784 if (!BN_copy(n0, b->Z))
786 } else if (b->Z_is_one) {
787 if (!BN_copy(n0, a->Z))
790 if (!field_mul(group, n0, a->Z, b->Z, ctx))
793 if (!field_mul(group, r->Z, n0, n5, ctx))
797 /* Z_r = Z_a * Z_b * n5 */
800 if (!field_sqr(group, n0, n6, ctx))
802 if (!field_sqr(group, n4, n5, ctx))
804 if (!field_mul(group, n3, n1, n4, ctx))
806 if (!BN_mod_sub_quick(r->X, n0, n3, p))
808 /* X_r = n6^2 - n5^2 * 'n7' */
811 if (!BN_mod_lshift1_quick(n0, r->X, p))
813 if (!BN_mod_sub_quick(n0, n3, n0, p))
815 /* n9 = n5^2 * 'n7' - 2 * X_r */
818 if (!field_mul(group, n0, n0, n6, ctx))
820 if (!field_mul(group, n5, n4, n5, ctx))
821 goto end; /* now n5 is n5^3 */
822 if (!field_mul(group, n1, n2, n5, ctx))
824 if (!BN_mod_sub_quick(n0, n0, n1, p))
827 if (!BN_add(n0, n0, p))
829 /* now 0 <= n0 < 2*p, and n0 is even */
830 if (!BN_rshift1(r->Y, n0))
832 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
837 if (ctx) /* otherwise we already called BN_CTX_end */
840 BN_CTX_free(new_ctx);
844 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
847 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
848 const BIGNUM *, BN_CTX *);
849 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
851 BN_CTX *new_ctx = NULL;
852 BIGNUM *n0, *n1, *n2, *n3;
855 if (EC_POINT_is_at_infinity(group, a)) {
861 field_mul = group->meth->field_mul;
862 field_sqr = group->meth->field_sqr;
866 ctx = new_ctx = BN_CTX_new();
872 n0 = BN_CTX_get(ctx);
873 n1 = BN_CTX_get(ctx);
874 n2 = BN_CTX_get(ctx);
875 n3 = BN_CTX_get(ctx);
880 * Note that in this function we must not read components of 'a' once we
881 * have written the corresponding components of 'r'. ('r' might the same
887 if (!field_sqr(group, n0, a->X, ctx))
889 if (!BN_mod_lshift1_quick(n1, n0, p))
891 if (!BN_mod_add_quick(n0, n0, n1, p))
893 if (!BN_mod_add_quick(n1, n0, group->a, p))
895 /* n1 = 3 * X_a^2 + a_curve */
896 } else if (group->a_is_minus3) {
897 if (!field_sqr(group, n1, a->Z, ctx))
899 if (!BN_mod_add_quick(n0, a->X, n1, p))
901 if (!BN_mod_sub_quick(n2, a->X, n1, p))
903 if (!field_mul(group, n1, n0, n2, ctx))
905 if (!BN_mod_lshift1_quick(n0, n1, p))
907 if (!BN_mod_add_quick(n1, n0, n1, p))
910 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
911 * = 3 * X_a^2 - 3 * Z_a^4
914 if (!field_sqr(group, n0, a->X, ctx))
916 if (!BN_mod_lshift1_quick(n1, n0, p))
918 if (!BN_mod_add_quick(n0, n0, n1, p))
920 if (!field_sqr(group, n1, a->Z, ctx))
922 if (!field_sqr(group, n1, n1, ctx))
924 if (!field_mul(group, n1, n1, group->a, ctx))
926 if (!BN_mod_add_quick(n1, n1, n0, p))
928 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
933 if (!BN_copy(n0, a->Y))
936 if (!field_mul(group, n0, a->Y, a->Z, ctx))
939 if (!BN_mod_lshift1_quick(r->Z, n0, p))
942 /* Z_r = 2 * Y_a * Z_a */
945 if (!field_sqr(group, n3, a->Y, ctx))
947 if (!field_mul(group, n2, a->X, n3, ctx))
949 if (!BN_mod_lshift_quick(n2, n2, 2, p))
951 /* n2 = 4 * X_a * Y_a^2 */
954 if (!BN_mod_lshift1_quick(n0, n2, p))
956 if (!field_sqr(group, r->X, n1, ctx))
958 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
960 /* X_r = n1^2 - 2 * n2 */
963 if (!field_sqr(group, n0, n3, ctx))
965 if (!BN_mod_lshift_quick(n3, n0, 3, p))
970 if (!BN_mod_sub_quick(n0, n2, r->X, p))
972 if (!field_mul(group, n0, n1, n0, ctx))
974 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
976 /* Y_r = n1 * (n2 - X_r) - n3 */
983 BN_CTX_free(new_ctx);
987 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
989 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
990 /* point is its own inverse */
993 return BN_usub(point->Y, group->field, point->Y);
996 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
998 return BN_is_zero(point->Z);
1001 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
1004 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1005 const BIGNUM *, BN_CTX *);
1006 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1008 BN_CTX *new_ctx = NULL;
1009 BIGNUM *rh, *tmp, *Z4, *Z6;
1012 if (EC_POINT_is_at_infinity(group, point))
1015 field_mul = group->meth->field_mul;
1016 field_sqr = group->meth->field_sqr;
1020 ctx = new_ctx = BN_CTX_new();
1026 rh = BN_CTX_get(ctx);
1027 tmp = BN_CTX_get(ctx);
1028 Z4 = BN_CTX_get(ctx);
1029 Z6 = BN_CTX_get(ctx);
1034 * We have a curve defined by a Weierstrass equation
1035 * y^2 = x^3 + a*x + b.
1036 * The point to consider is given in Jacobian projective coordinates
1037 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1038 * Substituting this and multiplying by Z^6 transforms the above equation into
1039 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1040 * To test this, we add up the right-hand side in 'rh'.
1044 if (!field_sqr(group, rh, point->X, ctx))
1047 if (!point->Z_is_one) {
1048 if (!field_sqr(group, tmp, point->Z, ctx))
1050 if (!field_sqr(group, Z4, tmp, ctx))
1052 if (!field_mul(group, Z6, Z4, tmp, ctx))
1055 /* rh := (rh + a*Z^4)*X */
1056 if (group->a_is_minus3) {
1057 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1059 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1061 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1063 if (!field_mul(group, rh, rh, point->X, ctx))
1066 if (!field_mul(group, tmp, Z4, group->a, ctx))
1068 if (!BN_mod_add_quick(rh, rh, tmp, p))
1070 if (!field_mul(group, rh, rh, point->X, ctx))
1074 /* rh := rh + b*Z^6 */
1075 if (!field_mul(group, tmp, group->b, Z6, ctx))
1077 if (!BN_mod_add_quick(rh, rh, tmp, p))
1080 /* point->Z_is_one */
1082 /* rh := (rh + a)*X */
1083 if (!BN_mod_add_quick(rh, rh, group->a, p))
1085 if (!field_mul(group, rh, rh, point->X, ctx))
1088 if (!BN_mod_add_quick(rh, rh, group->b, p))
1093 if (!field_sqr(group, tmp, point->Y, ctx))
1096 ret = (0 == BN_ucmp(tmp, rh));
1100 if (new_ctx != NULL)
1101 BN_CTX_free(new_ctx);
1105 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1106 const EC_POINT *b, BN_CTX *ctx)
1111 * 0 equal (in affine coordinates)
1115 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1116 const BIGNUM *, BN_CTX *);
1117 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1118 BN_CTX *new_ctx = NULL;
1119 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1120 const BIGNUM *tmp1_, *tmp2_;
1123 if (EC_POINT_is_at_infinity(group, a)) {
1124 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1127 if (EC_POINT_is_at_infinity(group, b))
1130 if (a->Z_is_one && b->Z_is_one) {
1131 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1134 field_mul = group->meth->field_mul;
1135 field_sqr = group->meth->field_sqr;
1138 ctx = new_ctx = BN_CTX_new();
1144 tmp1 = BN_CTX_get(ctx);
1145 tmp2 = BN_CTX_get(ctx);
1146 Za23 = BN_CTX_get(ctx);
1147 Zb23 = BN_CTX_get(ctx);
1152 * We have to decide whether
1153 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1154 * or equivalently, whether
1155 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1159 if (!field_sqr(group, Zb23, b->Z, ctx))
1161 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1167 if (!field_sqr(group, Za23, a->Z, ctx))
1169 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1175 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1176 if (BN_cmp(tmp1_, tmp2_) != 0) {
1177 ret = 1; /* points differ */
1182 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1184 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1190 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1192 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1198 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1199 if (BN_cmp(tmp1_, tmp2_) != 0) {
1200 ret = 1; /* points differ */
1204 /* points are equal */
1209 if (new_ctx != NULL)
1210 BN_CTX_free(new_ctx);
1214 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1217 BN_CTX *new_ctx = NULL;
1221 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1225 ctx = new_ctx = BN_CTX_new();
1231 x = BN_CTX_get(ctx);
1232 y = BN_CTX_get(ctx);
1236 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1238 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1240 if (!point->Z_is_one) {
1241 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1249 if (new_ctx != NULL)
1250 BN_CTX_free(new_ctx);
1254 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1255 EC_POINT *points[], BN_CTX *ctx)
1257 BN_CTX *new_ctx = NULL;
1258 BIGNUM *tmp, *tmp_Z;
1259 BIGNUM **prod_Z = NULL;
1267 ctx = new_ctx = BN_CTX_new();
1273 tmp = BN_CTX_get(ctx);
1274 tmp_Z = BN_CTX_get(ctx);
1275 if (tmp == NULL || tmp_Z == NULL)
1278 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1281 for (i = 0; i < num; i++) {
1282 prod_Z[i] = BN_new();
1283 if (prod_Z[i] == NULL)
1288 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1289 * skipping any zero-valued inputs (pretend that they're 1).
1292 if (!BN_is_zero(points[0]->Z)) {
1293 if (!BN_copy(prod_Z[0], points[0]->Z))
1296 if (group->meth->field_set_to_one != 0) {
1297 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1300 if (!BN_one(prod_Z[0]))
1305 for (i = 1; i < num; i++) {
1306 if (!BN_is_zero(points[i]->Z)) {
1308 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1312 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1318 * Now use a single explicit inversion to replace every non-zero
1319 * points[i]->Z by its inverse.
1322 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1323 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1326 if (group->meth->field_encode != 0) {
1328 * In the Montgomery case, we just turned R*H (representing H) into
1329 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1330 * multiply by the Montgomery factor twice.
1332 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1334 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1338 for (i = num - 1; i > 0; --i) {
1340 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1341 * .. points[i]->Z (zero-valued inputs skipped).
1343 if (!BN_is_zero(points[i]->Z)) {
1345 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1346 * inverses 0 .. i, Z values 0 .. i - 1).
1349 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1352 * Update tmp to satisfy the loop invariant for i - 1.
1354 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1356 /* Replace points[i]->Z by its inverse. */
1357 if (!BN_copy(points[i]->Z, tmp_Z))
1362 if (!BN_is_zero(points[0]->Z)) {
1363 /* Replace points[0]->Z by its inverse. */
1364 if (!BN_copy(points[0]->Z, tmp))
1368 /* Finally, fix up the X and Y coordinates for all points. */
1370 for (i = 0; i < num; i++) {
1371 EC_POINT *p = points[i];
1373 if (!BN_is_zero(p->Z)) {
1374 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1376 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1378 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1381 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1383 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1386 if (group->meth->field_set_to_one != 0) {
1387 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1401 if (new_ctx != NULL)
1402 BN_CTX_free(new_ctx);
1403 if (prod_Z != NULL) {
1404 for (i = 0; i < num; i++) {
1405 if (prod_Z[i] == NULL)
1407 BN_clear_free(prod_Z[i]);
1409 OPENSSL_free(prod_Z);
1414 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1415 const BIGNUM *b, BN_CTX *ctx)
1417 return BN_mod_mul(r, a, b, group->field, ctx);
1420 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1423 return BN_mod_sqr(r, a, group->field, ctx);