1 /* crypto/ec/ecp_smpl.c */
2 /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
3 * for the OpenSSL project.
4 * Includes code written by Bodo Moeller for the OpenSSL project.
6 /* ====================================================================
7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
16 * 2. Redistributions in binary form must reproduce the above copyright
17 * notice, this list of conditions and the following disclaimer in
18 * the documentation and/or other materials provided with the
21 * 3. All advertising materials mentioning features or use of this
22 * software must display the following acknowledgment:
23 * "This product includes software developed by the OpenSSL Project
24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
27 * endorse or promote products derived from this software without
28 * prior written permission. For written permission, please contact
29 * openssl-core@openssl.org.
31 * 5. Products derived from this software may not be called "OpenSSL"
32 * nor may "OpenSSL" appear in their names without prior written
33 * permission of the OpenSSL Project.
35 * 6. Redistributions of any form whatsoever must retain the following
37 * "This product includes software developed by the OpenSSL Project
38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
51 * OF THE POSSIBILITY OF SUCH DAMAGE.
52 * ====================================================================
54 * This product includes cryptographic software written by Eric Young
55 * (eay@cryptsoft.com). This product includes software written by Tim
56 * Hudson (tjh@cryptsoft.com).
59 /* ====================================================================
60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
62 * and contributed to the OpenSSL project.
65 #define OPENSSL_FIPSAPI
67 #include <openssl/err.h>
68 #include <openssl/symhacks.h>
72 const EC_METHOD *EC_GFp_simple_method(void)
74 static const EC_METHOD ret = {
76 NID_X9_62_prime_field,
77 ec_GFp_simple_group_init,
78 ec_GFp_simple_group_finish,
79 ec_GFp_simple_group_clear_finish,
80 ec_GFp_simple_group_copy,
81 ec_GFp_simple_group_set_curve,
82 ec_GFp_simple_group_get_curve,
83 ec_GFp_simple_group_get_degree,
84 ec_GFp_simple_group_check_discriminant,
85 ec_GFp_simple_point_init,
86 ec_GFp_simple_point_finish,
87 ec_GFp_simple_point_clear_finish,
88 ec_GFp_simple_point_copy,
89 ec_GFp_simple_point_set_to_infinity,
90 ec_GFp_simple_set_Jprojective_coordinates_GFp,
91 ec_GFp_simple_get_Jprojective_coordinates_GFp,
92 ec_GFp_simple_point_set_affine_coordinates,
93 ec_GFp_simple_point_get_affine_coordinates,
98 ec_GFp_simple_is_at_infinity,
99 ec_GFp_simple_is_on_curve,
101 ec_GFp_simple_make_affine,
102 ec_GFp_simple_points_make_affine,
104 0 /* precompute_mult */,
105 0 /* have_precompute_mult */,
106 ec_GFp_simple_field_mul,
107 ec_GFp_simple_field_sqr,
109 0 /* field_encode */,
110 0 /* field_decode */,
111 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).
131 int ec_GFp_simple_group_init(EC_GROUP *group)
133 BN_init(&group->field);
136 group->a_is_minus3 = 0;
141 void ec_GFp_simple_group_finish(EC_GROUP *group)
143 BN_free(&group->field);
149 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
151 BN_clear_free(&group->field);
152 BN_clear_free(&group->a);
153 BN_clear_free(&group->b);
157 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
159 if (!BN_copy(&dest->field, &src->field)) return 0;
160 if (!BN_copy(&dest->a, &src->a)) return 0;
161 if (!BN_copy(&dest->b, &src->b)) return 0;
163 dest->a_is_minus3 = src->a_is_minus3;
169 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
170 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
173 BN_CTX *new_ctx = NULL;
176 /* p must be a prime > 3 */
177 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
179 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
185 ctx = new_ctx = BN_CTX_new();
191 tmp_a = BN_CTX_get(ctx);
192 if (tmp_a == NULL) goto err;
195 if (!BN_copy(&group->field, p)) goto err;
196 BN_set_negative(&group->field, 0);
199 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
200 if (group->meth->field_encode)
201 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
203 if (!BN_copy(&group->a, tmp_a)) goto err;
206 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
207 if (group->meth->field_encode)
208 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
210 /* group->a_is_minus3 */
211 if (!BN_add_word(tmp_a, 3)) goto err;
212 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
219 BN_CTX_free(new_ctx);
224 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
227 BN_CTX *new_ctx = NULL;
231 if (!BN_copy(p, &group->field)) return 0;
234 if (a != NULL || b != NULL)
236 if (group->meth->field_decode)
240 ctx = new_ctx = BN_CTX_new();
246 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
250 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
257 if (!BN_copy(a, &group->a)) goto err;
261 if (!BN_copy(b, &group->b)) goto err;
270 BN_CTX_free(new_ctx);
275 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
277 return BN_num_bits(&group->field);
281 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
284 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
285 const BIGNUM *p = &group->field;
286 BN_CTX *new_ctx = NULL;
290 ctx = new_ctx = BN_CTX_new();
293 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
300 tmp_1 = BN_CTX_get(ctx);
301 tmp_2 = BN_CTX_get(ctx);
302 order = BN_CTX_get(ctx);
303 if (order == NULL) goto err;
305 if (group->meth->field_decode)
307 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
308 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
312 if (!BN_copy(a, &group->a)) goto err;
313 if (!BN_copy(b, &group->b)) goto err;
316 /* check the discriminant:
317 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
321 if (BN_is_zero(b)) goto err;
323 else if (!BN_is_zero(b))
325 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
326 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
327 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
330 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
331 if (!BN_mul_word(tmp_2, 27)) goto err;
334 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
335 if (BN_is_zero(a)) goto err;
343 BN_CTX_free(new_ctx);
348 int ec_GFp_simple_point_init(EC_POINT *point)
359 void ec_GFp_simple_point_finish(EC_POINT *point)
367 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
369 BN_clear_free(&point->X);
370 BN_clear_free(&point->Y);
371 BN_clear_free(&point->Z);
376 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
378 if (!BN_copy(&dest->X, &src->X)) return 0;
379 if (!BN_copy(&dest->Y, &src->Y)) return 0;
380 if (!BN_copy(&dest->Z, &src->Z)) return 0;
381 dest->Z_is_one = src->Z_is_one;
387 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
395 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
396 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
398 BN_CTX *new_ctx = NULL;
403 ctx = new_ctx = BN_CTX_new();
410 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
411 if (group->meth->field_encode)
413 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
419 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
420 if (group->meth->field_encode)
422 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
430 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
431 Z_is_one = BN_is_one(&point->Z);
432 if (group->meth->field_encode)
434 if (Z_is_one && (group->meth->field_set_to_one != 0))
436 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
440 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
443 point->Z_is_one = Z_is_one;
450 BN_CTX_free(new_ctx);
455 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
456 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
458 BN_CTX *new_ctx = NULL;
461 if (group->meth->field_decode != 0)
465 ctx = new_ctx = BN_CTX_new();
472 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
476 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
480 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
487 if (!BN_copy(x, &point->X)) goto err;
491 if (!BN_copy(y, &point->Y)) goto err;
495 if (!BN_copy(z, &point->Z)) goto err;
503 BN_CTX_free(new_ctx);
508 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
509 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
511 if (x == NULL || y == NULL)
513 /* unlike for projective coordinates, we do not tolerate this */
514 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
518 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
522 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
523 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
525 BN_CTX *new_ctx = NULL;
526 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
530 if (EC_POINT_is_at_infinity(group, point))
532 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
538 ctx = new_ctx = BN_CTX_new();
545 Z_1 = BN_CTX_get(ctx);
546 Z_2 = BN_CTX_get(ctx);
547 Z_3 = BN_CTX_get(ctx);
548 if (Z_3 == NULL) goto err;
550 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
552 if (group->meth->field_decode)
554 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
564 if (group->meth->field_decode)
568 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
572 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
579 if (!BN_copy(x, &point->X)) goto err;
583 if (!BN_copy(y, &point->Y)) goto err;
589 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
591 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
595 if (group->meth->field_encode == 0)
597 /* field_sqr works on standard representation */
598 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
602 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
607 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
608 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
613 if (group->meth->field_encode == 0)
615 /* field_mul works on standard representation */
616 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
620 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
623 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
624 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
633 BN_CTX_free(new_ctx);
637 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
639 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
640 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
642 BN_CTX *new_ctx = NULL;
643 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
647 return EC_POINT_dbl(group, r, a, ctx);
648 if (EC_POINT_is_at_infinity(group, a))
649 return EC_POINT_copy(r, b);
650 if (EC_POINT_is_at_infinity(group, b))
651 return EC_POINT_copy(r, a);
653 field_mul = group->meth->field_mul;
654 field_sqr = group->meth->field_sqr;
659 ctx = new_ctx = BN_CTX_new();
665 n0 = BN_CTX_get(ctx);
666 n1 = BN_CTX_get(ctx);
667 n2 = BN_CTX_get(ctx);
668 n3 = BN_CTX_get(ctx);
669 n4 = BN_CTX_get(ctx);
670 n5 = BN_CTX_get(ctx);
671 n6 = BN_CTX_get(ctx);
672 if (n6 == NULL) goto end;
674 /* Note that in this function we must not read components of 'a' or 'b'
675 * once we have written the corresponding components of 'r'.
676 * ('r' might be one of 'a' or 'b'.)
682 if (!BN_copy(n1, &a->X)) goto end;
683 if (!BN_copy(n2, &a->Y)) goto end;
689 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
690 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
691 /* n1 = X_a * Z_b^2 */
693 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
694 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
695 /* n2 = Y_a * Z_b^3 */
701 if (!BN_copy(n3, &b->X)) goto end;
702 if (!BN_copy(n4, &b->Y)) goto end;
708 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
709 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
710 /* n3 = X_b * Z_a^2 */
712 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
713 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
714 /* n4 = Y_b * Z_a^3 */
718 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
719 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
727 /* a is the same point as b */
729 ret = EC_POINT_dbl(group, r, a, ctx);
735 /* a is the inverse of b */
744 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
745 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
750 if (a->Z_is_one && b->Z_is_one)
752 if (!BN_copy(&r->Z, n5)) goto end;
757 { if (!BN_copy(n0, &b->Z)) goto end; }
758 else if (b->Z_is_one)
759 { if (!BN_copy(n0, &a->Z)) goto end; }
761 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
762 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
765 /* Z_r = Z_a * Z_b * n5 */
768 if (!field_sqr(group, n0, n6, ctx)) goto end;
769 if (!field_sqr(group, n4, n5, ctx)) goto end;
770 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
771 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
772 /* X_r = n6^2 - n5^2 * 'n7' */
775 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
776 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
777 /* n9 = n5^2 * 'n7' - 2 * X_r */
780 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
781 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
782 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
783 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
785 if (!BN_add(n0, n0, p)) goto end;
786 /* now 0 <= n0 < 2*p, and n0 is even */
787 if (!BN_rshift1(&r->Y, n0)) goto end;
788 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
793 if (ctx) /* otherwise we already called BN_CTX_end */
796 BN_CTX_free(new_ctx);
801 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
803 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
804 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
806 BN_CTX *new_ctx = NULL;
807 BIGNUM *n0, *n1, *n2, *n3;
810 if (EC_POINT_is_at_infinity(group, a))
817 field_mul = group->meth->field_mul;
818 field_sqr = group->meth->field_sqr;
823 ctx = new_ctx = BN_CTX_new();
829 n0 = BN_CTX_get(ctx);
830 n1 = BN_CTX_get(ctx);
831 n2 = BN_CTX_get(ctx);
832 n3 = BN_CTX_get(ctx);
833 if (n3 == NULL) goto err;
835 /* Note that in this function we must not read components of 'a'
836 * once we have written the corresponding components of 'r'.
837 * ('r' might the same as 'a'.)
843 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
844 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
845 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
846 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
847 /* n1 = 3 * X_a^2 + a_curve */
849 else if (group->a_is_minus3)
851 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
852 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
853 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
854 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
855 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
856 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
857 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
858 * = 3 * X_a^2 - 3 * Z_a^4 */
862 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
863 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
864 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
865 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
866 if (!field_sqr(group, n1, n1, ctx)) goto err;
867 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
868 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
869 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
875 if (!BN_copy(n0, &a->Y)) goto err;
879 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
881 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
883 /* Z_r = 2 * Y_a * Z_a */
886 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
887 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
888 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
889 /* n2 = 4 * X_a * Y_a^2 */
892 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
893 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
894 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
895 /* X_r = n1^2 - 2 * n2 */
898 if (!field_sqr(group, n0, n3, ctx)) goto err;
899 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
903 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
904 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
905 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
906 /* Y_r = n1 * (n2 - X_r) - n3 */
913 BN_CTX_free(new_ctx);
918 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
920 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
921 /* point is its own inverse */
924 return BN_usub(&point->Y, &group->field, &point->Y);
928 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
930 return BN_is_zero(&point->Z);
934 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
936 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
937 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
939 BN_CTX *new_ctx = NULL;
940 BIGNUM *rh, *tmp, *Z4, *Z6;
943 if (EC_POINT_is_at_infinity(group, point))
946 field_mul = group->meth->field_mul;
947 field_sqr = group->meth->field_sqr;
952 ctx = new_ctx = BN_CTX_new();
958 rh = BN_CTX_get(ctx);
959 tmp = BN_CTX_get(ctx);
960 Z4 = BN_CTX_get(ctx);
961 Z6 = BN_CTX_get(ctx);
962 if (Z6 == NULL) goto err;
964 /* We have a curve defined by a Weierstrass equation
965 * y^2 = x^3 + a*x + b.
966 * The point to consider is given in Jacobian projective coordinates
967 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
968 * Substituting this and multiplying by Z^6 transforms the above equation into
969 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
970 * To test this, we add up the right-hand side in 'rh'.
974 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
976 if (!point->Z_is_one)
978 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
979 if (!field_sqr(group, Z4, tmp, ctx)) goto err;
980 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
982 /* rh := (rh + a*Z^4)*X */
983 if (group->a_is_minus3)
985 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
986 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
987 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
988 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
992 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
993 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
994 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
997 /* rh := rh + b*Z^6 */
998 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
999 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1003 /* point->Z_is_one */
1005 /* rh := (rh + a)*X */
1006 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
1007 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1009 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1013 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
1015 ret = (0 == BN_ucmp(tmp, rh));
1019 if (new_ctx != NULL)
1020 BN_CTX_free(new_ctx);
1025 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1029 * 0 equal (in affine coordinates)
1033 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1034 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1035 BN_CTX *new_ctx = NULL;
1036 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1037 const BIGNUM *tmp1_, *tmp2_;
1040 if (EC_POINT_is_at_infinity(group, a))
1042 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1045 if (EC_POINT_is_at_infinity(group, b))
1048 if (a->Z_is_one && b->Z_is_one)
1050 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1053 field_mul = group->meth->field_mul;
1054 field_sqr = group->meth->field_sqr;
1058 ctx = new_ctx = BN_CTX_new();
1064 tmp1 = BN_CTX_get(ctx);
1065 tmp2 = BN_CTX_get(ctx);
1066 Za23 = BN_CTX_get(ctx);
1067 Zb23 = BN_CTX_get(ctx);
1068 if (Zb23 == NULL) goto end;
1070 /* We have to decide whether
1071 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1072 * or equivalently, whether
1073 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1078 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1079 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1086 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1087 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1093 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1094 if (BN_cmp(tmp1_, tmp2_) != 0)
1096 ret = 1; /* points differ */
1103 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1104 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1111 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1112 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1118 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1119 if (BN_cmp(tmp1_, tmp2_) != 0)
1121 ret = 1; /* points differ */
1125 /* points are equal */
1130 if (new_ctx != NULL)
1131 BN_CTX_free(new_ctx);
1136 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1138 BN_CTX *new_ctx = NULL;
1142 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1147 ctx = new_ctx = BN_CTX_new();
1153 x = BN_CTX_get(ctx);
1154 y = BN_CTX_get(ctx);
1155 if (y == NULL) goto err;
1157 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1158 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1159 if (!point->Z_is_one)
1161 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1169 if (new_ctx != NULL)
1170 BN_CTX_free(new_ctx);
1175 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1177 BN_CTX *new_ctx = NULL;
1178 BIGNUM *tmp, *tmp_Z;
1179 BIGNUM **prod_Z = NULL;
1188 ctx = new_ctx = BN_CTX_new();
1194 tmp = BN_CTX_get(ctx);
1195 tmp_Z = BN_CTX_get(ctx);
1196 if (tmp == NULL || tmp_Z == NULL) goto err;
1198 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1199 if (prod_Z == NULL) goto err;
1200 for (i = 0; i < num; i++)
1202 prod_Z[i] = BN_new();
1203 if (prod_Z[i] == NULL) goto err;
1206 /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1207 * skipping any zero-valued inputs (pretend that they're 1). */
1209 if (!BN_is_zero(&points[0]->Z))
1211 if (!BN_copy(prod_Z[0], &points[0]->Z)) goto err;
1215 if (group->meth->field_set_to_one != 0)
1217 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
1221 if (!BN_one(prod_Z[0])) goto err;
1225 for (i = 1; i < num; i++)
1227 if (!BN_is_zero(&points[i]->Z))
1229 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], &points[i]->Z, ctx)) goto err;
1233 if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
1237 /* Now use a single explicit inversion to replace every
1238 * non-zero points[i]->Z by its inverse. */
1240 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx))
1242 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1245 if (group->meth->field_encode != 0)
1247 /* In the Montgomery case, we just turned R*H (representing H)
1248 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1249 * i.e. we need to multiply by the Montgomery factor twice. */
1250 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1251 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1254 for (i = num - 1; i > 0; --i)
1256 /* Loop invariant: tmp is the product of the inverses of
1257 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
1258 if (!BN_is_zero(&points[i]->Z))
1260 /* Set tmp_Z to the inverse of points[i]->Z (as product
1261 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
1262 if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
1263 /* Update tmp to satisfy the loop invariant for i - 1. */
1264 if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) goto err;
1265 /* Replace points[i]->Z by its inverse. */
1266 if (!BN_copy(&points[i]->Z, tmp_Z)) goto err;
1270 if (!BN_is_zero(&points[0]->Z))
1272 /* Replace points[0]->Z by its inverse. */
1273 if (!BN_copy(&points[0]->Z, tmp)) goto err;
1276 /* Finally, fix up the X and Y coordinates for all points. */
1278 for (i = 0; i < num; i++)
1280 EC_POINT *p = points[i];
1282 if (!BN_is_zero(&p->Z))
1284 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1286 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) goto err;
1287 if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) goto err;
1289 if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) goto err;
1290 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) goto err;
1292 if (group->meth->field_set_to_one != 0)
1294 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1298 if (!BN_one(&p->Z)) goto err;
1308 if (new_ctx != NULL)
1309 BN_CTX_free(new_ctx);
1312 for (i = 0; i < num; i++)
1314 if (prod_Z[i] == NULL) break;
1315 BN_clear_free(prod_Z[i]);
1317 OPENSSL_free(prod_Z);
1323 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1325 return BN_mod_mul(r, a, b, &group->field, ctx);
1329 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1331 return BN_mod_sqr(r, a, &group->field, ctx);