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 #include <openssl/err.h>
66 #include <openssl/symhacks.h>
69 #include <openssl/fips.h>
74 const EC_METHOD *EC_GFp_simple_method(void)
76 static const EC_METHOD ret = {
78 NID_X9_62_prime_field,
79 ec_GFp_simple_group_init,
80 ec_GFp_simple_group_finish,
81 ec_GFp_simple_group_clear_finish,
82 ec_GFp_simple_group_copy,
83 ec_GFp_simple_group_set_curve,
84 ec_GFp_simple_group_get_curve,
85 ec_GFp_simple_group_get_degree,
86 ec_GFp_simple_group_check_discriminant,
87 ec_GFp_simple_point_init,
88 ec_GFp_simple_point_finish,
89 ec_GFp_simple_point_clear_finish,
90 ec_GFp_simple_point_copy,
91 ec_GFp_simple_point_set_to_infinity,
92 ec_GFp_simple_set_Jprojective_coordinates_GFp,
93 ec_GFp_simple_get_Jprojective_coordinates_GFp,
94 ec_GFp_simple_point_set_affine_coordinates,
95 ec_GFp_simple_point_get_affine_coordinates,
100 ec_GFp_simple_is_at_infinity,
101 ec_GFp_simple_is_on_curve,
103 ec_GFp_simple_make_affine,
104 ec_GFp_simple_points_make_affine,
106 0 /* precompute_mult */,
107 0 /* have_precompute_mult */,
108 ec_GFp_simple_field_mul,
109 ec_GFp_simple_field_sqr,
111 0 /* field_encode */,
112 0 /* field_decode */,
113 0 /* field_set_to_one */ };
117 return fips_ec_gfp_simple_method();
125 * Most method functions in this file are designed to work with
126 * non-trivial representations of field elements if necessary
127 * (see ecp_mont.c): while standard modular addition and subtraction
128 * are used, the field_mul and field_sqr methods will be used for
129 * multiplication, and field_encode and field_decode (if defined)
130 * will be used for converting between representations.
132 * Functions ec_GFp_simple_points_make_affine() and
133 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
134 * that if a non-trivial representation is used, it is a Montgomery
135 * 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;
149 void ec_GFp_simple_group_finish(EC_GROUP *group)
151 BN_free(&group->field);
157 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
159 BN_clear_free(&group->field);
160 BN_clear_free(&group->a);
161 BN_clear_free(&group->b);
165 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
167 if (!BN_copy(&dest->field, &src->field)) return 0;
168 if (!BN_copy(&dest->a, &src->a)) return 0;
169 if (!BN_copy(&dest->b, &src->b)) return 0;
171 dest->a_is_minus3 = src->a_is_minus3;
177 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
178 const BIGNUM *p, const BIGNUM *a, 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))
187 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
193 ctx = new_ctx = BN_CTX_new();
199 tmp_a = BN_CTX_get(ctx);
200 if (tmp_a == NULL) goto err;
203 if (!BN_copy(&group->field, p)) goto err;
204 BN_set_negative(&group->field, 0);
207 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
208 if (group->meth->field_encode)
209 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
211 if (!BN_copy(&group->a, tmp_a)) goto err;
214 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
215 if (group->meth->field_encode)
216 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
218 /* group->a_is_minus3 */
219 if (!BN_add_word(tmp_a, 3)) goto err;
220 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
227 BN_CTX_free(new_ctx);
232 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
235 BN_CTX *new_ctx = NULL;
239 if (!BN_copy(p, &group->field)) return 0;
242 if (a != NULL || b != NULL)
244 if (group->meth->field_decode)
248 ctx = new_ctx = BN_CTX_new();
254 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
258 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
265 if (!BN_copy(a, &group->a)) goto err;
269 if (!BN_copy(b, &group->b)) goto err;
278 BN_CTX_free(new_ctx);
283 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
285 return BN_num_bits(&group->field);
289 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
292 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
293 const BIGNUM *p = &group->field;
294 BN_CTX *new_ctx = NULL;
298 ctx = new_ctx = BN_CTX_new();
301 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
308 tmp_1 = BN_CTX_get(ctx);
309 tmp_2 = BN_CTX_get(ctx);
310 order = BN_CTX_get(ctx);
311 if (order == NULL) goto err;
313 if (group->meth->field_decode)
315 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
316 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
320 if (!BN_copy(a, &group->a)) goto err;
321 if (!BN_copy(b, &group->b)) goto err;
325 * check the discriminant:
326 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
331 if (BN_is_zero(b)) goto err;
333 else if (!BN_is_zero(b))
335 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
336 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
337 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
340 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
341 if (!BN_mul_word(tmp_2, 27)) goto err;
344 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
345 if (BN_is_zero(a)) goto err;
353 BN_CTX_free(new_ctx);
358 int ec_GFp_simple_point_init(EC_POINT *point)
369 void ec_GFp_simple_point_finish(EC_POINT *point)
377 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
379 BN_clear_free(&point->X);
380 BN_clear_free(&point->Y);
381 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)) return 0;
389 if (!BN_copy(&dest->Y, &src->Y)) return 0;
390 if (!BN_copy(&dest->Z, &src->Z)) return 0;
391 dest->Z_is_one = src->Z_is_one;
397 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
405 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
406 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
408 BN_CTX *new_ctx = NULL;
413 ctx = new_ctx = BN_CTX_new();
420 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
421 if (group->meth->field_encode)
423 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
429 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
430 if (group->meth->field_encode)
432 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
440 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
441 Z_is_one = BN_is_one(&point->Z);
442 if (group->meth->field_encode)
444 if (Z_is_one && (group->meth->field_set_to_one != 0))
446 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
450 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
453 point->Z_is_one = Z_is_one;
460 BN_CTX_free(new_ctx);
465 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
466 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
468 BN_CTX *new_ctx = NULL;
471 if (group->meth->field_decode != 0)
475 ctx = new_ctx = BN_CTX_new();
482 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
486 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
490 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
497 if (!BN_copy(x, &point->X)) goto err;
501 if (!BN_copy(y, &point->Y)) goto err;
505 if (!BN_copy(z, &point->Z)) goto err;
513 BN_CTX_free(new_ctx);
518 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
519 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
521 if (x == NULL || y == NULL)
523 /* unlike for projective coordinates, we do not tolerate this */
524 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
528 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
532 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
533 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
535 BN_CTX *new_ctx = NULL;
536 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
540 if (EC_POINT_is_at_infinity(group, point))
542 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
548 ctx = new_ctx = BN_CTX_new();
555 Z_1 = BN_CTX_get(ctx);
556 Z_2 = BN_CTX_get(ctx);
557 Z_3 = BN_CTX_get(ctx);
558 if (Z_3 == NULL) goto err;
560 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
562 if (group->meth->field_decode)
564 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
574 if (group->meth->field_decode)
578 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
582 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
589 if (!BN_copy(x, &point->X)) goto err;
593 if (!BN_copy(y, &point->Y)) goto err;
599 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
601 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
605 if (group->meth->field_encode == 0)
607 /* field_sqr works on standard representation */
608 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
612 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
617 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
618 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
623 if (group->meth->field_encode == 0)
625 /* field_mul works on standard representation */
626 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
630 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
633 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
634 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
643 BN_CTX_free(new_ctx);
647 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
649 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
650 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
652 BN_CTX *new_ctx = NULL;
653 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
657 return EC_POINT_dbl(group, r, a, ctx);
658 if (EC_POINT_is_at_infinity(group, a))
659 return EC_POINT_copy(r, b);
660 if (EC_POINT_is_at_infinity(group, b))
661 return EC_POINT_copy(r, a);
663 field_mul = group->meth->field_mul;
664 field_sqr = group->meth->field_sqr;
669 ctx = new_ctx = BN_CTX_new();
675 n0 = BN_CTX_get(ctx);
676 n1 = BN_CTX_get(ctx);
677 n2 = BN_CTX_get(ctx);
678 n3 = BN_CTX_get(ctx);
679 n4 = BN_CTX_get(ctx);
680 n5 = BN_CTX_get(ctx);
681 n6 = BN_CTX_get(ctx);
682 if (n6 == NULL) goto end;
684 /* Note that in this function we must not read components of 'a' or 'b'
685 * once we have written the corresponding components of 'r'.
686 * ('r' might be one of 'a' or 'b'.)
692 if (!BN_copy(n1, &a->X)) goto end;
693 if (!BN_copy(n2, &a->Y)) goto end;
699 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
700 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
701 /* n1 = X_a * Z_b^2 */
703 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
704 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
705 /* n2 = Y_a * Z_b^3 */
711 if (!BN_copy(n3, &b->X)) goto end;
712 if (!BN_copy(n4, &b->Y)) goto end;
718 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
719 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
720 /* n3 = X_b * Z_a^2 */
722 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
723 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
724 /* n4 = Y_b * Z_a^3 */
728 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
729 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
737 /* a is the same point as b */
739 ret = EC_POINT_dbl(group, r, a, ctx);
745 /* a is the inverse of b */
754 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
755 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
760 if (a->Z_is_one && b->Z_is_one)
762 if (!BN_copy(&r->Z, n5)) goto end;
767 { if (!BN_copy(n0, &b->Z)) goto end; }
768 else if (b->Z_is_one)
769 { if (!BN_copy(n0, &a->Z)) goto end; }
771 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
772 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
775 /* Z_r = Z_a * Z_b * n5 */
778 if (!field_sqr(group, n0, n6, ctx)) goto end;
779 if (!field_sqr(group, n4, n5, ctx)) goto end;
780 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
781 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
782 /* X_r = n6^2 - n5^2 * 'n7' */
785 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
786 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
787 /* n9 = n5^2 * 'n7' - 2 * X_r */
790 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
791 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
792 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
793 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
795 if (!BN_add(n0, n0, p)) goto end;
796 /* now 0 <= n0 < 2*p, and n0 is even */
797 if (!BN_rshift1(&r->Y, n0)) goto end;
798 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
803 if (ctx) /* otherwise we already called BN_CTX_end */
806 BN_CTX_free(new_ctx);
811 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
813 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
814 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
816 BN_CTX *new_ctx = NULL;
817 BIGNUM *n0, *n1, *n2, *n3;
820 if (EC_POINT_is_at_infinity(group, a))
827 field_mul = group->meth->field_mul;
828 field_sqr = group->meth->field_sqr;
833 ctx = new_ctx = BN_CTX_new();
839 n0 = BN_CTX_get(ctx);
840 n1 = BN_CTX_get(ctx);
841 n2 = BN_CTX_get(ctx);
842 n3 = BN_CTX_get(ctx);
843 if (n3 == NULL) goto err;
845 /* Note that in this function we must not read components of 'a'
846 * once we have written the corresponding components of 'r'.
847 * ('r' might the same as 'a'.)
853 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
854 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
855 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
856 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
857 /* n1 = 3 * X_a^2 + a_curve */
859 else if (group->a_is_minus3)
861 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
862 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
863 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
864 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
865 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
866 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
868 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
869 * = 3 * X_a^2 - 3 * Z_a^4
874 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
875 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
876 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
877 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
878 if (!field_sqr(group, n1, n1, ctx)) goto err;
879 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
880 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
881 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
887 if (!BN_copy(n0, &a->Y)) goto err;
891 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
893 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
895 /* Z_r = 2 * Y_a * Z_a */
898 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
899 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
900 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
901 /* n2 = 4 * X_a * Y_a^2 */
904 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
905 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
906 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
907 /* X_r = n1^2 - 2 * n2 */
910 if (!field_sqr(group, n0, n3, ctx)) goto err;
911 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
915 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
916 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
917 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
918 /* Y_r = n1 * (n2 - X_r) - n3 */
925 BN_CTX_free(new_ctx);
930 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
932 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
933 /* point is its own inverse */
936 return BN_usub(&point->Y, &group->field, &point->Y);
940 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
942 return BN_is_zero(&point->Z);
946 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
948 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
949 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
951 BN_CTX *new_ctx = NULL;
952 BIGNUM *rh, *tmp, *Z4, *Z6;
955 if (EC_POINT_is_at_infinity(group, point))
958 field_mul = group->meth->field_mul;
959 field_sqr = group->meth->field_sqr;
964 ctx = new_ctx = BN_CTX_new();
970 rh = BN_CTX_get(ctx);
971 tmp = BN_CTX_get(ctx);
972 Z4 = BN_CTX_get(ctx);
973 Z6 = BN_CTX_get(ctx);
974 if (Z6 == NULL) goto err;
977 * We have a curve defined by a Weierstrass equation
978 * y^2 = x^3 + a*x + b.
979 * The point to consider is given in Jacobian projective coordinates
980 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
981 * Substituting this and multiplying by Z^6 transforms the above equation into
982 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
983 * To test this, we add up the right-hand side in 'rh'.
987 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
989 if (!point->Z_is_one)
991 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
992 if (!field_sqr(group, Z4, tmp, ctx)) goto err;
993 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
995 /* rh := (rh + a*Z^4)*X */
996 if (group->a_is_minus3)
998 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
999 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
1000 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
1001 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1005 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
1006 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1007 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1010 /* rh := rh + b*Z^6 */
1011 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
1012 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1016 /* point->Z_is_one */
1018 /* rh := (rh + a)*X */
1019 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
1020 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1022 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1026 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
1028 ret = (0 == BN_ucmp(tmp, rh));
1032 if (new_ctx != NULL)
1033 BN_CTX_free(new_ctx);
1038 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1043 * 0 equal (in affine coordinates)
1047 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1048 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1049 BN_CTX *new_ctx = NULL;
1050 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1051 const BIGNUM *tmp1_, *tmp2_;
1054 if (EC_POINT_is_at_infinity(group, a))
1056 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1059 if (EC_POINT_is_at_infinity(group, b))
1062 if (a->Z_is_one && b->Z_is_one)
1064 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1067 field_mul = group->meth->field_mul;
1068 field_sqr = group->meth->field_sqr;
1072 ctx = new_ctx = BN_CTX_new();
1078 tmp1 = BN_CTX_get(ctx);
1079 tmp2 = BN_CTX_get(ctx);
1080 Za23 = BN_CTX_get(ctx);
1081 Zb23 = BN_CTX_get(ctx);
1082 if (Zb23 == NULL) goto end;
1085 * We have to decide whether
1086 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1087 * or equivalently, whether
1088 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1093 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1094 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1101 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1102 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1108 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1109 if (BN_cmp(tmp1_, tmp2_) != 0)
1111 ret = 1; /* points differ */
1118 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1119 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1126 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1127 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1133 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1134 if (BN_cmp(tmp1_, tmp2_) != 0)
1136 ret = 1; /* points differ */
1140 /* points are equal */
1145 if (new_ctx != NULL)
1146 BN_CTX_free(new_ctx);
1151 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1153 BN_CTX *new_ctx = NULL;
1157 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1162 ctx = new_ctx = BN_CTX_new();
1168 x = BN_CTX_get(ctx);
1169 y = BN_CTX_get(ctx);
1170 if (y == NULL) goto err;
1172 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1173 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1174 if (!point->Z_is_one)
1176 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1184 if (new_ctx != NULL)
1185 BN_CTX_free(new_ctx);
1190 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1192 BN_CTX *new_ctx = NULL;
1193 BIGNUM *tmp, *tmp_Z;
1194 BIGNUM **prod_Z = NULL;
1203 ctx = new_ctx = BN_CTX_new();
1209 tmp = BN_CTX_get(ctx);
1210 tmp_Z = BN_CTX_get(ctx);
1211 if (tmp == NULL || tmp_Z == NULL) goto err;
1213 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1214 if (prod_Z == NULL) goto err;
1215 for (i = 0; i < num; i++)
1217 prod_Z[i] = BN_new();
1218 if (prod_Z[i] == NULL) goto err;
1221 /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1222 * skipping any zero-valued inputs (pretend that they're 1). */
1224 if (!BN_is_zero(&points[0]->Z))
1226 if (!BN_copy(prod_Z[0], &points[0]->Z)) goto err;
1230 if (group->meth->field_set_to_one != 0)
1232 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
1236 if (!BN_one(prod_Z[0])) goto err;
1240 for (i = 1; i < num; i++)
1242 if (!BN_is_zero(&points[i]->Z))
1244 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], &points[i]->Z, ctx)) goto err;
1248 if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
1252 /* Now use a single explicit inversion to replace every
1253 * non-zero points[i]->Z by its inverse. */
1255 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx))
1257 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1260 if (group->meth->field_encode != 0)
1262 /* In the Montgomery case, we just turned R*H (representing H)
1263 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1264 * i.e. we need to multiply by the Montgomery factor twice. */
1265 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1266 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1269 for (i = num - 1; i > 0; --i)
1271 /* Loop invariant: tmp is the product of the inverses of
1272 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
1273 if (!BN_is_zero(&points[i]->Z))
1275 /* Set tmp_Z to the inverse of points[i]->Z (as product
1276 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
1277 if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
1278 /* Update tmp to satisfy the loop invariant for i - 1. */
1279 if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) goto err;
1280 /* Replace points[i]->Z by its inverse. */
1281 if (!BN_copy(&points[i]->Z, tmp_Z)) goto err;
1285 if (!BN_is_zero(&points[0]->Z))
1287 /* Replace points[0]->Z by its inverse. */
1288 if (!BN_copy(&points[0]->Z, tmp)) goto err;
1291 /* Finally, fix up the X and Y coordinates for all points. */
1293 for (i = 0; i < num; i++)
1295 EC_POINT *p = points[i];
1297 if (!BN_is_zero(&p->Z))
1299 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1301 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) goto err;
1302 if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) goto err;
1304 if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) goto err;
1305 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) goto err;
1307 if (group->meth->field_set_to_one != 0)
1309 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1313 if (!BN_one(&p->Z)) goto err;
1323 if (new_ctx != NULL)
1324 BN_CTX_free(new_ctx);
1327 for (i = 0; i < num; i++)
1329 if (prod_Z[i] == NULL) break;
1330 BN_clear_free(prod_Z[i]);
1332 OPENSSL_free(prod_Z);
1338 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1340 return BN_mod_mul(r, a, b, &group->field, ctx);
1344 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1346 return BN_mod_sqr(r, a, &group->field, ctx);