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>
70 const EC_METHOD *EC_GFp_simple_method(void)
72 static const EC_METHOD ret = {
73 NID_X9_62_prime_field,
74 ec_GFp_simple_group_init,
75 ec_GFp_simple_group_finish,
76 ec_GFp_simple_group_clear_finish,
77 ec_GFp_simple_group_copy,
78 ec_GFp_simple_group_set_curve,
79 ec_GFp_simple_group_get_curve,
80 ec_GFp_simple_group_get_degree,
81 ec_GFp_simple_group_check_discriminant,
82 ec_GFp_simple_point_init,
83 ec_GFp_simple_point_finish,
84 ec_GFp_simple_point_clear_finish,
85 ec_GFp_simple_point_copy,
86 ec_GFp_simple_point_set_to_infinity,
87 ec_GFp_simple_set_Jprojective_coordinates_GFp,
88 ec_GFp_simple_get_Jprojective_coordinates_GFp,
89 ec_GFp_simple_point_set_affine_coordinates,
90 ec_GFp_simple_point_get_affine_coordinates,
91 ec_GFp_simple_set_compressed_coordinates,
92 ec_GFp_simple_point2oct,
93 ec_GFp_simple_oct2point,
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).
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;
317 * check the discriminant:
318 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
323 if (BN_is_zero(b)) goto err;
325 else if (!BN_is_zero(b))
327 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
328 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
329 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
332 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
333 if (!BN_mul_word(tmp_2, 27)) goto err;
336 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
337 if (BN_is_zero(a)) goto err;
345 BN_CTX_free(new_ctx);
350 int ec_GFp_simple_point_init(EC_POINT *point)
361 void ec_GFp_simple_point_finish(EC_POINT *point)
369 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
371 BN_clear_free(&point->X);
372 BN_clear_free(&point->Y);
373 BN_clear_free(&point->Z);
378 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
380 if (!BN_copy(&dest->X, &src->X)) return 0;
381 if (!BN_copy(&dest->Y, &src->Y)) return 0;
382 if (!BN_copy(&dest->Z, &src->Z)) return 0;
383 dest->Z_is_one = src->Z_is_one;
389 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
397 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
398 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
400 BN_CTX *new_ctx = NULL;
405 ctx = new_ctx = BN_CTX_new();
412 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
413 if (group->meth->field_encode)
415 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
421 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
422 if (group->meth->field_encode)
424 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
432 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
433 Z_is_one = BN_is_one(&point->Z);
434 if (group->meth->field_encode)
436 if (Z_is_one && (group->meth->field_set_to_one != 0))
438 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
442 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
445 point->Z_is_one = Z_is_one;
452 BN_CTX_free(new_ctx);
457 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
458 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
460 BN_CTX *new_ctx = NULL;
463 if (group->meth->field_decode != 0)
467 ctx = new_ctx = BN_CTX_new();
474 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
478 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
482 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
489 if (!BN_copy(x, &point->X)) goto err;
493 if (!BN_copy(y, &point->Y)) goto err;
497 if (!BN_copy(z, &point->Z)) goto err;
505 BN_CTX_free(new_ctx);
510 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
511 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
513 if (x == NULL || y == NULL)
515 /* unlike for projective coordinates, we do not tolerate this */
516 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
520 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
524 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
525 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
527 BN_CTX *new_ctx = NULL;
528 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
532 if (EC_POINT_is_at_infinity(group, point))
534 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
540 ctx = new_ctx = BN_CTX_new();
547 Z_1 = BN_CTX_get(ctx);
548 Z_2 = BN_CTX_get(ctx);
549 Z_3 = BN_CTX_get(ctx);
550 if (Z_3 == NULL) goto err;
552 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
554 if (group->meth->field_decode)
556 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
566 if (group->meth->field_decode)
570 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
574 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
581 if (!BN_copy(x, &point->X)) goto err;
585 if (!BN_copy(y, &point->Y)) goto err;
591 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
593 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
597 if (group->meth->field_encode == 0)
599 /* field_sqr works on standard representation */
600 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
604 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
609 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
610 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
615 if (group->meth->field_encode == 0)
617 /* field_mul works on standard representation */
618 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
622 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
625 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
626 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
635 BN_CTX_free(new_ctx);
640 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
641 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
643 BN_CTX *new_ctx = NULL;
644 BIGNUM *tmp1, *tmp2, *x, *y;
647 /* clear error queue*/
652 ctx = new_ctx = BN_CTX_new();
657 y_bit = (y_bit != 0);
660 tmp1 = BN_CTX_get(ctx);
661 tmp2 = BN_CTX_get(ctx);
664 if (y == NULL) goto err;
666 /* Recover y. We have a Weierstrass equation
667 * y^2 = x^3 + a*x + b,
668 * so y is one of the square roots of x^3 + a*x + b.
672 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
673 if (group->meth->field_decode == 0)
675 /* field_{sqr,mul} work on standard representation */
676 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
677 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
681 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
682 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
685 /* tmp1 := tmp1 + a*x */
686 if (group->a_is_minus3)
688 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
689 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
690 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
694 if (group->meth->field_decode)
696 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
697 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
701 /* field_mul works on standard representation */
702 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
705 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
708 /* tmp1 := tmp1 + b */
709 if (group->meth->field_decode)
711 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
712 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
716 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
719 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
721 unsigned long err = ERR_peek_last_error();
723 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
726 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
729 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
733 if (y_bit != BN_is_odd(y))
739 kron = BN_kronecker(x, &group->field, ctx);
740 if (kron == -2) goto err;
743 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
745 /* BN_mod_sqrt() should have cought this error (not a square) */
746 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
749 if (!BN_usub(y, &group->field, y)) goto err;
751 if (y_bit != BN_is_odd(y))
753 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
757 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
764 BN_CTX_free(new_ctx);
769 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
770 unsigned char *buf, size_t len, BN_CTX *ctx)
773 BN_CTX *new_ctx = NULL;
776 size_t field_len, i, skip;
778 if ((form != POINT_CONVERSION_COMPRESSED)
779 && (form != POINT_CONVERSION_UNCOMPRESSED)
780 && (form != POINT_CONVERSION_HYBRID))
782 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
786 if (EC_POINT_is_at_infinity(group, point))
788 /* encodes to a single 0 octet */
793 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
802 /* ret := required output buffer length */
803 field_len = BN_num_bytes(&group->field);
804 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
806 /* if 'buf' is NULL, just return required length */
811 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
817 ctx = new_ctx = BN_CTX_new();
826 if (y == NULL) goto err;
828 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
830 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
837 skip = field_len - BN_num_bytes(x);
838 if (skip > field_len)
840 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
848 skip = BN_bn2bin(x, buf + i);
850 if (i != 1 + field_len)
852 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
856 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
858 skip = field_len - BN_num_bytes(y);
859 if (skip > field_len)
861 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
869 skip = BN_bn2bin(y, buf + i);
875 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
883 BN_CTX_free(new_ctx);
890 BN_CTX_free(new_ctx);
895 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
896 const unsigned char *buf, size_t len, BN_CTX *ctx)
898 point_conversion_form_t form;
900 BN_CTX *new_ctx = NULL;
902 size_t field_len, enc_len;
907 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
913 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
914 && (form != POINT_CONVERSION_UNCOMPRESSED)
915 && (form != POINT_CONVERSION_HYBRID))
917 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
920 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
922 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
930 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
934 return EC_POINT_set_to_infinity(group, point);
937 field_len = BN_num_bytes(&group->field);
938 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
942 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
948 ctx = new_ctx = BN_CTX_new();
956 if (y == NULL) goto err;
958 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
959 if (BN_ucmp(x, &group->field) >= 0)
961 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
965 if (form == POINT_CONVERSION_COMPRESSED)
967 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
971 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
972 if (BN_ucmp(y, &group->field) >= 0)
974 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
977 if (form == POINT_CONVERSION_HYBRID)
979 if (y_bit != BN_is_odd(y))
981 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
986 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
989 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
991 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
1000 BN_CTX_free(new_ctx);
1005 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1007 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1008 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1010 BN_CTX *new_ctx = NULL;
1011 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
1015 return EC_POINT_dbl(group, r, a, ctx);
1016 if (EC_POINT_is_at_infinity(group, a))
1017 return EC_POINT_copy(r, b);
1018 if (EC_POINT_is_at_infinity(group, b))
1019 return EC_POINT_copy(r, a);
1021 field_mul = group->meth->field_mul;
1022 field_sqr = group->meth->field_sqr;
1027 ctx = new_ctx = BN_CTX_new();
1033 n0 = BN_CTX_get(ctx);
1034 n1 = BN_CTX_get(ctx);
1035 n2 = BN_CTX_get(ctx);
1036 n3 = BN_CTX_get(ctx);
1037 n4 = BN_CTX_get(ctx);
1038 n5 = BN_CTX_get(ctx);
1039 n6 = BN_CTX_get(ctx);
1040 if (n6 == NULL) goto end;
1042 /* Note that in this function we must not read components of 'a' or 'b'
1043 * once we have written the corresponding components of 'r'.
1044 * ('r' might be one of 'a' or 'b'.)
1050 if (!BN_copy(n1, &a->X)) goto end;
1051 if (!BN_copy(n2, &a->Y)) goto end;
1057 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1058 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1059 /* n1 = X_a * Z_b^2 */
1061 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1062 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1063 /* n2 = Y_a * Z_b^3 */
1069 if (!BN_copy(n3, &b->X)) goto end;
1070 if (!BN_copy(n4, &b->Y)) goto end;
1076 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1077 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1078 /* n3 = X_b * Z_a^2 */
1080 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1081 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1082 /* n4 = Y_b * Z_a^3 */
1086 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1087 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1095 /* a is the same point as b */
1097 ret = EC_POINT_dbl(group, r, a, ctx);
1103 /* a is the inverse of b */
1112 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1113 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1114 /* 'n7' = n1 + n3 */
1115 /* 'n8' = n2 + n4 */
1118 if (a->Z_is_one && b->Z_is_one)
1120 if (!BN_copy(&r->Z, n5)) goto end;
1125 { if (!BN_copy(n0, &b->Z)) goto end; }
1126 else if (b->Z_is_one)
1127 { if (!BN_copy(n0, &a->Z)) goto end; }
1129 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1130 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1133 /* Z_r = Z_a * Z_b * n5 */
1136 if (!field_sqr(group, n0, n6, ctx)) goto end;
1137 if (!field_sqr(group, n4, n5, ctx)) goto end;
1138 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1139 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1140 /* X_r = n6^2 - n5^2 * 'n7' */
1143 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1144 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1145 /* n9 = n5^2 * 'n7' - 2 * X_r */
1148 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1149 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1150 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1151 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1153 if (!BN_add(n0, n0, p)) goto end;
1154 /* now 0 <= n0 < 2*p, and n0 is even */
1155 if (!BN_rshift1(&r->Y, n0)) goto end;
1156 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1161 if (ctx) /* otherwise we already called BN_CTX_end */
1163 if (new_ctx != NULL)
1164 BN_CTX_free(new_ctx);
1169 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1171 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1172 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1174 BN_CTX *new_ctx = NULL;
1175 BIGNUM *n0, *n1, *n2, *n3;
1178 if (EC_POINT_is_at_infinity(group, a))
1185 field_mul = group->meth->field_mul;
1186 field_sqr = group->meth->field_sqr;
1191 ctx = new_ctx = BN_CTX_new();
1197 n0 = BN_CTX_get(ctx);
1198 n1 = BN_CTX_get(ctx);
1199 n2 = BN_CTX_get(ctx);
1200 n3 = BN_CTX_get(ctx);
1201 if (n3 == NULL) goto err;
1203 /* Note that in this function we must not read components of 'a'
1204 * once we have written the corresponding components of 'r'.
1205 * ('r' might the same as 'a'.)
1211 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1212 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1213 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1214 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1215 /* n1 = 3 * X_a^2 + a_curve */
1217 else if (group->a_is_minus3)
1219 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1220 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1221 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1222 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1223 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1224 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1225 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1226 * = 3 * X_a^2 - 3 * Z_a^4 */
1230 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1231 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1232 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1233 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1234 if (!field_sqr(group, n1, n1, ctx)) goto err;
1235 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1236 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1237 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1243 if (!BN_copy(n0, &a->Y)) goto err;
1247 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1249 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1251 /* Z_r = 2 * Y_a * Z_a */
1254 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1255 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1256 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1257 /* n2 = 4 * X_a * Y_a^2 */
1260 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1261 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1262 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1263 /* X_r = n1^2 - 2 * n2 */
1266 if (!field_sqr(group, n0, n3, ctx)) goto err;
1267 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1268 /* n3 = 8 * Y_a^4 */
1271 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1272 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1273 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1274 /* Y_r = n1 * (n2 - X_r) - n3 */
1280 if (new_ctx != NULL)
1281 BN_CTX_free(new_ctx);
1286 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1288 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1289 /* point is its own inverse */
1292 return BN_usub(&point->Y, &group->field, &point->Y);
1296 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1298 return BN_is_zero(&point->Z);
1302 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1304 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1305 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1307 BN_CTX *new_ctx = NULL;
1308 BIGNUM *rh, *tmp, *Z4, *Z6;
1311 if (EC_POINT_is_at_infinity(group, point))
1314 field_mul = group->meth->field_mul;
1315 field_sqr = group->meth->field_sqr;
1320 ctx = new_ctx = BN_CTX_new();
1326 rh = BN_CTX_get(ctx);
1327 tmp = BN_CTX_get(ctx);
1328 Z4 = BN_CTX_get(ctx);
1329 Z6 = BN_CTX_get(ctx);
1330 if (Z6 == NULL) goto err;
1333 * We have a curve defined by a Weierstrass equation
1334 * y^2 = x^3 + a*x + b.
1335 * The point to consider is given in Jacobian projective coordinates
1336 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1337 * Substituting this and multiplying by Z^6 transforms the above equation into
1338 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1339 * To test this, we add up the right-hand side in 'rh'.
1343 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1345 if (!point->Z_is_one)
1347 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
1348 if (!field_sqr(group, Z4, tmp, ctx)) goto err;
1349 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
1351 /* rh := (rh + a*Z^4)*X */
1352 if (group->a_is_minus3)
1354 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
1355 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
1356 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
1357 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1361 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
1362 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1363 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1366 /* rh := rh + b*Z^6 */
1367 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
1368 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1372 /* point->Z_is_one */
1374 /* rh := (rh + a)*X */
1375 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
1376 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1378 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1382 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
1384 ret = (0 == BN_ucmp(tmp, rh));
1388 if (new_ctx != NULL)
1389 BN_CTX_free(new_ctx);
1394 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1398 * 0 equal (in affine coordinates)
1402 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1403 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1404 BN_CTX *new_ctx = NULL;
1405 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1406 const BIGNUM *tmp1_, *tmp2_;
1409 if (EC_POINT_is_at_infinity(group, a))
1411 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1414 if (EC_POINT_is_at_infinity(group, b))
1417 if (a->Z_is_one && b->Z_is_one)
1419 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1422 field_mul = group->meth->field_mul;
1423 field_sqr = group->meth->field_sqr;
1427 ctx = new_ctx = BN_CTX_new();
1433 tmp1 = BN_CTX_get(ctx);
1434 tmp2 = BN_CTX_get(ctx);
1435 Za23 = BN_CTX_get(ctx);
1436 Zb23 = BN_CTX_get(ctx);
1437 if (Zb23 == NULL) goto end;
1440 * We have to decide whether
1441 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1442 * or equivalently, whether
1443 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1448 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1449 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1456 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1457 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1463 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1464 if (BN_cmp(tmp1_, tmp2_) != 0)
1466 ret = 1; /* points differ */
1473 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1474 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1481 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1482 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1488 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1489 if (BN_cmp(tmp1_, tmp2_) != 0)
1491 ret = 1; /* points differ */
1495 /* points are equal */
1500 if (new_ctx != NULL)
1501 BN_CTX_free(new_ctx);
1506 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1508 BN_CTX *new_ctx = NULL;
1512 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1517 ctx = new_ctx = BN_CTX_new();
1523 x = BN_CTX_get(ctx);
1524 y = BN_CTX_get(ctx);
1525 if (y == NULL) goto err;
1527 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1528 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1529 if (!point->Z_is_one)
1531 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1539 if (new_ctx != NULL)
1540 BN_CTX_free(new_ctx);
1545 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1547 BN_CTX *new_ctx = NULL;
1548 BIGNUM *tmp, *tmp_Z;
1549 BIGNUM **prod_Z = NULL;
1558 ctx = new_ctx = BN_CTX_new();
1564 tmp = BN_CTX_get(ctx);
1565 tmp_Z = BN_CTX_get(ctx);
1566 if (tmp == NULL || tmp_Z == NULL) goto err;
1568 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1569 if (prod_Z == NULL) goto err;
1570 for (i = 0; i < num; i++)
1572 prod_Z[i] = BN_new();
1573 if (prod_Z[i] == NULL) goto err;
1576 /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1577 * skipping any zero-valued inputs (pretend that they're 1). */
1579 if (!BN_is_zero(&points[0]->Z))
1581 if (!BN_copy(prod_Z[0], &points[0]->Z)) goto err;
1585 if (group->meth->field_set_to_one != 0)
1587 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
1591 if (!BN_one(prod_Z[0])) goto err;
1595 for (i = 1; i < num; i++)
1597 if (!BN_is_zero(&points[i]->Z))
1599 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], &points[i]->Z, ctx)) goto err;
1603 if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
1607 /* Now use a single explicit inversion to replace every
1608 * non-zero points[i]->Z by its inverse. */
1610 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx))
1612 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1615 if (group->meth->field_encode != 0)
1617 /* In the Montgomery case, we just turned R*H (representing H)
1618 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1619 * i.e. we need to multiply by the Montgomery factor twice. */
1620 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1621 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1624 for (i = num - 1; i > 0; --i)
1626 /* Loop invariant: tmp is the product of the inverses of
1627 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
1628 if (!BN_is_zero(&points[i]->Z))
1630 /* Set tmp_Z to the inverse of points[i]->Z (as product
1631 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
1632 if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
1633 /* Update tmp to satisfy the loop invariant for i - 1. */
1634 if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) goto err;
1635 /* Replace points[i]->Z by its inverse. */
1636 if (!BN_copy(&points[i]->Z, tmp_Z)) goto err;
1640 if (!BN_is_zero(&points[0]->Z))
1642 /* Replace points[0]->Z by its inverse. */
1643 if (!BN_copy(&points[0]->Z, tmp)) goto err;
1646 /* Finally, fix up the X and Y coordinates for all points. */
1648 for (i = 0; i < num; i++)
1650 EC_POINT *p = points[i];
1652 if (!BN_is_zero(&p->Z))
1654 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1656 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) goto err;
1657 if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) goto err;
1659 if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) goto err;
1660 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) goto err;
1662 if (group->meth->field_set_to_one != 0)
1664 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1668 if (!BN_one(&p->Z)) goto err;
1678 if (new_ctx != NULL)
1679 BN_CTX_free(new_ctx);
1682 for (i = 0; i < num; i++)
1684 if (prod_Z[i] == NULL) break;
1685 BN_clear_free(prod_Z[i]);
1687 OPENSSL_free(prod_Z);
1693 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1695 return BN_mod_mul(r, a, b, &group->field, ctx);
1699 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1701 return BN_mod_sqr(r, a, &group->field, ctx);