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 /* ====================================================================
5 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
33 * 6. Redistributions of any form whatsoever must retain the following
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
57 /* ====================================================================
58 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
59 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
60 * and contributed to the OpenSSL project.
63 #include <openssl/err.h>
64 #include <openssl/symhacks.h>
68 const EC_METHOD *EC_GFp_simple_method(void)
70 static const EC_METHOD ret = {
71 NID_X9_62_prime_field,
72 ec_GFp_simple_group_init,
73 ec_GFp_simple_group_finish,
74 ec_GFp_simple_group_clear_finish,
75 ec_GFp_simple_group_copy,
76 ec_GFp_simple_group_set_curve_GFp,
77 ec_GFp_simple_group_get_curve_GFp,
78 ec_GFp_simple_group_get_degree,
79 ec_GFp_simple_group_check_discriminant,
80 ec_GFp_simple_point_init,
81 ec_GFp_simple_point_finish,
82 ec_GFp_simple_point_clear_finish,
83 ec_GFp_simple_point_copy,
84 ec_GFp_simple_point_set_to_infinity,
85 ec_GFp_simple_set_Jprojective_coordinates_GFp,
86 ec_GFp_simple_get_Jprojective_coordinates_GFp,
87 ec_GFp_simple_point_set_affine_coordinates_GFp,
88 ec_GFp_simple_point_get_affine_coordinates_GFp,
89 ec_GFp_simple_set_compressed_coordinates_GFp,
90 ec_GFp_simple_point2oct,
91 ec_GFp_simple_oct2point,
96 0 /* precompute_mult */,
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,
102 ec_GFp_simple_field_mul,
103 ec_GFp_simple_field_sqr,
105 0 /* field_encode */,
106 0 /* field_decode */,
107 0 /* field_set_to_one */ };
113 int ec_GFp_simple_group_init(EC_GROUP *group)
115 BN_init(&group->field);
118 group->a_is_minus3 = 0;
123 void ec_GFp_simple_group_finish(EC_GROUP *group)
125 BN_free(&group->field);
131 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
133 BN_clear_free(&group->field);
134 BN_clear_free(&group->a);
135 BN_clear_free(&group->b);
139 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
141 if (!BN_copy(&dest->field, &src->field)) return 0;
142 if (!BN_copy(&dest->a, &src->a)) return 0;
143 if (!BN_copy(&dest->b, &src->b)) return 0;
145 dest->a_is_minus3 = src->a_is_minus3;
151 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
152 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
155 BN_CTX *new_ctx = NULL;
158 /* p must be a prime > 3 */
159 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
161 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
167 ctx = new_ctx = BN_CTX_new();
173 tmp_a = BN_CTX_get(ctx);
174 if (tmp_a == NULL) goto err;
177 if (!BN_copy(&group->field, p)) goto err;
178 group->field.neg = 0;
181 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
182 if (group->meth->field_encode)
183 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
185 if (!BN_copy(&group->a, tmp_a)) goto err;
188 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
189 if (group->meth->field_encode)
190 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
192 /* group->a_is_minus3 */
193 if (!BN_add_word(tmp_a, 3)) goto err;
194 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
201 BN_CTX_free(new_ctx);
206 int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
209 BN_CTX *new_ctx = NULL;
213 if (!BN_copy(p, &group->field)) return 0;
216 if (a != NULL || b != NULL)
218 if (group->meth->field_decode)
222 ctx = new_ctx = BN_CTX_new();
228 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
232 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
239 if (!BN_copy(a, &group->a)) goto err;
243 if (!BN_copy(b, &group->b)) goto err;
252 BN_CTX_free(new_ctx);
257 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
259 return BN_num_bits(&group->field);
263 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
266 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
267 const BIGNUM *p = &group->field;
268 BN_CTX *new_ctx = NULL;
272 ctx = new_ctx = BN_CTX_new();
275 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
282 tmp_1 = BN_CTX_get(ctx);
283 tmp_2 = BN_CTX_get(ctx);
284 order = BN_CTX_get(ctx);
285 if (order == NULL) goto err;
287 if (group->meth->field_decode)
289 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
290 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
294 if (!BN_copy(a, &group->a)) goto err;
295 if (!BN_copy(b, &group->b)) goto err;
298 /* check the discriminant:
299 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
303 if (BN_is_zero(b)) goto err;
305 else if (!BN_is_zero(b))
307 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
308 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
309 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
312 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
313 if (!BN_mul_word(tmp_2, 27)) goto err;
316 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
317 if (BN_is_zero(a)) goto err;
324 BN_CTX_free(new_ctx);
329 int ec_GFp_simple_point_init(EC_POINT *point)
340 void ec_GFp_simple_point_finish(EC_POINT *point)
348 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
350 BN_clear_free(&point->X);
351 BN_clear_free(&point->Y);
352 BN_clear_free(&point->Z);
357 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
359 if (!BN_copy(&dest->X, &src->X)) return 0;
360 if (!BN_copy(&dest->Y, &src->Y)) return 0;
361 if (!BN_copy(&dest->Z, &src->Z)) return 0;
362 dest->Z_is_one = src->Z_is_one;
368 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
371 return (BN_zero(&point->Z));
375 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
376 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
378 BN_CTX *new_ctx = NULL;
383 ctx = new_ctx = BN_CTX_new();
390 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
391 if (group->meth->field_encode)
393 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
399 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
400 if (group->meth->field_encode)
402 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
410 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
411 Z_is_one = BN_is_one(&point->Z);
412 if (group->meth->field_encode)
414 if (Z_is_one && (group->meth->field_set_to_one != 0))
416 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
420 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
423 point->Z_is_one = Z_is_one;
430 BN_CTX_free(new_ctx);
435 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
436 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
438 BN_CTX *new_ctx = NULL;
441 if (group->meth->field_decode != 0)
445 ctx = new_ctx = BN_CTX_new();
452 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
456 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
460 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
467 if (!BN_copy(x, &point->X)) goto err;
471 if (!BN_copy(y, &point->Y)) goto err;
475 if (!BN_copy(z, &point->Z)) goto err;
483 BN_CTX_free(new_ctx);
488 int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
489 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
491 if (x == NULL || y == NULL)
493 /* unlike for projective coordinates, we do not tolerate this */
494 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
498 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
502 int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
503 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
505 BN_CTX *new_ctx = NULL;
506 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
507 const BIGNUM *X_, *Y_, *Z_;
510 if (EC_POINT_is_at_infinity(group, point))
512 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
518 ctx = new_ctx = BN_CTX_new();
527 Z_1 = BN_CTX_get(ctx);
528 Z_2 = BN_CTX_get(ctx);
529 Z_3 = BN_CTX_get(ctx);
530 if (Z_3 == NULL) goto err;
532 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
534 if (group->meth->field_decode)
536 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
537 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
538 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
539 X_ = X; Y_ = Y; Z_ = Z;
552 if (!BN_copy(x, X_)) goto err;
556 if (!BN_copy(y, Y_)) goto err;
561 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
563 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
567 if (group->meth->field_encode == 0)
569 /* field_sqr works on standard representation */
570 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
574 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
579 if (group->meth->field_encode == 0)
581 /* field_mul works on standard representation */
582 if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
586 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
592 if (group->meth->field_encode == 0)
594 /* field_mul works on standard representation */
595 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
596 if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
601 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
602 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
612 BN_CTX_free(new_ctx);
617 int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
618 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
620 BN_CTX *new_ctx = NULL;
621 BIGNUM *tmp1, *tmp2, *x, *y;
626 ctx = new_ctx = BN_CTX_new();
631 y_bit = (y_bit != 0);
634 tmp1 = BN_CTX_get(ctx);
635 tmp2 = BN_CTX_get(ctx);
638 if (y == NULL) goto err;
640 /* Recover y. We have a Weierstrass equation
641 * y^2 = x^3 + a*x + b,
642 * so y is one of the square roots of x^3 + a*x + b.
646 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
647 if (group->meth->field_decode == 0)
649 /* field_{sqr,mul} work on standard representation */
650 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
651 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
655 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
656 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
659 /* tmp1 := tmp1 + a*x */
660 if (group->a_is_minus3)
662 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
663 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
664 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
668 if (group->meth->field_decode)
670 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
671 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
675 /* field_mul works on standard representation */
676 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
679 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
682 /* tmp1 := tmp1 + b */
683 if (group->meth->field_decode)
685 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
686 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
690 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
693 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
695 unsigned long err = ERR_peek_error();
697 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
699 (void)ERR_get_error();
700 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
703 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_BN_LIB);
706 /* If tmp1 is not a square (i.e. there is no point on the curve with
707 * our x), then y now is a nonsense value too */
709 if (y_bit != BN_is_odd(y))
715 kron = BN_kronecker(x, &group->field, ctx);
716 if (kron == -2) goto err;
719 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
721 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
724 if (!BN_usub(y, &group->field, y)) goto err;
726 if (y_bit != BN_is_odd(y))
728 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_INTERNAL_ERROR);
732 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
739 BN_CTX_free(new_ctx);
744 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
745 unsigned char *buf, size_t len, BN_CTX *ctx)
748 BN_CTX *new_ctx = NULL;
751 size_t field_len, i, skip;
753 if ((form != POINT_CONVERSION_COMPRESSED)
754 && (form != POINT_CONVERSION_UNCOMPRESSED)
755 && (form != POINT_CONVERSION_HYBRID))
757 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
761 if (EC_POINT_is_at_infinity(group, point))
763 /* encodes to a single 0 octet */
768 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
777 /* ret := required output buffer length */
778 field_len = BN_num_bytes(&group->field);
779 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
781 /* if 'buf' is NULL, just return required length */
786 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
792 ctx = new_ctx = BN_CTX_new();
801 if (y == NULL) goto err;
803 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
805 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
812 skip = field_len - BN_num_bytes(x);
813 if (skip > field_len)
815 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
823 skip = BN_bn2bin(x, buf + i);
825 if (i != 1 + field_len)
827 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
831 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
833 skip = field_len - BN_num_bytes(y);
834 if (skip > field_len)
836 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
844 skip = BN_bn2bin(y, buf + i);
850 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
858 BN_CTX_free(new_ctx);
865 BN_CTX_free(new_ctx);
870 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
871 const unsigned char *buf, size_t len, BN_CTX *ctx)
873 point_conversion_form_t form;
875 BN_CTX *new_ctx = NULL;
877 size_t field_len, enc_len;
882 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
888 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
889 && (form != POINT_CONVERSION_UNCOMPRESSED)
890 && (form != POINT_CONVERSION_HYBRID))
892 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
895 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
897 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
905 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
909 return EC_POINT_set_to_infinity(group, point);
912 field_len = BN_num_bytes(&group->field);
913 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
917 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
923 ctx = new_ctx = BN_CTX_new();
931 if (y == NULL) goto err;
933 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
934 if (BN_ucmp(x, &group->field) >= 0)
936 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
940 if (form == POINT_CONVERSION_COMPRESSED)
942 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
946 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
947 if (BN_ucmp(y, &group->field) >= 0)
949 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
952 if (form == POINT_CONVERSION_HYBRID)
954 if (y_bit != BN_is_odd(y))
956 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
961 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
964 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
966 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
975 BN_CTX_free(new_ctx);
980 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
982 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
983 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
985 BN_CTX *new_ctx = NULL;
986 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
990 return EC_POINT_dbl(group, r, a, ctx);
991 if (EC_POINT_is_at_infinity(group, a))
992 return EC_POINT_copy(r, b);
993 if (EC_POINT_is_at_infinity(group, b))
994 return EC_POINT_copy(r, a);
996 field_mul = group->meth->field_mul;
997 field_sqr = group->meth->field_sqr;
1002 ctx = new_ctx = BN_CTX_new();
1008 n0 = BN_CTX_get(ctx);
1009 n1 = BN_CTX_get(ctx);
1010 n2 = BN_CTX_get(ctx);
1011 n3 = BN_CTX_get(ctx);
1012 n4 = BN_CTX_get(ctx);
1013 n5 = BN_CTX_get(ctx);
1014 n6 = BN_CTX_get(ctx);
1015 if (n6 == NULL) goto end;
1017 /* Note that in this function we must not read components of 'a' or 'b'
1018 * once we have written the corresponding components of 'r'.
1019 * ('r' might be one of 'a' or 'b'.)
1025 if (!BN_copy(n1, &a->X)) goto end;
1026 if (!BN_copy(n2, &a->Y)) goto end;
1032 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1033 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1034 /* n1 = X_a * Z_b^2 */
1036 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1037 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1038 /* n2 = Y_a * Z_b^3 */
1044 if (!BN_copy(n3, &b->X)) goto end;
1045 if (!BN_copy(n4, &b->Y)) goto end;
1051 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1052 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1053 /* n3 = X_b * Z_a^2 */
1055 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1056 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1057 /* n4 = Y_b * Z_a^3 */
1061 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1062 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1070 /* a is the same point as b */
1072 ret = EC_POINT_dbl(group, r, a, ctx);
1078 /* a is the inverse of b */
1079 if (!BN_zero(&r->Z)) goto end;
1087 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1088 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1089 /* 'n7' = n1 + n3 */
1090 /* 'n8' = n2 + n4 */
1093 if (a->Z_is_one && b->Z_is_one)
1095 if (!BN_copy(&r->Z, n5)) goto end;
1100 { if (!BN_copy(n0, &b->Z)) goto end; }
1101 else if (b->Z_is_one)
1102 { if (!BN_copy(n0, &a->Z)) goto end; }
1104 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1105 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1108 /* Z_r = Z_a * Z_b * n5 */
1111 if (!field_sqr(group, n0, n6, ctx)) goto end;
1112 if (!field_sqr(group, n4, n5, ctx)) goto end;
1113 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1114 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1115 /* X_r = n6^2 - n5^2 * 'n7' */
1118 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1119 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1120 /* n9 = n5^2 * 'n7' - 2 * X_r */
1123 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1124 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1125 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1126 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1128 if (!BN_add(n0, n0, p)) goto end;
1129 /* now 0 <= n0 < 2*p, and n0 is even */
1130 if (!BN_rshift1(&r->Y, n0)) goto end;
1131 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1136 if (ctx) /* otherwise we already called BN_CTX_end */
1138 if (new_ctx != NULL)
1139 BN_CTX_free(new_ctx);
1144 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1146 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1147 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1149 BN_CTX *new_ctx = NULL;
1150 BIGNUM *n0, *n1, *n2, *n3;
1153 if (EC_POINT_is_at_infinity(group, a))
1155 if (!BN_zero(&r->Z)) return 0;
1160 field_mul = group->meth->field_mul;
1161 field_sqr = group->meth->field_sqr;
1166 ctx = new_ctx = BN_CTX_new();
1172 n0 = BN_CTX_get(ctx);
1173 n1 = BN_CTX_get(ctx);
1174 n2 = BN_CTX_get(ctx);
1175 n3 = BN_CTX_get(ctx);
1176 if (n3 == NULL) goto err;
1178 /* Note that in this function we must not read components of 'a'
1179 * once we have written the corresponding components of 'r'.
1180 * ('r' might the same as 'a'.)
1186 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1187 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1188 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1189 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1190 /* n1 = 3 * X_a^2 + a_curve */
1192 else if (group->a_is_minus3)
1194 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1195 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1196 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1197 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1198 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1199 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1200 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1201 * = 3 * X_a^2 - 3 * Z_a^4 */
1205 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1206 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1207 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1208 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1209 if (!field_sqr(group, n1, n1, ctx)) goto err;
1210 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1211 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1212 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1218 if (!BN_copy(n0, &a->Y)) goto err;
1222 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1224 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1226 /* Z_r = 2 * Y_a * Z_a */
1229 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1230 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1231 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1232 /* n2 = 4 * X_a * Y_a^2 */
1235 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1236 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1237 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1238 /* X_r = n1^2 - 2 * n2 */
1241 if (!field_sqr(group, n0, n3, ctx)) goto err;
1242 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1243 /* n3 = 8 * Y_a^4 */
1246 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1247 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1248 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1249 /* Y_r = n1 * (n2 - X_r) - n3 */
1255 if (new_ctx != NULL)
1256 BN_CTX_free(new_ctx);
1261 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1263 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1264 /* point is its own inverse */
1267 return BN_usub(&point->Y, &group->field, &point->Y);
1271 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1273 return BN_is_zero(&point->Z);
1277 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1279 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1280 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1282 BN_CTX *new_ctx = NULL;
1283 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1286 if (EC_POINT_is_at_infinity(group, point))
1289 field_mul = group->meth->field_mul;
1290 field_sqr = group->meth->field_sqr;
1295 ctx = new_ctx = BN_CTX_new();
1301 rh = BN_CTX_get(ctx);
1302 tmp1 = BN_CTX_get(ctx);
1303 tmp2 = BN_CTX_get(ctx);
1304 Z4 = BN_CTX_get(ctx);
1305 Z6 = BN_CTX_get(ctx);
1306 if (Z6 == NULL) goto err;
1308 /* We have a curve defined by a Weierstrass equation
1309 * y^2 = x^3 + a*x + b.
1310 * The point to consider is given in Jacobian projective coordinates
1311 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1312 * Substituting this and multiplying by Z^6 transforms the above equation into
1313 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1314 * To test this, we add up the right-hand side in 'rh'.
1318 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1319 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1321 if (!point->Z_is_one)
1323 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1324 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1325 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1327 /* rh := rh + a*X*Z^4 */
1328 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1329 if (group->a_is_minus3)
1331 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1332 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1333 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1337 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1338 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1341 /* rh := rh + b*Z^6 */
1342 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1343 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1347 /* point->Z_is_one */
1349 /* rh := rh + a*X */
1350 if (group->a_is_minus3)
1352 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1353 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1354 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1358 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1359 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1363 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1367 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1369 ret = (0 == BN_cmp(tmp1, rh));
1373 if (new_ctx != NULL)
1374 BN_CTX_free(new_ctx);
1379 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1383 * 0 equal (in affine coordinates)
1387 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1388 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1389 BN_CTX *new_ctx = NULL;
1390 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1391 const BIGNUM *tmp1_, *tmp2_;
1394 if (EC_POINT_is_at_infinity(group, a))
1396 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1399 if (a->Z_is_one && b->Z_is_one)
1401 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1404 field_mul = group->meth->field_mul;
1405 field_sqr = group->meth->field_sqr;
1409 ctx = new_ctx = BN_CTX_new();
1415 tmp1 = BN_CTX_get(ctx);
1416 tmp2 = BN_CTX_get(ctx);
1417 Za23 = BN_CTX_get(ctx);
1418 Zb23 = BN_CTX_get(ctx);
1419 if (Zb23 == NULL) goto end;
1421 /* We have to decide whether
1422 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1423 * or equivalently, whether
1424 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1429 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1430 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1437 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1438 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1444 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1445 if (BN_cmp(tmp1_, tmp2_) != 0)
1447 ret = 1; /* points differ */
1454 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1455 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1462 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1463 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1469 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1470 if (BN_cmp(tmp1_, tmp2_) != 0)
1472 ret = 1; /* points differ */
1476 /* points are equal */
1481 if (new_ctx != NULL)
1482 BN_CTX_free(new_ctx);
1487 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1489 BN_CTX *new_ctx = NULL;
1493 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1498 ctx = new_ctx = BN_CTX_new();
1504 x = BN_CTX_get(ctx);
1505 y = BN_CTX_get(ctx);
1506 if (y == NULL) goto err;
1508 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1509 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1510 if (!point->Z_is_one)
1512 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1520 if (new_ctx != NULL)
1521 BN_CTX_free(new_ctx);
1526 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1528 BN_CTX *new_ctx = NULL;
1529 BIGNUM *tmp0, *tmp1;
1531 BIGNUM **heap = NULL;
1540 ctx = new_ctx = BN_CTX_new();
1546 tmp0 = BN_CTX_get(ctx);
1547 tmp1 = BN_CTX_get(ctx);
1548 if (tmp0 == NULL || tmp1 == NULL) goto err;
1550 /* Before converting the individual points, compute inverses of all Z values.
1551 * Modular inversion is rather slow, but luckily we can do with a single
1552 * explicit inversion, plus about 3 multiplications per input value.
1558 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1559 * We need twice that. */
1562 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1563 if (heap == NULL) goto err;
1565 /* The array is used as a binary tree, exactly as in heapsort:
1569 * heap[4] heap[5] heap[6] heap[7]
1570 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1572 * We put the Z's in the last line;
1573 * then we set each other node to the product of its two child-nodes (where
1574 * empty or 0 entries are treated as ones);
1575 * then we invert heap[1];
1576 * then we invert each other node by replacing it by the product of its
1577 * parent (after inversion) and its sibling (before inversion).
1580 for (i = pow2/2 - 1; i > 0; i--)
1582 for (i = 0; i < num; i++)
1583 heap[pow2/2 + i] = &points[i]->Z;
1584 for (i = pow2/2 + num; i < pow2; i++)
1587 /* set each node to the product of its children */
1588 for (i = pow2/2 - 1; i > 0; i--)
1591 if (heap[i] == NULL) goto err;
1593 if (heap[2*i] != NULL)
1595 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1597 if (!BN_copy(heap[i], heap[2*i])) goto err;
1601 if (BN_is_zero(heap[2*i]))
1603 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1607 if (!group->meth->field_mul(group, heap[i],
1608 heap[2*i], heap[2*i + 1], ctx)) goto err;
1614 /* invert heap[1] */
1615 if (!BN_is_zero(heap[1]))
1617 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1619 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1623 if (group->meth->field_encode != 0)
1625 /* in the Montgomery case, we just turned R*H (representing H)
1626 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1627 * i.e. we have need to multiply by the Montgomery factor twice */
1628 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1629 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1632 /* set other heap[i]'s to their inverses */
1633 for (i = 2; i < pow2/2 + num; i += 2)
1636 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1638 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1639 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1640 if (!BN_copy(heap[i], tmp0)) goto err;
1641 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1645 if (!BN_copy(heap[i], heap[i/2])) goto err;
1649 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1650 for (i = 0; i < num; i++)
1652 EC_POINT *p = points[i];
1654 if (!BN_is_zero(&p->Z))
1656 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1658 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1659 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1661 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1662 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1664 if (group->meth->field_set_to_one != 0)
1666 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1670 if (!BN_one(&p->Z)) goto err;
1680 if (new_ctx != NULL)
1681 BN_CTX_free(new_ctx);
1684 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1685 for (i = pow2/2 - 1; i > 0; i--)
1687 if (heap[i] != NULL)
1688 BN_clear_free(heap[i]);
1696 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1698 return BN_mod_mul(r, a, b, &group->field, ctx);
1702 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1704 return BN_mod_sqr(r, a, &group->field, ctx);