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,
98 0 /* precompute_mult */,
99 ec_GFp_simple_is_at_infinity,
100 ec_GFp_simple_is_on_curve,
102 ec_GFp_simple_make_affine,
103 ec_GFp_simple_points_make_affine,
104 ec_GFp_simple_field_mul,
105 ec_GFp_simple_field_sqr,
107 0 /* field_encode */,
108 0 /* field_decode */,
109 0 /* field_set_to_one */ };
115 /* Most method functions in this file are designed to work with
116 * non-trivial representations of field elements if necessary
117 * (see ecp_mont.c): while standard modular addition and subtraction
118 * are used, the field_mul and field_sqr methods will be used for
119 * multiplication, and field_encode and field_decode (if defined)
120 * will be used for converting between representations.
122 * Functions ec_GFp_simple_points_make_affine() and
123 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
124 * that if a non-trivial representation is used, it is a Montgomery
125 * representation (i.e. 'encoding' means multiplying by some factor R).
129 int ec_GFp_simple_group_init(EC_GROUP *group)
131 BN_init(&group->field);
134 group->a_is_minus3 = 0;
139 void ec_GFp_simple_group_finish(EC_GROUP *group)
141 BN_free(&group->field);
147 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
149 BN_clear_free(&group->field);
150 BN_clear_free(&group->a);
151 BN_clear_free(&group->b);
155 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
157 if (!BN_copy(&dest->field, &src->field)) return 0;
158 if (!BN_copy(&dest->a, &src->a)) return 0;
159 if (!BN_copy(&dest->b, &src->b)) return 0;
161 dest->a_is_minus3 = src->a_is_minus3;
167 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
168 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
171 BN_CTX *new_ctx = NULL;
174 /* p must be a prime > 3 */
175 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
177 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
183 ctx = new_ctx = BN_CTX_new();
189 tmp_a = BN_CTX_get(ctx);
190 if (tmp_a == NULL) goto err;
193 if (!BN_copy(&group->field, p)) goto err;
194 BN_set_sign(&group->field, 0);
197 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
198 if (group->meth->field_encode)
199 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
201 if (!BN_copy(&group->a, tmp_a)) goto err;
204 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
205 if (group->meth->field_encode)
206 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
208 /* group->a_is_minus3 */
209 if (!BN_add_word(tmp_a, 3)) goto err;
210 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
217 BN_CTX_free(new_ctx);
222 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
225 BN_CTX *new_ctx = NULL;
229 if (!BN_copy(p, &group->field)) return 0;
232 if (a != NULL || b != NULL)
234 if (group->meth->field_decode)
238 ctx = new_ctx = BN_CTX_new();
244 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
248 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
255 if (!BN_copy(a, &group->a)) goto err;
259 if (!BN_copy(b, &group->b)) goto err;
268 BN_CTX_free(new_ctx);
273 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
275 return BN_num_bits(&group->field);
279 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
282 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
283 const BIGNUM *p = &group->field;
284 BN_CTX *new_ctx = NULL;
288 ctx = new_ctx = BN_CTX_new();
291 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
298 tmp_1 = BN_CTX_get(ctx);
299 tmp_2 = BN_CTX_get(ctx);
300 order = BN_CTX_get(ctx);
301 if (order == NULL) goto err;
303 if (group->meth->field_decode)
305 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
306 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
310 if (!BN_copy(a, &group->a)) goto err;
311 if (!BN_copy(b, &group->b)) goto err;
314 /* check the discriminant:
315 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
319 if (BN_is_zero(b)) goto err;
321 else if (!BN_is_zero(b))
323 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
324 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
325 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
328 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
329 if (!BN_mul_word(tmp_2, 27)) goto err;
332 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
333 if (BN_is_zero(a)) goto err;
340 BN_CTX_free(new_ctx);
345 int ec_GFp_simple_point_init(EC_POINT *point)
356 void ec_GFp_simple_point_finish(EC_POINT *point)
364 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
366 BN_clear_free(&point->X);
367 BN_clear_free(&point->Y);
368 BN_clear_free(&point->Z);
373 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
375 if (!BN_copy(&dest->X, &src->X)) return 0;
376 if (!BN_copy(&dest->Y, &src->Y)) return 0;
377 if (!BN_copy(&dest->Z, &src->Z)) return 0;
378 dest->Z_is_one = src->Z_is_one;
384 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
387 return (BN_zero(&point->Z));
391 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
392 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
394 BN_CTX *new_ctx = NULL;
399 ctx = new_ctx = BN_CTX_new();
406 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
407 if (group->meth->field_encode)
409 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
415 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
416 if (group->meth->field_encode)
418 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
426 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
427 Z_is_one = BN_is_one(&point->Z);
428 if (group->meth->field_encode)
430 if (Z_is_one && (group->meth->field_set_to_one != 0))
432 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
436 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
439 point->Z_is_one = Z_is_one;
446 BN_CTX_free(new_ctx);
451 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
452 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
454 BN_CTX *new_ctx = NULL;
457 if (group->meth->field_decode != 0)
461 ctx = new_ctx = BN_CTX_new();
468 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
472 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
476 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
483 if (!BN_copy(x, &point->X)) goto err;
487 if (!BN_copy(y, &point->Y)) goto err;
491 if (!BN_copy(z, &point->Z)) goto err;
499 BN_CTX_free(new_ctx);
504 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
505 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
507 if (x == NULL || y == NULL)
509 /* unlike for projective coordinates, we do not tolerate this */
510 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
514 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
518 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
519 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
521 BN_CTX *new_ctx = NULL;
522 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
526 if (EC_POINT_is_at_infinity(group, point))
528 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
534 ctx = new_ctx = BN_CTX_new();
541 Z_1 = BN_CTX_get(ctx);
542 Z_2 = BN_CTX_get(ctx);
543 Z_3 = BN_CTX_get(ctx);
544 if (Z_3 == NULL) goto err;
546 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
548 if (group->meth->field_decode)
550 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
560 if (group->meth->field_decode)
564 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
568 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
575 if (!BN_copy(x, &point->X)) goto err;
579 if (!BN_copy(y, &point->Y)) goto err;
585 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
587 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
591 if (group->meth->field_encode == 0)
593 /* field_sqr works on standard representation */
594 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
598 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
603 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
604 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
609 if (group->meth->field_encode == 0)
611 /* field_mul works on standard representation */
612 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
616 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
619 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
620 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
629 BN_CTX_free(new_ctx);
634 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
635 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
637 BN_CTX *new_ctx = NULL;
638 BIGNUM *tmp1, *tmp2, *x, *y;
643 ctx = new_ctx = BN_CTX_new();
648 y_bit = (y_bit != 0);
651 tmp1 = BN_CTX_get(ctx);
652 tmp2 = BN_CTX_get(ctx);
655 if (y == NULL) goto err;
657 /* Recover y. We have a Weierstrass equation
658 * y^2 = x^3 + a*x + b,
659 * so y is one of the square roots of x^3 + a*x + b.
663 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
664 if (group->meth->field_decode == 0)
666 /* field_{sqr,mul} work on standard representation */
667 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
668 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
672 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
673 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
676 /* tmp1 := tmp1 + a*x */
677 if (group->a_is_minus3)
679 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
680 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
681 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
685 if (group->meth->field_decode)
687 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
688 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
692 /* field_mul works on standard representation */
693 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
696 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
699 /* tmp1 := tmp1 + b */
700 if (group->meth->field_decode)
702 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
703 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
707 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
710 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
712 unsigned long err = ERR_peek_error();
714 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
716 (void)ERR_get_error();
717 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
720 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
724 if (y_bit != BN_is_odd(y))
730 kron = BN_kronecker(x, &group->field, ctx);
731 if (kron == -2) goto err;
734 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
736 /* BN_mod_sqrt() should have cought this error (not a square) */
737 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
740 if (!BN_usub(y, &group->field, y)) goto err;
742 if (y_bit != BN_is_odd(y))
744 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
748 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
755 BN_CTX_free(new_ctx);
760 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
761 unsigned char *buf, size_t len, BN_CTX *ctx)
764 BN_CTX *new_ctx = NULL;
767 size_t field_len, i, skip;
769 if ((form != POINT_CONVERSION_COMPRESSED)
770 && (form != POINT_CONVERSION_UNCOMPRESSED)
771 && (form != POINT_CONVERSION_HYBRID))
773 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
777 if (EC_POINT_is_at_infinity(group, point))
779 /* encodes to a single 0 octet */
784 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
793 /* ret := required output buffer length */
794 field_len = BN_num_bytes(&group->field);
795 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
797 /* if 'buf' is NULL, just return required length */
802 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
808 ctx = new_ctx = BN_CTX_new();
817 if (y == NULL) goto err;
819 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
821 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
828 skip = field_len - BN_num_bytes(x);
829 if (skip > field_len)
831 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
839 skip = BN_bn2bin(x, buf + i);
841 if (i != 1 + field_len)
843 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
847 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
849 skip = field_len - BN_num_bytes(y);
850 if (skip > field_len)
852 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
860 skip = BN_bn2bin(y, buf + i);
866 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
874 BN_CTX_free(new_ctx);
881 BN_CTX_free(new_ctx);
886 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
887 const unsigned char *buf, size_t len, BN_CTX *ctx)
889 point_conversion_form_t form;
891 BN_CTX *new_ctx = NULL;
893 size_t field_len, enc_len;
898 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
904 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
905 && (form != POINT_CONVERSION_UNCOMPRESSED)
906 && (form != POINT_CONVERSION_HYBRID))
908 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
911 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
913 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
921 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
925 return EC_POINT_set_to_infinity(group, point);
928 field_len = BN_num_bytes(&group->field);
929 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
933 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
939 ctx = new_ctx = BN_CTX_new();
947 if (y == NULL) goto err;
949 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
950 if (BN_ucmp(x, &group->field) >= 0)
952 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
956 if (form == POINT_CONVERSION_COMPRESSED)
958 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
962 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
963 if (BN_ucmp(y, &group->field) >= 0)
965 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
968 if (form == POINT_CONVERSION_HYBRID)
970 if (y_bit != BN_is_odd(y))
972 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
977 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
980 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
982 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
991 BN_CTX_free(new_ctx);
996 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
998 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
999 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1001 BN_CTX *new_ctx = NULL;
1002 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
1006 return EC_POINT_dbl(group, r, a, ctx);
1007 if (EC_POINT_is_at_infinity(group, a))
1008 return EC_POINT_copy(r, b);
1009 if (EC_POINT_is_at_infinity(group, b))
1010 return EC_POINT_copy(r, a);
1012 field_mul = group->meth->field_mul;
1013 field_sqr = group->meth->field_sqr;
1018 ctx = new_ctx = BN_CTX_new();
1024 n0 = BN_CTX_get(ctx);
1025 n1 = BN_CTX_get(ctx);
1026 n2 = BN_CTX_get(ctx);
1027 n3 = BN_CTX_get(ctx);
1028 n4 = BN_CTX_get(ctx);
1029 n5 = BN_CTX_get(ctx);
1030 n6 = BN_CTX_get(ctx);
1031 if (n6 == NULL) goto end;
1033 /* Note that in this function we must not read components of 'a' or 'b'
1034 * once we have written the corresponding components of 'r'.
1035 * ('r' might be one of 'a' or 'b'.)
1041 if (!BN_copy(n1, &a->X)) goto end;
1042 if (!BN_copy(n2, &a->Y)) goto end;
1048 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1049 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1050 /* n1 = X_a * Z_b^2 */
1052 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1053 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1054 /* n2 = Y_a * Z_b^3 */
1060 if (!BN_copy(n3, &b->X)) goto end;
1061 if (!BN_copy(n4, &b->Y)) goto end;
1067 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1068 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1069 /* n3 = X_b * Z_a^2 */
1071 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1072 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1073 /* n4 = Y_b * Z_a^3 */
1077 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1078 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1086 /* a is the same point as b */
1088 ret = EC_POINT_dbl(group, r, a, ctx);
1094 /* a is the inverse of b */
1095 if (!BN_zero(&r->Z)) goto end;
1103 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1104 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1105 /* 'n7' = n1 + n3 */
1106 /* 'n8' = n2 + n4 */
1109 if (a->Z_is_one && b->Z_is_one)
1111 if (!BN_copy(&r->Z, n5)) goto end;
1116 { if (!BN_copy(n0, &b->Z)) goto end; }
1117 else if (b->Z_is_one)
1118 { if (!BN_copy(n0, &a->Z)) goto end; }
1120 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1121 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1124 /* Z_r = Z_a * Z_b * n5 */
1127 if (!field_sqr(group, n0, n6, ctx)) goto end;
1128 if (!field_sqr(group, n4, n5, ctx)) goto end;
1129 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1130 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1131 /* X_r = n6^2 - n5^2 * 'n7' */
1134 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1135 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1136 /* n9 = n5^2 * 'n7' - 2 * X_r */
1139 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1140 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1141 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1142 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1144 if (!BN_add(n0, n0, p)) goto end;
1145 /* now 0 <= n0 < 2*p, and n0 is even */
1146 if (!BN_rshift1(&r->Y, n0)) goto end;
1147 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1152 if (ctx) /* otherwise we already called BN_CTX_end */
1154 if (new_ctx != NULL)
1155 BN_CTX_free(new_ctx);
1160 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1162 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1163 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1165 BN_CTX *new_ctx = NULL;
1166 BIGNUM *n0, *n1, *n2, *n3;
1169 if (EC_POINT_is_at_infinity(group, a))
1171 if (!BN_zero(&r->Z)) return 0;
1176 field_mul = group->meth->field_mul;
1177 field_sqr = group->meth->field_sqr;
1182 ctx = new_ctx = BN_CTX_new();
1188 n0 = BN_CTX_get(ctx);
1189 n1 = BN_CTX_get(ctx);
1190 n2 = BN_CTX_get(ctx);
1191 n3 = BN_CTX_get(ctx);
1192 if (n3 == NULL) goto err;
1194 /* Note that in this function we must not read components of 'a'
1195 * once we have written the corresponding components of 'r'.
1196 * ('r' might the same as 'a'.)
1202 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1203 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1204 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1205 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1206 /* n1 = 3 * X_a^2 + a_curve */
1208 else if (group->a_is_minus3)
1210 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1211 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1212 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1213 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1214 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1215 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1216 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1217 * = 3 * X_a^2 - 3 * Z_a^4 */
1221 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1222 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1223 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1224 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1225 if (!field_sqr(group, n1, n1, ctx)) goto err;
1226 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1227 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1228 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1234 if (!BN_copy(n0, &a->Y)) goto err;
1238 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1240 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1242 /* Z_r = 2 * Y_a * Z_a */
1245 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1246 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1247 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1248 /* n2 = 4 * X_a * Y_a^2 */
1251 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1252 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1253 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1254 /* X_r = n1^2 - 2 * n2 */
1257 if (!field_sqr(group, n0, n3, ctx)) goto err;
1258 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1259 /* n3 = 8 * Y_a^4 */
1262 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1263 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1264 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1265 /* Y_r = n1 * (n2 - X_r) - n3 */
1271 if (new_ctx != NULL)
1272 BN_CTX_free(new_ctx);
1277 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1279 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1280 /* point is its own inverse */
1283 return BN_usub(&point->Y, &group->field, &point->Y);
1287 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1289 return BN_is_zero(&point->Z);
1293 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1295 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1296 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1298 BN_CTX *new_ctx = NULL;
1299 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1302 if (EC_POINT_is_at_infinity(group, point))
1305 field_mul = group->meth->field_mul;
1306 field_sqr = group->meth->field_sqr;
1311 ctx = new_ctx = BN_CTX_new();
1317 rh = BN_CTX_get(ctx);
1318 tmp1 = BN_CTX_get(ctx);
1319 tmp2 = BN_CTX_get(ctx);
1320 Z4 = BN_CTX_get(ctx);
1321 Z6 = BN_CTX_get(ctx);
1322 if (Z6 == NULL) goto err;
1324 /* We have a curve defined by a Weierstrass equation
1325 * y^2 = x^3 + a*x + b.
1326 * The point to consider is given in Jacobian projective coordinates
1327 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1328 * Substituting this and multiplying by Z^6 transforms the above equation into
1329 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1330 * To test this, we add up the right-hand side in 'rh'.
1334 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1335 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1337 if (!point->Z_is_one)
1339 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1340 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1341 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1343 /* rh := rh + a*X*Z^4 */
1344 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1345 if (group->a_is_minus3)
1347 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1348 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1349 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1353 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1354 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1357 /* rh := rh + b*Z^6 */
1358 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1359 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1363 /* point->Z_is_one */
1365 /* rh := rh + a*X */
1366 if (group->a_is_minus3)
1368 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1369 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1370 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1374 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1375 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1379 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1383 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1385 ret = (0 == BN_cmp(tmp1, rh));
1389 if (new_ctx != NULL)
1390 BN_CTX_free(new_ctx);
1395 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1399 * 0 equal (in affine coordinates)
1403 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1404 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1405 BN_CTX *new_ctx = NULL;
1406 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1407 const BIGNUM *tmp1_, *tmp2_;
1410 if (EC_POINT_is_at_infinity(group, a))
1412 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1415 if (a->Z_is_one && b->Z_is_one)
1417 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1420 field_mul = group->meth->field_mul;
1421 field_sqr = group->meth->field_sqr;
1425 ctx = new_ctx = BN_CTX_new();
1431 tmp1 = BN_CTX_get(ctx);
1432 tmp2 = BN_CTX_get(ctx);
1433 Za23 = BN_CTX_get(ctx);
1434 Zb23 = BN_CTX_get(ctx);
1435 if (Zb23 == NULL) goto end;
1437 /* We have to decide whether
1438 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1439 * or equivalently, whether
1440 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1445 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1446 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1453 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1454 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1460 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1461 if (BN_cmp(tmp1_, tmp2_) != 0)
1463 ret = 1; /* points differ */
1470 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1471 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1478 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1479 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1485 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1486 if (BN_cmp(tmp1_, tmp2_) != 0)
1488 ret = 1; /* points differ */
1492 /* points are equal */
1497 if (new_ctx != NULL)
1498 BN_CTX_free(new_ctx);
1503 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1505 BN_CTX *new_ctx = NULL;
1509 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1514 ctx = new_ctx = BN_CTX_new();
1520 x = BN_CTX_get(ctx);
1521 y = BN_CTX_get(ctx);
1522 if (y == NULL) goto err;
1524 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1525 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1526 if (!point->Z_is_one)
1528 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1536 if (new_ctx != NULL)
1537 BN_CTX_free(new_ctx);
1542 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1544 BN_CTX *new_ctx = NULL;
1545 BIGNUM *tmp0, *tmp1;
1547 BIGNUM **heap = NULL;
1556 ctx = new_ctx = BN_CTX_new();
1562 tmp0 = BN_CTX_get(ctx);
1563 tmp1 = BN_CTX_get(ctx);
1564 if (tmp0 == NULL || tmp1 == NULL) goto err;
1566 /* Before converting the individual points, compute inverses of all Z values.
1567 * Modular inversion is rather slow, but luckily we can do with a single
1568 * explicit inversion, plus about 3 multiplications per input value.
1574 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1575 * We need twice that. */
1578 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1579 if (heap == NULL) goto err;
1581 /* The array is used as a binary tree, exactly as in heapsort:
1585 * heap[4] heap[5] heap[6] heap[7]
1586 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1588 * We put the Z's in the last line;
1589 * then we set each other node to the product of its two child-nodes (where
1590 * empty or 0 entries are treated as ones);
1591 * then we invert heap[1];
1592 * then we invert each other node by replacing it by the product of its
1593 * parent (after inversion) and its sibling (before inversion).
1596 for (i = pow2/2 - 1; i > 0; i--)
1598 for (i = 0; i < num; i++)
1599 heap[pow2/2 + i] = &points[i]->Z;
1600 for (i = pow2/2 + num; i < pow2; i++)
1603 /* set each node to the product of its children */
1604 for (i = pow2/2 - 1; i > 0; i--)
1607 if (heap[i] == NULL) goto err;
1609 if (heap[2*i] != NULL)
1611 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1613 if (!BN_copy(heap[i], heap[2*i])) goto err;
1617 if (BN_is_zero(heap[2*i]))
1619 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1623 if (!group->meth->field_mul(group, heap[i],
1624 heap[2*i], heap[2*i + 1], ctx)) goto err;
1630 /* invert heap[1] */
1631 if (!BN_is_zero(heap[1]))
1633 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1635 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1639 if (group->meth->field_encode != 0)
1641 /* in the Montgomery case, we just turned R*H (representing H)
1642 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1643 * i.e. we have need to multiply by the Montgomery factor twice */
1644 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1645 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1648 /* set other heap[i]'s to their inverses */
1649 for (i = 2; i < pow2/2 + num; i += 2)
1652 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1654 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1655 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1656 if (!BN_copy(heap[i], tmp0)) goto err;
1657 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1661 if (!BN_copy(heap[i], heap[i/2])) goto err;
1665 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1666 for (i = 0; i < num; i++)
1668 EC_POINT *p = points[i];
1670 if (!BN_is_zero(&p->Z))
1672 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1674 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1675 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1677 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1678 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1680 if (group->meth->field_set_to_one != 0)
1682 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1686 if (!BN_one(&p->Z)) goto err;
1696 if (new_ctx != NULL)
1697 BN_CTX_free(new_ctx);
1700 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1701 for (i = pow2/2 - 1; i > 0; i--)
1703 if (heap[i] != NULL)
1704 BN_clear_free(heap[i]);
1712 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1714 return BN_mod_mul(r, a, b, &group->field, ctx);
1718 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1720 return BN_mod_sqr(r, a, &group->field, ctx);