1 /* crypto/ec/ec2_smpl.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
16 /* ====================================================================
17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
45 * 6. Redistributions of any form whatsoever must retain the following
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
70 #include <openssl/err.h>
74 const EC_METHOD *EC_GF2m_simple_method(void)
76 static const EC_METHOD ret = {
77 NID_X9_62_characteristic_two_field,
78 ec_GF2m_simple_group_init,
79 ec_GF2m_simple_group_finish,
80 ec_GF2m_simple_group_clear_finish,
81 ec_GF2m_simple_group_copy,
82 ec_GF2m_simple_group_set_curve,
83 ec_GF2m_simple_group_get_curve,
84 ec_GF2m_simple_group_get_degree,
85 ec_GF2m_simple_group_check_discriminant,
86 ec_GF2m_simple_point_init,
87 ec_GF2m_simple_point_finish,
88 ec_GF2m_simple_point_clear_finish,
89 ec_GF2m_simple_point_copy,
90 ec_GF2m_simple_point_set_to_infinity,
91 0 /* set_Jprojective_coordinates_GFp */ ,
92 0 /* get_Jprojective_coordinates_GFp */ ,
93 ec_GF2m_simple_point_set_affine_coordinates,
94 ec_GF2m_simple_point_get_affine_coordinates,
95 ec_GF2m_simple_set_compressed_coordinates,
96 ec_GF2m_simple_point2oct,
97 ec_GF2m_simple_oct2point,
100 ec_GF2m_simple_invert,
101 ec_GF2m_simple_is_at_infinity,
102 ec_GF2m_simple_is_on_curve,
104 ec_GF2m_simple_make_affine,
105 ec_GF2m_simple_points_make_affine,
108 * the following three method functions are defined in ec2_mult.c
111 ec_GF2m_precompute_mult,
112 ec_GF2m_have_precompute_mult,
114 ec_GF2m_simple_field_mul,
115 ec_GF2m_simple_field_sqr,
116 ec_GF2m_simple_field_div,
117 0 /* field_encode */ ,
118 0 /* field_decode */ ,
119 0 /* field_set_to_one */
126 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
127 * are handled by EC_GROUP_new.
129 int ec_GF2m_simple_group_init(EC_GROUP *group)
131 BN_init(&group->field);
138 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
139 * handled by EC_GROUP_free.
141 void ec_GF2m_simple_group_finish(EC_GROUP *group)
143 BN_free(&group->field);
149 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
150 * members are handled by EC_GROUP_clear_free.
152 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
154 BN_clear_free(&group->field);
155 BN_clear_free(&group->a);
156 BN_clear_free(&group->b);
165 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
166 * handled by EC_GROUP_copy.
168 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
171 if (!BN_copy(&dest->field, &src->field))
173 if (!BN_copy(&dest->a, &src->a))
175 if (!BN_copy(&dest->b, &src->b))
177 dest->poly[0] = src->poly[0];
178 dest->poly[1] = src->poly[1];
179 dest->poly[2] = src->poly[2];
180 dest->poly[3] = src->poly[3];
181 dest->poly[4] = src->poly[4];
182 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2)
185 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2)
188 for (i = dest->a.top; i < dest->a.dmax; i++)
190 for (i = dest->b.top; i < dest->b.dmax; i++)
195 /* Set the curve parameters of an EC_GROUP structure. */
196 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
197 const BIGNUM *p, const BIGNUM *a,
198 const BIGNUM *b, BN_CTX *ctx)
203 if (!BN_copy(&group->field, p))
205 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
206 if ((i != 5) && (i != 3)) {
207 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
212 if (!BN_GF2m_mod_arr(&group->a, a, group->poly))
214 if (bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
217 for (i = group->a.top; i < group->a.dmax; i++)
221 if (!BN_GF2m_mod_arr(&group->b, b, group->poly))
223 if (bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
226 for (i = group->b.top; i < group->b.dmax; i++)
235 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
236 * then there values will not be set but the method will return with success.
238 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
239 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
244 if (!BN_copy(p, &group->field))
249 if (!BN_copy(a, &group->a))
254 if (!BN_copy(b, &group->b))
265 * Gets the degree of the field. For a curve over GF(2^m) this is the value
268 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
270 return BN_num_bits(&group->field) - 1;
274 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
275 * elliptic curve <=> b != 0 (mod p)
277 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
282 BN_CTX *new_ctx = NULL;
285 ctx = new_ctx = BN_CTX_new();
287 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT,
288 ERR_R_MALLOC_FAILURE);
297 if (!BN_GF2m_mod_arr(b, &group->b, group->poly))
301 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
302 * curve <=> b != 0 (mod p)
313 BN_CTX_free(new_ctx);
317 /* Initializes an EC_POINT. */
318 int ec_GF2m_simple_point_init(EC_POINT *point)
326 /* Frees an EC_POINT. */
327 void ec_GF2m_simple_point_finish(EC_POINT *point)
334 /* Clears and frees an EC_POINT. */
335 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
337 BN_clear_free(&point->X);
338 BN_clear_free(&point->Y);
339 BN_clear_free(&point->Z);
344 * Copy the contents of one EC_POINT into another. Assumes dest is
347 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
349 if (!BN_copy(&dest->X, &src->X))
351 if (!BN_copy(&dest->Y, &src->Y))
353 if (!BN_copy(&dest->Z, &src->Z))
355 dest->Z_is_one = src->Z_is_one;
361 * Set an EC_POINT to the point at infinity. A point at infinity is
362 * represented by having Z=0.
364 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
373 * Set the coordinates of an EC_POINT using affine coordinates. Note that
374 * the simple implementation only uses affine coordinates.
376 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
379 const BIGNUM *y, BN_CTX *ctx)
382 if (x == NULL || y == NULL) {
383 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
384 ERR_R_PASSED_NULL_PARAMETER);
388 if (!BN_copy(&point->X, x))
390 BN_set_negative(&point->X, 0);
391 if (!BN_copy(&point->Y, y))
393 BN_set_negative(&point->Y, 0);
394 if (!BN_copy(&point->Z, BN_value_one()))
396 BN_set_negative(&point->Z, 0);
405 * Gets the affine coordinates of an EC_POINT. Note that the simple
406 * implementation only uses affine coordinates.
408 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
409 const EC_POINT *point,
410 BIGNUM *x, BIGNUM *y,
415 if (EC_POINT_is_at_infinity(group, point)) {
416 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
417 EC_R_POINT_AT_INFINITY);
421 if (BN_cmp(&point->Z, BN_value_one())) {
422 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
423 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
427 if (!BN_copy(x, &point->X))
429 BN_set_negative(x, 0);
432 if (!BN_copy(y, &point->Y))
434 BN_set_negative(y, 0);
442 /* Include patented algorithms. */
443 #include "ec2_smpt.c"
446 * Converts an EC_POINT to an octet string. If buf is NULL, the encoded
447 * length will be returned. If the length len of buf is smaller than required
448 * an error will be returned. The point compression section of this function
449 * is patented by Certicom Corp. under US Patent 6,141,420. Point
450 * compression is disabled by default and can be enabled by defining the
451 * preprocessor macro OPENSSL_EC_BIN_PT_COMP at Configure-time.
453 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
454 point_conversion_form_t form,
455 unsigned char *buf, size_t len, BN_CTX *ctx)
458 BN_CTX *new_ctx = NULL;
461 size_t field_len, i, skip;
463 #ifndef OPENSSL_EC_BIN_PT_COMP
464 if ((form == POINT_CONVERSION_COMPRESSED)
465 || (form == POINT_CONVERSION_HYBRID)) {
466 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
471 if ((form != POINT_CONVERSION_COMPRESSED)
472 && (form != POINT_CONVERSION_UNCOMPRESSED)
473 && (form != POINT_CONVERSION_HYBRID)) {
474 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
478 if (EC_POINT_is_at_infinity(group, point)) {
479 /* encodes to a single 0 octet */
482 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
490 /* ret := required output buffer length */
491 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
494 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
496 /* if 'buf' is NULL, just return required length */
499 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
504 ctx = new_ctx = BN_CTX_new();
513 yxi = BN_CTX_get(ctx);
517 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
521 #ifdef OPENSSL_EC_BIN_PT_COMP
522 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
523 if (!group->meth->field_div(group, yxi, y, x, ctx))
532 skip = field_len - BN_num_bytes(x);
533 if (skip > field_len) {
534 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
541 skip = BN_bn2bin(x, buf + i);
543 if (i != 1 + field_len) {
544 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
548 if (form == POINT_CONVERSION_UNCOMPRESSED
549 || form == POINT_CONVERSION_HYBRID) {
550 skip = field_len - BN_num_bytes(y);
551 if (skip > field_len) {
552 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
559 skip = BN_bn2bin(y, buf + i);
564 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
572 BN_CTX_free(new_ctx);
579 BN_CTX_free(new_ctx);
584 * Converts an octet string representation to an EC_POINT. Note that the
585 * simple implementation only uses affine coordinates.
587 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
588 const unsigned char *buf, size_t len,
591 point_conversion_form_t form;
593 BN_CTX *new_ctx = NULL;
595 size_t field_len, enc_len;
599 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
605 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
606 && (form != POINT_CONVERSION_UNCOMPRESSED)
607 && (form != POINT_CONVERSION_HYBRID)) {
608 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
611 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
612 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
618 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
622 return EC_POINT_set_to_infinity(group, point);
625 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
628 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
630 if (len != enc_len) {
631 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
636 ctx = new_ctx = BN_CTX_new();
644 yxi = BN_CTX_get(ctx);
648 if (!BN_bin2bn(buf + 1, field_len, x))
650 if (BN_ucmp(x, &group->field) >= 0) {
651 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
655 if (form == POINT_CONVERSION_COMPRESSED) {
656 if (!EC_POINT_set_compressed_coordinates_GF2m
657 (group, point, x, y_bit, ctx))
660 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
662 if (BN_ucmp(y, &group->field) >= 0) {
663 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
666 if (form == POINT_CONVERSION_HYBRID) {
667 if (!group->meth->field_div(group, yxi, y, x, ctx))
669 if (y_bit != BN_is_odd(yxi)) {
670 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
675 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx))
679 /* test required by X9.62 */
680 if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
681 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
690 BN_CTX_free(new_ctx);
695 * Computes a + b and stores the result in r. r could be a or b, a could be
696 * b. Uses algorithm A.10.2 of IEEE P1363.
698 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
699 const EC_POINT *b, BN_CTX *ctx)
701 BN_CTX *new_ctx = NULL;
702 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
705 if (EC_POINT_is_at_infinity(group, a)) {
706 if (!EC_POINT_copy(r, b))
711 if (EC_POINT_is_at_infinity(group, b)) {
712 if (!EC_POINT_copy(r, a))
718 ctx = new_ctx = BN_CTX_new();
724 x0 = BN_CTX_get(ctx);
725 y0 = BN_CTX_get(ctx);
726 x1 = BN_CTX_get(ctx);
727 y1 = BN_CTX_get(ctx);
728 x2 = BN_CTX_get(ctx);
729 y2 = BN_CTX_get(ctx);
736 if (!BN_copy(x0, &a->X))
738 if (!BN_copy(y0, &a->Y))
741 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx))
745 if (!BN_copy(x1, &b->X))
747 if (!BN_copy(y1, &b->Y))
750 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx))
754 if (BN_GF2m_cmp(x0, x1)) {
755 if (!BN_GF2m_add(t, x0, x1))
757 if (!BN_GF2m_add(s, y0, y1))
759 if (!group->meth->field_div(group, s, s, t, ctx))
761 if (!group->meth->field_sqr(group, x2, s, ctx))
763 if (!BN_GF2m_add(x2, x2, &group->a))
765 if (!BN_GF2m_add(x2, x2, s))
767 if (!BN_GF2m_add(x2, x2, t))
770 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
771 if (!EC_POINT_set_to_infinity(group, r))
776 if (!group->meth->field_div(group, s, y1, x1, ctx))
778 if (!BN_GF2m_add(s, s, x1))
781 if (!group->meth->field_sqr(group, x2, s, ctx))
783 if (!BN_GF2m_add(x2, x2, s))
785 if (!BN_GF2m_add(x2, x2, &group->a))
789 if (!BN_GF2m_add(y2, x1, x2))
791 if (!group->meth->field_mul(group, y2, y2, s, ctx))
793 if (!BN_GF2m_add(y2, y2, x2))
795 if (!BN_GF2m_add(y2, y2, y1))
798 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx))
806 BN_CTX_free(new_ctx);
811 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
812 * A.10.2 of IEEE P1363.
814 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
817 return ec_GF2m_simple_add(group, r, a, a, ctx);
820 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
822 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
823 /* point is its own inverse */
826 if (!EC_POINT_make_affine(group, point, ctx))
828 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
831 /* Indicates whether the given point is the point at infinity. */
832 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
833 const EC_POINT *point)
835 return BN_is_zero(&point->Z);
839 * Determines whether the given EC_POINT is an actual point on the curve defined
840 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
841 * y^2 + x*y = x^3 + a*x^2 + b.
843 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
847 BN_CTX *new_ctx = NULL;
849 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
850 const BIGNUM *, BN_CTX *);
851 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
853 if (EC_POINT_is_at_infinity(group, point))
856 field_mul = group->meth->field_mul;
857 field_sqr = group->meth->field_sqr;
859 /* only support affine coordinates */
860 if (!point->Z_is_one)
864 ctx = new_ctx = BN_CTX_new();
870 y2 = BN_CTX_get(ctx);
871 lh = BN_CTX_get(ctx);
876 * We have a curve defined by a Weierstrass equation
877 * y^2 + x*y = x^3 + a*x^2 + b.
878 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
879 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
881 if (!BN_GF2m_add(lh, &point->X, &group->a))
883 if (!field_mul(group, lh, lh, &point->X, ctx))
885 if (!BN_GF2m_add(lh, lh, &point->Y))
887 if (!field_mul(group, lh, lh, &point->X, ctx))
889 if (!BN_GF2m_add(lh, lh, &group->b))
891 if (!field_sqr(group, y2, &point->Y, ctx))
893 if (!BN_GF2m_add(lh, lh, y2))
895 ret = BN_is_zero(lh);
900 BN_CTX_free(new_ctx);
905 * Indicates whether two points are equal.
908 * 0 equal (in affine coordinates)
911 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
912 const EC_POINT *b, BN_CTX *ctx)
914 BIGNUM *aX, *aY, *bX, *bY;
915 BN_CTX *new_ctx = NULL;
918 if (EC_POINT_is_at_infinity(group, a)) {
919 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
922 if (EC_POINT_is_at_infinity(group, b))
925 if (a->Z_is_one && b->Z_is_one) {
926 return ((BN_cmp(&a->X, &b->X) == 0)
927 && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
931 ctx = new_ctx = BN_CTX_new();
937 aX = BN_CTX_get(ctx);
938 aY = BN_CTX_get(ctx);
939 bX = BN_CTX_get(ctx);
940 bY = BN_CTX_get(ctx);
944 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx))
946 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx))
948 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
954 BN_CTX_free(new_ctx);
958 /* Forces the given EC_POINT to internally use affine coordinates. */
959 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
962 BN_CTX *new_ctx = NULL;
966 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
970 ctx = new_ctx = BN_CTX_new();
981 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
983 if (!BN_copy(&point->X, x))
985 if (!BN_copy(&point->Y, y))
987 if (!BN_one(&point->Z))
996 BN_CTX_free(new_ctx);
1001 * Forces each of the EC_POINTs in the given array to use affine coordinates.
1003 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
1004 EC_POINT *points[], BN_CTX *ctx)
1008 for (i = 0; i < num; i++) {
1009 if (!group->meth->make_affine(group, points[i], ctx))
1016 /* Wrapper to simple binary polynomial field multiplication implementation. */
1017 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
1018 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1020 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1023 /* Wrapper to simple binary polynomial field squaring implementation. */
1024 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
1025 const BIGNUM *a, BN_CTX *ctx)
1027 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1030 /* Wrapper to simple binary polynomial field division implementation. */
1031 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
1032 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1034 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);