1 /* ====================================================================
2 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
5 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
6 * to the OpenSSL project.
8 * The ECC Code is licensed pursuant to the OpenSSL open source
9 * license provided below.
11 * The software is originally written by Sheueling Chang Shantz and
12 * Douglas Stebila of Sun Microsystems Laboratories.
15 /* ====================================================================
16 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
18 * Redistribution and use in source and binary forms, with or without
19 * modification, are permitted provided that the following conditions
22 * 1. Redistributions of source code must retain the above copyright
23 * notice, this list of conditions and the following disclaimer.
25 * 2. Redistributions in binary form must reproduce the above copyright
26 * notice, this list of conditions and the following disclaimer in
27 * the documentation and/or other materials provided with the
30 * 3. All advertising materials mentioning features or use of this
31 * software must display the following acknowledgment:
32 * "This product includes software developed by the OpenSSL Project
33 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
36 * endorse or promote products derived from this software without
37 * prior written permission. For written permission, please contact
38 * openssl-core@openssl.org.
40 * 5. Products derived from this software may not be called "OpenSSL"
41 * nor may "OpenSSL" appear in their names without prior written
42 * permission of the OpenSSL Project.
44 * 6. Redistributions of any form whatsoever must retain the following
46 * "This product includes software developed by the OpenSSL Project
47 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
50 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
51 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
52 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
53 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
54 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
55 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
56 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
57 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
58 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
59 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
60 * OF THE POSSIBILITY OF SUCH DAMAGE.
61 * ====================================================================
63 * This product includes cryptographic software written by Eric Young
64 * (eay@cryptsoft.com). This product includes software written by Tim
65 * Hudson (tjh@cryptsoft.com).
69 #include <openssl/err.h>
71 #include "internal/bn_int.h"
74 #ifndef OPENSSL_NO_EC2M
76 const EC_METHOD *EC_GF2m_simple_method(void)
78 static const EC_METHOD ret = {
80 NID_X9_62_characteristic_two_field,
81 ec_GF2m_simple_group_init,
82 ec_GF2m_simple_group_finish,
83 ec_GF2m_simple_group_clear_finish,
84 ec_GF2m_simple_group_copy,
85 ec_GF2m_simple_group_set_curve,
86 ec_GF2m_simple_group_get_curve,
87 ec_GF2m_simple_group_get_degree,
88 ec_GF2m_simple_group_check_discriminant,
89 ec_GF2m_simple_point_init,
90 ec_GF2m_simple_point_finish,
91 ec_GF2m_simple_point_clear_finish,
92 ec_GF2m_simple_point_copy,
93 ec_GF2m_simple_point_set_to_infinity,
94 0 /* set_Jprojective_coordinates_GFp */ ,
95 0 /* get_Jprojective_coordinates_GFp */ ,
96 ec_GF2m_simple_point_set_affine_coordinates,
97 ec_GF2m_simple_point_get_affine_coordinates,
101 ec_GF2m_simple_invert,
102 ec_GF2m_simple_is_at_infinity,
103 ec_GF2m_simple_is_on_curve,
105 ec_GF2m_simple_make_affine,
106 ec_GF2m_simple_points_make_affine,
109 * the following three method functions are defined in ec2_mult.c
112 ec_GF2m_precompute_mult,
113 ec_GF2m_have_precompute_mult,
115 ec_GF2m_simple_field_mul,
116 ec_GF2m_simple_field_sqr,
117 ec_GF2m_simple_field_div,
118 0 /* field_encode */ ,
119 0 /* field_decode */ ,
120 0 /* field_set_to_one */
127 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
128 * are handled by EC_GROUP_new.
130 int ec_GF2m_simple_group_init(EC_GROUP *group)
132 group->field = BN_new();
136 if (group->field == NULL || group->a == NULL || group->b == NULL) {
137 BN_free(group->field);
146 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
147 * handled by EC_GROUP_free.
149 void ec_GF2m_simple_group_finish(EC_GROUP *group)
151 BN_free(group->field);
157 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
158 * members are handled by EC_GROUP_clear_free.
160 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
162 BN_clear_free(group->field);
163 BN_clear_free(group->a);
164 BN_clear_free(group->b);
174 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
175 * handled by EC_GROUP_copy.
177 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
179 if (!BN_copy(dest->field, src->field))
181 if (!BN_copy(dest->a, src->a))
183 if (!BN_copy(dest->b, src->b))
185 dest->poly[0] = src->poly[0];
186 dest->poly[1] = src->poly[1];
187 dest->poly[2] = src->poly[2];
188 dest->poly[3] = src->poly[3];
189 dest->poly[4] = src->poly[4];
190 dest->poly[5] = src->poly[5];
191 if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
194 if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
197 bn_set_all_zero(dest->a);
198 bn_set_all_zero(dest->b);
202 /* Set the curve parameters of an EC_GROUP structure. */
203 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
204 const BIGNUM *p, const BIGNUM *a,
205 const BIGNUM *b, BN_CTX *ctx)
210 if (!BN_copy(group->field, p))
212 i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
213 if ((i != 5) && (i != 3)) {
214 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
219 if (!BN_GF2m_mod_arr(group->a, a, group->poly))
221 if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
224 bn_set_all_zero(group->a);
227 if (!BN_GF2m_mod_arr(group->b, b, group->poly))
229 if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
232 bn_set_all_zero(group->b);
240 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
241 * then there values will not be set but the method will return with success.
243 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
244 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
249 if (!BN_copy(p, group->field))
254 if (!BN_copy(a, group->a))
259 if (!BN_copy(b, group->b))
270 * Gets the degree of the field. For a curve over GF(2^m) this is the value
273 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
275 return BN_num_bits(group->field) - 1;
279 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
280 * elliptic curve <=> b != 0 (mod p)
282 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
287 BN_CTX *new_ctx = NULL;
290 ctx = new_ctx = BN_CTX_new();
292 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT,
293 ERR_R_MALLOC_FAILURE);
302 if (!BN_GF2m_mod_arr(b, group->b, group->poly))
306 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
307 * curve <=> b != 0 (mod p)
317 BN_CTX_free(new_ctx);
321 /* Initializes an EC_POINT. */
322 int ec_GF2m_simple_point_init(EC_POINT *point)
328 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
337 /* Frees an EC_POINT. */
338 void ec_GF2m_simple_point_finish(EC_POINT *point)
345 /* Clears and frees an EC_POINT. */
346 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
348 BN_clear_free(point->X);
349 BN_clear_free(point->Y);
350 BN_clear_free(point->Z);
355 * Copy the contents of one EC_POINT into another. Assumes dest is
358 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
360 if (!BN_copy(dest->X, src->X))
362 if (!BN_copy(dest->Y, src->Y))
364 if (!BN_copy(dest->Z, src->Z))
366 dest->Z_is_one = src->Z_is_one;
372 * Set an EC_POINT to the point at infinity. A point at infinity is
373 * represented by having Z=0.
375 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
384 * Set the coordinates of an EC_POINT using affine coordinates. Note that
385 * the simple implementation only uses affine coordinates.
387 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
390 const BIGNUM *y, BN_CTX *ctx)
393 if (x == NULL || y == NULL) {
394 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
395 ERR_R_PASSED_NULL_PARAMETER);
399 if (!BN_copy(point->X, x))
401 BN_set_negative(point->X, 0);
402 if (!BN_copy(point->Y, y))
404 BN_set_negative(point->Y, 0);
405 if (!BN_copy(point->Z, BN_value_one()))
407 BN_set_negative(point->Z, 0);
416 * Gets the affine coordinates of an EC_POINT. Note that the simple
417 * implementation only uses affine coordinates.
419 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
420 const EC_POINT *point,
421 BIGNUM *x, BIGNUM *y,
426 if (EC_POINT_is_at_infinity(group, point)) {
427 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
428 EC_R_POINT_AT_INFINITY);
432 if (BN_cmp(point->Z, BN_value_one())) {
433 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
434 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
438 if (!BN_copy(x, point->X))
440 BN_set_negative(x, 0);
443 if (!BN_copy(y, point->Y))
445 BN_set_negative(y, 0);
454 * Computes a + b and stores the result in r. r could be a or b, a could be
455 * b. Uses algorithm A.10.2 of IEEE P1363.
457 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
458 const EC_POINT *b, BN_CTX *ctx)
460 BN_CTX *new_ctx = NULL;
461 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
464 if (EC_POINT_is_at_infinity(group, a)) {
465 if (!EC_POINT_copy(r, b))
470 if (EC_POINT_is_at_infinity(group, b)) {
471 if (!EC_POINT_copy(r, a))
477 ctx = new_ctx = BN_CTX_new();
483 x0 = BN_CTX_get(ctx);
484 y0 = BN_CTX_get(ctx);
485 x1 = BN_CTX_get(ctx);
486 y1 = BN_CTX_get(ctx);
487 x2 = BN_CTX_get(ctx);
488 y2 = BN_CTX_get(ctx);
495 if (!BN_copy(x0, a->X))
497 if (!BN_copy(y0, a->Y))
500 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx))
504 if (!BN_copy(x1, b->X))
506 if (!BN_copy(y1, b->Y))
509 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx))
513 if (BN_GF2m_cmp(x0, x1)) {
514 if (!BN_GF2m_add(t, x0, x1))
516 if (!BN_GF2m_add(s, y0, y1))
518 if (!group->meth->field_div(group, s, s, t, ctx))
520 if (!group->meth->field_sqr(group, x2, s, ctx))
522 if (!BN_GF2m_add(x2, x2, group->a))
524 if (!BN_GF2m_add(x2, x2, s))
526 if (!BN_GF2m_add(x2, x2, t))
529 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
530 if (!EC_POINT_set_to_infinity(group, r))
535 if (!group->meth->field_div(group, s, y1, x1, ctx))
537 if (!BN_GF2m_add(s, s, x1))
540 if (!group->meth->field_sqr(group, x2, s, ctx))
542 if (!BN_GF2m_add(x2, x2, s))
544 if (!BN_GF2m_add(x2, x2, group->a))
548 if (!BN_GF2m_add(y2, x1, x2))
550 if (!group->meth->field_mul(group, y2, y2, s, ctx))
552 if (!BN_GF2m_add(y2, y2, x2))
554 if (!BN_GF2m_add(y2, y2, y1))
557 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx))
564 BN_CTX_free(new_ctx);
569 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
570 * A.10.2 of IEEE P1363.
572 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
575 return ec_GF2m_simple_add(group, r, a, a, ctx);
578 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
580 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
581 /* point is its own inverse */
584 if (!EC_POINT_make_affine(group, point, ctx))
586 return BN_GF2m_add(point->Y, point->X, point->Y);
589 /* Indicates whether the given point is the point at infinity. */
590 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
591 const EC_POINT *point)
593 return BN_is_zero(point->Z);
597 * Determines whether the given EC_POINT is an actual point on the curve defined
598 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
599 * y^2 + x*y = x^3 + a*x^2 + b.
601 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
605 BN_CTX *new_ctx = NULL;
607 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
608 const BIGNUM *, BN_CTX *);
609 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
611 if (EC_POINT_is_at_infinity(group, point))
614 field_mul = group->meth->field_mul;
615 field_sqr = group->meth->field_sqr;
617 /* only support affine coordinates */
618 if (!point->Z_is_one)
622 ctx = new_ctx = BN_CTX_new();
628 y2 = BN_CTX_get(ctx);
629 lh = BN_CTX_get(ctx);
634 * We have a curve defined by a Weierstrass equation
635 * y^2 + x*y = x^3 + a*x^2 + b.
636 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
637 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
639 if (!BN_GF2m_add(lh, point->X, group->a))
641 if (!field_mul(group, lh, lh, point->X, ctx))
643 if (!BN_GF2m_add(lh, lh, point->Y))
645 if (!field_mul(group, lh, lh, point->X, ctx))
647 if (!BN_GF2m_add(lh, lh, group->b))
649 if (!field_sqr(group, y2, point->Y, ctx))
651 if (!BN_GF2m_add(lh, lh, y2))
653 ret = BN_is_zero(lh);
657 BN_CTX_free(new_ctx);
662 * Indicates whether two points are equal.
665 * 0 equal (in affine coordinates)
668 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
669 const EC_POINT *b, BN_CTX *ctx)
671 BIGNUM *aX, *aY, *bX, *bY;
672 BN_CTX *new_ctx = NULL;
675 if (EC_POINT_is_at_infinity(group, a)) {
676 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
679 if (EC_POINT_is_at_infinity(group, b))
682 if (a->Z_is_one && b->Z_is_one) {
683 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
687 ctx = new_ctx = BN_CTX_new();
693 aX = BN_CTX_get(ctx);
694 aY = BN_CTX_get(ctx);
695 bX = BN_CTX_get(ctx);
696 bY = BN_CTX_get(ctx);
700 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx))
702 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx))
704 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
709 BN_CTX_free(new_ctx);
713 /* Forces the given EC_POINT to internally use affine coordinates. */
714 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
717 BN_CTX *new_ctx = NULL;
721 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
725 ctx = new_ctx = BN_CTX_new();
736 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
738 if (!BN_copy(point->X, x))
740 if (!BN_copy(point->Y, y))
742 if (!BN_one(point->Z))
751 BN_CTX_free(new_ctx);
756 * Forces each of the EC_POINTs in the given array to use affine coordinates.
758 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
759 EC_POINT *points[], BN_CTX *ctx)
763 for (i = 0; i < num; i++) {
764 if (!group->meth->make_affine(group, points[i], ctx))
771 /* Wrapper to simple binary polynomial field multiplication implementation. */
772 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
773 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
775 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
778 /* Wrapper to simple binary polynomial field squaring implementation. */
779 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
780 const BIGNUM *a, BN_CTX *ctx)
782 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
785 /* Wrapper to simple binary polynomial field division implementation. */
786 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
787 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
789 return BN_GF2m_mod_div(r, a, b, group->field, ctx);