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) 1998-2005 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).
72 #include <openssl/err.h>
74 #include "internal/bn_int.h"
77 #ifndef OPENSSL_NO_EC2M
80 const EC_METHOD *EC_GF2m_simple_method(void)
82 static const EC_METHOD ret = {
84 NID_X9_62_characteristic_two_field,
85 ec_GF2m_simple_group_init,
86 ec_GF2m_simple_group_finish,
87 ec_GF2m_simple_group_clear_finish,
88 ec_GF2m_simple_group_copy,
89 ec_GF2m_simple_group_set_curve,
90 ec_GF2m_simple_group_get_curve,
91 ec_GF2m_simple_group_get_degree,
92 ec_GF2m_simple_group_check_discriminant,
93 ec_GF2m_simple_point_init,
94 ec_GF2m_simple_point_finish,
95 ec_GF2m_simple_point_clear_finish,
96 ec_GF2m_simple_point_copy,
97 ec_GF2m_simple_point_set_to_infinity,
98 0 /* set_Jprojective_coordinates_GFp */,
99 0 /* get_Jprojective_coordinates_GFp */,
100 ec_GF2m_simple_point_set_affine_coordinates,
101 ec_GF2m_simple_point_get_affine_coordinates,
105 ec_GF2m_simple_invert,
106 ec_GF2m_simple_is_at_infinity,
107 ec_GF2m_simple_is_on_curve,
109 ec_GF2m_simple_make_affine,
110 ec_GF2m_simple_points_make_affine,
112 /* the following three method functions are defined in ec2_mult.c */
114 ec_GF2m_precompute_mult,
115 ec_GF2m_have_precompute_mult,
117 ec_GF2m_simple_field_mul,
118 ec_GF2m_simple_field_sqr,
119 ec_GF2m_simple_field_div,
120 0 /* field_encode */,
121 0 /* field_decode */,
122 0 /* field_set_to_one */ };
128 /* Initialize a GF(2^m)-based EC_GROUP structure.
129 * Note that all other members are handled by EC_GROUP_new.
131 int ec_GF2m_simple_group_init(EC_GROUP *group)
133 group->field = BN_new();
137 if(!group->field || !group->a || !group->b)
139 if(group->field) BN_free(group->field);
140 if(group->a) BN_free(group->a);
141 if(group->b) BN_free(group->b);
148 /* Free a GF(2^m)-based EC_GROUP structure.
149 * Note that all other members are handled by EC_GROUP_free.
151 void ec_GF2m_simple_group_finish(EC_GROUP *group)
153 BN_free(group->field);
159 /* Clear and free a GF(2^m)-based EC_GROUP structure.
160 * Note that all other members are handled by EC_GROUP_clear_free.
162 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
164 BN_clear_free(group->field);
165 BN_clear_free(group->a);
166 BN_clear_free(group->b);
176 /* Copy a GF(2^m)-based EC_GROUP structure.
177 * Note that all other members are handled by EC_GROUP_copy.
179 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
181 if (!BN_copy(dest->field, src->field)) return 0;
182 if (!BN_copy(dest->a, src->a)) return 0;
183 if (!BN_copy(dest->b, src->b)) return 0;
184 dest->poly[0] = src->poly[0];
185 dest->poly[1] = src->poly[1];
186 dest->poly[2] = src->poly[2];
187 dest->poly[3] = src->poly[3];
188 dest->poly[4] = src->poly[4];
189 dest->poly[5] = src->poly[5];
190 if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
191 if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
192 bn_set_all_zero(dest->a);
193 bn_set_all_zero(dest->b);
198 /* Set the curve parameters of an EC_GROUP structure. */
199 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
200 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
205 if (!BN_copy(group->field, p)) goto err;
206 i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
207 if ((i != 5) && (i != 3))
209 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
214 if (!BN_GF2m_mod_arr(group->a, a, group->poly)) goto err;
215 if(bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
216 bn_set_all_zero(group->a);
219 if (!BN_GF2m_mod_arr(group->b, b, group->poly)) goto err;
220 if(bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
221 bn_set_all_zero(group->b);
229 /* Get the curve parameters of an EC_GROUP structure.
230 * If p, a, or b are NULL then there values will not be set but the method will return with success.
232 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
238 if (!BN_copy(p, group->field)) return 0;
243 if (!BN_copy(a, group->a)) goto err;
248 if (!BN_copy(b, group->b)) goto err;
258 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
259 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
261 return BN_num_bits(group->field)-1;
265 /* Checks the discriminant of the curve.
266 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
268 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
272 BN_CTX *new_ctx = NULL;
276 ctx = new_ctx = BN_CTX_new();
279 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
285 if (b == NULL) goto err;
287 if (!BN_GF2m_mod_arr(b, group->b, group->poly)) goto err;
289 /* check the discriminant:
290 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
292 if (BN_is_zero(b)) goto err;
300 BN_CTX_free(new_ctx);
305 /* Initializes an EC_POINT. */
306 int ec_GF2m_simple_point_init(EC_POINT *point)
312 if(!point->X || !point->Y || !point->Z)
314 if(point->X) BN_free(point->X);
315 if(point->Y) BN_free(point->Y);
316 if(point->Z) BN_free(point->Z);
323 /* Frees an EC_POINT. */
324 void ec_GF2m_simple_point_finish(EC_POINT *point)
332 /* Clears and frees an EC_POINT. */
333 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
335 BN_clear_free(point->X);
336 BN_clear_free(point->Y);
337 BN_clear_free(point->Z);
342 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
343 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
345 if (!BN_copy(dest->X, src->X)) return 0;
346 if (!BN_copy(dest->Y, src->Y)) return 0;
347 if (!BN_copy(dest->Z, src->Z)) return 0;
348 dest->Z_is_one = src->Z_is_one;
354 /* Set an EC_POINT to the point at infinity.
355 * A point at infinity is represented by having Z=0.
357 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
365 /* Set the coordinates of an EC_POINT using affine coordinates.
366 * Note that the simple implementation only uses affine coordinates.
368 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
369 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
372 if (x == NULL || y == NULL)
374 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
378 if (!BN_copy(point->X, x)) goto err;
379 BN_set_negative(point->X, 0);
380 if (!BN_copy(point->Y, y)) goto err;
381 BN_set_negative(point->Y, 0);
382 if (!BN_copy(point->Z, BN_value_one())) goto err;
383 BN_set_negative(point->Z, 0);
392 /* Gets the affine coordinates of an EC_POINT.
393 * Note that the simple implementation only uses affine coordinates.
395 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
396 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
400 if (EC_POINT_is_at_infinity(group, point))
402 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
406 if (BN_cmp(point->Z, BN_value_one()))
408 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
413 if (!BN_copy(x, point->X)) goto err;
414 BN_set_negative(x, 0);
418 if (!BN_copy(y, point->Y)) goto err;
419 BN_set_negative(y, 0);
427 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
428 * Uses algorithm A.10.2 of IEEE P1363.
430 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
432 BN_CTX *new_ctx = NULL;
433 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
436 if (EC_POINT_is_at_infinity(group, a))
438 if (!EC_POINT_copy(r, b)) return 0;
442 if (EC_POINT_is_at_infinity(group, b))
444 if (!EC_POINT_copy(r, a)) return 0;
450 ctx = new_ctx = BN_CTX_new();
456 x0 = BN_CTX_get(ctx);
457 y0 = BN_CTX_get(ctx);
458 x1 = BN_CTX_get(ctx);
459 y1 = BN_CTX_get(ctx);
460 x2 = BN_CTX_get(ctx);
461 y2 = BN_CTX_get(ctx);
464 if (t == NULL) goto err;
468 if (!BN_copy(x0, a->X)) goto err;
469 if (!BN_copy(y0, a->Y)) goto err;
473 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
477 if (!BN_copy(x1, b->X)) goto err;
478 if (!BN_copy(y1, b->Y)) goto err;
482 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
486 if (BN_GF2m_cmp(x0, x1))
488 if (!BN_GF2m_add(t, x0, x1)) goto err;
489 if (!BN_GF2m_add(s, y0, y1)) goto err;
490 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
491 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
492 if (!BN_GF2m_add(x2, x2, group->a)) goto err;
493 if (!BN_GF2m_add(x2, x2, s)) goto err;
494 if (!BN_GF2m_add(x2, x2, t)) goto err;
498 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
500 if (!EC_POINT_set_to_infinity(group, r)) goto err;
504 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
505 if (!BN_GF2m_add(s, s, x1)) goto err;
507 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
508 if (!BN_GF2m_add(x2, x2, s)) goto err;
509 if (!BN_GF2m_add(x2, x2, group->a)) goto err;
512 if (!BN_GF2m_add(y2, x1, x2)) goto err;
513 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
514 if (!BN_GF2m_add(y2, y2, x2)) goto err;
515 if (!BN_GF2m_add(y2, y2, y1)) goto err;
517 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
524 BN_CTX_free(new_ctx);
529 /* Computes 2 * a and stores the result in r. r could be a.
530 * Uses algorithm A.10.2 of IEEE P1363.
532 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
534 return ec_GF2m_simple_add(group, r, a, a, ctx);
538 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
540 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
541 /* point is its own inverse */
544 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
545 return BN_GF2m_add(point->Y, point->X, point->Y);
549 /* Indicates whether the given point is the point at infinity. */
550 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
552 return BN_is_zero(point->Z);
556 /* Determines whether the given EC_POINT is an actual point on the curve defined
557 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
558 * y^2 + x*y = x^3 + a*x^2 + b.
560 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
563 BN_CTX *new_ctx = NULL;
565 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
566 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
568 if (EC_POINT_is_at_infinity(group, point))
571 field_mul = group->meth->field_mul;
572 field_sqr = group->meth->field_sqr;
574 /* only support affine coordinates */
575 if (!point->Z_is_one) return -1;
579 ctx = new_ctx = BN_CTX_new();
585 y2 = BN_CTX_get(ctx);
586 lh = BN_CTX_get(ctx);
587 if (lh == NULL) goto err;
590 * We have a curve defined by a Weierstrass equation
591 * y^2 + x*y = x^3 + a*x^2 + b.
592 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
593 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
595 if (!BN_GF2m_add(lh, point->X, group->a)) goto err;
596 if (!field_mul(group, lh, lh, point->X, ctx)) goto err;
597 if (!BN_GF2m_add(lh, lh, point->Y)) goto err;
598 if (!field_mul(group, lh, lh, point->X, ctx)) goto err;
599 if (!BN_GF2m_add(lh, lh, group->b)) goto err;
600 if (!field_sqr(group, y2, point->Y, ctx)) goto err;
601 if (!BN_GF2m_add(lh, lh, y2)) goto err;
602 ret = BN_is_zero(lh);
604 if (ctx) BN_CTX_end(ctx);
605 if (new_ctx) BN_CTX_free(new_ctx);
611 * Indicates whether two points are equal.
614 * 0 equal (in affine coordinates)
617 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
619 BIGNUM *aX, *aY, *bX, *bY;
620 BN_CTX *new_ctx = NULL;
623 if (EC_POINT_is_at_infinity(group, a))
625 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
628 if (EC_POINT_is_at_infinity(group, b))
631 if (a->Z_is_one && b->Z_is_one)
633 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
638 ctx = new_ctx = BN_CTX_new();
644 aX = BN_CTX_get(ctx);
645 aY = BN_CTX_get(ctx);
646 bX = BN_CTX_get(ctx);
647 bY = BN_CTX_get(ctx);
648 if (bY == NULL) goto err;
650 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
651 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
652 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
655 if (ctx) BN_CTX_end(ctx);
656 if (new_ctx) BN_CTX_free(new_ctx);
661 /* Forces the given EC_POINT to internally use affine coordinates. */
662 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
664 BN_CTX *new_ctx = NULL;
668 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
673 ctx = new_ctx = BN_CTX_new();
681 if (y == NULL) goto err;
683 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
684 if (!BN_copy(point->X, x)) goto err;
685 if (!BN_copy(point->Y, y)) goto err;
686 if (!BN_one(point->Z)) goto err;
691 if (ctx) BN_CTX_end(ctx);
692 if (new_ctx) BN_CTX_free(new_ctx);
697 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
698 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
702 for (i = 0; i < num; i++)
704 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
711 /* Wrapper to simple binary polynomial field multiplication implementation. */
712 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
714 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
718 /* Wrapper to simple binary polynomial field squaring implementation. */
719 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
721 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
725 /* Wrapper to simple binary polynomial field division implementation. */
726 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
728 return BN_GF2m_mod_div(r, a, b, group->field, ctx);