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).
70 #define OPENSSL_FIPSAPI
72 #include <openssl/err.h>
76 #ifndef OPENSSL_NO_EC2M
79 const EC_METHOD *EC_GF2m_simple_method(void)
81 static const EC_METHOD ret = {
83 NID_X9_62_characteristic_two_field,
84 ec_GF2m_simple_group_init,
85 ec_GF2m_simple_group_finish,
86 ec_GF2m_simple_group_clear_finish,
87 ec_GF2m_simple_group_copy,
88 ec_GF2m_simple_group_set_curve,
89 ec_GF2m_simple_group_get_curve,
90 ec_GF2m_simple_group_get_degree,
91 ec_GF2m_simple_group_check_discriminant,
92 ec_GF2m_simple_point_init,
93 ec_GF2m_simple_point_finish,
94 ec_GF2m_simple_point_clear_finish,
95 ec_GF2m_simple_point_copy,
96 ec_GF2m_simple_point_set_to_infinity,
97 0 /* set_Jprojective_coordinates_GFp */,
98 0 /* get_Jprojective_coordinates_GFp */,
99 ec_GF2m_simple_point_set_affine_coordinates,
100 ec_GF2m_simple_point_get_affine_coordinates,
104 ec_GF2m_simple_invert,
105 ec_GF2m_simple_is_at_infinity,
106 ec_GF2m_simple_is_on_curve,
108 ec_GF2m_simple_make_affine,
109 ec_GF2m_simple_points_make_affine,
111 /* the following three method functions are defined in ec2_mult.c */
113 ec_GF2m_precompute_mult,
114 ec_GF2m_have_precompute_mult,
116 ec_GF2m_simple_field_mul,
117 ec_GF2m_simple_field_sqr,
118 ec_GF2m_simple_field_div,
119 0 /* field_encode */,
120 0 /* field_decode */,
121 0 /* field_set_to_one */ };
127 /* Initialize a GF(2^m)-based EC_GROUP structure.
128 * Note that all other members are handled by EC_GROUP_new.
130 int ec_GF2m_simple_group_init(EC_GROUP *group)
132 BN_init(&group->field);
139 /* Free a GF(2^m)-based EC_GROUP structure.
140 * Note that all other members are handled by EC_GROUP_free.
142 void ec_GF2m_simple_group_finish(EC_GROUP *group)
144 BN_free(&group->field);
150 /* Clear and free a GF(2^m)-based EC_GROUP structure.
151 * Note that all other members are handled by EC_GROUP_clear_free.
153 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
155 BN_clear_free(&group->field);
156 BN_clear_free(&group->a);
157 BN_clear_free(&group->b);
167 /* Copy a GF(2^m)-based EC_GROUP structure.
168 * Note that all other members are handled by EC_GROUP_copy.
170 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
173 if (!BN_copy(&dest->field, &src->field)) return 0;
174 if (!BN_copy(&dest->a, &src->a)) return 0;
175 if (!BN_copy(&dest->b, &src->b)) return 0;
176 dest->poly[0] = src->poly[0];
177 dest->poly[1] = src->poly[1];
178 dest->poly[2] = src->poly[2];
179 dest->poly[3] = src->poly[3];
180 dest->poly[4] = src->poly[4];
181 dest->poly[5] = src->poly[5];
182 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
183 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
184 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
185 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
190 /* Set the curve parameters of an EC_GROUP structure. */
191 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
192 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
197 if (!BN_copy(&group->field, p)) goto err;
198 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
199 if ((i != 5) && (i != 3))
201 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
206 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
207 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
208 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
211 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
212 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
213 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
221 /* Get the curve parameters of an EC_GROUP structure.
222 * If p, a, or b are NULL then there values will not be set but the method will return with success.
224 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
230 if (!BN_copy(p, &group->field)) return 0;
235 if (!BN_copy(a, &group->a)) goto err;
240 if (!BN_copy(b, &group->b)) goto err;
250 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
251 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
253 return BN_num_bits(&group->field)-1;
257 /* Checks the discriminant of the curve.
258 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
260 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
264 BN_CTX *new_ctx = NULL;
268 ctx = new_ctx = BN_CTX_new();
271 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
277 if (b == NULL) goto err;
279 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
281 /* check the discriminant:
282 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
284 if (BN_is_zero(b)) goto err;
292 BN_CTX_free(new_ctx);
297 /* Initializes an EC_POINT. */
298 int ec_GF2m_simple_point_init(EC_POINT *point)
307 /* Frees an EC_POINT. */
308 void ec_GF2m_simple_point_finish(EC_POINT *point)
316 /* Clears and frees an EC_POINT. */
317 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
319 BN_clear_free(&point->X);
320 BN_clear_free(&point->Y);
321 BN_clear_free(&point->Z);
326 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
327 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
329 if (!BN_copy(&dest->X, &src->X)) return 0;
330 if (!BN_copy(&dest->Y, &src->Y)) return 0;
331 if (!BN_copy(&dest->Z, &src->Z)) return 0;
332 dest->Z_is_one = src->Z_is_one;
338 /* Set an EC_POINT to the point at infinity.
339 * A point at infinity is represented by having Z=0.
341 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
349 /* Set the coordinates of an EC_POINT using affine coordinates.
350 * Note that the simple implementation only uses affine coordinates.
352 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
353 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
356 if (x == NULL || y == NULL)
358 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
362 if (!BN_copy(&point->X, x)) goto err;
363 BN_set_negative(&point->X, 0);
364 if (!BN_copy(&point->Y, y)) goto err;
365 BN_set_negative(&point->Y, 0);
366 if (!BN_copy(&point->Z, BN_value_one())) goto err;
367 BN_set_negative(&point->Z, 0);
376 /* Gets the affine coordinates of an EC_POINT.
377 * Note that the simple implementation only uses affine coordinates.
379 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
380 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
384 if (EC_POINT_is_at_infinity(group, point))
386 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
390 if (BN_cmp(&point->Z, BN_value_one()))
392 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
397 if (!BN_copy(x, &point->X)) goto err;
398 BN_set_negative(x, 0);
402 if (!BN_copy(y, &point->Y)) goto err;
403 BN_set_negative(y, 0);
411 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
412 * Uses algorithm A.10.2 of IEEE P1363.
414 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
416 BN_CTX *new_ctx = NULL;
417 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
420 if (EC_POINT_is_at_infinity(group, a))
422 if (!EC_POINT_copy(r, b)) return 0;
426 if (EC_POINT_is_at_infinity(group, b))
428 if (!EC_POINT_copy(r, a)) return 0;
434 ctx = new_ctx = BN_CTX_new();
440 x0 = BN_CTX_get(ctx);
441 y0 = BN_CTX_get(ctx);
442 x1 = BN_CTX_get(ctx);
443 y1 = BN_CTX_get(ctx);
444 x2 = BN_CTX_get(ctx);
445 y2 = BN_CTX_get(ctx);
448 if (t == NULL) goto err;
452 if (!BN_copy(x0, &a->X)) goto err;
453 if (!BN_copy(y0, &a->Y)) goto err;
457 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
461 if (!BN_copy(x1, &b->X)) goto err;
462 if (!BN_copy(y1, &b->Y)) goto err;
466 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
470 if (BN_GF2m_cmp(x0, x1))
472 if (!BN_GF2m_add(t, x0, x1)) goto err;
473 if (!BN_GF2m_add(s, y0, y1)) goto err;
474 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
475 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
476 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
477 if (!BN_GF2m_add(x2, x2, s)) goto err;
478 if (!BN_GF2m_add(x2, x2, t)) goto err;
482 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
484 if (!EC_POINT_set_to_infinity(group, r)) goto err;
488 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
489 if (!BN_GF2m_add(s, s, x1)) goto err;
491 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
492 if (!BN_GF2m_add(x2, x2, s)) goto err;
493 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
496 if (!BN_GF2m_add(y2, x1, x2)) goto err;
497 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
498 if (!BN_GF2m_add(y2, y2, x2)) goto err;
499 if (!BN_GF2m_add(y2, y2, y1)) goto err;
501 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
508 BN_CTX_free(new_ctx);
513 /* Computes 2 * a and stores the result in r. r could be a.
514 * Uses algorithm A.10.2 of IEEE P1363.
516 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
518 return ec_GF2m_simple_add(group, r, a, a, ctx);
522 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
524 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
525 /* point is its own inverse */
528 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
529 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
533 /* Indicates whether the given point is the point at infinity. */
534 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
536 return BN_is_zero(&point->Z);
540 /* Determines whether the given EC_POINT is an actual point on the curve defined
541 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
542 * y^2 + x*y = x^3 + a*x^2 + b.
544 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
547 BN_CTX *new_ctx = NULL;
549 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
550 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
552 if (EC_POINT_is_at_infinity(group, point))
555 field_mul = group->meth->field_mul;
556 field_sqr = group->meth->field_sqr;
558 /* only support affine coordinates */
559 if (!point->Z_is_one) goto err;
563 ctx = new_ctx = BN_CTX_new();
569 y2 = BN_CTX_get(ctx);
570 lh = BN_CTX_get(ctx);
571 if (lh == NULL) goto err;
573 /* We have a curve defined by a Weierstrass equation
574 * y^2 + x*y = x^3 + a*x^2 + b.
575 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
576 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
578 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
579 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
580 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
581 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
582 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
583 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
584 if (!BN_GF2m_add(lh, lh, y2)) goto err;
585 ret = BN_is_zero(lh);
587 if (ctx) BN_CTX_end(ctx);
588 if (new_ctx) BN_CTX_free(new_ctx);
593 /* Indicates whether two points are equal.
596 * 0 equal (in affine coordinates)
599 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
601 BIGNUM *aX, *aY, *bX, *bY;
602 BN_CTX *new_ctx = NULL;
605 if (EC_POINT_is_at_infinity(group, a))
607 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
610 if (EC_POINT_is_at_infinity(group, b))
613 if (a->Z_is_one && b->Z_is_one)
615 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
620 ctx = new_ctx = BN_CTX_new();
626 aX = BN_CTX_get(ctx);
627 aY = BN_CTX_get(ctx);
628 bX = BN_CTX_get(ctx);
629 bY = BN_CTX_get(ctx);
630 if (bY == NULL) goto err;
632 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
633 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
634 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
637 if (ctx) BN_CTX_end(ctx);
638 if (new_ctx) BN_CTX_free(new_ctx);
643 /* Forces the given EC_POINT to internally use affine coordinates. */
644 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
646 BN_CTX *new_ctx = NULL;
650 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
655 ctx = new_ctx = BN_CTX_new();
663 if (y == NULL) goto err;
665 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
666 if (!BN_copy(&point->X, x)) goto err;
667 if (!BN_copy(&point->Y, y)) goto err;
668 if (!BN_one(&point->Z)) goto err;
673 if (ctx) BN_CTX_end(ctx);
674 if (new_ctx) BN_CTX_free(new_ctx);
679 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
680 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
684 for (i = 0; i < num; i++)
686 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
693 /* Wrapper to simple binary polynomial field multiplication implementation. */
694 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
696 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
700 /* Wrapper to simple binary polynomial field squaring implementation. */
701 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
703 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
707 /* Wrapper to simple binary polynomial field division implementation. */
708 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
710 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);