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 #include <openssl/err.h>
72 #include "internal/bn_int.h"
75 #ifndef OPENSSL_NO_EC2M
77 const EC_METHOD
*EC_GF2m_simple_method(void)
79 static const EC_METHOD ret
= {
81 NID_X9_62_characteristic_two_field
,
82 ec_GF2m_simple_group_init
,
83 ec_GF2m_simple_group_finish
,
84 ec_GF2m_simple_group_clear_finish
,
85 ec_GF2m_simple_group_copy
,
86 ec_GF2m_simple_group_set_curve
,
87 ec_GF2m_simple_group_get_curve
,
88 ec_GF2m_simple_group_get_degree
,
89 ec_GF2m_simple_group_check_discriminant
,
90 ec_GF2m_simple_point_init
,
91 ec_GF2m_simple_point_finish
,
92 ec_GF2m_simple_point_clear_finish
,
93 ec_GF2m_simple_point_copy
,
94 ec_GF2m_simple_point_set_to_infinity
,
95 0 /* set_Jprojective_coordinates_GFp */ ,
96 0 /* get_Jprojective_coordinates_GFp */ ,
97 ec_GF2m_simple_point_set_affine_coordinates
,
98 ec_GF2m_simple_point_get_affine_coordinates
,
102 ec_GF2m_simple_invert
,
103 ec_GF2m_simple_is_at_infinity
,
104 ec_GF2m_simple_is_on_curve
,
106 ec_GF2m_simple_make_affine
,
107 ec_GF2m_simple_points_make_affine
,
110 * 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 */
128 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
129 * 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 BN_free(group
->field
);
150 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
151 * handled by EC_GROUP_free.
153 void ec_GF2m_simple_group_finish(EC_GROUP
*group
)
155 BN_free(group
->field
);
161 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
162 * members are handled by EC_GROUP_clear_free.
164 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*group
)
166 BN_clear_free(group
->field
);
167 BN_clear_free(group
->a
);
168 BN_clear_free(group
->b
);
178 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
179 * handled by EC_GROUP_copy.
181 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
183 if (!BN_copy(dest
->field
, src
->field
))
185 if (!BN_copy(dest
->a
, src
->a
))
187 if (!BN_copy(dest
->b
, src
->b
))
189 dest
->poly
[0] = src
->poly
[0];
190 dest
->poly
[1] = src
->poly
[1];
191 dest
->poly
[2] = src
->poly
[2];
192 dest
->poly
[3] = src
->poly
[3];
193 dest
->poly
[4] = src
->poly
[4];
194 dest
->poly
[5] = src
->poly
[5];
195 if (bn_wexpand(dest
->a
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
198 if (bn_wexpand(dest
->b
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
201 bn_set_all_zero(dest
->a
);
202 bn_set_all_zero(dest
->b
);
206 /* Set the curve parameters of an EC_GROUP structure. */
207 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
208 const BIGNUM
*p
, const BIGNUM
*a
,
209 const BIGNUM
*b
, BN_CTX
*ctx
)
214 if (!BN_copy(group
->field
, p
))
216 i
= BN_GF2m_poly2arr(group
->field
, group
->poly
, 6) - 1;
217 if ((i
!= 5) && (i
!= 3)) {
218 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
223 if (!BN_GF2m_mod_arr(group
->a
, a
, group
->poly
))
225 if (bn_wexpand(group
->a
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
228 bn_set_all_zero(group
->a
);
231 if (!BN_GF2m_mod_arr(group
->b
, b
, group
->poly
))
233 if (bn_wexpand(group
->b
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
236 bn_set_all_zero(group
->b
);
244 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
245 * then there values will not be set but the method will return with success.
247 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
,
248 BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
253 if (!BN_copy(p
, group
->field
))
258 if (!BN_copy(a
, group
->a
))
263 if (!BN_copy(b
, group
->b
))
274 * Gets the degree of the field. For a curve over GF(2^m) this is the value
277 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
279 return BN_num_bits(group
->field
) - 1;
283 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
284 * elliptic curve <=> b != 0 (mod p)
286 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
,
291 BN_CTX
*new_ctx
= NULL
;
294 ctx
= new_ctx
= BN_CTX_new();
296 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
297 ERR_R_MALLOC_FAILURE
);
306 if (!BN_GF2m_mod_arr(b
, group
->b
, group
->poly
))
310 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
311 * curve <=> b != 0 (mod p)
322 BN_CTX_free(new_ctx
);
326 /* Initializes an EC_POINT. */
327 int ec_GF2m_simple_point_init(EC_POINT
*point
)
333 if (!point
->X
|| !point
->Y
|| !point
->Z
) {
345 /* Frees an EC_POINT. */
346 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
353 /* Clears and frees an EC_POINT. */
354 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
356 BN_clear_free(point
->X
);
357 BN_clear_free(point
->Y
);
358 BN_clear_free(point
->Z
);
363 * Copy the contents of one EC_POINT into another. Assumes dest is
366 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
368 if (!BN_copy(dest
->X
, src
->X
))
370 if (!BN_copy(dest
->Y
, src
->Y
))
372 if (!BN_copy(dest
->Z
, src
->Z
))
374 dest
->Z_is_one
= src
->Z_is_one
;
380 * Set an EC_POINT to the point at infinity. A point at infinity is
381 * represented by having Z=0.
383 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
392 * Set the coordinates of an EC_POINT using affine coordinates. Note that
393 * the simple implementation only uses affine coordinates.
395 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
398 const BIGNUM
*y
, BN_CTX
*ctx
)
401 if (x
== NULL
|| y
== NULL
) {
402 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
403 ERR_R_PASSED_NULL_PARAMETER
);
407 if (!BN_copy(point
->X
, x
))
409 BN_set_negative(point
->X
, 0);
410 if (!BN_copy(point
->Y
, y
))
412 BN_set_negative(point
->Y
, 0);
413 if (!BN_copy(point
->Z
, BN_value_one()))
415 BN_set_negative(point
->Z
, 0);
424 * Gets the affine coordinates of an EC_POINT. Note that the simple
425 * implementation only uses affine coordinates.
427 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
428 const EC_POINT
*point
,
429 BIGNUM
*x
, BIGNUM
*y
,
434 if (EC_POINT_is_at_infinity(group
, point
)) {
435 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
436 EC_R_POINT_AT_INFINITY
);
440 if (BN_cmp(point
->Z
, BN_value_one())) {
441 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
442 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
446 if (!BN_copy(x
, point
->X
))
448 BN_set_negative(x
, 0);
451 if (!BN_copy(y
, point
->Y
))
453 BN_set_negative(y
, 0);
462 * Computes a + b and stores the result in r. r could be a or b, a could be
463 * b. Uses algorithm A.10.2 of IEEE P1363.
465 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
466 const EC_POINT
*b
, BN_CTX
*ctx
)
468 BN_CTX
*new_ctx
= NULL
;
469 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
472 if (EC_POINT_is_at_infinity(group
, a
)) {
473 if (!EC_POINT_copy(r
, b
))
478 if (EC_POINT_is_at_infinity(group
, b
)) {
479 if (!EC_POINT_copy(r
, a
))
485 ctx
= new_ctx
= BN_CTX_new();
491 x0
= BN_CTX_get(ctx
);
492 y0
= BN_CTX_get(ctx
);
493 x1
= BN_CTX_get(ctx
);
494 y1
= BN_CTX_get(ctx
);
495 x2
= BN_CTX_get(ctx
);
496 y2
= BN_CTX_get(ctx
);
503 if (!BN_copy(x0
, a
->X
))
505 if (!BN_copy(y0
, a
->Y
))
508 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, x0
, y0
, ctx
))
512 if (!BN_copy(x1
, b
->X
))
514 if (!BN_copy(y1
, b
->Y
))
517 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, x1
, y1
, ctx
))
521 if (BN_GF2m_cmp(x0
, x1
)) {
522 if (!BN_GF2m_add(t
, x0
, x1
))
524 if (!BN_GF2m_add(s
, y0
, y1
))
526 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
528 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
530 if (!BN_GF2m_add(x2
, x2
, group
->a
))
532 if (!BN_GF2m_add(x2
, x2
, s
))
534 if (!BN_GF2m_add(x2
, x2
, t
))
537 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
538 if (!EC_POINT_set_to_infinity(group
, r
))
543 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
545 if (!BN_GF2m_add(s
, s
, x1
))
548 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
550 if (!BN_GF2m_add(x2
, x2
, s
))
552 if (!BN_GF2m_add(x2
, x2
, group
->a
))
556 if (!BN_GF2m_add(y2
, x1
, x2
))
558 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
560 if (!BN_GF2m_add(y2
, y2
, x2
))
562 if (!BN_GF2m_add(y2
, y2
, y1
))
565 if (!EC_POINT_set_affine_coordinates_GF2m(group
, r
, x2
, y2
, ctx
))
573 BN_CTX_free(new_ctx
);
578 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
579 * A.10.2 of IEEE P1363.
581 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
584 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
587 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
589 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(point
->Y
))
590 /* point is its own inverse */
593 if (!EC_POINT_make_affine(group
, point
, ctx
))
595 return BN_GF2m_add(point
->Y
, point
->X
, point
->Y
);
598 /* Indicates whether the given point is the point at infinity. */
599 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
600 const EC_POINT
*point
)
602 return BN_is_zero(point
->Z
);
606 * Determines whether the given EC_POINT is an actual point on the curve defined
607 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
608 * y^2 + x*y = x^3 + a*x^2 + b.
610 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
614 BN_CTX
*new_ctx
= NULL
;
616 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
617 const BIGNUM
*, BN_CTX
*);
618 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
620 if (EC_POINT_is_at_infinity(group
, point
))
623 field_mul
= group
->meth
->field_mul
;
624 field_sqr
= group
->meth
->field_sqr
;
626 /* only support affine coordinates */
627 if (!point
->Z_is_one
)
631 ctx
= new_ctx
= BN_CTX_new();
637 y2
= BN_CTX_get(ctx
);
638 lh
= BN_CTX_get(ctx
);
643 * We have a curve defined by a Weierstrass equation
644 * y^2 + x*y = x^3 + a*x^2 + b.
645 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
646 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
648 if (!BN_GF2m_add(lh
, point
->X
, group
->a
))
650 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
652 if (!BN_GF2m_add(lh
, lh
, point
->Y
))
654 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
656 if (!BN_GF2m_add(lh
, lh
, group
->b
))
658 if (!field_sqr(group
, y2
, point
->Y
, ctx
))
660 if (!BN_GF2m_add(lh
, lh
, y2
))
662 ret
= BN_is_zero(lh
);
667 BN_CTX_free(new_ctx
);
672 * Indicates whether two points are equal.
675 * 0 equal (in affine coordinates)
678 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
679 const EC_POINT
*b
, BN_CTX
*ctx
)
681 BIGNUM
*aX
, *aY
, *bX
, *bY
;
682 BN_CTX
*new_ctx
= NULL
;
685 if (EC_POINT_is_at_infinity(group
, a
)) {
686 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
689 if (EC_POINT_is_at_infinity(group
, b
))
692 if (a
->Z_is_one
&& b
->Z_is_one
) {
693 return ((BN_cmp(a
->X
, b
->X
) == 0) && BN_cmp(a
->Y
, b
->Y
) == 0) ? 0 : 1;
697 ctx
= new_ctx
= BN_CTX_new();
703 aX
= BN_CTX_get(ctx
);
704 aY
= BN_CTX_get(ctx
);
705 bX
= BN_CTX_get(ctx
);
706 bY
= BN_CTX_get(ctx
);
710 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
))
712 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
))
714 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
720 BN_CTX_free(new_ctx
);
724 /* Forces the given EC_POINT to internally use affine coordinates. */
725 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
728 BN_CTX
*new_ctx
= NULL
;
732 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
736 ctx
= new_ctx
= BN_CTX_new();
747 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
))
749 if (!BN_copy(point
->X
, x
))
751 if (!BN_copy(point
->Y
, y
))
753 if (!BN_one(point
->Z
))
762 BN_CTX_free(new_ctx
);
767 * Forces each of the EC_POINTs in the given array to use affine coordinates.
769 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
770 EC_POINT
*points
[], BN_CTX
*ctx
)
774 for (i
= 0; i
< num
; i
++) {
775 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
782 /* Wrapper to simple binary polynomial field multiplication implementation. */
783 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
784 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
786 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
789 /* Wrapper to simple binary polynomial field squaring implementation. */
790 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
791 const BIGNUM
*a
, BN_CTX
*ctx
)
793 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
796 /* Wrapper to simple binary polynomial field division implementation. */
797 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
798 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
800 return BN_GF2m_mod_div(r
, a
, b
, group
->field
, ctx
);