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>
74 #ifndef OPENSSL_NO_EC2M
77 # include <openssl/fips.h>
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
,
113 * the following three method functions are defined in ec2_mult.c
116 ec_GF2m_precompute_mult
,
117 ec_GF2m_have_precompute_mult
,
119 ec_GF2m_simple_field_mul
,
120 ec_GF2m_simple_field_sqr
,
121 ec_GF2m_simple_field_div
,
122 0 /* field_encode */ ,
123 0 /* field_decode */ ,
124 0 /* field_set_to_one */
129 return fips_ec_gf2m_simple_method();
136 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
137 * are handled by EC_GROUP_new.
139 int ec_GF2m_simple_group_init(EC_GROUP
*group
)
141 BN_init(&group
->field
);
148 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
149 * 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. Note that all other
160 * 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. Note that all other members are
177 * handled by EC_GROUP_copy.
179 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
182 if (!BN_copy(&dest
->field
, &src
->field
))
184 if (!BN_copy(&dest
->a
, &src
->a
))
186 if (!BN_copy(&dest
->b
, &src
->b
))
188 dest
->poly
[0] = src
->poly
[0];
189 dest
->poly
[1] = src
->poly
[1];
190 dest
->poly
[2] = src
->poly
[2];
191 dest
->poly
[3] = src
->poly
[3];
192 dest
->poly
[4] = src
->poly
[4];
193 dest
->poly
[5] = src
->poly
[5];
194 if (bn_wexpand(&dest
->a
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
197 if (bn_wexpand(&dest
->b
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
200 for (i
= dest
->a
.top
; i
< dest
->a
.dmax
; i
++)
202 for (i
= dest
->b
.top
; i
< dest
->b
.dmax
; i
++)
207 /* Set the curve parameters of an EC_GROUP structure. */
208 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
209 const BIGNUM
*p
, const BIGNUM
*a
,
210 const BIGNUM
*b
, BN_CTX
*ctx
)
215 if (!BN_copy(&group
->field
, p
))
217 i
= BN_GF2m_poly2arr(&group
->field
, group
->poly
, 6) - 1;
218 if ((i
!= 5) && (i
!= 3)) {
219 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
224 if (!BN_GF2m_mod_arr(&group
->a
, a
, group
->poly
))
226 if (bn_wexpand(&group
->a
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
229 for (i
= group
->a
.top
; i
< group
->a
.dmax
; i
++)
233 if (!BN_GF2m_mod_arr(&group
->b
, b
, group
->poly
))
235 if (bn_wexpand(&group
->b
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
238 for (i
= group
->b
.top
; i
< group
->b
.dmax
; i
++)
247 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
248 * then there values will not be set but the method will return with success.
250 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
,
251 BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
256 if (!BN_copy(p
, &group
->field
))
261 if (!BN_copy(a
, &group
->a
))
266 if (!BN_copy(b
, &group
->b
))
277 * Gets the degree of the field. For a curve over GF(2^m) this is the value
280 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
282 return BN_num_bits(&group
->field
) - 1;
286 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
287 * elliptic curve <=> b != 0 (mod p)
289 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
,
294 BN_CTX
*new_ctx
= NULL
;
297 ctx
= new_ctx
= BN_CTX_new();
299 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
300 ERR_R_MALLOC_FAILURE
);
309 if (!BN_GF2m_mod_arr(b
, &group
->b
, group
->poly
))
313 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
314 * curve <=> b != 0 (mod p)
325 BN_CTX_free(new_ctx
);
329 /* Initializes an EC_POINT. */
330 int ec_GF2m_simple_point_init(EC_POINT
*point
)
338 /* Frees an EC_POINT. */
339 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
346 /* Clears and frees an EC_POINT. */
347 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
349 BN_clear_free(&point
->X
);
350 BN_clear_free(&point
->Y
);
351 BN_clear_free(&point
->Z
);
356 * Copy the contents of one EC_POINT into another. Assumes dest is
359 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
361 if (!BN_copy(&dest
->X
, &src
->X
))
363 if (!BN_copy(&dest
->Y
, &src
->Y
))
365 if (!BN_copy(&dest
->Z
, &src
->Z
))
367 dest
->Z_is_one
= src
->Z_is_one
;
373 * Set an EC_POINT to the point at infinity. A point at infinity is
374 * represented by having Z=0.
376 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
385 * Set the coordinates of an EC_POINT using affine coordinates. Note that
386 * the simple implementation only uses affine coordinates.
388 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
391 const BIGNUM
*y
, BN_CTX
*ctx
)
394 if (x
== NULL
|| y
== NULL
) {
395 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
396 ERR_R_PASSED_NULL_PARAMETER
);
400 if (!BN_copy(&point
->X
, x
))
402 BN_set_negative(&point
->X
, 0);
403 if (!BN_copy(&point
->Y
, y
))
405 BN_set_negative(&point
->Y
, 0);
406 if (!BN_copy(&point
->Z
, BN_value_one()))
408 BN_set_negative(&point
->Z
, 0);
417 * Gets the affine coordinates of an EC_POINT. Note that the simple
418 * implementation only uses affine coordinates.
420 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
421 const EC_POINT
*point
,
422 BIGNUM
*x
, BIGNUM
*y
,
427 if (EC_POINT_is_at_infinity(group
, point
)) {
428 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
429 EC_R_POINT_AT_INFINITY
);
433 if (BN_cmp(&point
->Z
, BN_value_one())) {
434 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
435 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
439 if (!BN_copy(x
, &point
->X
))
441 BN_set_negative(x
, 0);
444 if (!BN_copy(y
, &point
->Y
))
446 BN_set_negative(y
, 0);
455 * Computes a + b and stores the result in r. r could be a or b, a could be
456 * b. Uses algorithm A.10.2 of IEEE P1363.
458 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
459 const EC_POINT
*b
, BN_CTX
*ctx
)
461 BN_CTX
*new_ctx
= NULL
;
462 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
465 if (EC_POINT_is_at_infinity(group
, a
)) {
466 if (!EC_POINT_copy(r
, b
))
471 if (EC_POINT_is_at_infinity(group
, b
)) {
472 if (!EC_POINT_copy(r
, a
))
478 ctx
= new_ctx
= BN_CTX_new();
484 x0
= BN_CTX_get(ctx
);
485 y0
= BN_CTX_get(ctx
);
486 x1
= BN_CTX_get(ctx
);
487 y1
= BN_CTX_get(ctx
);
488 x2
= BN_CTX_get(ctx
);
489 y2
= BN_CTX_get(ctx
);
496 if (!BN_copy(x0
, &a
->X
))
498 if (!BN_copy(y0
, &a
->Y
))
501 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, x0
, y0
, ctx
))
505 if (!BN_copy(x1
, &b
->X
))
507 if (!BN_copy(y1
, &b
->Y
))
510 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, x1
, y1
, ctx
))
514 if (BN_GF2m_cmp(x0
, x1
)) {
515 if (!BN_GF2m_add(t
, x0
, x1
))
517 if (!BN_GF2m_add(s
, y0
, y1
))
519 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
521 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
523 if (!BN_GF2m_add(x2
, x2
, &group
->a
))
525 if (!BN_GF2m_add(x2
, x2
, s
))
527 if (!BN_GF2m_add(x2
, x2
, t
))
530 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
531 if (!EC_POINT_set_to_infinity(group
, r
))
536 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
538 if (!BN_GF2m_add(s
, s
, x1
))
541 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
543 if (!BN_GF2m_add(x2
, x2
, s
))
545 if (!BN_GF2m_add(x2
, x2
, &group
->a
))
549 if (!BN_GF2m_add(y2
, x1
, x2
))
551 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
553 if (!BN_GF2m_add(y2
, y2
, x2
))
555 if (!BN_GF2m_add(y2
, y2
, y1
))
558 if (!EC_POINT_set_affine_coordinates_GF2m(group
, r
, x2
, y2
, ctx
))
566 BN_CTX_free(new_ctx
);
571 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
572 * A.10.2 of IEEE P1363.
574 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
577 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
580 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
582 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(&point
->Y
))
583 /* point is its own inverse */
586 if (!EC_POINT_make_affine(group
, point
, ctx
))
588 return BN_GF2m_add(&point
->Y
, &point
->X
, &point
->Y
);
591 /* Indicates whether the given point is the point at infinity. */
592 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
593 const EC_POINT
*point
)
595 return BN_is_zero(&point
->Z
);
599 * Determines whether the given EC_POINT is an actual point on the curve defined
600 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
601 * y^2 + x*y = x^3 + a*x^2 + b.
603 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
607 BN_CTX
*new_ctx
= NULL
;
609 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
610 const BIGNUM
*, BN_CTX
*);
611 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
613 if (EC_POINT_is_at_infinity(group
, point
))
616 field_mul
= group
->meth
->field_mul
;
617 field_sqr
= group
->meth
->field_sqr
;
619 /* only support affine coordinates */
620 if (!point
->Z_is_one
)
624 ctx
= new_ctx
= BN_CTX_new();
630 y2
= BN_CTX_get(ctx
);
631 lh
= BN_CTX_get(ctx
);
636 * We have a curve defined by a Weierstrass equation
637 * y^2 + x*y = x^3 + a*x^2 + b.
638 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
639 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
641 if (!BN_GF2m_add(lh
, &point
->X
, &group
->a
))
643 if (!field_mul(group
, lh
, lh
, &point
->X
, ctx
))
645 if (!BN_GF2m_add(lh
, lh
, &point
->Y
))
647 if (!field_mul(group
, lh
, lh
, &point
->X
, ctx
))
649 if (!BN_GF2m_add(lh
, lh
, &group
->b
))
651 if (!field_sqr(group
, y2
, &point
->Y
, ctx
))
653 if (!BN_GF2m_add(lh
, lh
, y2
))
655 ret
= BN_is_zero(lh
);
660 BN_CTX_free(new_ctx
);
665 * Indicates whether two points are equal.
668 * 0 equal (in affine coordinates)
671 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
672 const EC_POINT
*b
, BN_CTX
*ctx
)
674 BIGNUM
*aX
, *aY
, *bX
, *bY
;
675 BN_CTX
*new_ctx
= NULL
;
678 if (EC_POINT_is_at_infinity(group
, a
)) {
679 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
682 if (EC_POINT_is_at_infinity(group
, b
))
685 if (a
->Z_is_one
&& b
->Z_is_one
) {
686 return ((BN_cmp(&a
->X
, &b
->X
) == 0)
687 && BN_cmp(&a
->Y
, &b
->Y
) == 0) ? 0 : 1;
691 ctx
= new_ctx
= BN_CTX_new();
697 aX
= BN_CTX_get(ctx
);
698 aY
= BN_CTX_get(ctx
);
699 bX
= BN_CTX_get(ctx
);
700 bY
= BN_CTX_get(ctx
);
704 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
))
706 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
))
708 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
714 BN_CTX_free(new_ctx
);
718 /* Forces the given EC_POINT to internally use affine coordinates. */
719 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
722 BN_CTX
*new_ctx
= NULL
;
726 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
730 ctx
= new_ctx
= BN_CTX_new();
741 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
))
743 if (!BN_copy(&point
->X
, x
))
745 if (!BN_copy(&point
->Y
, y
))
747 if (!BN_one(&point
->Z
))
757 BN_CTX_free(new_ctx
);
762 * Forces each of the EC_POINTs in the given array to use affine coordinates.
764 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
765 EC_POINT
*points
[], BN_CTX
*ctx
)
769 for (i
= 0; i
< num
; i
++) {
770 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
777 /* Wrapper to simple binary polynomial field multiplication implementation. */
778 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
779 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
781 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
784 /* Wrapper to simple binary polynomial field squaring implementation. */
785 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
786 const BIGNUM
*a
, BN_CTX
*ctx
)
788 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
791 /* Wrapper to simple binary polynomial field division implementation. */
792 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
793 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
795 return BN_GF2m_mod_div(r
, a
, b
, &group
->field
, ctx
);