2 * Copyright 2002-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
11 #include <openssl/err.h>
13 #include "crypto/bn.h"
16 #ifndef OPENSSL_NO_EC2M
19 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
20 * are handled by EC_GROUP_new.
22 int ec_GF2m_simple_group_init(EC_GROUP
*group
)
24 group
->field
= BN_new();
28 if (group
->field
== NULL
|| group
->a
== NULL
|| group
->b
== NULL
) {
29 BN_free(group
->field
);
38 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
39 * handled by EC_GROUP_free.
41 void ec_GF2m_simple_group_finish(EC_GROUP
*group
)
43 BN_free(group
->field
);
49 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
50 * members are handled by EC_GROUP_clear_free.
52 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*group
)
54 BN_clear_free(group
->field
);
55 BN_clear_free(group
->a
);
56 BN_clear_free(group
->b
);
66 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
67 * handled by EC_GROUP_copy.
69 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
71 if (!BN_copy(dest
->field
, src
->field
))
73 if (!BN_copy(dest
->a
, src
->a
))
75 if (!BN_copy(dest
->b
, src
->b
))
77 dest
->poly
[0] = src
->poly
[0];
78 dest
->poly
[1] = src
->poly
[1];
79 dest
->poly
[2] = src
->poly
[2];
80 dest
->poly
[3] = src
->poly
[3];
81 dest
->poly
[4] = src
->poly
[4];
82 dest
->poly
[5] = src
->poly
[5];
83 if (bn_wexpand(dest
->a
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
86 if (bn_wexpand(dest
->b
, (int)(dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
) ==
89 bn_set_all_zero(dest
->a
);
90 bn_set_all_zero(dest
->b
);
94 /* Set the curve parameters of an EC_GROUP structure. */
95 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
96 const BIGNUM
*p
, const BIGNUM
*a
,
97 const BIGNUM
*b
, BN_CTX
*ctx
)
102 if (!BN_copy(group
->field
, p
))
104 i
= BN_GF2m_poly2arr(group
->field
, group
->poly
, 6) - 1;
105 if ((i
!= 5) && (i
!= 3)) {
106 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
111 if (!BN_GF2m_mod_arr(group
->a
, a
, group
->poly
))
113 if (bn_wexpand(group
->a
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
116 bn_set_all_zero(group
->a
);
119 if (!BN_GF2m_mod_arr(group
->b
, b
, group
->poly
))
121 if (bn_wexpand(group
->b
, (int)(group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
)
124 bn_set_all_zero(group
->b
);
132 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
133 * then there values will not be set but the method will return with success.
135 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
,
136 BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
141 if (!BN_copy(p
, group
->field
))
146 if (!BN_copy(a
, group
->a
))
151 if (!BN_copy(b
, group
->b
))
162 * Gets the degree of the field. For a curve over GF(2^m) this is the value
165 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
167 return BN_num_bits(group
->field
) - 1;
171 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
172 * elliptic curve <=> b != 0 (mod p)
174 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
,
180 BN_CTX
*new_ctx
= NULL
;
183 ctx
= new_ctx
= BN_CTX_new();
185 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
186 ERR_R_MALLOC_FAILURE
);
196 if (!BN_GF2m_mod_arr(b
, group
->b
, group
->poly
))
200 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
201 * curve <=> b != 0 (mod p)
211 BN_CTX_free(new_ctx
);
216 /* Initializes an EC_POINT. */
217 int ec_GF2m_simple_point_init(EC_POINT
*point
)
223 if (point
->X
== NULL
|| point
->Y
== NULL
|| point
->Z
== NULL
) {
232 /* Frees an EC_POINT. */
233 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
240 /* Clears and frees an EC_POINT. */
241 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
243 BN_clear_free(point
->X
);
244 BN_clear_free(point
->Y
);
245 BN_clear_free(point
->Z
);
250 * Copy the contents of one EC_POINT into another. Assumes dest is
253 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
255 if (!BN_copy(dest
->X
, src
->X
))
257 if (!BN_copy(dest
->Y
, src
->Y
))
259 if (!BN_copy(dest
->Z
, src
->Z
))
261 dest
->Z_is_one
= src
->Z_is_one
;
262 dest
->curve_name
= src
->curve_name
;
268 * Set an EC_POINT to the point at infinity. A point at infinity is
269 * represented by having Z=0.
271 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
280 * Set the coordinates of an EC_POINT using affine coordinates. Note that
281 * the simple implementation only uses affine coordinates.
283 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
286 const BIGNUM
*y
, BN_CTX
*ctx
)
289 if (x
== NULL
|| y
== NULL
) {
290 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
291 ERR_R_PASSED_NULL_PARAMETER
);
295 if (!BN_copy(point
->X
, x
))
297 BN_set_negative(point
->X
, 0);
298 if (!BN_copy(point
->Y
, y
))
300 BN_set_negative(point
->Y
, 0);
301 if (!BN_copy(point
->Z
, BN_value_one()))
303 BN_set_negative(point
->Z
, 0);
312 * Gets the affine coordinates of an EC_POINT. Note that the simple
313 * implementation only uses affine coordinates.
315 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
316 const EC_POINT
*point
,
317 BIGNUM
*x
, BIGNUM
*y
,
322 if (EC_POINT_is_at_infinity(group
, point
)) {
323 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
324 EC_R_POINT_AT_INFINITY
);
328 if (BN_cmp(point
->Z
, BN_value_one())) {
329 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
330 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
334 if (!BN_copy(x
, point
->X
))
336 BN_set_negative(x
, 0);
339 if (!BN_copy(y
, point
->Y
))
341 BN_set_negative(y
, 0);
350 * Computes a + b and stores the result in r. r could be a or b, a could be
351 * b. Uses algorithm A.10.2 of IEEE P1363.
353 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
354 const EC_POINT
*b
, BN_CTX
*ctx
)
356 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
359 BN_CTX
*new_ctx
= NULL
;
362 if (EC_POINT_is_at_infinity(group
, a
)) {
363 if (!EC_POINT_copy(r
, b
))
368 if (EC_POINT_is_at_infinity(group
, b
)) {
369 if (!EC_POINT_copy(r
, a
))
376 ctx
= new_ctx
= BN_CTX_new();
383 x0
= BN_CTX_get(ctx
);
384 y0
= BN_CTX_get(ctx
);
385 x1
= BN_CTX_get(ctx
);
386 y1
= BN_CTX_get(ctx
);
387 x2
= BN_CTX_get(ctx
);
388 y2
= BN_CTX_get(ctx
);
395 if (!BN_copy(x0
, a
->X
))
397 if (!BN_copy(y0
, a
->Y
))
400 if (!EC_POINT_get_affine_coordinates(group
, a
, x0
, y0
, ctx
))
404 if (!BN_copy(x1
, b
->X
))
406 if (!BN_copy(y1
, b
->Y
))
409 if (!EC_POINT_get_affine_coordinates(group
, b
, x1
, y1
, ctx
))
413 if (BN_GF2m_cmp(x0
, x1
)) {
414 if (!BN_GF2m_add(t
, x0
, x1
))
416 if (!BN_GF2m_add(s
, y0
, y1
))
418 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
420 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
422 if (!BN_GF2m_add(x2
, x2
, group
->a
))
424 if (!BN_GF2m_add(x2
, x2
, s
))
426 if (!BN_GF2m_add(x2
, x2
, t
))
429 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
430 if (!EC_POINT_set_to_infinity(group
, r
))
435 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
437 if (!BN_GF2m_add(s
, s
, x1
))
440 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
442 if (!BN_GF2m_add(x2
, x2
, s
))
444 if (!BN_GF2m_add(x2
, x2
, group
->a
))
448 if (!BN_GF2m_add(y2
, x1
, x2
))
450 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
452 if (!BN_GF2m_add(y2
, y2
, x2
))
454 if (!BN_GF2m_add(y2
, y2
, y1
))
457 if (!EC_POINT_set_affine_coordinates(group
, r
, x2
, y2
, ctx
))
465 BN_CTX_free(new_ctx
);
471 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
472 * A.10.2 of IEEE P1363.
474 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
477 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
480 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
482 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(point
->Y
))
483 /* point is its own inverse */
486 if (!EC_POINT_make_affine(group
, point
, ctx
))
488 return BN_GF2m_add(point
->Y
, point
->X
, point
->Y
);
491 /* Indicates whether the given point is the point at infinity. */
492 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
493 const EC_POINT
*point
)
495 return BN_is_zero(point
->Z
);
499 * Determines whether the given EC_POINT is an actual point on the curve defined
500 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
501 * y^2 + x*y = x^3 + a*x^2 + b.
503 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
508 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
509 const BIGNUM
*, BN_CTX
*);
510 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
512 BN_CTX
*new_ctx
= NULL
;
515 if (EC_POINT_is_at_infinity(group
, point
))
518 field_mul
= group
->meth
->field_mul
;
519 field_sqr
= group
->meth
->field_sqr
;
521 /* only support affine coordinates */
522 if (!point
->Z_is_one
)
527 ctx
= new_ctx
= BN_CTX_new();
534 y2
= BN_CTX_get(ctx
);
535 lh
= BN_CTX_get(ctx
);
540 * We have a curve defined by a Weierstrass equation
541 * y^2 + x*y = x^3 + a*x^2 + b.
542 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
543 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
545 if (!BN_GF2m_add(lh
, point
->X
, group
->a
))
547 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
549 if (!BN_GF2m_add(lh
, lh
, point
->Y
))
551 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
553 if (!BN_GF2m_add(lh
, lh
, group
->b
))
555 if (!field_sqr(group
, y2
, point
->Y
, ctx
))
557 if (!BN_GF2m_add(lh
, lh
, y2
))
559 ret
= BN_is_zero(lh
);
564 BN_CTX_free(new_ctx
);
570 * Indicates whether two points are equal.
573 * 0 equal (in affine coordinates)
576 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
577 const EC_POINT
*b
, BN_CTX
*ctx
)
579 BIGNUM
*aX
, *aY
, *bX
, *bY
;
582 BN_CTX
*new_ctx
= NULL
;
585 if (EC_POINT_is_at_infinity(group
, a
)) {
586 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
589 if (EC_POINT_is_at_infinity(group
, b
))
592 if (a
->Z_is_one
&& b
->Z_is_one
) {
593 return ((BN_cmp(a
->X
, b
->X
) == 0) && BN_cmp(a
->Y
, b
->Y
) == 0) ? 0 : 1;
598 ctx
= new_ctx
= BN_CTX_new();
605 aX
= BN_CTX_get(ctx
);
606 aY
= BN_CTX_get(ctx
);
607 bX
= BN_CTX_get(ctx
);
608 bY
= BN_CTX_get(ctx
);
612 if (!EC_POINT_get_affine_coordinates(group
, a
, aX
, aY
, ctx
))
614 if (!EC_POINT_get_affine_coordinates(group
, b
, bX
, bY
, ctx
))
616 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
621 BN_CTX_free(new_ctx
);
626 /* Forces the given EC_POINT to internally use affine coordinates. */
627 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
633 BN_CTX
*new_ctx
= NULL
;
636 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
641 ctx
= new_ctx
= BN_CTX_new();
653 if (!EC_POINT_get_affine_coordinates(group
, point
, x
, y
, ctx
))
655 if (!BN_copy(point
->X
, x
))
657 if (!BN_copy(point
->Y
, y
))
659 if (!BN_one(point
->Z
))
668 BN_CTX_free(new_ctx
);
674 * Forces each of the EC_POINTs in the given array to use affine coordinates.
676 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
677 EC_POINT
*points
[], BN_CTX
*ctx
)
681 for (i
= 0; i
< num
; i
++) {
682 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
689 /* Wrapper to simple binary polynomial field multiplication implementation. */
690 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
691 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
693 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
696 /* Wrapper to simple binary polynomial field squaring implementation. */
697 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
698 const BIGNUM
*a
, BN_CTX
*ctx
)
700 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
703 /* Wrapper to simple binary polynomial field division implementation. */
704 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
705 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
707 return BN_GF2m_mod_div(r
, a
, b
, group
->field
, ctx
);
711 * Lopez-Dahab ladder, pre step.
712 * See e.g. "Guide to ECC" Alg 3.40.
713 * Modified to blind s and r independently.
717 int ec_GF2m_simple_ladder_pre(const EC_GROUP
*group
,
718 EC_POINT
*r
, EC_POINT
*s
,
719 EC_POINT
*p
, BN_CTX
*ctx
)
721 /* if p is not affine, something is wrong */
722 if (p
->Z_is_one
== 0)
725 /* s blinding: make sure lambda (s->Z here) is not zero */
727 if (!BN_priv_rand_ex(s
->Z
, BN_num_bits(group
->field
) - 1,
728 BN_RAND_TOP_ANY
, BN_RAND_BOTTOM_ANY
, ctx
)) {
729 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE
, ERR_R_BN_LIB
);
732 } while (BN_is_zero(s
->Z
));
734 /* if field_encode defined convert between representations */
735 if ((group
->meth
->field_encode
!= NULL
736 && !group
->meth
->field_encode(group
, s
->Z
, s
->Z
, ctx
))
737 || !group
->meth
->field_mul(group
, s
->X
, p
->X
, s
->Z
, ctx
))
740 /* r blinding: make sure lambda (r->Y here for storage) is not zero */
742 if (!BN_priv_rand_ex(r
->Y
, BN_num_bits(group
->field
) - 1,
743 BN_RAND_TOP_ANY
, BN_RAND_BOTTOM_ANY
, ctx
)) {
744 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE
, ERR_R_BN_LIB
);
747 } while (BN_is_zero(r
->Y
));
749 if ((group
->meth
->field_encode
!= NULL
750 && !group
->meth
->field_encode(group
, r
->Y
, r
->Y
, ctx
))
751 || !group
->meth
->field_sqr(group
, r
->Z
, p
->X
, ctx
)
752 || !group
->meth
->field_sqr(group
, r
->X
, r
->Z
, ctx
)
753 || !BN_GF2m_add(r
->X
, r
->X
, group
->b
)
754 || !group
->meth
->field_mul(group
, r
->Z
, r
->Z
, r
->Y
, ctx
)
755 || !group
->meth
->field_mul(group
, r
->X
, r
->X
, r
->Y
, ctx
))
765 * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
766 * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
767 * s := r + s, r := 2r
770 int ec_GF2m_simple_ladder_step(const EC_GROUP
*group
,
771 EC_POINT
*r
, EC_POINT
*s
,
772 EC_POINT
*p
, BN_CTX
*ctx
)
774 if (!group
->meth
->field_mul(group
, r
->Y
, r
->Z
, s
->X
, ctx
)
775 || !group
->meth
->field_mul(group
, s
->X
, r
->X
, s
->Z
, ctx
)
776 || !group
->meth
->field_sqr(group
, s
->Y
, r
->Z
, ctx
)
777 || !group
->meth
->field_sqr(group
, r
->Z
, r
->X
, ctx
)
778 || !BN_GF2m_add(s
->Z
, r
->Y
, s
->X
)
779 || !group
->meth
->field_sqr(group
, s
->Z
, s
->Z
, ctx
)
780 || !group
->meth
->field_mul(group
, s
->X
, r
->Y
, s
->X
, ctx
)
781 || !group
->meth
->field_mul(group
, r
->Y
, s
->Z
, p
->X
, ctx
)
782 || !BN_GF2m_add(s
->X
, s
->X
, r
->Y
)
783 || !group
->meth
->field_sqr(group
, r
->Y
, r
->Z
, ctx
)
784 || !group
->meth
->field_mul(group
, r
->Z
, r
->Z
, s
->Y
, ctx
)
785 || !group
->meth
->field_sqr(group
, s
->Y
, s
->Y
, ctx
)
786 || !group
->meth
->field_mul(group
, s
->Y
, s
->Y
, group
->b
, ctx
)
787 || !BN_GF2m_add(r
->X
, r
->Y
, s
->Y
))
794 * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
795 * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
796 * without Precomputation" (Lopez and Dahab, CHES 1999),
800 int ec_GF2m_simple_ladder_post(const EC_GROUP
*group
,
801 EC_POINT
*r
, EC_POINT
*s
,
802 EC_POINT
*p
, BN_CTX
*ctx
)
805 BIGNUM
*t0
, *t1
, *t2
= NULL
;
807 if (BN_is_zero(r
->Z
))
808 return EC_POINT_set_to_infinity(group
, r
);
810 if (BN_is_zero(s
->Z
)) {
811 if (!EC_POINT_copy(r
, p
)
812 || !EC_POINT_invert(group
, r
, ctx
)) {
813 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST
, ERR_R_EC_LIB
);
820 t0
= BN_CTX_get(ctx
);
821 t1
= BN_CTX_get(ctx
);
822 t2
= BN_CTX_get(ctx
);
824 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST
, ERR_R_MALLOC_FAILURE
);
828 if (!group
->meth
->field_mul(group
, t0
, r
->Z
, s
->Z
, ctx
)
829 || !group
->meth
->field_mul(group
, t1
, p
->X
, r
->Z
, ctx
)
830 || !BN_GF2m_add(t1
, r
->X
, t1
)
831 || !group
->meth
->field_mul(group
, t2
, p
->X
, s
->Z
, ctx
)
832 || !group
->meth
->field_mul(group
, r
->Z
, r
->X
, t2
, ctx
)
833 || !BN_GF2m_add(t2
, t2
, s
->X
)
834 || !group
->meth
->field_mul(group
, t1
, t1
, t2
, ctx
)
835 || !group
->meth
->field_sqr(group
, t2
, p
->X
, ctx
)
836 || !BN_GF2m_add(t2
, p
->Y
, t2
)
837 || !group
->meth
->field_mul(group
, t2
, t2
, t0
, ctx
)
838 || !BN_GF2m_add(t1
, t2
, t1
)
839 || !group
->meth
->field_mul(group
, t2
, p
->X
, t0
, ctx
)
840 || !group
->meth
->field_inv(group
, t2
, t2
, ctx
)
841 || !group
->meth
->field_mul(group
, t1
, t1
, t2
, ctx
)
842 || !group
->meth
->field_mul(group
, r
->X
, r
->Z
, t2
, ctx
)
843 || !BN_GF2m_add(t2
, p
->X
, r
->X
)
844 || !group
->meth
->field_mul(group
, t2
, t2
, t1
, ctx
)
845 || !BN_GF2m_add(r
->Y
, p
->Y
, t2
)
851 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
852 BN_set_negative(r
->X
, 0);
853 BN_set_negative(r
->Y
, 0);
863 int ec_GF2m_simple_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
864 const BIGNUM
*scalar
, size_t num
,
865 const EC_POINT
*points
[],
866 const BIGNUM
*scalars
[],
873 * We limit use of the ladder only to the following cases:
875 * Fixed point mul: scalar != NULL && num == 0;
876 * - r := scalars[0] * points[0]
877 * Variable point mul: scalar == NULL && num == 1;
878 * - r := scalar * G + scalars[0] * points[0]
879 * used, e.g., in ECDSA verification: scalar != NULL && num == 1
881 * In any other case (num > 1) we use the default wNAF implementation.
883 * We also let the default implementation handle degenerate cases like group
884 * order or cofactor set to 0.
886 if (num
> 1 || BN_is_zero(group
->order
) || BN_is_zero(group
->cofactor
))
887 return ec_wNAF_mul(group
, r
, scalar
, num
, points
, scalars
, ctx
);
889 if (scalar
!= NULL
&& num
== 0)
890 /* Fixed point multiplication */
891 return ec_scalar_mul_ladder(group
, r
, scalar
, NULL
, ctx
);
893 if (scalar
== NULL
&& num
== 1)
894 /* Variable point multiplication */
895 return ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
);
898 * Double point multiplication:
899 * r := scalar * G + scalars[0] * points[0]
902 if ((t
= EC_POINT_new(group
)) == NULL
) {
903 ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL
, ERR_R_MALLOC_FAILURE
);
907 if (!ec_scalar_mul_ladder(group
, t
, scalar
, NULL
, ctx
)
908 || !ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
)
909 || !EC_POINT_add(group
, r
, t
, r
, ctx
))
920 * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
921 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
922 * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
924 static int ec_GF2m_simple_field_inv(const EC_GROUP
*group
, BIGNUM
*r
,
925 const BIGNUM
*a
, BN_CTX
*ctx
)
929 if (!(ret
= BN_GF2m_mod_inv(r
, a
, group
->field
, ctx
)))
930 ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV
, EC_R_CANNOT_INVERT
);
934 const EC_METHOD
*EC_GF2m_simple_method(void)
936 static const EC_METHOD ret
= {
937 EC_FLAGS_DEFAULT_OCT
,
938 NID_X9_62_characteristic_two_field
,
939 ec_GF2m_simple_group_init
,
940 ec_GF2m_simple_group_finish
,
941 ec_GF2m_simple_group_clear_finish
,
942 ec_GF2m_simple_group_copy
,
943 ec_GF2m_simple_group_set_curve
,
944 ec_GF2m_simple_group_get_curve
,
945 ec_GF2m_simple_group_get_degree
,
946 ec_group_simple_order_bits
,
947 ec_GF2m_simple_group_check_discriminant
,
948 ec_GF2m_simple_point_init
,
949 ec_GF2m_simple_point_finish
,
950 ec_GF2m_simple_point_clear_finish
,
951 ec_GF2m_simple_point_copy
,
952 ec_GF2m_simple_point_set_to_infinity
,
953 0, /* set_Jprojective_coordinates_GFp */
954 0, /* get_Jprojective_coordinates_GFp */
955 ec_GF2m_simple_point_set_affine_coordinates
,
956 ec_GF2m_simple_point_get_affine_coordinates
,
957 0, /* point_set_compressed_coordinates */
962 ec_GF2m_simple_invert
,
963 ec_GF2m_simple_is_at_infinity
,
964 ec_GF2m_simple_is_on_curve
,
966 ec_GF2m_simple_make_affine
,
967 ec_GF2m_simple_points_make_affine
,
968 ec_GF2m_simple_points_mul
,
969 0, /* precompute_mult */
970 0, /* have_precompute_mult */
971 ec_GF2m_simple_field_mul
,
972 ec_GF2m_simple_field_sqr
,
973 ec_GF2m_simple_field_div
,
974 ec_GF2m_simple_field_inv
,
975 0, /* field_encode */
976 0, /* field_decode */
977 0, /* field_set_to_one */
978 ec_key_simple_priv2oct
,
979 ec_key_simple_oct2priv
,
981 ec_key_simple_generate_key
,
982 ec_key_simple_check_key
,
983 ec_key_simple_generate_public_key
,
986 ecdh_simple_compute_key
,
987 ecdsa_simple_sign_setup
,
988 ecdsa_simple_sign_sig
,
989 ecdsa_simple_verify_sig
,
990 0, /* field_inverse_mod_ord */
991 0, /* blind_coordinates */
992 ec_GF2m_simple_ladder_pre
,
993 ec_GF2m_simple_ladder_step
,
994 ec_GF2m_simple_ladder_post