2 * Copyright 2002-2019 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (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
,
179 BN_CTX
*new_ctx
= NULL
;
182 ctx
= new_ctx
= BN_CTX_new();
184 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
,
185 ERR_R_MALLOC_FAILURE
);
194 if (!BN_GF2m_mod_arr(b
, group
->b
, group
->poly
))
198 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
199 * curve <=> b != 0 (mod p)
208 BN_CTX_free(new_ctx
);
212 /* Initializes an EC_POINT. */
213 int ec_GF2m_simple_point_init(EC_POINT
*point
)
219 if (point
->X
== NULL
|| point
->Y
== NULL
|| point
->Z
== NULL
) {
228 /* Frees an EC_POINT. */
229 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
236 /* Clears and frees an EC_POINT. */
237 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
239 BN_clear_free(point
->X
);
240 BN_clear_free(point
->Y
);
241 BN_clear_free(point
->Z
);
246 * Copy the contents of one EC_POINT into another. Assumes dest is
249 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
251 if (!BN_copy(dest
->X
, src
->X
))
253 if (!BN_copy(dest
->Y
, src
->Y
))
255 if (!BN_copy(dest
->Z
, src
->Z
))
257 dest
->Z_is_one
= src
->Z_is_one
;
258 dest
->curve_name
= src
->curve_name
;
264 * Set an EC_POINT to the point at infinity. A point at infinity is
265 * represented by having Z=0.
267 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
,
276 * Set the coordinates of an EC_POINT using affine coordinates. Note that
277 * the simple implementation only uses affine coordinates.
279 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
,
282 const BIGNUM
*y
, BN_CTX
*ctx
)
285 if (x
== NULL
|| y
== NULL
) {
286 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
,
287 ERR_R_PASSED_NULL_PARAMETER
);
291 if (!BN_copy(point
->X
, x
))
293 BN_set_negative(point
->X
, 0);
294 if (!BN_copy(point
->Y
, y
))
296 BN_set_negative(point
->Y
, 0);
297 if (!BN_copy(point
->Z
, BN_value_one()))
299 BN_set_negative(point
->Z
, 0);
308 * Gets the affine coordinates of an EC_POINT. Note that the simple
309 * implementation only uses affine coordinates.
311 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
,
312 const EC_POINT
*point
,
313 BIGNUM
*x
, BIGNUM
*y
,
318 if (EC_POINT_is_at_infinity(group
, point
)) {
319 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
320 EC_R_POINT_AT_INFINITY
);
324 if (BN_cmp(point
->Z
, BN_value_one())) {
325 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
,
326 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
330 if (!BN_copy(x
, point
->X
))
332 BN_set_negative(x
, 0);
335 if (!BN_copy(y
, point
->Y
))
337 BN_set_negative(y
, 0);
346 * Computes a + b and stores the result in r. r could be a or b, a could be
347 * b. Uses algorithm A.10.2 of IEEE P1363.
349 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
350 const EC_POINT
*b
, BN_CTX
*ctx
)
352 BN_CTX
*new_ctx
= NULL
;
353 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
356 if (EC_POINT_is_at_infinity(group
, a
)) {
357 if (!EC_POINT_copy(r
, b
))
362 if (EC_POINT_is_at_infinity(group
, b
)) {
363 if (!EC_POINT_copy(r
, a
))
369 ctx
= new_ctx
= BN_CTX_new();
375 x0
= BN_CTX_get(ctx
);
376 y0
= BN_CTX_get(ctx
);
377 x1
= BN_CTX_get(ctx
);
378 y1
= BN_CTX_get(ctx
);
379 x2
= BN_CTX_get(ctx
);
380 y2
= BN_CTX_get(ctx
);
387 if (!BN_copy(x0
, a
->X
))
389 if (!BN_copy(y0
, a
->Y
))
392 if (!EC_POINT_get_affine_coordinates(group
, a
, x0
, y0
, ctx
))
396 if (!BN_copy(x1
, b
->X
))
398 if (!BN_copy(y1
, b
->Y
))
401 if (!EC_POINT_get_affine_coordinates(group
, b
, x1
, y1
, ctx
))
405 if (BN_GF2m_cmp(x0
, x1
)) {
406 if (!BN_GF2m_add(t
, x0
, x1
))
408 if (!BN_GF2m_add(s
, y0
, y1
))
410 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
))
412 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
414 if (!BN_GF2m_add(x2
, x2
, group
->a
))
416 if (!BN_GF2m_add(x2
, x2
, s
))
418 if (!BN_GF2m_add(x2
, x2
, t
))
421 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
)) {
422 if (!EC_POINT_set_to_infinity(group
, r
))
427 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
))
429 if (!BN_GF2m_add(s
, s
, x1
))
432 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
))
434 if (!BN_GF2m_add(x2
, x2
, s
))
436 if (!BN_GF2m_add(x2
, x2
, group
->a
))
440 if (!BN_GF2m_add(y2
, x1
, x2
))
442 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
))
444 if (!BN_GF2m_add(y2
, y2
, x2
))
446 if (!BN_GF2m_add(y2
, y2
, y1
))
449 if (!EC_POINT_set_affine_coordinates(group
, r
, x2
, y2
, ctx
))
456 BN_CTX_free(new_ctx
);
461 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
462 * A.10.2 of IEEE P1363.
464 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
,
467 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
470 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
472 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(point
->Y
))
473 /* point is its own inverse */
476 if (!EC_POINT_make_affine(group
, point
, ctx
))
478 return BN_GF2m_add(point
->Y
, point
->X
, point
->Y
);
481 /* Indicates whether the given point is the point at infinity. */
482 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
,
483 const EC_POINT
*point
)
485 return BN_is_zero(point
->Z
);
489 * Determines whether the given EC_POINT is an actual point on the curve defined
490 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
491 * y^2 + x*y = x^3 + a*x^2 + b.
493 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
,
497 BN_CTX
*new_ctx
= NULL
;
499 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*,
500 const BIGNUM
*, BN_CTX
*);
501 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
503 if (EC_POINT_is_at_infinity(group
, point
))
506 field_mul
= group
->meth
->field_mul
;
507 field_sqr
= group
->meth
->field_sqr
;
509 /* only support affine coordinates */
510 if (!point
->Z_is_one
)
514 ctx
= new_ctx
= BN_CTX_new();
520 y2
= BN_CTX_get(ctx
);
521 lh
= BN_CTX_get(ctx
);
526 * We have a curve defined by a Weierstrass equation
527 * y^2 + x*y = x^3 + a*x^2 + b.
528 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
529 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
531 if (!BN_GF2m_add(lh
, point
->X
, group
->a
))
533 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
535 if (!BN_GF2m_add(lh
, lh
, point
->Y
))
537 if (!field_mul(group
, lh
, lh
, point
->X
, ctx
))
539 if (!BN_GF2m_add(lh
, lh
, group
->b
))
541 if (!field_sqr(group
, y2
, point
->Y
, ctx
))
543 if (!BN_GF2m_add(lh
, lh
, y2
))
545 ret
= BN_is_zero(lh
);
549 BN_CTX_free(new_ctx
);
554 * Indicates whether two points are equal.
557 * 0 equal (in affine coordinates)
560 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
,
561 const EC_POINT
*b
, BN_CTX
*ctx
)
563 BIGNUM
*aX
, *aY
, *bX
, *bY
;
564 BN_CTX
*new_ctx
= NULL
;
567 if (EC_POINT_is_at_infinity(group
, a
)) {
568 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
571 if (EC_POINT_is_at_infinity(group
, b
))
574 if (a
->Z_is_one
&& b
->Z_is_one
) {
575 return ((BN_cmp(a
->X
, b
->X
) == 0) && BN_cmp(a
->Y
, b
->Y
) == 0) ? 0 : 1;
579 ctx
= new_ctx
= BN_CTX_new();
585 aX
= BN_CTX_get(ctx
);
586 aY
= BN_CTX_get(ctx
);
587 bX
= BN_CTX_get(ctx
);
588 bY
= BN_CTX_get(ctx
);
592 if (!EC_POINT_get_affine_coordinates(group
, a
, aX
, aY
, ctx
))
594 if (!EC_POINT_get_affine_coordinates(group
, b
, bX
, bY
, ctx
))
596 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
600 BN_CTX_free(new_ctx
);
604 /* Forces the given EC_POINT to internally use affine coordinates. */
605 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
,
608 BN_CTX
*new_ctx
= NULL
;
612 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
616 ctx
= new_ctx
= BN_CTX_new();
627 if (!EC_POINT_get_affine_coordinates(group
, point
, x
, y
, ctx
))
629 if (!BN_copy(point
->X
, x
))
631 if (!BN_copy(point
->Y
, y
))
633 if (!BN_one(point
->Z
))
641 BN_CTX_free(new_ctx
);
646 * Forces each of the EC_POINTs in the given array to use affine coordinates.
648 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
,
649 EC_POINT
*points
[], BN_CTX
*ctx
)
653 for (i
= 0; i
< num
; i
++) {
654 if (!group
->meth
->make_affine(group
, points
[i
], ctx
))
661 /* Wrapper to simple binary polynomial field multiplication implementation. */
662 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
,
663 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
665 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
668 /* Wrapper to simple binary polynomial field squaring implementation. */
669 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
,
670 const BIGNUM
*a
, BN_CTX
*ctx
)
672 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
675 /* Wrapper to simple binary polynomial field division implementation. */
676 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
,
677 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
679 return BN_GF2m_mod_div(r
, a
, b
, group
->field
, ctx
);
683 * Lopez-Dahab ladder, pre step.
684 * See e.g. "Guide to ECC" Alg 3.40.
685 * Modified to blind s and r independently.
689 int ec_GF2m_simple_ladder_pre(const EC_GROUP
*group
,
690 EC_POINT
*r
, EC_POINT
*s
,
691 EC_POINT
*p
, BN_CTX
*ctx
)
693 /* if p is not affine, something is wrong */
694 if (p
->Z_is_one
== 0)
697 /* s blinding: make sure lambda (s->Z here) is not zero */
699 if (!BN_priv_rand(s
->Z
, BN_num_bits(group
->field
) - 1,
700 BN_RAND_TOP_ANY
, BN_RAND_BOTTOM_ANY
)) {
701 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE
, ERR_R_BN_LIB
);
704 } while (BN_is_zero(s
->Z
));
706 /* if field_encode defined convert between representations */
707 if ((group
->meth
->field_encode
!= NULL
708 && !group
->meth
->field_encode(group
, s
->Z
, s
->Z
, ctx
))
709 || !group
->meth
->field_mul(group
, s
->X
, p
->X
, s
->Z
, ctx
))
712 /* r blinding: make sure lambda (r->Y here for storage) is not zero */
714 if (!BN_priv_rand(r
->Y
, BN_num_bits(group
->field
) - 1,
715 BN_RAND_TOP_ANY
, BN_RAND_BOTTOM_ANY
)) {
716 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE
, ERR_R_BN_LIB
);
719 } while (BN_is_zero(r
->Y
));
721 if ((group
->meth
->field_encode
!= NULL
722 && !group
->meth
->field_encode(group
, r
->Y
, r
->Y
, ctx
))
723 || !group
->meth
->field_sqr(group
, r
->Z
, p
->X
, ctx
)
724 || !group
->meth
->field_sqr(group
, r
->X
, r
->Z
, ctx
)
725 || !BN_GF2m_add(r
->X
, r
->X
, group
->b
)
726 || !group
->meth
->field_mul(group
, r
->Z
, r
->Z
, r
->Y
, ctx
)
727 || !group
->meth
->field_mul(group
, r
->X
, r
->X
, r
->Y
, ctx
))
737 * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
738 * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
739 * s := r + s, r := 2r
742 int ec_GF2m_simple_ladder_step(const EC_GROUP
*group
,
743 EC_POINT
*r
, EC_POINT
*s
,
744 EC_POINT
*p
, BN_CTX
*ctx
)
746 if (!group
->meth
->field_mul(group
, r
->Y
, r
->Z
, s
->X
, ctx
)
747 || !group
->meth
->field_mul(group
, s
->X
, r
->X
, s
->Z
, ctx
)
748 || !group
->meth
->field_sqr(group
, s
->Y
, r
->Z
, ctx
)
749 || !group
->meth
->field_sqr(group
, r
->Z
, r
->X
, ctx
)
750 || !BN_GF2m_add(s
->Z
, r
->Y
, s
->X
)
751 || !group
->meth
->field_sqr(group
, s
->Z
, s
->Z
, ctx
)
752 || !group
->meth
->field_mul(group
, s
->X
, r
->Y
, s
->X
, ctx
)
753 || !group
->meth
->field_mul(group
, r
->Y
, s
->Z
, p
->X
, ctx
)
754 || !BN_GF2m_add(s
->X
, s
->X
, r
->Y
)
755 || !group
->meth
->field_sqr(group
, r
->Y
, r
->Z
, ctx
)
756 || !group
->meth
->field_mul(group
, r
->Z
, r
->Z
, s
->Y
, ctx
)
757 || !group
->meth
->field_sqr(group
, s
->Y
, s
->Y
, ctx
)
758 || !group
->meth
->field_mul(group
, s
->Y
, s
->Y
, group
->b
, ctx
)
759 || !BN_GF2m_add(r
->X
, r
->Y
, s
->Y
))
766 * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
767 * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
768 * without Precomputation" (Lopez and Dahab, CHES 1999),
772 int ec_GF2m_simple_ladder_post(const EC_GROUP
*group
,
773 EC_POINT
*r
, EC_POINT
*s
,
774 EC_POINT
*p
, BN_CTX
*ctx
)
777 BIGNUM
*t0
, *t1
, *t2
= NULL
;
779 if (BN_is_zero(r
->Z
))
780 return EC_POINT_set_to_infinity(group
, r
);
782 if (BN_is_zero(s
->Z
)) {
783 if (!EC_POINT_copy(r
, p
)
784 || !EC_POINT_invert(group
, r
, ctx
)) {
785 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST
, ERR_R_EC_LIB
);
792 t0
= BN_CTX_get(ctx
);
793 t1
= BN_CTX_get(ctx
);
794 t2
= BN_CTX_get(ctx
);
796 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST
, ERR_R_MALLOC_FAILURE
);
800 if (!group
->meth
->field_mul(group
, t0
, r
->Z
, s
->Z
, ctx
)
801 || !group
->meth
->field_mul(group
, t1
, p
->X
, r
->Z
, ctx
)
802 || !BN_GF2m_add(t1
, r
->X
, t1
)
803 || !group
->meth
->field_mul(group
, t2
, p
->X
, s
->Z
, ctx
)
804 || !group
->meth
->field_mul(group
, r
->Z
, r
->X
, t2
, ctx
)
805 || !BN_GF2m_add(t2
, t2
, s
->X
)
806 || !group
->meth
->field_mul(group
, t1
, t1
, t2
, ctx
)
807 || !group
->meth
->field_sqr(group
, t2
, p
->X
, ctx
)
808 || !BN_GF2m_add(t2
, p
->Y
, t2
)
809 || !group
->meth
->field_mul(group
, t2
, t2
, t0
, ctx
)
810 || !BN_GF2m_add(t1
, t2
, t1
)
811 || !group
->meth
->field_mul(group
, t2
, p
->X
, t0
, ctx
)
812 || !group
->meth
->field_inv(group
, t2
, t2
, ctx
)
813 || !group
->meth
->field_mul(group
, t1
, t1
, t2
, ctx
)
814 || !group
->meth
->field_mul(group
, r
->X
, r
->Z
, t2
, ctx
)
815 || !BN_GF2m_add(t2
, p
->X
, r
->X
)
816 || !group
->meth
->field_mul(group
, t2
, t2
, t1
, ctx
)
817 || !BN_GF2m_add(r
->Y
, p
->Y
, t2
)
823 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
824 BN_set_negative(r
->X
, 0);
825 BN_set_negative(r
->Y
, 0);
835 int ec_GF2m_simple_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
836 const BIGNUM
*scalar
, size_t num
,
837 const EC_POINT
*points
[],
838 const BIGNUM
*scalars
[],
845 * We limit use of the ladder only to the following cases:
847 * Fixed point mul: scalar != NULL && num == 0;
848 * - r := scalars[0] * points[0]
849 * Variable point mul: scalar == NULL && num == 1;
850 * - r := scalar * G + scalars[0] * points[0]
851 * used, e.g., in ECDSA verification: scalar != NULL && num == 1
853 * In any other case (num > 1) we use the default wNAF implementation.
855 * We also let the default implementation handle degenerate cases like group
856 * order or cofactor set to 0.
858 if (num
> 1 || BN_is_zero(group
->order
) || BN_is_zero(group
->cofactor
))
859 return ec_wNAF_mul(group
, r
, scalar
, num
, points
, scalars
, ctx
);
861 if (scalar
!= NULL
&& num
== 0)
862 /* Fixed point multiplication */
863 return ec_scalar_mul_ladder(group
, r
, scalar
, NULL
, ctx
);
865 if (scalar
== NULL
&& num
== 1)
866 /* Variable point multiplication */
867 return ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
);
870 * Double point multiplication:
871 * r := scalar * G + scalars[0] * points[0]
874 if ((t
= EC_POINT_new(group
)) == NULL
) {
875 ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL
, ERR_R_MALLOC_FAILURE
);
879 if (!ec_scalar_mul_ladder(group
, t
, scalar
, NULL
, ctx
)
880 || !ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
)
881 || !EC_POINT_add(group
, r
, t
, r
, ctx
))
892 * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
893 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
894 * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
896 static int ec_GF2m_simple_field_inv(const EC_GROUP
*group
, BIGNUM
*r
,
897 const BIGNUM
*a
, BN_CTX
*ctx
)
901 if (!(ret
= BN_GF2m_mod_inv(r
, a
, group
->field
, ctx
)))
902 ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV
, EC_R_CANNOT_INVERT
);
906 const EC_METHOD
*EC_GF2m_simple_method(void)
908 static const EC_METHOD ret
= {
909 EC_FLAGS_DEFAULT_OCT
,
910 NID_X9_62_characteristic_two_field
,
911 ec_GF2m_simple_group_init
,
912 ec_GF2m_simple_group_finish
,
913 ec_GF2m_simple_group_clear_finish
,
914 ec_GF2m_simple_group_copy
,
915 ec_GF2m_simple_group_set_curve
,
916 ec_GF2m_simple_group_get_curve
,
917 ec_GF2m_simple_group_get_degree
,
918 ec_group_simple_order_bits
,
919 ec_GF2m_simple_group_check_discriminant
,
920 ec_GF2m_simple_point_init
,
921 ec_GF2m_simple_point_finish
,
922 ec_GF2m_simple_point_clear_finish
,
923 ec_GF2m_simple_point_copy
,
924 ec_GF2m_simple_point_set_to_infinity
,
925 0, /* set_Jprojective_coordinates_GFp */
926 0, /* get_Jprojective_coordinates_GFp */
927 ec_GF2m_simple_point_set_affine_coordinates
,
928 ec_GF2m_simple_point_get_affine_coordinates
,
929 0, /* point_set_compressed_coordinates */
934 ec_GF2m_simple_invert
,
935 ec_GF2m_simple_is_at_infinity
,
936 ec_GF2m_simple_is_on_curve
,
938 ec_GF2m_simple_make_affine
,
939 ec_GF2m_simple_points_make_affine
,
940 ec_GF2m_simple_points_mul
,
941 0, /* precompute_mult */
942 0, /* have_precompute_mult */
943 ec_GF2m_simple_field_mul
,
944 ec_GF2m_simple_field_sqr
,
945 ec_GF2m_simple_field_div
,
946 ec_GF2m_simple_field_inv
,
947 0, /* field_encode */
948 0, /* field_decode */
949 0, /* field_set_to_one */
950 ec_key_simple_priv2oct
,
951 ec_key_simple_oct2priv
,
953 ec_key_simple_generate_key
,
954 ec_key_simple_check_key
,
955 ec_key_simple_generate_public_key
,
958 ecdh_simple_compute_key
,
959 0, /* field_inverse_mod_ord */
960 0, /* blind_coordinates */
961 ec_GF2m_simple_ladder_pre
,
962 ec_GF2m_simple_ladder_step
,
963 ec_GF2m_simple_ladder_post