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
12 * ECDSA low level APIs are deprecated for public use, but still ok for
15 #include "internal/deprecated.h"
17 #include <openssl/err.h>
19 #include "crypto/bn.h"
22 #ifndef OPENSSL_NO_EC2M
25 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
26 * are handled by EC_GROUP_new.
28 int ec_GF2m_simple_group_init(EC_GROUP *group)
30 group->field = BN_new();
34 if (group->field == NULL || group->a == NULL || group->b == NULL) {
35 BN_free(group->field);
44 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
45 * handled by EC_GROUP_free.
47 void ec_GF2m_simple_group_finish(EC_GROUP *group)
49 BN_free(group->field);
55 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
56 * members are handled by EC_GROUP_clear_free.
58 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
60 BN_clear_free(group->field);
61 BN_clear_free(group->a);
62 BN_clear_free(group->b);
72 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
73 * handled by EC_GROUP_copy.
75 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
77 if (!BN_copy(dest->field, src->field))
79 if (!BN_copy(dest->a, src->a))
81 if (!BN_copy(dest->b, src->b))
83 dest->poly[0] = src->poly[0];
84 dest->poly[1] = src->poly[1];
85 dest->poly[2] = src->poly[2];
86 dest->poly[3] = src->poly[3];
87 dest->poly[4] = src->poly[4];
88 dest->poly[5] = src->poly[5];
89 if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
92 if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
95 bn_set_all_zero(dest->a);
96 bn_set_all_zero(dest->b);
100 /* Set the curve parameters of an EC_GROUP structure. */
101 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
102 const BIGNUM *p, const BIGNUM *a,
103 const BIGNUM *b, BN_CTX *ctx)
108 if (!BN_copy(group->field, p))
110 i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
111 if ((i != 5) && (i != 3)) {
112 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
117 if (!BN_GF2m_mod_arr(group->a, a, group->poly))
119 if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
122 bn_set_all_zero(group->a);
125 if (!BN_GF2m_mod_arr(group->b, b, group->poly))
127 if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
130 bn_set_all_zero(group->b);
138 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
139 * then there values will not be set but the method will return with success.
141 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
142 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
147 if (!BN_copy(p, group->field))
152 if (!BN_copy(a, group->a))
157 if (!BN_copy(b, group->b))
168 * Gets the degree of the field. For a curve over GF(2^m) this is the value
171 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
173 return BN_num_bits(group->field) - 1;
177 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
178 * elliptic curve <=> b != 0 (mod p)
180 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
186 BN_CTX *new_ctx = NULL;
189 ctx = new_ctx = BN_CTX_new();
191 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT,
192 ERR_R_MALLOC_FAILURE);
202 if (!BN_GF2m_mod_arr(b, group->b, group->poly))
206 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
207 * curve <=> b != 0 (mod p)
217 BN_CTX_free(new_ctx);
222 /* Initializes an EC_POINT. */
223 int ec_GF2m_simple_point_init(EC_POINT *point)
229 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
238 /* Frees an EC_POINT. */
239 void ec_GF2m_simple_point_finish(EC_POINT *point)
246 /* Clears and frees an EC_POINT. */
247 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
249 BN_clear_free(point->X);
250 BN_clear_free(point->Y);
251 BN_clear_free(point->Z);
256 * Copy the contents of one EC_POINT into another. Assumes dest is
259 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
261 if (!BN_copy(dest->X, src->X))
263 if (!BN_copy(dest->Y, src->Y))
265 if (!BN_copy(dest->Z, src->Z))
267 dest->Z_is_one = src->Z_is_one;
268 dest->curve_name = src->curve_name;
274 * Set an EC_POINT to the point at infinity. A point at infinity is
275 * represented by having Z=0.
277 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
286 * Set the coordinates of an EC_POINT using affine coordinates. Note that
287 * the simple implementation only uses affine coordinates.
289 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
292 const BIGNUM *y, BN_CTX *ctx)
295 if (x == NULL || y == NULL) {
296 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
297 ERR_R_PASSED_NULL_PARAMETER);
301 if (!BN_copy(point->X, x))
303 BN_set_negative(point->X, 0);
304 if (!BN_copy(point->Y, y))
306 BN_set_negative(point->Y, 0);
307 if (!BN_copy(point->Z, BN_value_one()))
309 BN_set_negative(point->Z, 0);
318 * Gets the affine coordinates of an EC_POINT. Note that the simple
319 * implementation only uses affine coordinates.
321 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
322 const EC_POINT *point,
323 BIGNUM *x, BIGNUM *y,
328 if (EC_POINT_is_at_infinity(group, point)) {
329 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
330 EC_R_POINT_AT_INFINITY);
334 if (BN_cmp(point->Z, BN_value_one())) {
335 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
336 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
340 if (!BN_copy(x, point->X))
342 BN_set_negative(x, 0);
345 if (!BN_copy(y, point->Y))
347 BN_set_negative(y, 0);
356 * Computes a + b and stores the result in r. r could be a or b, a could be
357 * b. Uses algorithm A.10.2 of IEEE P1363.
359 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
360 const EC_POINT *b, BN_CTX *ctx)
362 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
365 BN_CTX *new_ctx = NULL;
368 if (EC_POINT_is_at_infinity(group, a)) {
369 if (!EC_POINT_copy(r, b))
374 if (EC_POINT_is_at_infinity(group, b)) {
375 if (!EC_POINT_copy(r, a))
382 ctx = new_ctx = BN_CTX_new();
389 x0 = BN_CTX_get(ctx);
390 y0 = BN_CTX_get(ctx);
391 x1 = BN_CTX_get(ctx);
392 y1 = BN_CTX_get(ctx);
393 x2 = BN_CTX_get(ctx);
394 y2 = BN_CTX_get(ctx);
401 if (!BN_copy(x0, a->X))
403 if (!BN_copy(y0, a->Y))
406 if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx))
410 if (!BN_copy(x1, b->X))
412 if (!BN_copy(y1, b->Y))
415 if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx))
419 if (BN_GF2m_cmp(x0, x1)) {
420 if (!BN_GF2m_add(t, x0, x1))
422 if (!BN_GF2m_add(s, y0, y1))
424 if (!group->meth->field_div(group, s, s, t, ctx))
426 if (!group->meth->field_sqr(group, x2, s, ctx))
428 if (!BN_GF2m_add(x2, x2, group->a))
430 if (!BN_GF2m_add(x2, x2, s))
432 if (!BN_GF2m_add(x2, x2, t))
435 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
436 if (!EC_POINT_set_to_infinity(group, r))
441 if (!group->meth->field_div(group, s, y1, x1, ctx))
443 if (!BN_GF2m_add(s, s, x1))
446 if (!group->meth->field_sqr(group, x2, s, ctx))
448 if (!BN_GF2m_add(x2, x2, s))
450 if (!BN_GF2m_add(x2, x2, group->a))
454 if (!BN_GF2m_add(y2, x1, x2))
456 if (!group->meth->field_mul(group, y2, y2, s, ctx))
458 if (!BN_GF2m_add(y2, y2, x2))
460 if (!BN_GF2m_add(y2, y2, y1))
463 if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx))
471 BN_CTX_free(new_ctx);
477 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
478 * A.10.2 of IEEE P1363.
480 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
483 return ec_GF2m_simple_add(group, r, a, a, ctx);
486 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
488 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
489 /* point is its own inverse */
492 if (!EC_POINT_make_affine(group, point, ctx))
494 return BN_GF2m_add(point->Y, point->X, point->Y);
497 /* Indicates whether the given point is the point at infinity. */
498 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
499 const EC_POINT *point)
501 return BN_is_zero(point->Z);
505 * Determines whether the given EC_POINT is an actual point on the curve defined
506 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
507 * y^2 + x*y = x^3 + a*x^2 + b.
509 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
514 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
515 const BIGNUM *, BN_CTX *);
516 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
518 BN_CTX *new_ctx = NULL;
521 if (EC_POINT_is_at_infinity(group, point))
524 field_mul = group->meth->field_mul;
525 field_sqr = group->meth->field_sqr;
527 /* only support affine coordinates */
528 if (!point->Z_is_one)
533 ctx = new_ctx = BN_CTX_new();
540 y2 = BN_CTX_get(ctx);
541 lh = BN_CTX_get(ctx);
546 * We have a curve defined by a Weierstrass equation
547 * y^2 + x*y = x^3 + a*x^2 + b.
548 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
549 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
551 if (!BN_GF2m_add(lh, point->X, group->a))
553 if (!field_mul(group, lh, lh, point->X, ctx))
555 if (!BN_GF2m_add(lh, lh, point->Y))
557 if (!field_mul(group, lh, lh, point->X, ctx))
559 if (!BN_GF2m_add(lh, lh, group->b))
561 if (!field_sqr(group, y2, point->Y, ctx))
563 if (!BN_GF2m_add(lh, lh, y2))
565 ret = BN_is_zero(lh);
570 BN_CTX_free(new_ctx);
576 * Indicates whether two points are equal.
579 * 0 equal (in affine coordinates)
582 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
583 const EC_POINT *b, BN_CTX *ctx)
585 BIGNUM *aX, *aY, *bX, *bY;
588 BN_CTX *new_ctx = NULL;
591 if (EC_POINT_is_at_infinity(group, a)) {
592 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
595 if (EC_POINT_is_at_infinity(group, b))
598 if (a->Z_is_one && b->Z_is_one) {
599 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
604 ctx = new_ctx = BN_CTX_new();
611 aX = BN_CTX_get(ctx);
612 aY = BN_CTX_get(ctx);
613 bX = BN_CTX_get(ctx);
614 bY = BN_CTX_get(ctx);
618 if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx))
620 if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx))
622 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
627 BN_CTX_free(new_ctx);
632 /* Forces the given EC_POINT to internally use affine coordinates. */
633 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
639 BN_CTX *new_ctx = NULL;
642 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
647 ctx = new_ctx = BN_CTX_new();
659 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
661 if (!BN_copy(point->X, x))
663 if (!BN_copy(point->Y, y))
665 if (!BN_one(point->Z))
674 BN_CTX_free(new_ctx);
680 * Forces each of the EC_POINTs in the given array to use affine coordinates.
682 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
683 EC_POINT *points[], BN_CTX *ctx)
687 for (i = 0; i < num; i++) {
688 if (!group->meth->make_affine(group, points[i], ctx))
695 /* Wrapper to simple binary polynomial field multiplication implementation. */
696 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
697 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
699 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
702 /* Wrapper to simple binary polynomial field squaring implementation. */
703 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
704 const BIGNUM *a, BN_CTX *ctx)
706 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
709 /* Wrapper to simple binary polynomial field division implementation. */
710 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
711 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
713 return BN_GF2m_mod_div(r, a, b, group->field, ctx);
717 * Lopez-Dahab ladder, pre step.
718 * See e.g. "Guide to ECC" Alg 3.40.
719 * Modified to blind s and r independently.
723 int ec_GF2m_simple_ladder_pre(const EC_GROUP *group,
724 EC_POINT *r, EC_POINT *s,
725 EC_POINT *p, BN_CTX *ctx)
727 /* if p is not affine, something is wrong */
728 if (p->Z_is_one == 0)
731 /* s blinding: make sure lambda (s->Z here) is not zero */
733 if (!BN_priv_rand_ex(s->Z, BN_num_bits(group->field) - 1,
734 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) {
735 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
738 } while (BN_is_zero(s->Z));
740 /* if field_encode defined convert between representations */
741 if ((group->meth->field_encode != NULL
742 && !group->meth->field_encode(group, s->Z, s->Z, ctx))
743 || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx))
746 /* r blinding: make sure lambda (r->Y here for storage) is not zero */
748 if (!BN_priv_rand_ex(r->Y, BN_num_bits(group->field) - 1,
749 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) {
750 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
753 } while (BN_is_zero(r->Y));
755 if ((group->meth->field_encode != NULL
756 && !group->meth->field_encode(group, r->Y, r->Y, ctx))
757 || !group->meth->field_sqr(group, r->Z, p->X, ctx)
758 || !group->meth->field_sqr(group, r->X, r->Z, ctx)
759 || !BN_GF2m_add(r->X, r->X, group->b)
760 || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
761 || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx))
771 * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
772 * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
773 * s := r + s, r := 2r
776 int ec_GF2m_simple_ladder_step(const EC_GROUP *group,
777 EC_POINT *r, EC_POINT *s,
778 EC_POINT *p, BN_CTX *ctx)
780 if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx)
781 || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx)
782 || !group->meth->field_sqr(group, s->Y, r->Z, ctx)
783 || !group->meth->field_sqr(group, r->Z, r->X, ctx)
784 || !BN_GF2m_add(s->Z, r->Y, s->X)
785 || !group->meth->field_sqr(group, s->Z, s->Z, ctx)
786 || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx)
787 || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx)
788 || !BN_GF2m_add(s->X, s->X, r->Y)
789 || !group->meth->field_sqr(group, r->Y, r->Z, ctx)
790 || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx)
791 || !group->meth->field_sqr(group, s->Y, s->Y, ctx)
792 || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx)
793 || !BN_GF2m_add(r->X, r->Y, s->Y))
800 * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
801 * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
802 * without Precomputation" (Lopez and Dahab, CHES 1999),
806 int ec_GF2m_simple_ladder_post(const EC_GROUP *group,
807 EC_POINT *r, EC_POINT *s,
808 EC_POINT *p, BN_CTX *ctx)
811 BIGNUM *t0, *t1, *t2 = NULL;
813 if (BN_is_zero(r->Z))
814 return EC_POINT_set_to_infinity(group, r);
816 if (BN_is_zero(s->Z)) {
817 if (!EC_POINT_copy(r, p)
818 || !EC_POINT_invert(group, r, ctx)) {
819 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_EC_LIB);
826 t0 = BN_CTX_get(ctx);
827 t1 = BN_CTX_get(ctx);
828 t2 = BN_CTX_get(ctx);
830 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_MALLOC_FAILURE);
834 if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
835 || !group->meth->field_mul(group, t1, p->X, r->Z, ctx)
836 || !BN_GF2m_add(t1, r->X, t1)
837 || !group->meth->field_mul(group, t2, p->X, s->Z, ctx)
838 || !group->meth->field_mul(group, r->Z, r->X, t2, ctx)
839 || !BN_GF2m_add(t2, t2, s->X)
840 || !group->meth->field_mul(group, t1, t1, t2, ctx)
841 || !group->meth->field_sqr(group, t2, p->X, ctx)
842 || !BN_GF2m_add(t2, p->Y, t2)
843 || !group->meth->field_mul(group, t2, t2, t0, ctx)
844 || !BN_GF2m_add(t1, t2, t1)
845 || !group->meth->field_mul(group, t2, p->X, t0, ctx)
846 || !group->meth->field_inv(group, t2, t2, ctx)
847 || !group->meth->field_mul(group, t1, t1, t2, ctx)
848 || !group->meth->field_mul(group, r->X, r->Z, t2, ctx)
849 || !BN_GF2m_add(t2, p->X, r->X)
850 || !group->meth->field_mul(group, t2, t2, t1, ctx)
851 || !BN_GF2m_add(r->Y, p->Y, t2)
857 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
858 BN_set_negative(r->X, 0);
859 BN_set_negative(r->Y, 0);
869 int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r,
870 const BIGNUM *scalar, size_t num,
871 const EC_POINT *points[],
872 const BIGNUM *scalars[],
879 * We limit use of the ladder only to the following cases:
881 * Fixed point mul: scalar != NULL && num == 0;
882 * - r := scalars[0] * points[0]
883 * Variable point mul: scalar == NULL && num == 1;
884 * - r := scalar * G + scalars[0] * points[0]
885 * used, e.g., in ECDSA verification: scalar != NULL && num == 1
887 * In any other case (num > 1) we use the default wNAF implementation.
889 * We also let the default implementation handle degenerate cases like group
890 * order or cofactor set to 0.
892 if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor))
893 return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
895 if (scalar != NULL && num == 0)
896 /* Fixed point multiplication */
897 return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
899 if (scalar == NULL && num == 1)
900 /* Variable point multiplication */
901 return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
904 * Double point multiplication:
905 * r := scalar * G + scalars[0] * points[0]
908 if ((t = EC_POINT_new(group)) == NULL) {
909 ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL, ERR_R_MALLOC_FAILURE);
913 if (!ec_scalar_mul_ladder(group, t, scalar, NULL, ctx)
914 || !ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx)
915 || !EC_POINT_add(group, r, t, r, ctx))
926 * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
927 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
928 * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
930 static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
931 const BIGNUM *a, BN_CTX *ctx)
935 if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx)))
936 ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
940 const EC_METHOD *EC_GF2m_simple_method(void)
942 static const EC_METHOD ret = {
943 EC_FLAGS_DEFAULT_OCT,
944 NID_X9_62_characteristic_two_field,
945 ec_GF2m_simple_group_init,
946 ec_GF2m_simple_group_finish,
947 ec_GF2m_simple_group_clear_finish,
948 ec_GF2m_simple_group_copy,
949 ec_GF2m_simple_group_set_curve,
950 ec_GF2m_simple_group_get_curve,
951 ec_GF2m_simple_group_get_degree,
952 ec_group_simple_order_bits,
953 ec_GF2m_simple_group_check_discriminant,
954 ec_GF2m_simple_point_init,
955 ec_GF2m_simple_point_finish,
956 ec_GF2m_simple_point_clear_finish,
957 ec_GF2m_simple_point_copy,
958 ec_GF2m_simple_point_set_to_infinity,
959 0, /* set_Jprojective_coordinates_GFp */
960 0, /* get_Jprojective_coordinates_GFp */
961 ec_GF2m_simple_point_set_affine_coordinates,
962 ec_GF2m_simple_point_get_affine_coordinates,
963 0, /* point_set_compressed_coordinates */
968 ec_GF2m_simple_invert,
969 ec_GF2m_simple_is_at_infinity,
970 ec_GF2m_simple_is_on_curve,
972 ec_GF2m_simple_make_affine,
973 ec_GF2m_simple_points_make_affine,
974 ec_GF2m_simple_points_mul,
975 0, /* precompute_mult */
976 0, /* have_precompute_mult */
977 ec_GF2m_simple_field_mul,
978 ec_GF2m_simple_field_sqr,
979 ec_GF2m_simple_field_div,
980 ec_GF2m_simple_field_inv,
981 0, /* field_encode */
982 0, /* field_decode */
983 0, /* field_set_to_one */
984 ec_key_simple_priv2oct,
985 ec_key_simple_oct2priv,
987 ec_key_simple_generate_key,
988 ec_key_simple_check_key,
989 ec_key_simple_generate_public_key,
992 ecdh_simple_compute_key,
993 ecdsa_simple_sign_setup,
994 ecdsa_simple_sign_sig,
995 ecdsa_simple_verify_sig,
996 0, /* field_inverse_mod_ord */
997 0, /* blind_coordinates */
998 ec_GF2m_simple_ladder_pre,
999 ec_GF2m_simple_ladder_step,
1000 ec_GF2m_simple_ladder_post