2 * Copyright 2002-2021 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 ossl_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 ossl_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 ossl_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 ossl_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 ossl_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 ERR_raise(ERR_LIB_EC, 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 ossl_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 ossl_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 ossl_ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
186 BN_CTX *new_ctx = NULL;
189 ctx = new_ctx = BN_CTX_new();
191 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
201 if (!BN_GF2m_mod_arr(b, group->b, group->poly))
205 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
206 * curve <=> b != 0 (mod p)
216 BN_CTX_free(new_ctx);
221 /* Initializes an EC_POINT. */
222 int ossl_ec_GF2m_simple_point_init(EC_POINT *point)
228 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
237 /* Frees an EC_POINT. */
238 void ossl_ec_GF2m_simple_point_finish(EC_POINT *point)
245 /* Clears and frees an EC_POINT. */
246 void ossl_ec_GF2m_simple_point_clear_finish(EC_POINT *point)
248 BN_clear_free(point->X);
249 BN_clear_free(point->Y);
250 BN_clear_free(point->Z);
255 * Copy the contents of one EC_POINT into another. Assumes dest is
258 int ossl_ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
260 if (!BN_copy(dest->X, src->X))
262 if (!BN_copy(dest->Y, src->Y))
264 if (!BN_copy(dest->Z, src->Z))
266 dest->Z_is_one = src->Z_is_one;
267 dest->curve_name = src->curve_name;
273 * Set an EC_POINT to the point at infinity. A point at infinity is
274 * represented by having Z=0.
276 int ossl_ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
285 * Set the coordinates of an EC_POINT using affine coordinates. Note that
286 * the simple implementation only uses affine coordinates.
288 int ossl_ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
295 if (x == NULL || y == NULL) {
296 ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER);
300 if (!BN_copy(point->X, x))
302 BN_set_negative(point->X, 0);
303 if (!BN_copy(point->Y, y))
305 BN_set_negative(point->Y, 0);
306 if (!BN_copy(point->Z, BN_value_one()))
308 BN_set_negative(point->Z, 0);
317 * Gets the affine coordinates of an EC_POINT. Note that the simple
318 * implementation only uses affine coordinates.
320 int ossl_ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
321 const EC_POINT *point,
322 BIGNUM *x, BIGNUM *y,
327 if (EC_POINT_is_at_infinity(group, point)) {
328 ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
332 if (BN_cmp(point->Z, BN_value_one())) {
333 ERR_raise(ERR_LIB_EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
337 if (!BN_copy(x, point->X))
339 BN_set_negative(x, 0);
342 if (!BN_copy(y, point->Y))
344 BN_set_negative(y, 0);
353 * Computes a + b and stores the result in r. r could be a or b, a could be
354 * b. Uses algorithm A.10.2 of IEEE P1363.
356 int ossl_ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r,
357 const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
359 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
362 BN_CTX *new_ctx = NULL;
365 if (EC_POINT_is_at_infinity(group, a)) {
366 if (!EC_POINT_copy(r, b))
371 if (EC_POINT_is_at_infinity(group, b)) {
372 if (!EC_POINT_copy(r, a))
379 ctx = new_ctx = BN_CTX_new();
386 x0 = BN_CTX_get(ctx);
387 y0 = BN_CTX_get(ctx);
388 x1 = BN_CTX_get(ctx);
389 y1 = BN_CTX_get(ctx);
390 x2 = BN_CTX_get(ctx);
391 y2 = BN_CTX_get(ctx);
398 if (!BN_copy(x0, a->X))
400 if (!BN_copy(y0, a->Y))
403 if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx))
407 if (!BN_copy(x1, b->X))
409 if (!BN_copy(y1, b->Y))
412 if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx))
416 if (BN_GF2m_cmp(x0, x1)) {
417 if (!BN_GF2m_add(t, x0, x1))
419 if (!BN_GF2m_add(s, y0, y1))
421 if (!group->meth->field_div(group, s, s, t, ctx))
423 if (!group->meth->field_sqr(group, x2, s, ctx))
425 if (!BN_GF2m_add(x2, x2, group->a))
427 if (!BN_GF2m_add(x2, x2, s))
429 if (!BN_GF2m_add(x2, x2, t))
432 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
433 if (!EC_POINT_set_to_infinity(group, r))
438 if (!group->meth->field_div(group, s, y1, x1, ctx))
440 if (!BN_GF2m_add(s, s, x1))
443 if (!group->meth->field_sqr(group, x2, s, ctx))
445 if (!BN_GF2m_add(x2, x2, s))
447 if (!BN_GF2m_add(x2, x2, group->a))
451 if (!BN_GF2m_add(y2, x1, x2))
453 if (!group->meth->field_mul(group, y2, y2, s, ctx))
455 if (!BN_GF2m_add(y2, y2, x2))
457 if (!BN_GF2m_add(y2, y2, y1))
460 if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx))
468 BN_CTX_free(new_ctx);
474 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
475 * A.10.2 of IEEE P1363.
477 int ossl_ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r,
478 const EC_POINT *a, BN_CTX *ctx)
480 return ossl_ec_GF2m_simple_add(group, r, a, a, ctx);
483 int ossl_ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point,
486 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
487 /* point is its own inverse */
490 if (group->meth->make_affine == NULL
491 || !group->meth->make_affine(group, point, ctx))
493 return BN_GF2m_add(point->Y, point->X, point->Y);
496 /* Indicates whether the given point is the point at infinity. */
497 int ossl_ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
498 const EC_POINT *point)
500 return BN_is_zero(point->Z);
504 * Determines whether the given EC_POINT is an actual point on the curve defined
505 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
506 * y^2 + x*y = x^3 + a*x^2 + b.
508 int ossl_ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
513 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
514 const BIGNUM *, BN_CTX *);
515 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
517 BN_CTX *new_ctx = NULL;
520 if (EC_POINT_is_at_infinity(group, point))
523 field_mul = group->meth->field_mul;
524 field_sqr = group->meth->field_sqr;
526 /* only support affine coordinates */
527 if (!point->Z_is_one)
532 ctx = new_ctx = BN_CTX_new();
539 y2 = BN_CTX_get(ctx);
540 lh = BN_CTX_get(ctx);
545 * We have a curve defined by a Weierstrass equation
546 * y^2 + x*y = x^3 + a*x^2 + b.
547 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
548 * <=> ((x + a) * x + y) * x + b + y^2 = 0
550 if (!BN_GF2m_add(lh, point->X, group->a))
552 if (!field_mul(group, lh, lh, point->X, ctx))
554 if (!BN_GF2m_add(lh, lh, point->Y))
556 if (!field_mul(group, lh, lh, point->X, ctx))
558 if (!BN_GF2m_add(lh, lh, group->b))
560 if (!field_sqr(group, y2, point->Y, ctx))
562 if (!BN_GF2m_add(lh, lh, y2))
564 ret = BN_is_zero(lh);
569 BN_CTX_free(new_ctx);
575 * Indicates whether two points are equal.
578 * 0 equal (in affine coordinates)
581 int ossl_ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
582 const EC_POINT *b, BN_CTX *ctx)
584 BIGNUM *aX, *aY, *bX, *bY;
587 BN_CTX *new_ctx = NULL;
590 if (EC_POINT_is_at_infinity(group, a)) {
591 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
594 if (EC_POINT_is_at_infinity(group, b))
597 if (a->Z_is_one && b->Z_is_one) {
598 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
603 ctx = new_ctx = BN_CTX_new();
610 aX = BN_CTX_get(ctx);
611 aY = BN_CTX_get(ctx);
612 bX = BN_CTX_get(ctx);
613 bY = BN_CTX_get(ctx);
617 if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx))
619 if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx))
621 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
626 BN_CTX_free(new_ctx);
631 /* Forces the given EC_POINT to internally use affine coordinates. */
632 int ossl_ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
638 BN_CTX *new_ctx = NULL;
641 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
646 ctx = new_ctx = BN_CTX_new();
658 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
660 if (!BN_copy(point->X, x))
662 if (!BN_copy(point->Y, y))
664 if (!BN_one(point->Z))
673 BN_CTX_free(new_ctx);
679 * Forces each of the EC_POINTs in the given array to use affine coordinates.
681 int ossl_ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
682 EC_POINT *points[], BN_CTX *ctx)
686 for (i = 0; i < num; i++) {
687 if (!group->meth->make_affine(group, points[i], ctx))
694 /* Wrapper to simple binary polynomial field multiplication implementation. */
695 int ossl_ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
696 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
698 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
701 /* Wrapper to simple binary polynomial field squaring implementation. */
702 int ossl_ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
703 const BIGNUM *a, BN_CTX *ctx)
705 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
708 /* Wrapper to simple binary polynomial field division implementation. */
709 int ossl_ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
710 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
712 return BN_GF2m_mod_div(r, a, b, group->field, ctx);
716 * Lopez-Dahab ladder, pre step.
717 * See e.g. "Guide to ECC" Alg 3.40.
718 * Modified to blind s and r independently.
722 int ec_GF2m_simple_ladder_pre(const EC_GROUP *group,
723 EC_POINT *r, EC_POINT *s,
724 EC_POINT *p, BN_CTX *ctx)
726 /* if p is not affine, something is wrong */
727 if (p->Z_is_one == 0)
730 /* s blinding: make sure lambda (s->Z here) is not zero */
732 if (!BN_priv_rand_ex(s->Z, BN_num_bits(group->field) - 1,
733 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, 0, ctx)) {
734 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
737 } while (BN_is_zero(s->Z));
739 /* if field_encode defined convert between representations */
740 if ((group->meth->field_encode != NULL
741 && !group->meth->field_encode(group, s->Z, s->Z, ctx))
742 || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx))
745 /* r blinding: make sure lambda (r->Y here for storage) is not zero */
747 if (!BN_priv_rand_ex(r->Y, BN_num_bits(group->field) - 1,
748 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, 0, ctx)) {
749 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
752 } while (BN_is_zero(r->Y));
754 if ((group->meth->field_encode != NULL
755 && !group->meth->field_encode(group, r->Y, r->Y, ctx))
756 || !group->meth->field_sqr(group, r->Z, p->X, ctx)
757 || !group->meth->field_sqr(group, r->X, r->Z, ctx)
758 || !BN_GF2m_add(r->X, r->X, group->b)
759 || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
760 || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx))
770 * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
771 * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
772 * s := r + s, r := 2r
775 int ec_GF2m_simple_ladder_step(const EC_GROUP *group,
776 EC_POINT *r, EC_POINT *s,
777 EC_POINT *p, BN_CTX *ctx)
779 if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx)
780 || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx)
781 || !group->meth->field_sqr(group, s->Y, r->Z, ctx)
782 || !group->meth->field_sqr(group, r->Z, r->X, ctx)
783 || !BN_GF2m_add(s->Z, r->Y, s->X)
784 || !group->meth->field_sqr(group, s->Z, s->Z, ctx)
785 || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx)
786 || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx)
787 || !BN_GF2m_add(s->X, s->X, r->Y)
788 || !group->meth->field_sqr(group, r->Y, r->Z, ctx)
789 || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx)
790 || !group->meth->field_sqr(group, s->Y, s->Y, ctx)
791 || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx)
792 || !BN_GF2m_add(r->X, r->Y, s->Y))
799 * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
800 * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
801 * without Precomputation" (Lopez and Dahab, CHES 1999),
805 int ec_GF2m_simple_ladder_post(const EC_GROUP *group,
806 EC_POINT *r, EC_POINT *s,
807 EC_POINT *p, BN_CTX *ctx)
810 BIGNUM *t0, *t1, *t2 = NULL;
812 if (BN_is_zero(r->Z))
813 return EC_POINT_set_to_infinity(group, r);
815 if (BN_is_zero(s->Z)) {
816 if (!EC_POINT_copy(r, p)
817 || !EC_POINT_invert(group, r, ctx)) {
818 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
825 t0 = BN_CTX_get(ctx);
826 t1 = BN_CTX_get(ctx);
827 t2 = BN_CTX_get(ctx);
829 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
833 if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
834 || !group->meth->field_mul(group, t1, p->X, r->Z, ctx)
835 || !BN_GF2m_add(t1, r->X, t1)
836 || !group->meth->field_mul(group, t2, p->X, s->Z, ctx)
837 || !group->meth->field_mul(group, r->Z, r->X, t2, ctx)
838 || !BN_GF2m_add(t2, t2, s->X)
839 || !group->meth->field_mul(group, t1, t1, t2, ctx)
840 || !group->meth->field_sqr(group, t2, p->X, ctx)
841 || !BN_GF2m_add(t2, p->Y, t2)
842 || !group->meth->field_mul(group, t2, t2, t0, ctx)
843 || !BN_GF2m_add(t1, t2, t1)
844 || !group->meth->field_mul(group, t2, p->X, t0, ctx)
845 || !group->meth->field_inv(group, t2, t2, ctx)
846 || !group->meth->field_mul(group, t1, t1, t2, ctx)
847 || !group->meth->field_mul(group, r->X, r->Z, t2, ctx)
848 || !BN_GF2m_add(t2, p->X, r->X)
849 || !group->meth->field_mul(group, t2, t2, t1, ctx)
850 || !BN_GF2m_add(r->Y, p->Y, t2)
856 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
857 BN_set_negative(r->X, 0);
858 BN_set_negative(r->Y, 0);
868 int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r,
869 const BIGNUM *scalar, size_t num,
870 const EC_POINT *points[],
871 const BIGNUM *scalars[],
878 * We limit use of the ladder only to the following cases:
880 * Fixed point mul: scalar != NULL && num == 0;
881 * - r := scalars[0] * points[0]
882 * Variable point mul: scalar == NULL && num == 1;
883 * - r := scalar * G + scalars[0] * points[0]
884 * used, e.g., in ECDSA verification: scalar != NULL && num == 1
886 * In any other case (num > 1) we use the default wNAF implementation.
888 * We also let the default implementation handle degenerate cases like group
889 * order or cofactor set to 0.
891 if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor))
892 return ossl_ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
894 if (scalar != NULL && num == 0)
895 /* Fixed point multiplication */
896 return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
898 if (scalar == NULL && num == 1)
899 /* Variable point multiplication */
900 return ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
903 * Double point multiplication:
904 * r := scalar * G + scalars[0] * points[0]
907 if ((t = EC_POINT_new(group)) == NULL) {
908 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
912 if (!ossl_ec_scalar_mul_ladder(group, t, scalar, NULL, ctx)
913 || !ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx)
914 || !EC_POINT_add(group, r, t, r, ctx))
925 * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
926 * If a is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error.
927 * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
929 static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
930 const BIGNUM *a, BN_CTX *ctx)
934 if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx)))
935 ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT);
939 const EC_METHOD *EC_GF2m_simple_method(void)
941 static const EC_METHOD ret = {
942 EC_FLAGS_DEFAULT_OCT,
943 NID_X9_62_characteristic_two_field,
944 ossl_ec_GF2m_simple_group_init,
945 ossl_ec_GF2m_simple_group_finish,
946 ossl_ec_GF2m_simple_group_clear_finish,
947 ossl_ec_GF2m_simple_group_copy,
948 ossl_ec_GF2m_simple_group_set_curve,
949 ossl_ec_GF2m_simple_group_get_curve,
950 ossl_ec_GF2m_simple_group_get_degree,
951 ossl_ec_group_simple_order_bits,
952 ossl_ec_GF2m_simple_group_check_discriminant,
953 ossl_ec_GF2m_simple_point_init,
954 ossl_ec_GF2m_simple_point_finish,
955 ossl_ec_GF2m_simple_point_clear_finish,
956 ossl_ec_GF2m_simple_point_copy,
957 ossl_ec_GF2m_simple_point_set_to_infinity,
958 ossl_ec_GF2m_simple_point_set_affine_coordinates,
959 ossl_ec_GF2m_simple_point_get_affine_coordinates,
960 0, /* point_set_compressed_coordinates */
963 ossl_ec_GF2m_simple_add,
964 ossl_ec_GF2m_simple_dbl,
965 ossl_ec_GF2m_simple_invert,
966 ossl_ec_GF2m_simple_is_at_infinity,
967 ossl_ec_GF2m_simple_is_on_curve,
968 ossl_ec_GF2m_simple_cmp,
969 ossl_ec_GF2m_simple_make_affine,
970 ossl_ec_GF2m_simple_points_make_affine,
971 ec_GF2m_simple_points_mul,
972 0, /* precompute_mult */
973 0, /* have_precompute_mult */
974 ossl_ec_GF2m_simple_field_mul,
975 ossl_ec_GF2m_simple_field_sqr,
976 ossl_ec_GF2m_simple_field_div,
977 ec_GF2m_simple_field_inv,
978 0, /* field_encode */
979 0, /* field_decode */
980 0, /* field_set_to_one */
981 ossl_ec_key_simple_priv2oct,
982 ossl_ec_key_simple_oct2priv,
984 ossl_ec_key_simple_generate_key,
985 ossl_ec_key_simple_check_key,
986 ossl_ec_key_simple_generate_public_key,
989 ossl_ecdh_simple_compute_key,
990 ossl_ecdsa_simple_sign_setup,
991 ossl_ecdsa_simple_sign_sig,
992 ossl_ecdsa_simple_verify_sig,
993 0, /* field_inverse_mod_ord */
994 0, /* blind_coordinates */
995 ec_GF2m_simple_ladder_pre,
996 ec_GF2m_simple_ladder_step,
997 ec_GF2m_simple_ladder_post