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 "internal/bn_int.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