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)
209 BN_CTX_free(new_ctx);
213 /* Initializes an EC_POINT. */
214 int ec_GF2m_simple_point_init(EC_POINT *point)
220 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
229 /* Frees an EC_POINT. */
230 void ec_GF2m_simple_point_finish(EC_POINT *point)
237 /* Clears and frees an EC_POINT. */
238 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
240 BN_clear_free(point->X);
241 BN_clear_free(point->Y);
242 BN_clear_free(point->Z);
247 * Copy the contents of one EC_POINT into another. Assumes dest is
250 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
252 if (!BN_copy(dest->X, src->X))
254 if (!BN_copy(dest->Y, src->Y))
256 if (!BN_copy(dest->Z, src->Z))
258 dest->Z_is_one = src->Z_is_one;
259 dest->curve_name = src->curve_name;
265 * Set an EC_POINT to the point at infinity. A point at infinity is
266 * represented by having Z=0.
268 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
277 * Set the coordinates of an EC_POINT using affine coordinates. Note that
278 * the simple implementation only uses affine coordinates.
280 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
283 const BIGNUM *y, BN_CTX *ctx)
286 if (x == NULL || y == NULL) {
287 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
288 ERR_R_PASSED_NULL_PARAMETER);
292 if (!BN_copy(point->X, x))
294 BN_set_negative(point->X, 0);
295 if (!BN_copy(point->Y, y))
297 BN_set_negative(point->Y, 0);
298 if (!BN_copy(point->Z, BN_value_one()))
300 BN_set_negative(point->Z, 0);
309 * Gets the affine coordinates of an EC_POINT. Note that the simple
310 * implementation only uses affine coordinates.
312 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
313 const EC_POINT *point,
314 BIGNUM *x, BIGNUM *y,
319 if (EC_POINT_is_at_infinity(group, point)) {
320 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
321 EC_R_POINT_AT_INFINITY);
325 if (BN_cmp(point->Z, BN_value_one())) {
326 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
327 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
331 if (!BN_copy(x, point->X))
333 BN_set_negative(x, 0);
336 if (!BN_copy(y, point->Y))
338 BN_set_negative(y, 0);
347 * Computes a + b and stores the result in r. r could be a or b, a could be
348 * b. Uses algorithm A.10.2 of IEEE P1363.
350 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
351 const EC_POINT *b, BN_CTX *ctx)
353 BN_CTX *new_ctx = NULL;
354 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
357 if (EC_POINT_is_at_infinity(group, a)) {
358 if (!EC_POINT_copy(r, b))
363 if (EC_POINT_is_at_infinity(group, b)) {
364 if (!EC_POINT_copy(r, a))
370 ctx = new_ctx = BN_CTX_new();
376 x0 = BN_CTX_get(ctx);
377 y0 = BN_CTX_get(ctx);
378 x1 = BN_CTX_get(ctx);
379 y1 = BN_CTX_get(ctx);
380 x2 = BN_CTX_get(ctx);
381 y2 = BN_CTX_get(ctx);
388 if (!BN_copy(x0, a->X))
390 if (!BN_copy(y0, a->Y))
393 if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx))
397 if (!BN_copy(x1, b->X))
399 if (!BN_copy(y1, b->Y))
402 if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx))
406 if (BN_GF2m_cmp(x0, x1)) {
407 if (!BN_GF2m_add(t, x0, x1))
409 if (!BN_GF2m_add(s, y0, y1))
411 if (!group->meth->field_div(group, s, s, t, ctx))
413 if (!group->meth->field_sqr(group, x2, s, ctx))
415 if (!BN_GF2m_add(x2, x2, group->a))
417 if (!BN_GF2m_add(x2, x2, s))
419 if (!BN_GF2m_add(x2, x2, t))
422 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
423 if (!EC_POINT_set_to_infinity(group, r))
428 if (!group->meth->field_div(group, s, y1, x1, ctx))
430 if (!BN_GF2m_add(s, s, x1))
433 if (!group->meth->field_sqr(group, x2, s, ctx))
435 if (!BN_GF2m_add(x2, x2, s))
437 if (!BN_GF2m_add(x2, x2, group->a))
441 if (!BN_GF2m_add(y2, x1, x2))
443 if (!group->meth->field_mul(group, y2, y2, s, ctx))
445 if (!BN_GF2m_add(y2, y2, x2))
447 if (!BN_GF2m_add(y2, y2, y1))
450 if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx))
457 BN_CTX_free(new_ctx);
462 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
463 * A.10.2 of IEEE P1363.
465 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
468 return ec_GF2m_simple_add(group, r, a, a, ctx);
471 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
473 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
474 /* point is its own inverse */
477 if (!EC_POINT_make_affine(group, point, ctx))
479 return BN_GF2m_add(point->Y, point->X, point->Y);
482 /* Indicates whether the given point is the point at infinity. */
483 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
484 const EC_POINT *point)
486 return BN_is_zero(point->Z);
490 * Determines whether the given EC_POINT is an actual point on the curve defined
491 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
492 * y^2 + x*y = x^3 + a*x^2 + b.
494 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
498 BN_CTX *new_ctx = NULL;
500 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
501 const BIGNUM *, BN_CTX *);
502 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
504 if (EC_POINT_is_at_infinity(group, point))
507 field_mul = group->meth->field_mul;
508 field_sqr = group->meth->field_sqr;
510 /* only support affine coordinates */
511 if (!point->Z_is_one)
515 ctx = new_ctx = BN_CTX_new();
521 y2 = BN_CTX_get(ctx);
522 lh = BN_CTX_get(ctx);
527 * We have a curve defined by a Weierstrass equation
528 * y^2 + x*y = x^3 + a*x^2 + b.
529 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
530 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
532 if (!BN_GF2m_add(lh, point->X, group->a))
534 if (!field_mul(group, lh, lh, point->X, ctx))
536 if (!BN_GF2m_add(lh, lh, point->Y))
538 if (!field_mul(group, lh, lh, point->X, ctx))
540 if (!BN_GF2m_add(lh, lh, group->b))
542 if (!field_sqr(group, y2, point->Y, ctx))
544 if (!BN_GF2m_add(lh, lh, y2))
546 ret = BN_is_zero(lh);
550 BN_CTX_free(new_ctx);
555 * Indicates whether two points are equal.
558 * 0 equal (in affine coordinates)
561 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
562 const EC_POINT *b, BN_CTX *ctx)
564 BIGNUM *aX, *aY, *bX, *bY;
565 BN_CTX *new_ctx = NULL;
568 if (EC_POINT_is_at_infinity(group, a)) {
569 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
572 if (EC_POINT_is_at_infinity(group, b))
575 if (a->Z_is_one && b->Z_is_one) {
576 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
580 ctx = new_ctx = BN_CTX_new();
586 aX = BN_CTX_get(ctx);
587 aY = BN_CTX_get(ctx);
588 bX = BN_CTX_get(ctx);
589 bY = BN_CTX_get(ctx);
593 if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx))
595 if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx))
597 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
601 BN_CTX_free(new_ctx);
605 /* Forces the given EC_POINT to internally use affine coordinates. */
606 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
609 BN_CTX *new_ctx = NULL;
613 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
617 ctx = new_ctx = BN_CTX_new();
628 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
630 if (!BN_copy(point->X, x))
632 if (!BN_copy(point->Y, y))
634 if (!BN_one(point->Z))
642 BN_CTX_free(new_ctx);
647 * Forces each of the EC_POINTs in the given array to use affine coordinates.
649 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
650 EC_POINT *points[], BN_CTX *ctx)
654 for (i = 0; i < num; i++) {
655 if (!group->meth->make_affine(group, points[i], ctx))
662 /* Wrapper to simple binary polynomial field multiplication implementation. */
663 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
664 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
666 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
669 /* Wrapper to simple binary polynomial field squaring implementation. */
670 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
671 const BIGNUM *a, BN_CTX *ctx)
673 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
676 /* Wrapper to simple binary polynomial field division implementation. */
677 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
678 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
680 return BN_GF2m_mod_div(r, a, b, group->field, ctx);
684 * Lopez-Dahab ladder, pre step.
685 * See e.g. "Guide to ECC" Alg 3.40.
686 * Modified to blind s and r independently.
690 int ec_GF2m_simple_ladder_pre(const EC_GROUP *group,
691 EC_POINT *r, EC_POINT *s,
692 EC_POINT *p, BN_CTX *ctx)
694 /* if p is not affine, something is wrong */
695 if (p->Z_is_one == 0)
698 /* s blinding: make sure lambda (s->Z here) is not zero */
700 if (!BN_priv_rand(s->Z, BN_num_bits(group->field) - 1,
701 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) {
702 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
705 } while (BN_is_zero(s->Z));
707 /* if field_encode defined convert between representations */
708 if ((group->meth->field_encode != NULL
709 && !group->meth->field_encode(group, s->Z, s->Z, ctx))
710 || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx))
713 /* r blinding: make sure lambda (r->Y here for storage) is not zero */
715 if (!BN_priv_rand(r->Y, BN_num_bits(group->field) - 1,
716 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) {
717 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB);
720 } while (BN_is_zero(r->Y));
722 if ((group->meth->field_encode != NULL
723 && !group->meth->field_encode(group, r->Y, r->Y, ctx))
724 || !group->meth->field_sqr(group, r->Z, p->X, ctx)
725 || !group->meth->field_sqr(group, r->X, r->Z, ctx)
726 || !BN_GF2m_add(r->X, r->X, group->b)
727 || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
728 || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx))
738 * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords.
739 * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3
740 * s := r + s, r := 2r
743 int ec_GF2m_simple_ladder_step(const EC_GROUP *group,
744 EC_POINT *r, EC_POINT *s,
745 EC_POINT *p, BN_CTX *ctx)
747 if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx)
748 || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx)
749 || !group->meth->field_sqr(group, s->Y, r->Z, ctx)
750 || !group->meth->field_sqr(group, r->Z, r->X, ctx)
751 || !BN_GF2m_add(s->Z, r->Y, s->X)
752 || !group->meth->field_sqr(group, s->Z, s->Z, ctx)
753 || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx)
754 || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx)
755 || !BN_GF2m_add(s->X, s->X, r->Y)
756 || !group->meth->field_sqr(group, r->Y, r->Z, ctx)
757 || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx)
758 || !group->meth->field_sqr(group, s->Y, s->Y, ctx)
759 || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx)
760 || !BN_GF2m_add(r->X, r->Y, s->Y))
767 * Recover affine (x,y) result from Lopez-Dahab r and s, affine p.
768 * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m)
769 * without Precomputation" (Lopez and Dahab, CHES 1999),
773 int ec_GF2m_simple_ladder_post(const EC_GROUP *group,
774 EC_POINT *r, EC_POINT *s,
775 EC_POINT *p, BN_CTX *ctx)
778 BIGNUM *t0, *t1, *t2 = NULL;
780 if (BN_is_zero(r->Z))
781 return EC_POINT_set_to_infinity(group, r);
783 if (BN_is_zero(s->Z)) {
784 if (!EC_POINT_copy(r, p)
785 || !EC_POINT_invert(group, r, ctx)) {
786 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_EC_LIB);
793 t0 = BN_CTX_get(ctx);
794 t1 = BN_CTX_get(ctx);
795 t2 = BN_CTX_get(ctx);
797 ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_MALLOC_FAILURE);
801 if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
802 || !group->meth->field_mul(group, t1, p->X, r->Z, ctx)
803 || !BN_GF2m_add(t1, r->X, t1)
804 || !group->meth->field_mul(group, t2, p->X, s->Z, ctx)
805 || !group->meth->field_mul(group, r->Z, r->X, t2, ctx)
806 || !BN_GF2m_add(t2, t2, s->X)
807 || !group->meth->field_mul(group, t1, t1, t2, ctx)
808 || !group->meth->field_sqr(group, t2, p->X, ctx)
809 || !BN_GF2m_add(t2, p->Y, t2)
810 || !group->meth->field_mul(group, t2, t2, t0, ctx)
811 || !BN_GF2m_add(t1, t2, t1)
812 || !group->meth->field_mul(group, t2, p->X, t0, ctx)
813 || !group->meth->field_inv(group, t2, t2, ctx)
814 || !group->meth->field_mul(group, t1, t1, t2, ctx)
815 || !group->meth->field_mul(group, r->X, r->Z, t2, ctx)
816 || !BN_GF2m_add(t2, p->X, r->X)
817 || !group->meth->field_mul(group, t2, t2, t1, ctx)
818 || !BN_GF2m_add(r->Y, p->Y, t2)
824 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
825 BN_set_negative(r->X, 0);
826 BN_set_negative(r->Y, 0);
836 int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r,
837 const BIGNUM *scalar, size_t num,
838 const EC_POINT *points[],
839 const BIGNUM *scalars[],
846 * We limit use of the ladder only to the following cases:
848 * Fixed point mul: scalar != NULL && num == 0;
849 * - r := scalars[0] * points[0]
850 * Variable point mul: scalar == NULL && num == 1;
851 * - r := scalar * G + scalars[0] * points[0]
852 * used, e.g., in ECDSA verification: scalar != NULL && num == 1
854 * In any other case (num > 1) we use the default wNAF implementation.
856 * We also let the default implementation handle degenerate cases like group
857 * order or cofactor set to 0.
859 if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor))
860 return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
862 if (scalar != NULL && num == 0)
863 /* Fixed point multiplication */
864 return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
866 if (scalar == NULL && num == 1)
867 /* Variable point multiplication */
868 return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
871 * Double point multiplication:
872 * r := scalar * G + scalars[0] * points[0]
875 if ((t = EC_POINT_new(group)) == NULL) {
876 ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL, ERR_R_MALLOC_FAILURE);
880 if (!ec_scalar_mul_ladder(group, t, scalar, NULL, ctx)
881 || !ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx)
882 || !EC_POINT_add(group, r, t, r, ctx))
893 * Computes the multiplicative inverse of a in GF(2^m), storing the result in r.
894 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
895 * SCA hardening is with blinding: BN_GF2m_mod_inv does that.
897 static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
898 const BIGNUM *a, BN_CTX *ctx)
902 if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx)))
903 ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
907 const EC_METHOD *EC_GF2m_simple_method(void)
909 static const EC_METHOD ret = {
910 EC_FLAGS_DEFAULT_OCT,
911 NID_X9_62_characteristic_two_field,
912 ec_GF2m_simple_group_init,
913 ec_GF2m_simple_group_finish,
914 ec_GF2m_simple_group_clear_finish,
915 ec_GF2m_simple_group_copy,
916 ec_GF2m_simple_group_set_curve,
917 ec_GF2m_simple_group_get_curve,
918 ec_GF2m_simple_group_get_degree,
919 ec_group_simple_order_bits,
920 ec_GF2m_simple_group_check_discriminant,
921 ec_GF2m_simple_point_init,
922 ec_GF2m_simple_point_finish,
923 ec_GF2m_simple_point_clear_finish,
924 ec_GF2m_simple_point_copy,
925 ec_GF2m_simple_point_set_to_infinity,
926 0, /* set_Jprojective_coordinates_GFp */
927 0, /* get_Jprojective_coordinates_GFp */
928 ec_GF2m_simple_point_set_affine_coordinates,
929 ec_GF2m_simple_point_get_affine_coordinates,
930 0, /* point_set_compressed_coordinates */
935 ec_GF2m_simple_invert,
936 ec_GF2m_simple_is_at_infinity,
937 ec_GF2m_simple_is_on_curve,
939 ec_GF2m_simple_make_affine,
940 ec_GF2m_simple_points_make_affine,
941 ec_GF2m_simple_points_mul,
942 0, /* precompute_mult */
943 0, /* have_precompute_mult */
944 ec_GF2m_simple_field_mul,
945 ec_GF2m_simple_field_sqr,
946 ec_GF2m_simple_field_div,
947 ec_GF2m_simple_field_inv,
948 0, /* field_encode */
949 0, /* field_decode */
950 0, /* field_set_to_one */
951 ec_key_simple_priv2oct,
952 ec_key_simple_oct2priv,
954 ec_key_simple_generate_key,
955 ec_key_simple_check_key,
956 ec_key_simple_generate_public_key,
959 ecdh_simple_compute_key,
960 0, /* field_inverse_mod_ord */
961 0, /* blind_coordinates */
962 ec_GF2m_simple_ladder_pre,
963 ec_GF2m_simple_ladder_step,
964 ec_GF2m_simple_ladder_post