2 * Copyright 2002-2016 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
18 const EC_METHOD *EC_GF2m_simple_method(void)
20 static const EC_METHOD ret = {
22 NID_X9_62_characteristic_two_field,
23 ec_GF2m_simple_group_init,
24 ec_GF2m_simple_group_finish,
25 ec_GF2m_simple_group_clear_finish,
26 ec_GF2m_simple_group_copy,
27 ec_GF2m_simple_group_set_curve,
28 ec_GF2m_simple_group_get_curve,
29 ec_GF2m_simple_group_get_degree,
30 ec_group_simple_order_bits,
31 ec_GF2m_simple_group_check_discriminant,
32 ec_GF2m_simple_point_init,
33 ec_GF2m_simple_point_finish,
34 ec_GF2m_simple_point_clear_finish,
35 ec_GF2m_simple_point_copy,
36 ec_GF2m_simple_point_set_to_infinity,
37 0 /* set_Jprojective_coordinates_GFp */ ,
38 0 /* get_Jprojective_coordinates_GFp */ ,
39 ec_GF2m_simple_point_set_affine_coordinates,
40 ec_GF2m_simple_point_get_affine_coordinates,
44 ec_GF2m_simple_invert,
45 ec_GF2m_simple_is_at_infinity,
46 ec_GF2m_simple_is_on_curve,
48 ec_GF2m_simple_make_affine,
49 ec_GF2m_simple_points_make_affine,
51 0 /* precompute_mul */,
52 0 /* have_precompute_mul */,
53 ec_GF2m_simple_field_mul,
54 ec_GF2m_simple_field_sqr,
55 ec_GF2m_simple_field_div,
56 0 /* field_encode */ ,
57 0 /* field_decode */ ,
58 0, /* field_set_to_one */
59 ec_key_simple_priv2oct,
60 ec_key_simple_oct2priv,
62 ec_key_simple_generate_key,
63 ec_key_simple_check_key,
64 ec_key_simple_generate_public_key,
67 ecdh_simple_compute_key
74 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
75 * are handled by EC_GROUP_new.
77 int ec_GF2m_simple_group_init(EC_GROUP *group)
79 group->field = BN_new();
83 if (group->field == NULL || group->a == NULL || group->b == NULL) {
84 BN_free(group->field);
93 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
94 * handled by EC_GROUP_free.
96 void ec_GF2m_simple_group_finish(EC_GROUP *group)
98 BN_free(group->field);
104 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
105 * members are handled by EC_GROUP_clear_free.
107 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
109 BN_clear_free(group->field);
110 BN_clear_free(group->a);
111 BN_clear_free(group->b);
121 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
122 * handled by EC_GROUP_copy.
124 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
126 if (!BN_copy(dest->field, src->field))
128 if (!BN_copy(dest->a, src->a))
130 if (!BN_copy(dest->b, src->b))
132 dest->poly[0] = src->poly[0];
133 dest->poly[1] = src->poly[1];
134 dest->poly[2] = src->poly[2];
135 dest->poly[3] = src->poly[3];
136 dest->poly[4] = src->poly[4];
137 dest->poly[5] = src->poly[5];
138 if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
141 if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
144 bn_set_all_zero(dest->a);
145 bn_set_all_zero(dest->b);
149 /* Set the curve parameters of an EC_GROUP structure. */
150 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
151 const BIGNUM *p, const BIGNUM *a,
152 const BIGNUM *b, BN_CTX *ctx)
157 if (!BN_copy(group->field, p))
159 i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
160 if ((i != 5) && (i != 3)) {
161 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
166 if (!BN_GF2m_mod_arr(group->a, a, group->poly))
168 if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
171 bn_set_all_zero(group->a);
174 if (!BN_GF2m_mod_arr(group->b, b, group->poly))
176 if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
179 bn_set_all_zero(group->b);
187 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
188 * then there values will not be set but the method will return with success.
190 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
191 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
196 if (!BN_copy(p, group->field))
201 if (!BN_copy(a, group->a))
206 if (!BN_copy(b, group->b))
217 * Gets the degree of the field. For a curve over GF(2^m) this is the value
220 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
222 return BN_num_bits(group->field) - 1;
226 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
227 * elliptic curve <=> b != 0 (mod p)
229 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
234 BN_CTX *new_ctx = NULL;
237 ctx = new_ctx = BN_CTX_new();
239 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT,
240 ERR_R_MALLOC_FAILURE);
249 if (!BN_GF2m_mod_arr(b, group->b, group->poly))
253 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
254 * curve <=> b != 0 (mod p)
264 BN_CTX_free(new_ctx);
268 /* Initializes an EC_POINT. */
269 int ec_GF2m_simple_point_init(EC_POINT *point)
275 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
284 /* Frees an EC_POINT. */
285 void ec_GF2m_simple_point_finish(EC_POINT *point)
292 /* Clears and frees an EC_POINT. */
293 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
295 BN_clear_free(point->X);
296 BN_clear_free(point->Y);
297 BN_clear_free(point->Z);
302 * Copy the contents of one EC_POINT into another. Assumes dest is
305 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
307 if (!BN_copy(dest->X, src->X))
309 if (!BN_copy(dest->Y, src->Y))
311 if (!BN_copy(dest->Z, src->Z))
313 dest->Z_is_one = src->Z_is_one;
314 dest->curve_name = src->curve_name;
320 * Set an EC_POINT to the point at infinity. A point at infinity is
321 * represented by having Z=0.
323 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
332 * Set the coordinates of an EC_POINT using affine coordinates. Note that
333 * the simple implementation only uses affine coordinates.
335 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
338 const BIGNUM *y, BN_CTX *ctx)
341 if (x == NULL || y == NULL) {
342 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
343 ERR_R_PASSED_NULL_PARAMETER);
347 if (!BN_copy(point->X, x))
349 BN_set_negative(point->X, 0);
350 if (!BN_copy(point->Y, y))
352 BN_set_negative(point->Y, 0);
353 if (!BN_copy(point->Z, BN_value_one()))
355 BN_set_negative(point->Z, 0);
364 * Gets the affine coordinates of an EC_POINT. Note that the simple
365 * implementation only uses affine coordinates.
367 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
368 const EC_POINT *point,
369 BIGNUM *x, BIGNUM *y,
374 if (EC_POINT_is_at_infinity(group, point)) {
375 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
376 EC_R_POINT_AT_INFINITY);
380 if (BN_cmp(point->Z, BN_value_one())) {
381 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
382 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
386 if (!BN_copy(x, point->X))
388 BN_set_negative(x, 0);
391 if (!BN_copy(y, point->Y))
393 BN_set_negative(y, 0);
402 * Computes a + b and stores the result in r. r could be a or b, a could be
403 * b. Uses algorithm A.10.2 of IEEE P1363.
405 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
406 const EC_POINT *b, BN_CTX *ctx)
408 BN_CTX *new_ctx = NULL;
409 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
412 if (EC_POINT_is_at_infinity(group, a)) {
413 if (!EC_POINT_copy(r, b))
418 if (EC_POINT_is_at_infinity(group, b)) {
419 if (!EC_POINT_copy(r, a))
425 ctx = new_ctx = BN_CTX_new();
431 x0 = BN_CTX_get(ctx);
432 y0 = BN_CTX_get(ctx);
433 x1 = BN_CTX_get(ctx);
434 y1 = BN_CTX_get(ctx);
435 x2 = BN_CTX_get(ctx);
436 y2 = BN_CTX_get(ctx);
443 if (!BN_copy(x0, a->X))
445 if (!BN_copy(y0, a->Y))
448 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx))
452 if (!BN_copy(x1, b->X))
454 if (!BN_copy(y1, b->Y))
457 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx))
461 if (BN_GF2m_cmp(x0, x1)) {
462 if (!BN_GF2m_add(t, x0, x1))
464 if (!BN_GF2m_add(s, y0, y1))
466 if (!group->meth->field_div(group, s, s, t, ctx))
468 if (!group->meth->field_sqr(group, x2, s, ctx))
470 if (!BN_GF2m_add(x2, x2, group->a))
472 if (!BN_GF2m_add(x2, x2, s))
474 if (!BN_GF2m_add(x2, x2, t))
477 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
478 if (!EC_POINT_set_to_infinity(group, r))
483 if (!group->meth->field_div(group, s, y1, x1, ctx))
485 if (!BN_GF2m_add(s, s, x1))
488 if (!group->meth->field_sqr(group, x2, s, ctx))
490 if (!BN_GF2m_add(x2, x2, s))
492 if (!BN_GF2m_add(x2, x2, group->a))
496 if (!BN_GF2m_add(y2, x1, x2))
498 if (!group->meth->field_mul(group, y2, y2, s, ctx))
500 if (!BN_GF2m_add(y2, y2, x2))
502 if (!BN_GF2m_add(y2, y2, y1))
505 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx))
512 BN_CTX_free(new_ctx);
517 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
518 * A.10.2 of IEEE P1363.
520 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
523 return ec_GF2m_simple_add(group, r, a, a, ctx);
526 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
528 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
529 /* point is its own inverse */
532 if (!EC_POINT_make_affine(group, point, ctx))
534 return BN_GF2m_add(point->Y, point->X, point->Y);
537 /* Indicates whether the given point is the point at infinity. */
538 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
539 const EC_POINT *point)
541 return BN_is_zero(point->Z);
545 * Determines whether the given EC_POINT is an actual point on the curve defined
546 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
547 * y^2 + x*y = x^3 + a*x^2 + b.
549 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
553 BN_CTX *new_ctx = NULL;
555 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
556 const BIGNUM *, BN_CTX *);
557 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
559 if (EC_POINT_is_at_infinity(group, point))
562 field_mul = group->meth->field_mul;
563 field_sqr = group->meth->field_sqr;
565 /* only support affine coordinates */
566 if (!point->Z_is_one)
570 ctx = new_ctx = BN_CTX_new();
576 y2 = BN_CTX_get(ctx);
577 lh = BN_CTX_get(ctx);
582 * We have a curve defined by a Weierstrass equation
583 * y^2 + x*y = x^3 + a*x^2 + b.
584 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
585 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
587 if (!BN_GF2m_add(lh, point->X, group->a))
589 if (!field_mul(group, lh, lh, point->X, ctx))
591 if (!BN_GF2m_add(lh, lh, point->Y))
593 if (!field_mul(group, lh, lh, point->X, ctx))
595 if (!BN_GF2m_add(lh, lh, group->b))
597 if (!field_sqr(group, y2, point->Y, ctx))
599 if (!BN_GF2m_add(lh, lh, y2))
601 ret = BN_is_zero(lh);
605 BN_CTX_free(new_ctx);
610 * Indicates whether two points are equal.
613 * 0 equal (in affine coordinates)
616 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
617 const EC_POINT *b, BN_CTX *ctx)
619 BIGNUM *aX, *aY, *bX, *bY;
620 BN_CTX *new_ctx = NULL;
623 if (EC_POINT_is_at_infinity(group, a)) {
624 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
627 if (EC_POINT_is_at_infinity(group, b))
630 if (a->Z_is_one && b->Z_is_one) {
631 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
635 ctx = new_ctx = BN_CTX_new();
641 aX = BN_CTX_get(ctx);
642 aY = BN_CTX_get(ctx);
643 bX = BN_CTX_get(ctx);
644 bY = BN_CTX_get(ctx);
648 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx))
650 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx))
652 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
656 BN_CTX_free(new_ctx);
660 /* Forces the given EC_POINT to internally use affine coordinates. */
661 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
664 BN_CTX *new_ctx = NULL;
668 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
672 ctx = new_ctx = BN_CTX_new();
683 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
685 if (!BN_copy(point->X, x))
687 if (!BN_copy(point->Y, y))
689 if (!BN_one(point->Z))
697 BN_CTX_free(new_ctx);
702 * Forces each of the EC_POINTs in the given array to use affine coordinates.
704 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
705 EC_POINT *points[], BN_CTX *ctx)
709 for (i = 0; i < num; i++) {
710 if (!group->meth->make_affine(group, points[i], ctx))
717 /* Wrapper to simple binary polynomial field multiplication implementation. */
718 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
719 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
721 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
724 /* Wrapper to simple binary polynomial field squaring implementation. */
725 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
726 const BIGNUM *a, BN_CTX *ctx)
728 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
731 /* Wrapper to simple binary polynomial field division implementation. */
732 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
733 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
735 return BN_GF2m_mod_div(r, a, b, group->field, ctx);