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,
52 * the following three method functions are defined in ec2_mult.c
55 ec_GF2m_precompute_mult,
56 ec_GF2m_have_precompute_mult,
58 ec_GF2m_simple_field_mul,
59 ec_GF2m_simple_field_sqr,
60 ec_GF2m_simple_field_div,
61 0 /* field_encode */ ,
62 0 /* field_decode */ ,
63 0, /* field_set_to_one */
64 ec_key_simple_priv2oct,
65 ec_key_simple_oct2priv,
67 ec_key_simple_generate_key,
68 ec_key_simple_check_key,
69 ec_key_simple_generate_public_key,
72 ecdh_simple_compute_key
79 * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members
80 * are handled by EC_GROUP_new.
82 int ec_GF2m_simple_group_init(EC_GROUP *group)
84 group->field = BN_new();
88 if (group->field == NULL || group->a == NULL || group->b == NULL) {
89 BN_free(group->field);
98 * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are
99 * handled by EC_GROUP_free.
101 void ec_GF2m_simple_group_finish(EC_GROUP *group)
103 BN_free(group->field);
109 * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other
110 * members are handled by EC_GROUP_clear_free.
112 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
114 BN_clear_free(group->field);
115 BN_clear_free(group->a);
116 BN_clear_free(group->b);
126 * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are
127 * handled by EC_GROUP_copy.
129 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
131 if (!BN_copy(dest->field, src->field))
133 if (!BN_copy(dest->a, src->a))
135 if (!BN_copy(dest->b, src->b))
137 dest->poly[0] = src->poly[0];
138 dest->poly[1] = src->poly[1];
139 dest->poly[2] = src->poly[2];
140 dest->poly[3] = src->poly[3];
141 dest->poly[4] = src->poly[4];
142 dest->poly[5] = src->poly[5];
143 if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
146 if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) ==
149 bn_set_all_zero(dest->a);
150 bn_set_all_zero(dest->b);
154 /* Set the curve parameters of an EC_GROUP structure. */
155 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
156 const BIGNUM *p, const BIGNUM *a,
157 const BIGNUM *b, BN_CTX *ctx)
162 if (!BN_copy(group->field, p))
164 i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
165 if ((i != 5) && (i != 3)) {
166 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
171 if (!BN_GF2m_mod_arr(group->a, a, group->poly))
173 if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
176 bn_set_all_zero(group->a);
179 if (!BN_GF2m_mod_arr(group->b, b, group->poly))
181 if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2)
184 bn_set_all_zero(group->b);
192 * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL
193 * then there values will not be set but the method will return with success.
195 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
196 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
201 if (!BN_copy(p, group->field))
206 if (!BN_copy(a, group->a))
211 if (!BN_copy(b, group->b))
222 * Gets the degree of the field. For a curve over GF(2^m) this is the value
225 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
227 return BN_num_bits(group->field) - 1;
231 * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an
232 * elliptic curve <=> b != 0 (mod p)
234 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,
239 BN_CTX *new_ctx = NULL;
242 ctx = new_ctx = BN_CTX_new();
244 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT,
245 ERR_R_MALLOC_FAILURE);
254 if (!BN_GF2m_mod_arr(b, group->b, group->poly))
258 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic
259 * curve <=> b != 0 (mod p)
269 BN_CTX_free(new_ctx);
273 /* Initializes an EC_POINT. */
274 int ec_GF2m_simple_point_init(EC_POINT *point)
280 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
289 /* Frees an EC_POINT. */
290 void ec_GF2m_simple_point_finish(EC_POINT *point)
297 /* Clears and frees an EC_POINT. */
298 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
300 BN_clear_free(point->X);
301 BN_clear_free(point->Y);
302 BN_clear_free(point->Z);
307 * Copy the contents of one EC_POINT into another. Assumes dest is
310 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
312 if (!BN_copy(dest->X, src->X))
314 if (!BN_copy(dest->Y, src->Y))
316 if (!BN_copy(dest->Z, src->Z))
318 dest->Z_is_one = src->Z_is_one;
324 * Set an EC_POINT to the point at infinity. A point at infinity is
325 * represented by having Z=0.
327 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group,
336 * Set the coordinates of an EC_POINT using affine coordinates. Note that
337 * the simple implementation only uses affine coordinates.
339 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group,
342 const BIGNUM *y, BN_CTX *ctx)
345 if (x == NULL || y == NULL) {
346 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES,
347 ERR_R_PASSED_NULL_PARAMETER);
351 if (!BN_copy(point->X, x))
353 BN_set_negative(point->X, 0);
354 if (!BN_copy(point->Y, y))
356 BN_set_negative(point->Y, 0);
357 if (!BN_copy(point->Z, BN_value_one()))
359 BN_set_negative(point->Z, 0);
368 * Gets the affine coordinates of an EC_POINT. Note that the simple
369 * implementation only uses affine coordinates.
371 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group,
372 const EC_POINT *point,
373 BIGNUM *x, BIGNUM *y,
378 if (EC_POINT_is_at_infinity(group, point)) {
379 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
380 EC_R_POINT_AT_INFINITY);
384 if (BN_cmp(point->Z, BN_value_one())) {
385 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES,
386 ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
390 if (!BN_copy(x, point->X))
392 BN_set_negative(x, 0);
395 if (!BN_copy(y, point->Y))
397 BN_set_negative(y, 0);
406 * Computes a + b and stores the result in r. r could be a or b, a could be
407 * b. Uses algorithm A.10.2 of IEEE P1363.
409 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
410 const EC_POINT *b, BN_CTX *ctx)
412 BN_CTX *new_ctx = NULL;
413 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
416 if (EC_POINT_is_at_infinity(group, a)) {
417 if (!EC_POINT_copy(r, b))
422 if (EC_POINT_is_at_infinity(group, b)) {
423 if (!EC_POINT_copy(r, a))
429 ctx = new_ctx = BN_CTX_new();
435 x0 = BN_CTX_get(ctx);
436 y0 = BN_CTX_get(ctx);
437 x1 = BN_CTX_get(ctx);
438 y1 = BN_CTX_get(ctx);
439 x2 = BN_CTX_get(ctx);
440 y2 = BN_CTX_get(ctx);
447 if (!BN_copy(x0, a->X))
449 if (!BN_copy(y0, a->Y))
452 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx))
456 if (!BN_copy(x1, b->X))
458 if (!BN_copy(y1, b->Y))
461 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx))
465 if (BN_GF2m_cmp(x0, x1)) {
466 if (!BN_GF2m_add(t, x0, x1))
468 if (!BN_GF2m_add(s, y0, y1))
470 if (!group->meth->field_div(group, s, s, t, ctx))
472 if (!group->meth->field_sqr(group, x2, s, ctx))
474 if (!BN_GF2m_add(x2, x2, group->a))
476 if (!BN_GF2m_add(x2, x2, s))
478 if (!BN_GF2m_add(x2, x2, t))
481 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) {
482 if (!EC_POINT_set_to_infinity(group, r))
487 if (!group->meth->field_div(group, s, y1, x1, ctx))
489 if (!BN_GF2m_add(s, s, x1))
492 if (!group->meth->field_sqr(group, x2, s, ctx))
494 if (!BN_GF2m_add(x2, x2, s))
496 if (!BN_GF2m_add(x2, x2, group->a))
500 if (!BN_GF2m_add(y2, x1, x2))
502 if (!group->meth->field_mul(group, y2, y2, s, ctx))
504 if (!BN_GF2m_add(y2, y2, x2))
506 if (!BN_GF2m_add(y2, y2, y1))
509 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx))
516 BN_CTX_free(new_ctx);
521 * Computes 2 * a and stores the result in r. r could be a. Uses algorithm
522 * A.10.2 of IEEE P1363.
524 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
527 return ec_GF2m_simple_add(group, r, a, a, ctx);
530 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
532 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
533 /* point is its own inverse */
536 if (!EC_POINT_make_affine(group, point, ctx))
538 return BN_GF2m_add(point->Y, point->X, point->Y);
541 /* Indicates whether the given point is the point at infinity. */
542 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group,
543 const EC_POINT *point)
545 return BN_is_zero(point->Z);
549 * Determines whether the given EC_POINT is an actual point on the curve defined
550 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
551 * y^2 + x*y = x^3 + a*x^2 + b.
553 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
557 BN_CTX *new_ctx = NULL;
559 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
560 const BIGNUM *, BN_CTX *);
561 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
563 if (EC_POINT_is_at_infinity(group, point))
566 field_mul = group->meth->field_mul;
567 field_sqr = group->meth->field_sqr;
569 /* only support affine coordinates */
570 if (!point->Z_is_one)
574 ctx = new_ctx = BN_CTX_new();
580 y2 = BN_CTX_get(ctx);
581 lh = BN_CTX_get(ctx);
586 * We have a curve defined by a Weierstrass equation
587 * y^2 + x*y = x^3 + a*x^2 + b.
588 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
589 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
591 if (!BN_GF2m_add(lh, point->X, group->a))
593 if (!field_mul(group, lh, lh, point->X, ctx))
595 if (!BN_GF2m_add(lh, lh, point->Y))
597 if (!field_mul(group, lh, lh, point->X, ctx))
599 if (!BN_GF2m_add(lh, lh, group->b))
601 if (!field_sqr(group, y2, point->Y, ctx))
603 if (!BN_GF2m_add(lh, lh, y2))
605 ret = BN_is_zero(lh);
609 BN_CTX_free(new_ctx);
614 * Indicates whether two points are equal.
617 * 0 equal (in affine coordinates)
620 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
621 const EC_POINT *b, BN_CTX *ctx)
623 BIGNUM *aX, *aY, *bX, *bY;
624 BN_CTX *new_ctx = NULL;
627 if (EC_POINT_is_at_infinity(group, a)) {
628 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
631 if (EC_POINT_is_at_infinity(group, b))
634 if (a->Z_is_one && b->Z_is_one) {
635 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
639 ctx = new_ctx = BN_CTX_new();
645 aX = BN_CTX_get(ctx);
646 aY = BN_CTX_get(ctx);
647 bX = BN_CTX_get(ctx);
648 bY = BN_CTX_get(ctx);
652 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx))
654 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx))
656 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
660 BN_CTX_free(new_ctx);
664 /* Forces the given EC_POINT to internally use affine coordinates. */
665 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
668 BN_CTX *new_ctx = NULL;
672 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
676 ctx = new_ctx = BN_CTX_new();
687 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
689 if (!BN_copy(point->X, x))
691 if (!BN_copy(point->Y, y))
693 if (!BN_one(point->Z))
701 BN_CTX_free(new_ctx);
706 * Forces each of the EC_POINTs in the given array to use affine coordinates.
708 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num,
709 EC_POINT *points[], BN_CTX *ctx)
713 for (i = 0; i < num; i++) {
714 if (!group->meth->make_affine(group, points[i], ctx))
721 /* Wrapper to simple binary polynomial field multiplication implementation. */
722 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r,
723 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
725 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
728 /* Wrapper to simple binary polynomial field squaring implementation. */
729 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r,
730 const BIGNUM *a, BN_CTX *ctx)
732 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
735 /* Wrapper to simple binary polynomial field division implementation. */
736 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r,
737 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
739 return BN_GF2m_mod_div(r, a, b, group->field, ctx);