1 /* crypto/ec/ec2_smpl.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
16 /* ====================================================================
17 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
45 * 6. Redistributions of any form whatsoever must retain the following
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
70 #include <openssl/err.h>
75 const EC_METHOD *EC_GF2m_simple_method(void)
77 static const EC_METHOD ret = {
78 NID_X9_62_characteristic_two_field,
79 ec_GF2m_simple_group_init,
80 ec_GF2m_simple_group_finish,
81 ec_GF2m_simple_group_clear_finish,
82 ec_GF2m_simple_group_copy,
83 ec_GF2m_simple_group_set_curve,
84 ec_GF2m_simple_group_get_curve,
85 ec_GF2m_simple_group_get_degree,
86 ec_GF2m_simple_group_check_discriminant,
87 ec_GF2m_simple_point_init,
88 ec_GF2m_simple_point_finish,
89 ec_GF2m_simple_point_clear_finish,
90 ec_GF2m_simple_point_copy,
91 ec_GF2m_simple_point_set_to_infinity,
92 0 /* set_Jprojective_coordinates_GFp */,
93 0 /* get_Jprojective_coordinates_GFp */,
94 ec_GF2m_simple_point_set_affine_coordinates,
95 ec_GF2m_simple_point_get_affine_coordinates,
96 ec_GF2m_simple_set_compressed_coordinates,
97 ec_GF2m_simple_point2oct,
98 ec_GF2m_simple_oct2point,
101 ec_GF2m_simple_invert,
102 ec_GF2m_simple_is_at_infinity,
103 ec_GF2m_simple_is_on_curve,
105 ec_GF2m_simple_make_affine,
106 ec_GF2m_simple_points_make_affine,
108 /* the following three method functions are defined in ec2_mult.c */
110 ec_GF2m_precompute_mult,
111 ec_GF2m_have_precompute_mult,
113 ec_GF2m_simple_field_mul,
114 ec_GF2m_simple_field_sqr,
115 ec_GF2m_simple_field_div,
116 0 /* field_encode */,
117 0 /* field_decode */,
118 0 /* field_set_to_one */ };
124 /* Initialize a GF(2^m)-based EC_GROUP structure.
125 * Note that all other members are handled by EC_GROUP_new.
127 int ec_GF2m_simple_group_init(EC_GROUP *group)
129 BN_init(&group->field);
136 /* Free a GF(2^m)-based EC_GROUP structure.
137 * Note that all other members are handled by EC_GROUP_free.
139 void ec_GF2m_simple_group_finish(EC_GROUP *group)
141 BN_free(&group->field);
147 /* Clear and free a GF(2^m)-based EC_GROUP structure.
148 * Note that all other members are handled by EC_GROUP_clear_free.
150 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
152 BN_clear_free(&group->field);
153 BN_clear_free(&group->a);
154 BN_clear_free(&group->b);
164 /* Copy a GF(2^m)-based EC_GROUP structure.
165 * Note that all other members are handled by EC_GROUP_copy.
167 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
170 if (!BN_copy(&dest->field, &src->field)) return 0;
171 if (!BN_copy(&dest->a, &src->a)) return 0;
172 if (!BN_copy(&dest->b, &src->b)) return 0;
173 dest->poly[0] = src->poly[0];
174 dest->poly[1] = src->poly[1];
175 dest->poly[2] = src->poly[2];
176 dest->poly[3] = src->poly[3];
177 dest->poly[4] = src->poly[4];
178 dest->poly[5] = src->poly[5];
179 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
180 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
181 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
182 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
187 /* Set the curve parameters of an EC_GROUP structure. */
188 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
189 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
194 if (!BN_copy(&group->field, p)) goto err;
195 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
196 if ((i != 5) && (i != 3))
198 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
203 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
204 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
205 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
208 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
209 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
210 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
218 /* Get the curve parameters of an EC_GROUP structure.
219 * If p, a, or b are NULL then there values will not be set but the method will return with success.
221 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
227 if (!BN_copy(p, &group->field)) return 0;
232 if (!BN_copy(a, &group->a)) goto err;
237 if (!BN_copy(b, &group->b)) goto err;
247 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
248 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
250 return BN_num_bits(&group->field)-1;
254 /* Checks the discriminant of the curve.
255 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
257 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
261 BN_CTX *new_ctx = NULL;
265 ctx = new_ctx = BN_CTX_new();
268 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
274 if (b == NULL) goto err;
276 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
278 /* check the discriminant:
279 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
281 if (BN_is_zero(b)) goto err;
289 BN_CTX_free(new_ctx);
294 /* Initializes an EC_POINT. */
295 int ec_GF2m_simple_point_init(EC_POINT *point)
304 /* Frees an EC_POINT. */
305 void ec_GF2m_simple_point_finish(EC_POINT *point)
313 /* Clears and frees an EC_POINT. */
314 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
316 BN_clear_free(&point->X);
317 BN_clear_free(&point->Y);
318 BN_clear_free(&point->Z);
323 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
324 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
326 if (!BN_copy(&dest->X, &src->X)) return 0;
327 if (!BN_copy(&dest->Y, &src->Y)) return 0;
328 if (!BN_copy(&dest->Z, &src->Z)) return 0;
329 dest->Z_is_one = src->Z_is_one;
335 /* Set an EC_POINT to the point at infinity.
336 * A point at infinity is represented by having Z=0.
338 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
346 /* Set the coordinates of an EC_POINT using affine coordinates.
347 * Note that the simple implementation only uses affine coordinates.
349 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
350 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
353 if (x == NULL || y == NULL)
355 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
359 if (!BN_copy(&point->X, x)) goto err;
360 BN_set_negative(&point->X, 0);
361 if (!BN_copy(&point->Y, y)) goto err;
362 BN_set_negative(&point->Y, 0);
363 if (!BN_copy(&point->Z, BN_value_one())) goto err;
364 BN_set_negative(&point->Z, 0);
373 /* Gets the affine coordinates of an EC_POINT.
374 * Note that the simple implementation only uses affine coordinates.
376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
377 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
381 if (EC_POINT_is_at_infinity(group, point))
383 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
387 if (BN_cmp(&point->Z, BN_value_one()))
389 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
394 if (!BN_copy(x, &point->X)) goto err;
395 BN_set_negative(x, 0);
399 if (!BN_copy(y, &point->Y)) goto err;
400 BN_set_negative(y, 0);
409 /* Calculates and sets the affine coordinates of an EC_POINT from the given
410 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
411 * Note that the simple implementation only uses affine coordinates.
413 * The method is from the following publication:
415 * Harper, Menezes, Vanstone:
416 * "Public-Key Cryptosystems with Very Small Key Lengths",
417 * EUROCRYPT '92, Springer-Verlag LNCS 658,
418 * published February 1993
420 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
421 * the same method, but claim no priority date earlier than July 29, 1994
422 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
424 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
425 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
427 BN_CTX *new_ctx = NULL;
428 BIGNUM *tmp, *x, *y, *z;
431 /* clear error queue */
436 ctx = new_ctx = BN_CTX_new();
441 y_bit = (y_bit != 0) ? 1 : 0;
444 tmp = BN_CTX_get(ctx);
448 if (z == NULL) goto err;
450 if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
453 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
457 if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
458 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
459 if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
460 if (!BN_GF2m_add(tmp, x, tmp)) goto err;
461 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
463 unsigned long err = ERR_peek_last_error();
465 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
468 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
471 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
474 z0 = (BN_is_odd(z)) ? 1 : 0;
475 if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
478 if (!BN_GF2m_add(y, y, x)) goto err;
482 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
489 BN_CTX_free(new_ctx);
494 /* Converts an EC_POINT to an octet string.
495 * If buf is NULL, the encoded length will be returned.
496 * If the length len of buf is smaller than required an error will be returned.
498 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
499 unsigned char *buf, size_t len, BN_CTX *ctx)
502 BN_CTX *new_ctx = NULL;
505 size_t field_len, i, skip;
507 if ((form != POINT_CONVERSION_COMPRESSED)
508 && (form != POINT_CONVERSION_UNCOMPRESSED)
509 && (form != POINT_CONVERSION_HYBRID))
511 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
515 if (EC_POINT_is_at_infinity(group, point))
517 /* encodes to a single 0 octet */
522 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
531 /* ret := required output buffer length */
532 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
533 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
535 /* if 'buf' is NULL, just return required length */
540 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
546 ctx = new_ctx = BN_CTX_new();
555 yxi = BN_CTX_get(ctx);
556 if (yxi == NULL) goto err;
558 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
561 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
563 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
564 if (BN_is_odd(yxi)) buf[0]++;
569 skip = field_len - BN_num_bytes(x);
570 if (skip > field_len)
572 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
580 skip = BN_bn2bin(x, buf + i);
582 if (i != 1 + field_len)
584 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
588 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
590 skip = field_len - BN_num_bytes(y);
591 if (skip > field_len)
593 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
601 skip = BN_bn2bin(y, buf + i);
607 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
615 BN_CTX_free(new_ctx);
622 BN_CTX_free(new_ctx);
627 /* Converts an octet string representation to an EC_POINT.
628 * Note that the simple implementation only uses affine coordinates.
630 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
631 const unsigned char *buf, size_t len, BN_CTX *ctx)
633 point_conversion_form_t form;
635 BN_CTX *new_ctx = NULL;
637 size_t field_len, enc_len;
642 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
648 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
649 && (form != POINT_CONVERSION_UNCOMPRESSED)
650 && (form != POINT_CONVERSION_HYBRID))
652 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
655 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
657 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
665 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
669 return EC_POINT_set_to_infinity(group, point);
672 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
673 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
677 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
683 ctx = new_ctx = BN_CTX_new();
691 yxi = BN_CTX_get(ctx);
692 if (yxi == NULL) goto err;
694 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
695 if (BN_ucmp(x, &group->field) >= 0)
697 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
701 if (form == POINT_CONVERSION_COMPRESSED)
703 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
707 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
708 if (BN_ucmp(y, &group->field) >= 0)
710 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
713 if (form == POINT_CONVERSION_HYBRID)
715 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
716 if (y_bit != BN_is_odd(yxi))
718 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
723 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
726 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
728 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
737 BN_CTX_free(new_ctx);
742 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
743 * Uses algorithm A.10.2 of IEEE P1363.
745 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
747 BN_CTX *new_ctx = NULL;
748 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
751 if (EC_POINT_is_at_infinity(group, a))
753 if (!EC_POINT_copy(r, b)) return 0;
757 if (EC_POINT_is_at_infinity(group, b))
759 if (!EC_POINT_copy(r, a)) return 0;
765 ctx = new_ctx = BN_CTX_new();
771 x0 = BN_CTX_get(ctx);
772 y0 = BN_CTX_get(ctx);
773 x1 = BN_CTX_get(ctx);
774 y1 = BN_CTX_get(ctx);
775 x2 = BN_CTX_get(ctx);
776 y2 = BN_CTX_get(ctx);
779 if (t == NULL) goto err;
783 if (!BN_copy(x0, &a->X)) goto err;
784 if (!BN_copy(y0, &a->Y)) goto err;
788 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
792 if (!BN_copy(x1, &b->X)) goto err;
793 if (!BN_copy(y1, &b->Y)) goto err;
797 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
801 if (BN_GF2m_cmp(x0, x1))
803 if (!BN_GF2m_add(t, x0, x1)) goto err;
804 if (!BN_GF2m_add(s, y0, y1)) goto err;
805 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
806 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
807 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
808 if (!BN_GF2m_add(x2, x2, s)) goto err;
809 if (!BN_GF2m_add(x2, x2, t)) goto err;
813 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
815 if (!EC_POINT_set_to_infinity(group, r)) goto err;
819 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
820 if (!BN_GF2m_add(s, s, x1)) goto err;
822 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
823 if (!BN_GF2m_add(x2, x2, s)) goto err;
824 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
827 if (!BN_GF2m_add(y2, x1, x2)) goto err;
828 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
829 if (!BN_GF2m_add(y2, y2, x2)) goto err;
830 if (!BN_GF2m_add(y2, y2, y1)) goto err;
832 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
839 BN_CTX_free(new_ctx);
844 /* Computes 2 * a and stores the result in r. r could be a.
845 * Uses algorithm A.10.2 of IEEE P1363.
847 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
849 return ec_GF2m_simple_add(group, r, a, a, ctx);
853 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
855 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
856 /* point is its own inverse */
859 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
860 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
864 /* Indicates whether the given point is the point at infinity. */
865 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
867 return BN_is_zero(&point->Z);
871 /* Determines whether the given EC_POINT is an actual point on the curve defined
872 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
873 * y^2 + x*y = x^3 + a*x^2 + b.
875 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
878 BN_CTX *new_ctx = NULL;
880 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
881 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
883 if (EC_POINT_is_at_infinity(group, point))
886 field_mul = group->meth->field_mul;
887 field_sqr = group->meth->field_sqr;
889 /* only support affine coordinates */
890 if (!point->Z_is_one) goto err;
894 ctx = new_ctx = BN_CTX_new();
900 y2 = BN_CTX_get(ctx);
901 lh = BN_CTX_get(ctx);
902 if (lh == NULL) goto err;
904 /* We have a curve defined by a Weierstrass equation
905 * y^2 + x*y = x^3 + a*x^2 + b.
906 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
907 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
909 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
910 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
911 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
912 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
913 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
914 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
915 if (!BN_GF2m_add(lh, lh, y2)) goto err;
916 ret = BN_is_zero(lh);
918 if (ctx) BN_CTX_end(ctx);
919 if (new_ctx) BN_CTX_free(new_ctx);
924 /* Indicates whether two points are equal.
927 * 0 equal (in affine coordinates)
930 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
932 BIGNUM *aX, *aY, *bX, *bY;
933 BN_CTX *new_ctx = NULL;
936 if (EC_POINT_is_at_infinity(group, a))
938 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
941 if (a->Z_is_one && b->Z_is_one)
943 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
948 ctx = new_ctx = BN_CTX_new();
954 aX = BN_CTX_get(ctx);
955 aY = BN_CTX_get(ctx);
956 bX = BN_CTX_get(ctx);
957 bY = BN_CTX_get(ctx);
958 if (bY == NULL) goto err;
960 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
961 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
962 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
965 if (ctx) BN_CTX_end(ctx);
966 if (new_ctx) BN_CTX_free(new_ctx);
971 /* Forces the given EC_POINT to internally use affine coordinates. */
972 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
974 BN_CTX *new_ctx = NULL;
978 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
983 ctx = new_ctx = BN_CTX_new();
991 if (y == NULL) goto err;
993 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
994 if (!BN_copy(&point->X, x)) goto err;
995 if (!BN_copy(&point->Y, y)) goto err;
996 if (!BN_one(&point->Z)) goto err;
1001 if (ctx) BN_CTX_end(ctx);
1002 if (new_ctx) BN_CTX_free(new_ctx);
1007 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
1008 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1012 for (i = 0; i < num; i++)
1014 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1021 /* Wrapper to simple binary polynomial field multiplication implementation. */
1022 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1024 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1028 /* Wrapper to simple binary polynomial field squaring implementation. */
1029 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1031 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1035 /* Wrapper to simple binary polynomial field division implementation. */
1036 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1038 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);