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 * In addition, Sun covenants to all licensees who provide a reciprocal
13 * covenant with respect to their own patents if any, not to sue under
14 * current and future patent claims necessarily infringed by the making,
15 * using, practicing, selling, offering for sale and/or otherwise
16 * disposing of the ECC Code as delivered hereunder (or portions thereof),
17 * provided that such covenant shall not apply:
18 * 1) for code that a licensee deletes from the ECC Code;
19 * 2) separates from the ECC Code; or
20 * 3) for infringements caused by:
21 * i) the modification of the ECC Code or
22 * ii) the combination of the ECC Code with other software or
23 * devices where such combination causes the infringement.
25 * The software is originally written by Sheueling Chang Shantz and
26 * Douglas Stebila of Sun Microsystems Laboratories.
29 /* ====================================================================
30 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
32 * Redistribution and use in source and binary forms, with or without
33 * modification, are permitted provided that the following conditions
36 * 1. Redistributions of source code must retain the above copyright
37 * notice, this list of conditions and the following disclaimer.
39 * 2. Redistributions in binary form must reproduce the above copyright
40 * notice, this list of conditions and the following disclaimer in
41 * the documentation and/or other materials provided with the
44 * 3. All advertising materials mentioning features or use of this
45 * software must display the following acknowledgment:
46 * "This product includes software developed by the OpenSSL Project
47 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
49 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
50 * endorse or promote products derived from this software without
51 * prior written permission. For written permission, please contact
52 * openssl-core@openssl.org.
54 * 5. Products derived from this software may not be called "OpenSSL"
55 * nor may "OpenSSL" appear in their names without prior written
56 * permission of the OpenSSL Project.
58 * 6. Redistributions of any form whatsoever must retain the following
60 * "This product includes software developed by the OpenSSL Project
61 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
63 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
64 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
65 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
66 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
67 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
68 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
69 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
70 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
71 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
72 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
73 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
74 * OF THE POSSIBILITY OF SUCH DAMAGE.
75 * ====================================================================
77 * This product includes cryptographic software written by Eric Young
78 * (eay@cryptsoft.com). This product includes software written by Tim
79 * Hudson (tjh@cryptsoft.com).
83 #include <openssl/err.h>
88 const EC_METHOD *EC_GF2m_simple_method(void)
90 static const EC_METHOD ret = {
91 NID_X9_62_characteristic_two_field,
92 ec_GF2m_simple_group_init,
93 ec_GF2m_simple_group_finish,
94 ec_GF2m_simple_group_clear_finish,
95 ec_GF2m_simple_group_copy,
96 ec_GF2m_simple_group_set_curve,
97 ec_GF2m_simple_group_get_curve,
98 ec_GF2m_simple_group_get_degree,
99 ec_GF2m_simple_group_check_discriminant,
100 ec_GF2m_simple_point_init,
101 ec_GF2m_simple_point_finish,
102 ec_GF2m_simple_point_clear_finish,
103 ec_GF2m_simple_point_copy,
104 ec_GF2m_simple_point_set_to_infinity,
105 0 /* set_Jprojective_coordinates_GFp */,
106 0 /* get_Jprojective_coordinates_GFp */,
107 ec_GF2m_simple_point_set_affine_coordinates,
108 ec_GF2m_simple_point_get_affine_coordinates,
109 ec_GF2m_simple_set_compressed_coordinates,
110 ec_GF2m_simple_point2oct,
111 ec_GF2m_simple_oct2point,
114 ec_GF2m_simple_invert,
116 ec_GF2m_mont_precompute_mult,
117 ec_GF2m_simple_is_at_infinity,
118 ec_GF2m_simple_is_on_curve,
120 ec_GF2m_simple_make_affine,
121 ec_GF2m_simple_points_make_affine,
122 ec_GF2m_simple_field_mul,
123 ec_GF2m_simple_field_sqr,
124 ec_GF2m_simple_field_div,
125 0 /* field_encode */,
126 0 /* field_decode */,
127 0 /* field_set_to_one */ };
133 /* Initialize a GF(2^m)-based EC_GROUP structure.
134 * Note that all other members are handled by EC_GROUP_new.
136 int ec_GF2m_simple_group_init(EC_GROUP *group)
138 BN_init(&group->field);
145 /* Free a GF(2^m)-based EC_GROUP structure.
146 * Note that all other members are handled by EC_GROUP_free.
148 void ec_GF2m_simple_group_finish(EC_GROUP *group)
150 BN_free(&group->field);
156 /* Clear and free a GF(2^m)-based EC_GROUP structure.
157 * Note that all other members are handled by EC_GROUP_clear_free.
159 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
161 BN_clear_free(&group->field);
162 BN_clear_free(&group->a);
163 BN_clear_free(&group->b);
172 /* Copy a GF(2^m)-based EC_GROUP structure.
173 * Note that all other members are handled by EC_GROUP_copy.
175 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
178 if (!BN_copy(&dest->field, &src->field)) return 0;
179 if (!BN_copy(&dest->a, &src->a)) return 0;
180 if (!BN_copy(&dest->b, &src->b)) return 0;
181 dest->poly[0] = src->poly[0];
182 dest->poly[1] = src->poly[1];
183 dest->poly[2] = src->poly[2];
184 dest->poly[3] = src->poly[3];
185 dest->poly[4] = src->poly[4];
186 bn_wexpand(&dest->a, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
187 bn_wexpand(&dest->b, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
188 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
189 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
194 /* Set the curve parameters of an EC_GROUP structure. */
195 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
196 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
201 if (!BN_copy(&group->field, p)) goto err;
202 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
203 if ((i != 5) && (i != 3)) goto err;
206 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
207 bn_wexpand(&group->a, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
208 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
211 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
212 bn_wexpand(&group->b, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
213 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
221 /* Get the curve parameters of an EC_GROUP structure.
222 * If p, a, or b are NULL then there values will not be set but the method will return with success.
224 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
230 if (!BN_copy(p, &group->field)) return 0;
233 if (a != NULL || b != NULL)
237 if (!BN_copy(a, &group->a)) goto err;
241 if (!BN_copy(b, &group->b)) goto err;
252 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
253 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
255 return BN_num_bits(&group->field)-1;
259 /* Checks the discriminant of the curve.
260 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
262 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
266 BN_CTX *new_ctx = NULL;
270 ctx = new_ctx = BN_CTX_new();
273 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
279 if (b == NULL) goto err;
281 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
283 /* check the discriminant:
284 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
286 if (BN_is_zero(b)) goto err;
293 BN_CTX_free(new_ctx);
298 /* Initializes an EC_POINT. */
299 int ec_GF2m_simple_point_init(EC_POINT *point)
308 /* Frees an EC_POINT. */
309 void ec_GF2m_simple_point_finish(EC_POINT *point)
317 /* Clears and frees an EC_POINT. */
318 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
320 BN_clear_free(&point->X);
321 BN_clear_free(&point->Y);
322 BN_clear_free(&point->Z);
327 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
328 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
330 if (!BN_copy(&dest->X, &src->X)) return 0;
331 if (!BN_copy(&dest->Y, &src->Y)) return 0;
332 if (!BN_copy(&dest->Z, &src->Z)) return 0;
333 dest->Z_is_one = src->Z_is_one;
339 /* Set an EC_POINT to the point at infinity.
340 * A point at infinity is represented by having Z=0.
342 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
345 return (BN_zero(&point->Z));
349 /* Set the coordinates of an EC_POINT using affine coordinates.
350 * Note that the simple implementation only uses affine coordinates.
352 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
353 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
356 if (x == NULL || y == NULL)
358 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
362 if (!BN_copy(&point->X, x)) goto err;
363 if (!BN_copy(&point->Y, y)) goto err;
364 if (!BN_copy(&point->Z, BN_value_one())) goto err;
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;
398 if (!BN_copy(y, &point->Y)) goto err;
407 /* Include patented algorithms. */
408 #include "ec2_smpt.c"
411 /* Converts an EC_POINT to an octet string.
412 * If buf is NULL, the encoded length will be returned.
413 * If the length len of buf is smaller than required an error will be returned.
415 * The point compression section of this function is patented by Certicom Corp.
416 * under US Patent 6,141,420. Point compression is disabled by default and can
417 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
420 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
421 unsigned char *buf, size_t len, BN_CTX *ctx)
424 BN_CTX *new_ctx = NULL;
427 size_t field_len, i, skip;
429 #ifndef OPENSSL_EC_BIN_PT_COMP
430 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
432 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
437 if ((form != POINT_CONVERSION_COMPRESSED)
438 && (form != POINT_CONVERSION_UNCOMPRESSED)
439 && (form != POINT_CONVERSION_HYBRID))
441 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
445 if (EC_POINT_is_at_infinity(group, point))
447 /* encodes to a single 0 octet */
452 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
461 /* ret := required output buffer length */
462 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
463 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
465 /* if 'buf' is NULL, just return required length */
470 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
476 ctx = new_ctx = BN_CTX_new();
485 yxi = BN_CTX_get(ctx);
486 if (yxi == NULL) goto err;
488 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
491 #ifdef OPENSSL_EC_BIN_PT_COMP
492 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
494 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
495 if (BN_is_odd(yxi)) buf[0]++;
501 skip = field_len - BN_num_bytes(x);
502 if (skip > field_len)
504 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
512 skip = BN_bn2bin(x, buf + i);
514 if (i != 1 + field_len)
516 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
520 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
522 skip = field_len - BN_num_bytes(y);
523 if (skip > field_len)
525 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
533 skip = BN_bn2bin(y, buf + i);
539 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
547 BN_CTX_free(new_ctx);
554 BN_CTX_free(new_ctx);
559 /* Converts an octet string representation to an EC_POINT.
560 * Note that the simple implementation only uses affine coordinates.
562 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
563 const unsigned char *buf, size_t len, BN_CTX *ctx)
565 point_conversion_form_t form;
567 BN_CTX *new_ctx = NULL;
569 size_t field_len, enc_len;
574 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
580 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
581 && (form != POINT_CONVERSION_UNCOMPRESSED)
582 && (form != POINT_CONVERSION_HYBRID))
584 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
587 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
589 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
597 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
601 return EC_POINT_set_to_infinity(group, point);
604 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
605 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
609 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
615 ctx = new_ctx = BN_CTX_new();
623 yxi = BN_CTX_get(ctx);
624 if (yxi == NULL) goto err;
626 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
627 if (BN_ucmp(x, &group->field) >= 0)
629 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
633 if (form == POINT_CONVERSION_COMPRESSED)
635 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
639 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
640 if (BN_ucmp(y, &group->field) >= 0)
642 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
645 if (form == POINT_CONVERSION_HYBRID)
647 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
648 if (y_bit != BN_is_odd(yxi))
650 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
655 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
658 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
660 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
669 BN_CTX_free(new_ctx);
674 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
675 * Uses algorithm A.10.2 of IEEE P1363.
677 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
679 BN_CTX *new_ctx = NULL;
680 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
683 if (EC_POINT_is_at_infinity(group, a))
685 if (!EC_POINT_copy(r, b)) return 0;
689 if (EC_POINT_is_at_infinity(group, b))
691 if (!EC_POINT_copy(r, a)) return 0;
697 ctx = new_ctx = BN_CTX_new();
703 x0 = BN_CTX_get(ctx);
704 y0 = BN_CTX_get(ctx);
705 x1 = BN_CTX_get(ctx);
706 y1 = BN_CTX_get(ctx);
707 x2 = BN_CTX_get(ctx);
708 y2 = BN_CTX_get(ctx);
711 if (t == NULL) goto err;
715 if (!BN_copy(x0, &a->X)) goto err;
716 if (!BN_copy(y0, &a->Y)) goto err;
720 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
724 if (!BN_copy(x1, &b->X)) goto err;
725 if (!BN_copy(y1, &b->Y)) goto err;
729 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
733 if (BN_GF2m_cmp(x0, x1))
735 if (!BN_GF2m_add(t, x0, x1)) goto err;
736 if (!BN_GF2m_add(s, y0, y1)) goto err;
737 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
738 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
739 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
740 if (!BN_GF2m_add(x2, x2, s)) goto err;
741 if (!BN_GF2m_add(x2, x2, t)) goto err;
745 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
747 if (!EC_POINT_set_to_infinity(group, r)) goto err;
751 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
752 if (!BN_GF2m_add(s, s, x1)) goto err;
754 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
755 if (!BN_GF2m_add(x2, x2, s)) goto err;
756 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
759 if (!BN_GF2m_add(y2, x1, x2)) goto err;
760 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
761 if (!BN_GF2m_add(y2, y2, x2)) goto err;
762 if (!BN_GF2m_add(y2, y2, y1)) goto err;
764 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
771 BN_CTX_free(new_ctx);
776 /* Computes 2 * a and stores the result in r. r could be a.
777 * Uses algorithm A.10.2 of IEEE P1363.
779 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
781 return ec_GF2m_simple_add(group, r, a, a, ctx);
785 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
787 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
788 /* point is its own inverse */
791 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
792 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
796 /* Indicates whether the given point is the point at infinity. */
797 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
799 return BN_is_zero(&point->Z);
803 /* Determines whether the given EC_POINT is an actual point on the curve defined
804 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
805 * y^2 + x*y = x^3 + a*x^2 + b.
807 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
809 BN_CTX *new_ctx = NULL;
810 BIGNUM *rh, *lh, *tmp1;
813 if (EC_POINT_is_at_infinity(group, point))
816 /* only support affine coordinates */
817 if (!point->Z_is_one) goto err;
821 ctx = new_ctx = BN_CTX_new();
827 rh = BN_CTX_get(ctx);
828 lh = BN_CTX_get(ctx);
829 tmp1 = BN_CTX_get(ctx);
830 if (tmp1 == NULL) goto err;
832 /* We have a curve defined by a Weierstrass equation
833 * y^2 + x*y = x^3 + a*x^2 + b.
834 * To test this, we add up the right-hand side in 'rh'
835 * and the left-hand side in 'lh'.
839 if (!group->meth->field_sqr(group, tmp1, &point->X, ctx)) goto err;
840 if (!group->meth->field_mul(group, rh, tmp1, &point->X, ctx)) goto err;
842 /* rh := rh + a*X^2 */
843 if (!group->meth->field_mul(group, tmp1, tmp1, &group->a, ctx)) goto err;
844 if (!BN_GF2m_add(rh, rh, tmp1)) goto err;
847 if (!BN_GF2m_add(rh, rh, &group->b)) goto err;
850 if (!group->meth->field_sqr(group, lh, &point->Y, ctx)) goto err;
853 if (!group->meth->field_mul(group, tmp1, &point->X, &point->Y, ctx)) goto err;
854 if (!BN_GF2m_add(lh, lh, tmp1)) goto err;
856 ret = (0 == BN_GF2m_cmp(lh, rh));
859 if (ctx) BN_CTX_end(ctx);
860 if (new_ctx) BN_CTX_free(new_ctx);
865 /* Indicates whether two points are equal.
868 * 0 equal (in affine coordinates)
871 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
873 BIGNUM *aX, *aY, *bX, *bY;
874 BN_CTX *new_ctx = NULL;
877 if (EC_POINT_is_at_infinity(group, a))
879 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
882 if (a->Z_is_one && b->Z_is_one)
884 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
889 ctx = new_ctx = BN_CTX_new();
895 aX = BN_CTX_get(ctx);
896 aY = BN_CTX_get(ctx);
897 bX = BN_CTX_get(ctx);
898 bY = BN_CTX_get(ctx);
899 if (bY == NULL) goto err;
901 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
902 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
903 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
906 if (ctx) BN_CTX_end(ctx);
907 if (new_ctx) BN_CTX_free(new_ctx);
912 /* Forces the given EC_POINT to internally use affine coordinates. */
913 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
915 BN_CTX *new_ctx = NULL;
919 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
924 ctx = new_ctx = BN_CTX_new();
932 if (y == NULL) goto err;
934 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
935 if (!BN_copy(&point->X, x)) goto err;
936 if (!BN_copy(&point->Y, y)) goto err;
937 if (!BN_one(&point->Z)) goto err;
942 if (ctx) BN_CTX_end(ctx);
943 if (new_ctx) BN_CTX_free(new_ctx);
948 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
949 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
953 for (i = 0; i < num; i++)
955 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
962 /* Wrapper to simple binary polynomial field multiplication implementation. */
963 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
965 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
969 /* Wrapper to simple binary polynomial field squaring implementation. */
970 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
972 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
976 /* Wrapper to simple binary polynomial field division implementation. */
977 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
979 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);