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) 1998-2003 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);
163 /* Copy a GF(2^m)-based EC_GROUP structure.
164 * Note that all other members are handled by EC_GROUP_copy.
166 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
169 if (!BN_copy(&dest->field, &src->field)) return 0;
170 if (!BN_copy(&dest->a, &src->a)) return 0;
171 if (!BN_copy(&dest->b, &src->b)) return 0;
172 dest->poly[0] = src->poly[0];
173 dest->poly[1] = src->poly[1];
174 dest->poly[2] = src->poly[2];
175 dest->poly[3] = src->poly[3];
176 dest->poly[4] = src->poly[4];
177 bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
178 bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
179 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
180 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
185 /* Set the curve parameters of an EC_GROUP structure. */
186 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
187 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
192 if (!BN_copy(&group->field, p)) goto err;
193 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
194 if ((i != 5) && (i != 3))
196 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
201 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
202 bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
203 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
206 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
207 bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
208 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
216 /* Get the curve parameters of an EC_GROUP structure.
217 * If p, a, or b are NULL then there values will not be set but the method will return with success.
219 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
225 if (!BN_copy(p, &group->field)) return 0;
230 if (!BN_copy(a, &group->a)) goto err;
235 if (!BN_copy(b, &group->b)) goto err;
245 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
246 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
248 return BN_num_bits(&group->field)-1;
252 /* Checks the discriminant of the curve.
253 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
255 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
259 BN_CTX *new_ctx = NULL;
263 ctx = new_ctx = BN_CTX_new();
266 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
272 if (b == NULL) goto err;
274 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
276 /* check the discriminant:
277 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
279 if (BN_is_zero(b)) goto err;
286 BN_CTX_free(new_ctx);
291 /* Initializes an EC_POINT. */
292 int ec_GF2m_simple_point_init(EC_POINT *point)
301 /* Frees an EC_POINT. */
302 void ec_GF2m_simple_point_finish(EC_POINT *point)
310 /* Clears and frees an EC_POINT. */
311 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
313 BN_clear_free(&point->X);
314 BN_clear_free(&point->Y);
315 BN_clear_free(&point->Z);
320 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
321 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
323 if (!BN_copy(&dest->X, &src->X)) return 0;
324 if (!BN_copy(&dest->Y, &src->Y)) return 0;
325 if (!BN_copy(&dest->Z, &src->Z)) return 0;
326 dest->Z_is_one = src->Z_is_one;
332 /* Set an EC_POINT to the point at infinity.
333 * A point at infinity is represented by having Z=0.
335 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
343 /* Set the coordinates of an EC_POINT using affine coordinates.
344 * Note that the simple implementation only uses affine coordinates.
346 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
347 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
350 if (x == NULL || y == NULL)
352 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
356 if (!BN_copy(&point->X, x)) goto err;
357 BN_set_negative(&point->X, 0);
358 if (!BN_copy(&point->Y, y)) goto err;
359 BN_set_negative(&point->Y, 0);
360 if (!BN_copy(&point->Z, BN_value_one())) goto err;
361 BN_set_negative(&point->Z, 0);
370 /* Gets the affine coordinates of an EC_POINT.
371 * Note that the simple implementation only uses affine coordinates.
373 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
374 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
378 if (EC_POINT_is_at_infinity(group, point))
380 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
384 if (BN_cmp(&point->Z, BN_value_one()))
386 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
391 if (!BN_copy(x, &point->X)) goto err;
392 BN_set_negative(x, 0);
396 if (!BN_copy(y, &point->Y)) goto err;
397 BN_set_negative(y, 0);
406 /* Include patented algorithms. */
407 #include "ec2_smpt.c"
410 /* Converts an EC_POINT to an octet string.
411 * If buf is NULL, the encoded length will be returned.
412 * If the length len of buf is smaller than required an error will be returned.
414 * The point compression section of this function is patented by Certicom Corp.
415 * under US Patent 6,141,420. Point compression is disabled by default and can
416 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
419 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
420 unsigned char *buf, size_t len, BN_CTX *ctx)
423 BN_CTX *new_ctx = NULL;
426 size_t field_len, i, skip;
428 #ifndef OPENSSL_EC_BIN_PT_COMP
429 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
431 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
436 if ((form != POINT_CONVERSION_COMPRESSED)
437 && (form != POINT_CONVERSION_UNCOMPRESSED)
438 && (form != POINT_CONVERSION_HYBRID))
440 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
444 if (EC_POINT_is_at_infinity(group, point))
446 /* encodes to a single 0 octet */
451 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
460 /* ret := required output buffer length */
461 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
462 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
464 /* if 'buf' is NULL, just return required length */
469 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
475 ctx = new_ctx = BN_CTX_new();
484 yxi = BN_CTX_get(ctx);
485 if (yxi == NULL) goto err;
487 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
490 #ifdef OPENSSL_EC_BIN_PT_COMP
491 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
493 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
494 if (BN_is_odd(yxi)) buf[0]++;
500 skip = field_len - BN_num_bytes(x);
501 if (skip > field_len)
503 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
511 skip = BN_bn2bin(x, buf + i);
513 if (i != 1 + field_len)
515 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
519 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
521 skip = field_len - BN_num_bytes(y);
522 if (skip > field_len)
524 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
532 skip = BN_bn2bin(y, buf + i);
538 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
546 BN_CTX_free(new_ctx);
553 BN_CTX_free(new_ctx);
558 /* Converts an octet string representation to an EC_POINT.
559 * Note that the simple implementation only uses affine coordinates.
561 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
562 const unsigned char *buf, size_t len, BN_CTX *ctx)
564 point_conversion_form_t form;
566 BN_CTX *new_ctx = NULL;
568 size_t field_len, enc_len;
573 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
579 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
580 && (form != POINT_CONVERSION_UNCOMPRESSED)
581 && (form != POINT_CONVERSION_HYBRID))
583 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
586 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
588 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
596 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
600 return EC_POINT_set_to_infinity(group, point);
603 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
604 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
608 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
614 ctx = new_ctx = BN_CTX_new();
622 yxi = BN_CTX_get(ctx);
623 if (yxi == NULL) goto err;
625 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
626 if (BN_ucmp(x, &group->field) >= 0)
628 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
632 if (form == POINT_CONVERSION_COMPRESSED)
634 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
638 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
639 if (BN_ucmp(y, &group->field) >= 0)
641 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
644 if (form == POINT_CONVERSION_HYBRID)
646 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
647 if (y_bit != BN_is_odd(yxi))
649 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
654 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
657 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
659 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
668 BN_CTX_free(new_ctx);
673 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
674 * Uses algorithm A.10.2 of IEEE P1363.
676 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
678 BN_CTX *new_ctx = NULL;
679 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
682 if (EC_POINT_is_at_infinity(group, a))
684 if (!EC_POINT_copy(r, b)) return 0;
688 if (EC_POINT_is_at_infinity(group, b))
690 if (!EC_POINT_copy(r, a)) return 0;
696 ctx = new_ctx = BN_CTX_new();
702 x0 = BN_CTX_get(ctx);
703 y0 = BN_CTX_get(ctx);
704 x1 = BN_CTX_get(ctx);
705 y1 = BN_CTX_get(ctx);
706 x2 = BN_CTX_get(ctx);
707 y2 = BN_CTX_get(ctx);
710 if (t == NULL) goto err;
714 if (!BN_copy(x0, &a->X)) goto err;
715 if (!BN_copy(y0, &a->Y)) goto err;
719 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
723 if (!BN_copy(x1, &b->X)) goto err;
724 if (!BN_copy(y1, &b->Y)) goto err;
728 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
732 if (BN_GF2m_cmp(x0, x1))
734 if (!BN_GF2m_add(t, x0, x1)) goto err;
735 if (!BN_GF2m_add(s, y0, y1)) goto err;
736 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
737 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
738 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
739 if (!BN_GF2m_add(x2, x2, s)) goto err;
740 if (!BN_GF2m_add(x2, x2, t)) goto err;
744 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
746 if (!EC_POINT_set_to_infinity(group, r)) goto err;
750 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
751 if (!BN_GF2m_add(s, s, x1)) goto err;
753 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
754 if (!BN_GF2m_add(x2, x2, s)) goto err;
755 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
758 if (!BN_GF2m_add(y2, x1, x2)) goto err;
759 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
760 if (!BN_GF2m_add(y2, y2, x2)) goto err;
761 if (!BN_GF2m_add(y2, y2, y1)) goto err;
763 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
770 BN_CTX_free(new_ctx);
775 /* Computes 2 * a and stores the result in r. r could be a.
776 * Uses algorithm A.10.2 of IEEE P1363.
778 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
780 return ec_GF2m_simple_add(group, r, a, a, ctx);
784 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
786 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
787 /* point is its own inverse */
790 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
791 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
795 /* Indicates whether the given point is the point at infinity. */
796 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
798 return BN_is_zero(&point->Z);
802 /* Determines whether the given EC_POINT is an actual point on the curve defined
803 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
804 * y^2 + x*y = x^3 + a*x^2 + b.
806 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
809 BN_CTX *new_ctx = NULL;
811 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
812 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
814 if (EC_POINT_is_at_infinity(group, point))
817 field_mul = group->meth->field_mul;
818 field_sqr = group->meth->field_sqr;
820 /* only support affine coordinates */
821 if (!point->Z_is_one) goto err;
825 ctx = new_ctx = BN_CTX_new();
831 y2 = BN_CTX_get(ctx);
832 lh = BN_CTX_get(ctx);
833 if (lh == NULL) goto err;
835 /* We have a curve defined by a Weierstrass equation
836 * y^2 + x*y = x^3 + a*x^2 + b.
837 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
838 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
840 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
841 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
842 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
843 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
844 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
845 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
846 if (!BN_GF2m_add(lh, lh, y2)) goto err;
847 ret = BN_is_zero(lh);
849 if (ctx) BN_CTX_end(ctx);
850 if (new_ctx) BN_CTX_free(new_ctx);
855 /* Indicates whether two points are equal.
858 * 0 equal (in affine coordinates)
861 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
863 BIGNUM *aX, *aY, *bX, *bY;
864 BN_CTX *new_ctx = NULL;
867 if (EC_POINT_is_at_infinity(group, a))
869 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
872 if (a->Z_is_one && b->Z_is_one)
874 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
879 ctx = new_ctx = BN_CTX_new();
885 aX = BN_CTX_get(ctx);
886 aY = BN_CTX_get(ctx);
887 bX = BN_CTX_get(ctx);
888 bY = BN_CTX_get(ctx);
889 if (bY == NULL) goto err;
891 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
892 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
893 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
896 if (ctx) BN_CTX_end(ctx);
897 if (new_ctx) BN_CTX_free(new_ctx);
902 /* Forces the given EC_POINT to internally use affine coordinates. */
903 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
905 BN_CTX *new_ctx = NULL;
909 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
914 ctx = new_ctx = BN_CTX_new();
922 if (y == NULL) goto err;
924 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
925 if (!BN_copy(&point->X, x)) goto err;
926 if (!BN_copy(&point->Y, y)) goto err;
927 if (!BN_one(&point->Z)) goto err;
932 if (ctx) BN_CTX_end(ctx);
933 if (new_ctx) BN_CTX_free(new_ctx);
938 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
939 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
943 for (i = 0; i < num; i++)
945 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
952 /* Wrapper to simple binary polynomial field multiplication implementation. */
953 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
955 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
959 /* Wrapper to simple binary polynomial field squaring implementation. */
960 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
962 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
966 /* Wrapper to simple binary polynomial field division implementation. */
967 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
969 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);