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) 1998-2002 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
,
103 ec_GF2m_mont_precompute_mult
,
104 ec_GF2m_simple_is_at_infinity
,
105 ec_GF2m_simple_is_on_curve
,
107 ec_GF2m_simple_make_affine
,
108 ec_GF2m_simple_points_make_affine
,
109 ec_GF2m_simple_field_mul
,
110 ec_GF2m_simple_field_sqr
,
111 ec_GF2m_simple_field_div
,
112 0 /* field_encode */,
113 0 /* field_decode */,
114 0 /* field_set_to_one */ };
120 /* Initialize a GF(2^m)-based EC_GROUP structure.
121 * Note that all other members are handled by EC_GROUP_new.
123 int ec_GF2m_simple_group_init(EC_GROUP
*group
)
125 BN_init(&group
->field
);
132 /* Free a GF(2^m)-based EC_GROUP structure.
133 * Note that all other members are handled by EC_GROUP_free.
135 void ec_GF2m_simple_group_finish(EC_GROUP
*group
)
137 BN_free(&group
->field
);
143 /* Clear and free a GF(2^m)-based EC_GROUP structure.
144 * Note that all other members are handled by EC_GROUP_clear_free.
146 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*group
)
148 BN_clear_free(&group
->field
);
149 BN_clear_free(&group
->a
);
150 BN_clear_free(&group
->b
);
159 /* Copy a GF(2^m)-based EC_GROUP structure.
160 * Note that all other members are handled by EC_GROUP_copy.
162 int ec_GF2m_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
165 if (!BN_copy(&dest
->field
, &src
->field
)) return 0;
166 if (!BN_copy(&dest
->a
, &src
->a
)) return 0;
167 if (!BN_copy(&dest
->b
, &src
->b
)) return 0;
168 dest
->poly
[0] = src
->poly
[0];
169 dest
->poly
[1] = src
->poly
[1];
170 dest
->poly
[2] = src
->poly
[2];
171 dest
->poly
[3] = src
->poly
[3];
172 dest
->poly
[4] = src
->poly
[4];
173 bn_wexpand(&dest
->a
, (dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
);
174 bn_wexpand(&dest
->b
, (dest
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
);
175 for (i
= dest
->a
.top
; i
< dest
->a
.dmax
; i
++) dest
->a
.d
[i
] = 0;
176 for (i
= dest
->b
.top
; i
< dest
->b
.dmax
; i
++) dest
->b
.d
[i
] = 0;
181 /* Set the curve parameters of an EC_GROUP structure. */
182 int ec_GF2m_simple_group_set_curve(EC_GROUP
*group
,
183 const BIGNUM
*p
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
188 if (!BN_copy(&group
->field
, p
)) goto err
;
189 i
= BN_GF2m_poly2arr(&group
->field
, group
->poly
, 5);
190 if ((i
!= 5) && (i
!= 3))
192 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
, EC_R_UNSUPPORTED_FIELD
);
197 if (!BN_GF2m_mod_arr(&group
->a
, a
, group
->poly
)) goto err
;
198 bn_wexpand(&group
->a
, (group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
);
199 for (i
= group
->a
.top
; i
< group
->a
.dmax
; i
++) group
->a
.d
[i
] = 0;
202 if (!BN_GF2m_mod_arr(&group
->b
, b
, group
->poly
)) goto err
;
203 bn_wexpand(&group
->b
, (group
->poly
[0] + BN_BITS2
- 1) / BN_BITS2
);
204 for (i
= group
->b
.top
; i
< group
->b
.dmax
; i
++) group
->b
.d
[i
] = 0;
212 /* Get the curve parameters of an EC_GROUP structure.
213 * If p, a, or b are NULL then there values will not be set but the method will return with success.
215 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
221 if (!BN_copy(p
, &group
->field
)) return 0;
226 if (!BN_copy(a
, &group
->a
)) goto err
;
231 if (!BN_copy(b
, &group
->b
)) goto err
;
241 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
242 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*group
)
244 return BN_num_bits(&group
->field
)-1;
248 /* Checks the discriminant of the curve.
249 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
251 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*group
, BN_CTX
*ctx
)
255 BN_CTX
*new_ctx
= NULL
;
259 ctx
= new_ctx
= BN_CTX_new();
262 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
, ERR_R_MALLOC_FAILURE
);
268 if (b
== NULL
) goto err
;
270 if (!BN_GF2m_mod_arr(b
, &group
->b
, group
->poly
)) goto err
;
272 /* check the discriminant:
273 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
275 if (BN_is_zero(b
)) goto err
;
282 BN_CTX_free(new_ctx
);
287 /* Initializes an EC_POINT. */
288 int ec_GF2m_simple_point_init(EC_POINT
*point
)
297 /* Frees an EC_POINT. */
298 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
306 /* Clears and frees an EC_POINT. */
307 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
309 BN_clear_free(&point
->X
);
310 BN_clear_free(&point
->Y
);
311 BN_clear_free(&point
->Z
);
316 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
317 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
319 if (!BN_copy(&dest
->X
, &src
->X
)) return 0;
320 if (!BN_copy(&dest
->Y
, &src
->Y
)) return 0;
321 if (!BN_copy(&dest
->Z
, &src
->Z
)) return 0;
322 dest
->Z_is_one
= src
->Z_is_one
;
328 /* Set an EC_POINT to the point at infinity.
329 * A point at infinity is represented by having Z=0.
331 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
, EC_POINT
*point
)
334 return (BN_zero(&point
->Z
));
338 /* Set the coordinates of an EC_POINT using affine coordinates.
339 * Note that the simple implementation only uses affine coordinates.
341 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
, EC_POINT
*point
,
342 const BIGNUM
*x
, const BIGNUM
*y
, BN_CTX
*ctx
)
345 if (x
== NULL
|| y
== NULL
)
347 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
, ERR_R_PASSED_NULL_PARAMETER
);
351 if (!BN_copy(&point
->X
, x
)) goto err
;
353 if (!BN_copy(&point
->Y
, y
)) goto err
;
355 if (!BN_copy(&point
->Z
, BN_value_one())) goto err
;
365 /* Gets the affine coordinates of an EC_POINT.
366 * Note that the simple implementation only uses affine coordinates.
368 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
, const EC_POINT
*point
,
369 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*ctx
)
373 if (EC_POINT_is_at_infinity(group
, point
))
375 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
, EC_R_POINT_AT_INFINITY
);
379 if (BN_cmp(&point
->Z
, BN_value_one()))
381 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
386 if (!BN_copy(x
, &point
->X
)) goto err
;
391 if (!BN_copy(y
, &point
->Y
)) goto err
;
401 /* Include patented algorithms. */
402 #include "ec2_smpt.c"
405 /* Converts an EC_POINT to an octet string.
406 * If buf is NULL, the encoded length will be returned.
407 * If the length len of buf is smaller than required an error will be returned.
409 * The point compression section of this function is patented by Certicom Corp.
410 * under US Patent 6,141,420. Point compression is disabled by default and can
411 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
414 size_t ec_GF2m_simple_point2oct(const EC_GROUP
*group
, const EC_POINT
*point
, point_conversion_form_t form
,
415 unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
418 BN_CTX
*new_ctx
= NULL
;
421 size_t field_len
, i
, skip
;
423 #ifndef OPENSSL_EC_BIN_PT_COMP
424 if ((form
== POINT_CONVERSION_COMPRESSED
) || (form
== POINT_CONVERSION_HYBRID
))
426 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, ERR_R_DISABLED
);
431 if ((form
!= POINT_CONVERSION_COMPRESSED
)
432 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
433 && (form
!= POINT_CONVERSION_HYBRID
))
435 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, EC_R_INVALID_FORM
);
439 if (EC_POINT_is_at_infinity(group
, point
))
441 /* encodes to a single 0 octet */
446 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
455 /* ret := required output buffer length */
456 field_len
= (EC_GROUP_get_degree(group
) + 7) / 8;
457 ret
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
459 /* if 'buf' is NULL, just return required length */
464 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
470 ctx
= new_ctx
= BN_CTX_new();
479 yxi
= BN_CTX_get(ctx
);
480 if (yxi
== NULL
) goto err
;
482 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
)) goto err
;
485 #ifdef OPENSSL_EC_BIN_PT_COMP
486 if ((form
!= POINT_CONVERSION_UNCOMPRESSED
) && !BN_is_zero(x
))
488 if (!group
->meth
->field_div(group
, yxi
, y
, x
, ctx
)) goto err
;
489 if (BN_is_odd(yxi
)) buf
[0]++;
495 skip
= field_len
- BN_num_bytes(x
);
496 if (skip
> field_len
)
498 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
506 skip
= BN_bn2bin(x
, buf
+ i
);
508 if (i
!= 1 + field_len
)
510 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
514 if (form
== POINT_CONVERSION_UNCOMPRESSED
|| form
== POINT_CONVERSION_HYBRID
)
516 skip
= field_len
- BN_num_bytes(y
);
517 if (skip
> field_len
)
519 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
527 skip
= BN_bn2bin(y
, buf
+ i
);
533 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
541 BN_CTX_free(new_ctx
);
548 BN_CTX_free(new_ctx
);
553 /* Converts an octet string representation to an EC_POINT.
554 * Note that the simple implementation only uses affine coordinates.
556 int ec_GF2m_simple_oct2point(const EC_GROUP
*group
, EC_POINT
*point
,
557 const unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
559 point_conversion_form_t form
;
561 BN_CTX
*new_ctx
= NULL
;
563 size_t field_len
, enc_len
;
568 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_BUFFER_TOO_SMALL
);
574 if ((form
!= 0) && (form
!= POINT_CONVERSION_COMPRESSED
)
575 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
576 && (form
!= POINT_CONVERSION_HYBRID
))
578 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
581 if ((form
== 0 || form
== POINT_CONVERSION_UNCOMPRESSED
) && y_bit
)
583 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
591 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
595 return EC_POINT_set_to_infinity(group
, point
);
598 field_len
= (EC_GROUP_get_degree(group
) + 7) / 8;
599 enc_len
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
603 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
609 ctx
= new_ctx
= BN_CTX_new();
617 yxi
= BN_CTX_get(ctx
);
618 if (yxi
== NULL
) goto err
;
620 if (!BN_bin2bn(buf
+ 1, field_len
, x
)) goto err
;
621 if (BN_ucmp(x
, &group
->field
) >= 0)
623 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
627 if (form
== POINT_CONVERSION_COMPRESSED
)
629 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, point
, x
, y_bit
, ctx
)) goto err
;
633 if (!BN_bin2bn(buf
+ 1 + field_len
, field_len
, y
)) goto err
;
634 if (BN_ucmp(y
, &group
->field
) >= 0)
636 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
639 if (form
== POINT_CONVERSION_HYBRID
)
641 if (!group
->meth
->field_div(group
, yxi
, y
, x
, ctx
)) goto err
;
642 if (y_bit
!= BN_is_odd(yxi
))
644 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
649 if (!EC_POINT_set_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
)) goto err
;
652 if (!EC_POINT_is_on_curve(group
, point
, ctx
)) /* test required by X9.62 */
654 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT
, EC_R_POINT_IS_NOT_ON_CURVE
);
663 BN_CTX_free(new_ctx
);
668 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
669 * Uses algorithm A.10.2 of IEEE P1363.
671 int ec_GF2m_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
673 BN_CTX
*new_ctx
= NULL
;
674 BIGNUM
*x0
, *y0
, *x1
, *y1
, *x2
, *y2
, *s
, *t
;
677 if (EC_POINT_is_at_infinity(group
, a
))
679 if (!EC_POINT_copy(r
, b
)) return 0;
683 if (EC_POINT_is_at_infinity(group
, b
))
685 if (!EC_POINT_copy(r
, a
)) return 0;
691 ctx
= new_ctx
= BN_CTX_new();
697 x0
= BN_CTX_get(ctx
);
698 y0
= BN_CTX_get(ctx
);
699 x1
= BN_CTX_get(ctx
);
700 y1
= BN_CTX_get(ctx
);
701 x2
= BN_CTX_get(ctx
);
702 y2
= BN_CTX_get(ctx
);
705 if (t
== NULL
) goto err
;
709 if (!BN_copy(x0
, &a
->X
)) goto err
;
710 if (!BN_copy(y0
, &a
->Y
)) goto err
;
714 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, x0
, y0
, ctx
)) goto err
;
718 if (!BN_copy(x1
, &b
->X
)) goto err
;
719 if (!BN_copy(y1
, &b
->Y
)) goto err
;
723 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, x1
, y1
, ctx
)) goto err
;
727 if (BN_GF2m_cmp(x0
, x1
))
729 if (!BN_GF2m_add(t
, x0
, x1
)) goto err
;
730 if (!BN_GF2m_add(s
, y0
, y1
)) goto err
;
731 if (!group
->meth
->field_div(group
, s
, s
, t
, ctx
)) goto err
;
732 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
)) goto err
;
733 if (!BN_GF2m_add(x2
, x2
, &group
->a
)) goto err
;
734 if (!BN_GF2m_add(x2
, x2
, s
)) goto err
;
735 if (!BN_GF2m_add(x2
, x2
, t
)) goto err
;
739 if (BN_GF2m_cmp(y0
, y1
) || BN_is_zero(x1
))
741 if (!EC_POINT_set_to_infinity(group
, r
)) goto err
;
745 if (!group
->meth
->field_div(group
, s
, y1
, x1
, ctx
)) goto err
;
746 if (!BN_GF2m_add(s
, s
, x1
)) goto err
;
748 if (!group
->meth
->field_sqr(group
, x2
, s
, ctx
)) goto err
;
749 if (!BN_GF2m_add(x2
, x2
, s
)) goto err
;
750 if (!BN_GF2m_add(x2
, x2
, &group
->a
)) goto err
;
753 if (!BN_GF2m_add(y2
, x1
, x2
)) goto err
;
754 if (!group
->meth
->field_mul(group
, y2
, y2
, s
, ctx
)) goto err
;
755 if (!BN_GF2m_add(y2
, y2
, x2
)) goto err
;
756 if (!BN_GF2m_add(y2
, y2
, y1
)) goto err
;
758 if (!EC_POINT_set_affine_coordinates_GF2m(group
, r
, x2
, y2
, ctx
)) goto err
;
765 BN_CTX_free(new_ctx
);
770 /* Computes 2 * a and stores the result in r. r could be a.
771 * Uses algorithm A.10.2 of IEEE P1363.
773 int ec_GF2m_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, BN_CTX
*ctx
)
775 return ec_GF2m_simple_add(group
, r
, a
, a
, ctx
);
779 int ec_GF2m_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
781 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(&point
->Y
))
782 /* point is its own inverse */
785 if (!EC_POINT_make_affine(group
, point
, ctx
)) return 0;
786 return BN_GF2m_add(&point
->Y
, &point
->X
, &point
->Y
);
790 /* Indicates whether the given point is the point at infinity. */
791 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*group
, const EC_POINT
*point
)
793 return BN_is_zero(&point
->Z
);
797 /* Determines whether the given EC_POINT is an actual point on the curve defined
798 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
799 * y^2 + x*y = x^3 + a*x^2 + b.
801 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
, BN_CTX
*ctx
)
803 BN_CTX
*new_ctx
= NULL
;
804 BIGNUM
*rh
, *lh
, *tmp1
;
807 if (EC_POINT_is_at_infinity(group
, point
))
810 /* only support affine coordinates */
811 if (!point
->Z_is_one
) goto err
;
815 ctx
= new_ctx
= BN_CTX_new();
821 rh
= BN_CTX_get(ctx
);
822 lh
= BN_CTX_get(ctx
);
823 tmp1
= BN_CTX_get(ctx
);
824 if (tmp1
== NULL
) goto err
;
826 /* We have a curve defined by a Weierstrass equation
827 * y^2 + x*y = x^3 + a*x^2 + b.
828 * To test this, we add up the right-hand side in 'rh'
829 * and the left-hand side in 'lh'.
833 if (!group
->meth
->field_sqr(group
, tmp1
, &point
->X
, ctx
)) goto err
;
834 if (!group
->meth
->field_mul(group
, rh
, tmp1
, &point
->X
, ctx
)) goto err
;
836 /* rh := rh + a*X^2 */
837 if (!group
->meth
->field_mul(group
, tmp1
, tmp1
, &group
->a
, ctx
)) goto err
;
838 if (!BN_GF2m_add(rh
, rh
, tmp1
)) goto err
;
841 if (!BN_GF2m_add(rh
, rh
, &group
->b
)) goto err
;
844 if (!group
->meth
->field_sqr(group
, lh
, &point
->Y
, ctx
)) goto err
;
847 if (!group
->meth
->field_mul(group
, tmp1
, &point
->X
, &point
->Y
, ctx
)) goto err
;
848 if (!BN_GF2m_add(lh
, lh
, tmp1
)) goto err
;
850 ret
= (0 == BN_GF2m_cmp(lh
, rh
));
853 if (ctx
) BN_CTX_end(ctx
);
854 if (new_ctx
) BN_CTX_free(new_ctx
);
859 /* Indicates whether two points are equal.
862 * 0 equal (in affine coordinates)
865 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
867 BIGNUM
*aX
, *aY
, *bX
, *bY
;
868 BN_CTX
*new_ctx
= NULL
;
871 if (EC_POINT_is_at_infinity(group
, a
))
873 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
876 if (a
->Z_is_one
&& b
->Z_is_one
)
878 return ((BN_cmp(&a
->X
, &b
->X
) == 0) && BN_cmp(&a
->Y
, &b
->Y
) == 0) ? 0 : 1;
883 ctx
= new_ctx
= BN_CTX_new();
889 aX
= BN_CTX_get(ctx
);
890 aY
= BN_CTX_get(ctx
);
891 bX
= BN_CTX_get(ctx
);
892 bY
= BN_CTX_get(ctx
);
893 if (bY
== NULL
) goto err
;
895 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
)) goto err
;
896 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
)) goto err
;
897 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
900 if (ctx
) BN_CTX_end(ctx
);
901 if (new_ctx
) BN_CTX_free(new_ctx
);
906 /* Forces the given EC_POINT to internally use affine coordinates. */
907 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
909 BN_CTX
*new_ctx
= NULL
;
913 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
918 ctx
= new_ctx
= BN_CTX_new();
926 if (y
== NULL
) goto err
;
928 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
)) goto err
;
929 if (!BN_copy(&point
->X
, x
)) goto err
;
930 if (!BN_copy(&point
->Y
, y
)) goto err
;
931 if (!BN_one(&point
->Z
)) goto err
;
936 if (ctx
) BN_CTX_end(ctx
);
937 if (new_ctx
) BN_CTX_free(new_ctx
);
942 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
943 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
, EC_POINT
*points
[], BN_CTX
*ctx
)
947 for (i
= 0; i
< num
; i
++)
949 if (!group
->meth
->make_affine(group
, points
[i
], ctx
)) return 0;
956 /* Wrapper to simple binary polynomial field multiplication implementation. */
957 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
959 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
963 /* Wrapper to simple binary polynomial field squaring implementation. */
964 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*ctx
)
966 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
970 /* Wrapper to simple binary polynomial field division implementation. */
971 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
973 return BN_GF2m_mod_div(r
, a
, b
, &group
->field
, ctx
);