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
;
287 BN_CTX_free(new_ctx
);
292 /* Initializes an EC_POINT. */
293 int ec_GF2m_simple_point_init(EC_POINT
*point
)
302 /* Frees an EC_POINT. */
303 void ec_GF2m_simple_point_finish(EC_POINT
*point
)
311 /* Clears and frees an EC_POINT. */
312 void ec_GF2m_simple_point_clear_finish(EC_POINT
*point
)
314 BN_clear_free(&point
->X
);
315 BN_clear_free(&point
->Y
);
316 BN_clear_free(&point
->Z
);
321 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
322 int ec_GF2m_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
324 if (!BN_copy(&dest
->X
, &src
->X
)) return 0;
325 if (!BN_copy(&dest
->Y
, &src
->Y
)) return 0;
326 if (!BN_copy(&dest
->Z
, &src
->Z
)) return 0;
327 dest
->Z_is_one
= src
->Z_is_one
;
333 /* Set an EC_POINT to the point at infinity.
334 * A point at infinity is represented by having Z=0.
336 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*group
, EC_POINT
*point
)
344 /* Set the coordinates of an EC_POINT using affine coordinates.
345 * Note that the simple implementation only uses affine coordinates.
347 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*group
, EC_POINT
*point
,
348 const BIGNUM
*x
, const BIGNUM
*y
, BN_CTX
*ctx
)
351 if (x
== NULL
|| y
== NULL
)
353 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
, ERR_R_PASSED_NULL_PARAMETER
);
357 if (!BN_copy(&point
->X
, x
)) goto err
;
358 BN_set_negative(&point
->X
, 0);
359 if (!BN_copy(&point
->Y
, y
)) goto err
;
360 BN_set_negative(&point
->Y
, 0);
361 if (!BN_copy(&point
->Z
, BN_value_one())) goto err
;
362 BN_set_negative(&point
->Z
, 0);
371 /* Gets the affine coordinates of an EC_POINT.
372 * Note that the simple implementation only uses affine coordinates.
374 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*group
, const EC_POINT
*point
,
375 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*ctx
)
379 if (EC_POINT_is_at_infinity(group
, point
))
381 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
, EC_R_POINT_AT_INFINITY
);
385 if (BN_cmp(&point
->Z
, BN_value_one()))
387 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
392 if (!BN_copy(x
, &point
->X
)) goto err
;
393 BN_set_negative(x
, 0);
397 if (!BN_copy(y
, &point
->Y
)) goto err
;
398 BN_set_negative(y
, 0);
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
)
810 BN_CTX
*new_ctx
= NULL
;
812 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
813 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
815 if (EC_POINT_is_at_infinity(group
, point
))
818 field_mul
= group
->meth
->field_mul
;
819 field_sqr
= group
->meth
->field_sqr
;
821 /* only support affine coordinates */
822 if (!point
->Z_is_one
) goto err
;
826 ctx
= new_ctx
= BN_CTX_new();
832 y2
= BN_CTX_get(ctx
);
833 lh
= BN_CTX_get(ctx
);
834 if (lh
== NULL
) goto err
;
836 /* We have a curve defined by a Weierstrass equation
837 * y^2 + x*y = x^3 + a*x^2 + b.
838 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
839 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
841 if (!BN_GF2m_add(lh
, &point
->X
, &group
->a
)) goto err
;
842 if (!field_mul(group
, lh
, lh
, &point
->X
, ctx
)) goto err
;
843 if (!BN_GF2m_add(lh
, lh
, &point
->Y
)) goto err
;
844 if (!field_mul(group
, lh
, lh
, &point
->X
, ctx
)) goto err
;
845 if (!BN_GF2m_add(lh
, lh
, &group
->b
)) goto err
;
846 if (!field_sqr(group
, y2
, &point
->Y
, ctx
)) goto err
;
847 if (!BN_GF2m_add(lh
, lh
, y2
)) goto err
;
848 ret
= BN_is_zero(lh
);
850 if (ctx
) BN_CTX_end(ctx
);
851 if (new_ctx
) BN_CTX_free(new_ctx
);
856 /* Indicates whether two points are equal.
859 * 0 equal (in affine coordinates)
862 int ec_GF2m_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
864 BIGNUM
*aX
, *aY
, *bX
, *bY
;
865 BN_CTX
*new_ctx
= NULL
;
868 if (EC_POINT_is_at_infinity(group
, a
))
870 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
873 if (a
->Z_is_one
&& b
->Z_is_one
)
875 return ((BN_cmp(&a
->X
, &b
->X
) == 0) && BN_cmp(&a
->Y
, &b
->Y
) == 0) ? 0 : 1;
880 ctx
= new_ctx
= BN_CTX_new();
886 aX
= BN_CTX_get(ctx
);
887 aY
= BN_CTX_get(ctx
);
888 bX
= BN_CTX_get(ctx
);
889 bY
= BN_CTX_get(ctx
);
890 if (bY
== NULL
) goto err
;
892 if (!EC_POINT_get_affine_coordinates_GF2m(group
, a
, aX
, aY
, ctx
)) goto err
;
893 if (!EC_POINT_get_affine_coordinates_GF2m(group
, b
, bX
, bY
, ctx
)) goto err
;
894 ret
= ((BN_cmp(aX
, bX
) == 0) && BN_cmp(aY
, bY
) == 0) ? 0 : 1;
897 if (ctx
) BN_CTX_end(ctx
);
898 if (new_ctx
) BN_CTX_free(new_ctx
);
903 /* Forces the given EC_POINT to internally use affine coordinates. */
904 int ec_GF2m_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
906 BN_CTX
*new_ctx
= NULL
;
910 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
915 ctx
= new_ctx
= BN_CTX_new();
923 if (y
== NULL
) goto err
;
925 if (!EC_POINT_get_affine_coordinates_GF2m(group
, point
, x
, y
, ctx
)) goto err
;
926 if (!BN_copy(&point
->X
, x
)) goto err
;
927 if (!BN_copy(&point
->Y
, y
)) goto err
;
928 if (!BN_one(&point
->Z
)) goto err
;
933 if (ctx
) BN_CTX_end(ctx
);
934 if (new_ctx
) BN_CTX_free(new_ctx
);
939 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
940 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*group
, size_t num
, EC_POINT
*points
[], BN_CTX
*ctx
)
944 for (i
= 0; i
< num
; i
++)
946 if (!group
->meth
->make_affine(group
, points
[i
], ctx
)) return 0;
953 /* Wrapper to simple binary polynomial field multiplication implementation. */
954 int ec_GF2m_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
956 return BN_GF2m_mod_mul_arr(r
, a
, b
, group
->poly
, ctx
);
960 /* Wrapper to simple binary polynomial field squaring implementation. */
961 int ec_GF2m_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*ctx
)
963 return BN_GF2m_mod_sqr_arr(r
, a
, group
->poly
, ctx
);
967 /* Wrapper to simple binary polynomial field division implementation. */
968 int ec_GF2m_simple_field_div(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
970 return BN_GF2m_mod_div(r
, a
, b
, &group
->field
, ctx
);