1 /* crypto/ec/ecp_smpl.c */
2 /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
3 * for the OpenSSL project.
4 * Includes code written by Bodo Moeller for the OpenSSL project.
6 /* ====================================================================
7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
16 * 2. Redistributions in binary form must reproduce the above copyright
17 * notice, this list of conditions and the following disclaimer in
18 * the documentation and/or other materials provided with the
21 * 3. All advertising materials mentioning features or use of this
22 * software must display the following acknowledgment:
23 * "This product includes software developed by the OpenSSL Project
24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
27 * endorse or promote products derived from this software without
28 * prior written permission. For written permission, please contact
29 * openssl-core@openssl.org.
31 * 5. Products derived from this software may not be called "OpenSSL"
32 * nor may "OpenSSL" appear in their names without prior written
33 * permission of the OpenSSL Project.
35 * 6. Redistributions of any form whatsoever must retain the following
37 * "This product includes software developed by the OpenSSL Project
38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
51 * OF THE POSSIBILITY OF SUCH DAMAGE.
52 * ====================================================================
54 * This product includes cryptographic software written by Eric Young
55 * (eay@cryptsoft.com). This product includes software written by Tim
56 * Hudson (tjh@cryptsoft.com).
59 /* ====================================================================
60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
62 * and contributed to the OpenSSL project.
65 #include <openssl/err.h>
66 #include <openssl/symhacks.h>
70 const EC_METHOD
*EC_GFp_simple_method(void)
72 static const EC_METHOD ret
= {
73 NID_X9_62_prime_field
,
74 ec_GFp_simple_group_init
,
75 ec_GFp_simple_group_finish
,
76 ec_GFp_simple_group_clear_finish
,
77 ec_GFp_simple_group_copy
,
78 ec_GFp_simple_group_set_curve
,
79 ec_GFp_simple_group_get_curve
,
80 ec_GFp_simple_group_get_degree
,
81 ec_GFp_simple_group_check_discriminant
,
82 ec_GFp_simple_point_init
,
83 ec_GFp_simple_point_finish
,
84 ec_GFp_simple_point_clear_finish
,
85 ec_GFp_simple_point_copy
,
86 ec_GFp_simple_point_set_to_infinity
,
87 ec_GFp_simple_set_Jprojective_coordinates_GFp
,
88 ec_GFp_simple_get_Jprojective_coordinates_GFp
,
89 ec_GFp_simple_point_set_affine_coordinates
,
90 ec_GFp_simple_point_get_affine_coordinates
,
91 ec_GFp_simple_set_compressed_coordinates
,
92 ec_GFp_simple_point2oct
,
93 ec_GFp_simple_oct2point
,
97 ec_GFp_simple_is_at_infinity
,
98 ec_GFp_simple_is_on_curve
,
100 ec_GFp_simple_make_affine
,
101 ec_GFp_simple_points_make_affine
,
103 0 /* precompute_mult */,
104 0 /* have_precompute_mult */,
105 ec_GFp_simple_field_mul
,
106 ec_GFp_simple_field_sqr
,
108 0 /* field_encode */,
109 0 /* field_decode */,
110 0 /* field_set_to_one */ };
116 /* Most method functions in this file are designed to work with
117 * non-trivial representations of field elements if necessary
118 * (see ecp_mont.c): while standard modular addition and subtraction
119 * are used, the field_mul and field_sqr methods will be used for
120 * multiplication, and field_encode and field_decode (if defined)
121 * will be used for converting between representations.
123 * Functions ec_GFp_simple_points_make_affine() and
124 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
125 * that if a non-trivial representation is used, it is a Montgomery
126 * representation (i.e. 'encoding' means multiplying by some factor R).
130 int ec_GFp_simple_group_init(EC_GROUP
*group
)
132 BN_init(&group
->field
);
135 group
->a_is_minus3
= 0;
140 void ec_GFp_simple_group_finish(EC_GROUP
*group
)
142 BN_free(&group
->field
);
148 void ec_GFp_simple_group_clear_finish(EC_GROUP
*group
)
150 BN_clear_free(&group
->field
);
151 BN_clear_free(&group
->a
);
152 BN_clear_free(&group
->b
);
156 int ec_GFp_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
158 if (!BN_copy(&dest
->field
, &src
->field
)) return 0;
159 if (!BN_copy(&dest
->a
, &src
->a
)) return 0;
160 if (!BN_copy(&dest
->b
, &src
->b
)) return 0;
162 dest
->a_is_minus3
= src
->a_is_minus3
;
168 int ec_GFp_simple_group_set_curve(EC_GROUP
*group
,
169 const BIGNUM
*p
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
172 BN_CTX
*new_ctx
= NULL
;
175 /* p must be a prime > 3 */
176 if (BN_num_bits(p
) <= 2 || !BN_is_odd(p
))
178 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE
, EC_R_INVALID_FIELD
);
184 ctx
= new_ctx
= BN_CTX_new();
190 tmp_a
= BN_CTX_get(ctx
);
191 if (tmp_a
== NULL
) goto err
;
194 if (!BN_copy(&group
->field
, p
)) goto err
;
195 BN_set_negative(&group
->field
, 0);
198 if (!BN_nnmod(tmp_a
, a
, p
, ctx
)) goto err
;
199 if (group
->meth
->field_encode
)
200 { if (!group
->meth
->field_encode(group
, &group
->a
, tmp_a
, ctx
)) goto err
; }
202 if (!BN_copy(&group
->a
, tmp_a
)) goto err
;
205 if (!BN_nnmod(&group
->b
, b
, p
, ctx
)) goto err
;
206 if (group
->meth
->field_encode
)
207 if (!group
->meth
->field_encode(group
, &group
->b
, &group
->b
, ctx
)) goto err
;
209 /* group->a_is_minus3 */
210 if (!BN_add_word(tmp_a
, 3)) goto err
;
211 group
->a_is_minus3
= (0 == BN_cmp(tmp_a
, &group
->field
));
218 BN_CTX_free(new_ctx
);
223 int ec_GFp_simple_group_get_curve(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
226 BN_CTX
*new_ctx
= NULL
;
230 if (!BN_copy(p
, &group
->field
)) return 0;
233 if (a
!= NULL
|| b
!= NULL
)
235 if (group
->meth
->field_decode
)
239 ctx
= new_ctx
= BN_CTX_new();
245 if (!group
->meth
->field_decode(group
, a
, &group
->a
, ctx
)) goto err
;
249 if (!group
->meth
->field_decode(group
, b
, &group
->b
, ctx
)) goto err
;
256 if (!BN_copy(a
, &group
->a
)) goto err
;
260 if (!BN_copy(b
, &group
->b
)) goto err
;
269 BN_CTX_free(new_ctx
);
274 int ec_GFp_simple_group_get_degree(const EC_GROUP
*group
)
276 return BN_num_bits(&group
->field
);
280 int ec_GFp_simple_group_check_discriminant(const EC_GROUP
*group
, BN_CTX
*ctx
)
283 BIGNUM
*a
,*b
,*order
,*tmp_1
,*tmp_2
;
284 const BIGNUM
*p
= &group
->field
;
285 BN_CTX
*new_ctx
= NULL
;
289 ctx
= new_ctx
= BN_CTX_new();
292 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT
, ERR_R_MALLOC_FAILURE
);
299 tmp_1
= BN_CTX_get(ctx
);
300 tmp_2
= BN_CTX_get(ctx
);
301 order
= BN_CTX_get(ctx
);
302 if (order
== NULL
) goto err
;
304 if (group
->meth
->field_decode
)
306 if (!group
->meth
->field_decode(group
, a
, &group
->a
, ctx
)) goto err
;
307 if (!group
->meth
->field_decode(group
, b
, &group
->b
, ctx
)) goto err
;
311 if (!BN_copy(a
, &group
->a
)) goto err
;
312 if (!BN_copy(b
, &group
->b
)) goto err
;
315 /* check the discriminant:
316 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
320 if (BN_is_zero(b
)) goto err
;
322 else if (!BN_is_zero(b
))
324 if (!BN_mod_sqr(tmp_1
, a
, p
, ctx
)) goto err
;
325 if (!BN_mod_mul(tmp_2
, tmp_1
, a
, p
, ctx
)) goto err
;
326 if (!BN_lshift(tmp_1
, tmp_2
, 2)) goto err
;
329 if (!BN_mod_sqr(tmp_2
, b
, p
, ctx
)) goto err
;
330 if (!BN_mul_word(tmp_2
, 27)) goto err
;
333 if (!BN_mod_add(a
, tmp_1
, tmp_2
, p
, ctx
)) goto err
;
334 if (BN_is_zero(a
)) goto err
;
342 BN_CTX_free(new_ctx
);
347 int ec_GFp_simple_point_init(EC_POINT
*point
)
358 void ec_GFp_simple_point_finish(EC_POINT
*point
)
366 void ec_GFp_simple_point_clear_finish(EC_POINT
*point
)
368 BN_clear_free(&point
->X
);
369 BN_clear_free(&point
->Y
);
370 BN_clear_free(&point
->Z
);
375 int ec_GFp_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
377 if (!BN_copy(&dest
->X
, &src
->X
)) return 0;
378 if (!BN_copy(&dest
->Y
, &src
->Y
)) return 0;
379 if (!BN_copy(&dest
->Z
, &src
->Z
)) return 0;
380 dest
->Z_is_one
= src
->Z_is_one
;
386 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP
*group
, EC_POINT
*point
)
394 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP
*group
, EC_POINT
*point
,
395 const BIGNUM
*x
, const BIGNUM
*y
, const BIGNUM
*z
, BN_CTX
*ctx
)
397 BN_CTX
*new_ctx
= NULL
;
402 ctx
= new_ctx
= BN_CTX_new();
409 if (!BN_nnmod(&point
->X
, x
, &group
->field
, ctx
)) goto err
;
410 if (group
->meth
->field_encode
)
412 if (!group
->meth
->field_encode(group
, &point
->X
, &point
->X
, ctx
)) goto err
;
418 if (!BN_nnmod(&point
->Y
, y
, &group
->field
, ctx
)) goto err
;
419 if (group
->meth
->field_encode
)
421 if (!group
->meth
->field_encode(group
, &point
->Y
, &point
->Y
, ctx
)) goto err
;
429 if (!BN_nnmod(&point
->Z
, z
, &group
->field
, ctx
)) goto err
;
430 Z_is_one
= BN_is_one(&point
->Z
);
431 if (group
->meth
->field_encode
)
433 if (Z_is_one
&& (group
->meth
->field_set_to_one
!= 0))
435 if (!group
->meth
->field_set_to_one(group
, &point
->Z
, ctx
)) goto err
;
439 if (!group
->meth
->field_encode(group
, &point
->Z
, &point
->Z
, ctx
)) goto err
;
442 point
->Z_is_one
= Z_is_one
;
449 BN_CTX_free(new_ctx
);
454 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP
*group
, const EC_POINT
*point
,
455 BIGNUM
*x
, BIGNUM
*y
, BIGNUM
*z
, BN_CTX
*ctx
)
457 BN_CTX
*new_ctx
= NULL
;
460 if (group
->meth
->field_decode
!= 0)
464 ctx
= new_ctx
= BN_CTX_new();
471 if (!group
->meth
->field_decode(group
, x
, &point
->X
, ctx
)) goto err
;
475 if (!group
->meth
->field_decode(group
, y
, &point
->Y
, ctx
)) goto err
;
479 if (!group
->meth
->field_decode(group
, z
, &point
->Z
, ctx
)) goto err
;
486 if (!BN_copy(x
, &point
->X
)) goto err
;
490 if (!BN_copy(y
, &point
->Y
)) goto err
;
494 if (!BN_copy(z
, &point
->Z
)) goto err
;
502 BN_CTX_free(new_ctx
);
507 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP
*group
, EC_POINT
*point
,
508 const BIGNUM
*x
, const BIGNUM
*y
, BN_CTX
*ctx
)
510 if (x
== NULL
|| y
== NULL
)
512 /* unlike for projective coordinates, we do not tolerate this */
513 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES
, ERR_R_PASSED_NULL_PARAMETER
);
517 return EC_POINT_set_Jprojective_coordinates_GFp(group
, point
, x
, y
, BN_value_one(), ctx
);
521 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP
*group
, const EC_POINT
*point
,
522 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*ctx
)
524 BN_CTX
*new_ctx
= NULL
;
525 BIGNUM
*Z
, *Z_1
, *Z_2
, *Z_3
;
529 if (EC_POINT_is_at_infinity(group
, point
))
531 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES
, EC_R_POINT_AT_INFINITY
);
537 ctx
= new_ctx
= BN_CTX_new();
544 Z_1
= BN_CTX_get(ctx
);
545 Z_2
= BN_CTX_get(ctx
);
546 Z_3
= BN_CTX_get(ctx
);
547 if (Z_3
== NULL
) goto err
;
549 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
551 if (group
->meth
->field_decode
)
553 if (!group
->meth
->field_decode(group
, Z
, &point
->Z
, ctx
)) goto err
;
563 if (group
->meth
->field_decode
)
567 if (!group
->meth
->field_decode(group
, x
, &point
->X
, ctx
)) goto err
;
571 if (!group
->meth
->field_decode(group
, y
, &point
->Y
, ctx
)) goto err
;
578 if (!BN_copy(x
, &point
->X
)) goto err
;
582 if (!BN_copy(y
, &point
->Y
)) goto err
;
588 if (!BN_mod_inverse(Z_1
, Z_
, &group
->field
, ctx
))
590 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES
, ERR_R_BN_LIB
);
594 if (group
->meth
->field_encode
== 0)
596 /* field_sqr works on standard representation */
597 if (!group
->meth
->field_sqr(group
, Z_2
, Z_1
, ctx
)) goto err
;
601 if (!BN_mod_sqr(Z_2
, Z_1
, &group
->field
, ctx
)) goto err
;
606 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
607 if (!group
->meth
->field_mul(group
, x
, &point
->X
, Z_2
, ctx
)) goto err
;
612 if (group
->meth
->field_encode
== 0)
614 /* field_mul works on standard representation */
615 if (!group
->meth
->field_mul(group
, Z_3
, Z_2
, Z_1
, ctx
)) goto err
;
619 if (!BN_mod_mul(Z_3
, Z_2
, Z_1
, &group
->field
, ctx
)) goto err
;
622 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
623 if (!group
->meth
->field_mul(group
, y
, &point
->Y
, Z_3
, ctx
)) goto err
;
632 BN_CTX_free(new_ctx
);
637 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP
*group
, EC_POINT
*point
,
638 const BIGNUM
*x_
, int y_bit
, BN_CTX
*ctx
)
640 BN_CTX
*new_ctx
= NULL
;
641 BIGNUM
*tmp1
, *tmp2
, *x
, *y
;
644 /* clear error queue*/
649 ctx
= new_ctx
= BN_CTX_new();
654 y_bit
= (y_bit
!= 0);
657 tmp1
= BN_CTX_get(ctx
);
658 tmp2
= BN_CTX_get(ctx
);
661 if (y
== NULL
) goto err
;
663 /* Recover y. We have a Weierstrass equation
664 * y^2 = x^3 + a*x + b,
665 * so y is one of the square roots of x^3 + a*x + b.
669 if (!BN_nnmod(x
, x_
, &group
->field
,ctx
)) goto err
;
670 if (group
->meth
->field_decode
== 0)
672 /* field_{sqr,mul} work on standard representation */
673 if (!group
->meth
->field_sqr(group
, tmp2
, x_
, ctx
)) goto err
;
674 if (!group
->meth
->field_mul(group
, tmp1
, tmp2
, x_
, ctx
)) goto err
;
678 if (!BN_mod_sqr(tmp2
, x_
, &group
->field
, ctx
)) goto err
;
679 if (!BN_mod_mul(tmp1
, tmp2
, x_
, &group
->field
, ctx
)) goto err
;
682 /* tmp1 := tmp1 + a*x */
683 if (group
->a_is_minus3
)
685 if (!BN_mod_lshift1_quick(tmp2
, x
, &group
->field
)) goto err
;
686 if (!BN_mod_add_quick(tmp2
, tmp2
, x
, &group
->field
)) goto err
;
687 if (!BN_mod_sub_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
691 if (group
->meth
->field_decode
)
693 if (!group
->meth
->field_decode(group
, tmp2
, &group
->a
, ctx
)) goto err
;
694 if (!BN_mod_mul(tmp2
, tmp2
, x
, &group
->field
, ctx
)) goto err
;
698 /* field_mul works on standard representation */
699 if (!group
->meth
->field_mul(group
, tmp2
, &group
->a
, x
, ctx
)) goto err
;
702 if (!BN_mod_add_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
705 /* tmp1 := tmp1 + b */
706 if (group
->meth
->field_decode
)
708 if (!group
->meth
->field_decode(group
, tmp2
, &group
->b
, ctx
)) goto err
;
709 if (!BN_mod_add_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
713 if (!BN_mod_add_quick(tmp1
, tmp1
, &group
->b
, &group
->field
)) goto err
;
716 if (!BN_mod_sqrt(y
, tmp1
, &group
->field
, ctx
))
718 unsigned long err
= ERR_peek_last_error();
720 if (ERR_GET_LIB(err
) == ERR_LIB_BN
&& ERR_GET_REASON(err
) == BN_R_NOT_A_SQUARE
)
723 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
, EC_R_INVALID_COMPRESSED_POINT
);
726 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
, ERR_R_BN_LIB
);
730 if (y_bit
!= BN_is_odd(y
))
736 kron
= BN_kronecker(x
, &group
->field
, ctx
);
737 if (kron
== -2) goto err
;
740 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
, EC_R_INVALID_COMPRESSION_BIT
);
742 /* BN_mod_sqrt() should have cought this error (not a square) */
743 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
, EC_R_INVALID_COMPRESSED_POINT
);
746 if (!BN_usub(y
, &group
->field
, y
)) goto err
;
748 if (y_bit
!= BN_is_odd(y
))
750 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
, ERR_R_INTERNAL_ERROR
);
754 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
761 BN_CTX_free(new_ctx
);
766 size_t ec_GFp_simple_point2oct(const EC_GROUP
*group
, const EC_POINT
*point
, point_conversion_form_t form
,
767 unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
770 BN_CTX
*new_ctx
= NULL
;
773 size_t field_len
, i
, skip
;
775 if ((form
!= POINT_CONVERSION_COMPRESSED
)
776 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
777 && (form
!= POINT_CONVERSION_HYBRID
))
779 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_INVALID_FORM
);
783 if (EC_POINT_is_at_infinity(group
, point
))
785 /* encodes to a single 0 octet */
790 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
799 /* ret := required output buffer length */
800 field_len
= BN_num_bytes(&group
->field
);
801 ret
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
803 /* if 'buf' is NULL, just return required length */
808 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
814 ctx
= new_ctx
= BN_CTX_new();
823 if (y
== NULL
) goto err
;
825 if (!EC_POINT_get_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
827 if ((form
== POINT_CONVERSION_COMPRESSED
|| form
== POINT_CONVERSION_HYBRID
) && BN_is_odd(y
))
834 skip
= field_len
- BN_num_bytes(x
);
835 if (skip
> field_len
)
837 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
845 skip
= BN_bn2bin(x
, buf
+ i
);
847 if (i
!= 1 + field_len
)
849 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
853 if (form
== POINT_CONVERSION_UNCOMPRESSED
|| form
== POINT_CONVERSION_HYBRID
)
855 skip
= field_len
- BN_num_bytes(y
);
856 if (skip
> field_len
)
858 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
866 skip
= BN_bn2bin(y
, buf
+ i
);
872 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
880 BN_CTX_free(new_ctx
);
887 BN_CTX_free(new_ctx
);
892 int ec_GFp_simple_oct2point(const EC_GROUP
*group
, EC_POINT
*point
,
893 const unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
895 point_conversion_form_t form
;
897 BN_CTX
*new_ctx
= NULL
;
899 size_t field_len
, enc_len
;
904 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_BUFFER_TOO_SMALL
);
910 if ((form
!= 0) && (form
!= POINT_CONVERSION_COMPRESSED
)
911 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
912 && (form
!= POINT_CONVERSION_HYBRID
))
914 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
917 if ((form
== 0 || form
== POINT_CONVERSION_UNCOMPRESSED
) && y_bit
)
919 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
927 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
931 return EC_POINT_set_to_infinity(group
, point
);
934 field_len
= BN_num_bytes(&group
->field
);
935 enc_len
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
939 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
945 ctx
= new_ctx
= BN_CTX_new();
953 if (y
== NULL
) goto err
;
955 if (!BN_bin2bn(buf
+ 1, field_len
, x
)) goto err
;
956 if (BN_ucmp(x
, &group
->field
) >= 0)
958 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
962 if (form
== POINT_CONVERSION_COMPRESSED
)
964 if (!EC_POINT_set_compressed_coordinates_GFp(group
, point
, x
, y_bit
, ctx
)) goto err
;
968 if (!BN_bin2bn(buf
+ 1 + field_len
, field_len
, y
)) goto err
;
969 if (BN_ucmp(y
, &group
->field
) >= 0)
971 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
974 if (form
== POINT_CONVERSION_HYBRID
)
976 if (y_bit
!= BN_is_odd(y
))
978 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
983 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
986 if (!EC_POINT_is_on_curve(group
, point
, ctx
)) /* test required by X9.62 */
988 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_POINT_IS_NOT_ON_CURVE
);
997 BN_CTX_free(new_ctx
);
1002 int ec_GFp_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
1004 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1005 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1007 BN_CTX
*new_ctx
= NULL
;
1008 BIGNUM
*n0
, *n1
, *n2
, *n3
, *n4
, *n5
, *n6
;
1012 return EC_POINT_dbl(group
, r
, a
, ctx
);
1013 if (EC_POINT_is_at_infinity(group
, a
))
1014 return EC_POINT_copy(r
, b
);
1015 if (EC_POINT_is_at_infinity(group
, b
))
1016 return EC_POINT_copy(r
, a
);
1018 field_mul
= group
->meth
->field_mul
;
1019 field_sqr
= group
->meth
->field_sqr
;
1024 ctx
= new_ctx
= BN_CTX_new();
1030 n0
= BN_CTX_get(ctx
);
1031 n1
= BN_CTX_get(ctx
);
1032 n2
= BN_CTX_get(ctx
);
1033 n3
= BN_CTX_get(ctx
);
1034 n4
= BN_CTX_get(ctx
);
1035 n5
= BN_CTX_get(ctx
);
1036 n6
= BN_CTX_get(ctx
);
1037 if (n6
== NULL
) goto end
;
1039 /* Note that in this function we must not read components of 'a' or 'b'
1040 * once we have written the corresponding components of 'r'.
1041 * ('r' might be one of 'a' or 'b'.)
1047 if (!BN_copy(n1
, &a
->X
)) goto end
;
1048 if (!BN_copy(n2
, &a
->Y
)) goto end
;
1054 if (!field_sqr(group
, n0
, &b
->Z
, ctx
)) goto end
;
1055 if (!field_mul(group
, n1
, &a
->X
, n0
, ctx
)) goto end
;
1056 /* n1 = X_a * Z_b^2 */
1058 if (!field_mul(group
, n0
, n0
, &b
->Z
, ctx
)) goto end
;
1059 if (!field_mul(group
, n2
, &a
->Y
, n0
, ctx
)) goto end
;
1060 /* n2 = Y_a * Z_b^3 */
1066 if (!BN_copy(n3
, &b
->X
)) goto end
;
1067 if (!BN_copy(n4
, &b
->Y
)) goto end
;
1073 if (!field_sqr(group
, n0
, &a
->Z
, ctx
)) goto end
;
1074 if (!field_mul(group
, n3
, &b
->X
, n0
, ctx
)) goto end
;
1075 /* n3 = X_b * Z_a^2 */
1077 if (!field_mul(group
, n0
, n0
, &a
->Z
, ctx
)) goto end
;
1078 if (!field_mul(group
, n4
, &b
->Y
, n0
, ctx
)) goto end
;
1079 /* n4 = Y_b * Z_a^3 */
1083 if (!BN_mod_sub_quick(n5
, n1
, n3
, p
)) goto end
;
1084 if (!BN_mod_sub_quick(n6
, n2
, n4
, p
)) goto end
;
1092 /* a is the same point as b */
1094 ret
= EC_POINT_dbl(group
, r
, a
, ctx
);
1100 /* a is the inverse of b */
1109 if (!BN_mod_add_quick(n1
, n1
, n3
, p
)) goto end
;
1110 if (!BN_mod_add_quick(n2
, n2
, n4
, p
)) goto end
;
1111 /* 'n7' = n1 + n3 */
1112 /* 'n8' = n2 + n4 */
1115 if (a
->Z_is_one
&& b
->Z_is_one
)
1117 if (!BN_copy(&r
->Z
, n5
)) goto end
;
1122 { if (!BN_copy(n0
, &b
->Z
)) goto end
; }
1123 else if (b
->Z_is_one
)
1124 { if (!BN_copy(n0
, &a
->Z
)) goto end
; }
1126 { if (!field_mul(group
, n0
, &a
->Z
, &b
->Z
, ctx
)) goto end
; }
1127 if (!field_mul(group
, &r
->Z
, n0
, n5
, ctx
)) goto end
;
1130 /* Z_r = Z_a * Z_b * n5 */
1133 if (!field_sqr(group
, n0
, n6
, ctx
)) goto end
;
1134 if (!field_sqr(group
, n4
, n5
, ctx
)) goto end
;
1135 if (!field_mul(group
, n3
, n1
, n4
, ctx
)) goto end
;
1136 if (!BN_mod_sub_quick(&r
->X
, n0
, n3
, p
)) goto end
;
1137 /* X_r = n6^2 - n5^2 * 'n7' */
1140 if (!BN_mod_lshift1_quick(n0
, &r
->X
, p
)) goto end
;
1141 if (!BN_mod_sub_quick(n0
, n3
, n0
, p
)) goto end
;
1142 /* n9 = n5^2 * 'n7' - 2 * X_r */
1145 if (!field_mul(group
, n0
, n0
, n6
, ctx
)) goto end
;
1146 if (!field_mul(group
, n5
, n4
, n5
, ctx
)) goto end
; /* now n5 is n5^3 */
1147 if (!field_mul(group
, n1
, n2
, n5
, ctx
)) goto end
;
1148 if (!BN_mod_sub_quick(n0
, n0
, n1
, p
)) goto end
;
1150 if (!BN_add(n0
, n0
, p
)) goto end
;
1151 /* now 0 <= n0 < 2*p, and n0 is even */
1152 if (!BN_rshift1(&r
->Y
, n0
)) goto end
;
1153 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1158 if (ctx
) /* otherwise we already called BN_CTX_end */
1160 if (new_ctx
!= NULL
)
1161 BN_CTX_free(new_ctx
);
1166 int ec_GFp_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, BN_CTX
*ctx
)
1168 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1169 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1171 BN_CTX
*new_ctx
= NULL
;
1172 BIGNUM
*n0
, *n1
, *n2
, *n3
;
1175 if (EC_POINT_is_at_infinity(group
, a
))
1182 field_mul
= group
->meth
->field_mul
;
1183 field_sqr
= group
->meth
->field_sqr
;
1188 ctx
= new_ctx
= BN_CTX_new();
1194 n0
= BN_CTX_get(ctx
);
1195 n1
= BN_CTX_get(ctx
);
1196 n2
= BN_CTX_get(ctx
);
1197 n3
= BN_CTX_get(ctx
);
1198 if (n3
== NULL
) goto err
;
1200 /* Note that in this function we must not read components of 'a'
1201 * once we have written the corresponding components of 'r'.
1202 * ('r' might the same as 'a'.)
1208 if (!field_sqr(group
, n0
, &a
->X
, ctx
)) goto err
;
1209 if (!BN_mod_lshift1_quick(n1
, n0
, p
)) goto err
;
1210 if (!BN_mod_add_quick(n0
, n0
, n1
, p
)) goto err
;
1211 if (!BN_mod_add_quick(n1
, n0
, &group
->a
, p
)) goto err
;
1212 /* n1 = 3 * X_a^2 + a_curve */
1214 else if (group
->a_is_minus3
)
1216 if (!field_sqr(group
, n1
, &a
->Z
, ctx
)) goto err
;
1217 if (!BN_mod_add_quick(n0
, &a
->X
, n1
, p
)) goto err
;
1218 if (!BN_mod_sub_quick(n2
, &a
->X
, n1
, p
)) goto err
;
1219 if (!field_mul(group
, n1
, n0
, n2
, ctx
)) goto err
;
1220 if (!BN_mod_lshift1_quick(n0
, n1
, p
)) goto err
;
1221 if (!BN_mod_add_quick(n1
, n0
, n1
, p
)) goto err
;
1222 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1223 * = 3 * X_a^2 - 3 * Z_a^4 */
1227 if (!field_sqr(group
, n0
, &a
->X
, ctx
)) goto err
;
1228 if (!BN_mod_lshift1_quick(n1
, n0
, p
)) goto err
;
1229 if (!BN_mod_add_quick(n0
, n0
, n1
, p
)) goto err
;
1230 if (!field_sqr(group
, n1
, &a
->Z
, ctx
)) goto err
;
1231 if (!field_sqr(group
, n1
, n1
, ctx
)) goto err
;
1232 if (!field_mul(group
, n1
, n1
, &group
->a
, ctx
)) goto err
;
1233 if (!BN_mod_add_quick(n1
, n1
, n0
, p
)) goto err
;
1234 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1240 if (!BN_copy(n0
, &a
->Y
)) goto err
;
1244 if (!field_mul(group
, n0
, &a
->Y
, &a
->Z
, ctx
)) goto err
;
1246 if (!BN_mod_lshift1_quick(&r
->Z
, n0
, p
)) goto err
;
1248 /* Z_r = 2 * Y_a * Z_a */
1251 if (!field_sqr(group
, n3
, &a
->Y
, ctx
)) goto err
;
1252 if (!field_mul(group
, n2
, &a
->X
, n3
, ctx
)) goto err
;
1253 if (!BN_mod_lshift_quick(n2
, n2
, 2, p
)) goto err
;
1254 /* n2 = 4 * X_a * Y_a^2 */
1257 if (!BN_mod_lshift1_quick(n0
, n2
, p
)) goto err
;
1258 if (!field_sqr(group
, &r
->X
, n1
, ctx
)) goto err
;
1259 if (!BN_mod_sub_quick(&r
->X
, &r
->X
, n0
, p
)) goto err
;
1260 /* X_r = n1^2 - 2 * n2 */
1263 if (!field_sqr(group
, n0
, n3
, ctx
)) goto err
;
1264 if (!BN_mod_lshift_quick(n3
, n0
, 3, p
)) goto err
;
1265 /* n3 = 8 * Y_a^4 */
1268 if (!BN_mod_sub_quick(n0
, n2
, &r
->X
, p
)) goto err
;
1269 if (!field_mul(group
, n0
, n1
, n0
, ctx
)) goto err
;
1270 if (!BN_mod_sub_quick(&r
->Y
, n0
, n3
, p
)) goto err
;
1271 /* Y_r = n1 * (n2 - X_r) - n3 */
1277 if (new_ctx
!= NULL
)
1278 BN_CTX_free(new_ctx
);
1283 int ec_GFp_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
1285 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(&point
->Y
))
1286 /* point is its own inverse */
1289 return BN_usub(&point
->Y
, &group
->field
, &point
->Y
);
1293 int ec_GFp_simple_is_at_infinity(const EC_GROUP
*group
, const EC_POINT
*point
)
1295 return BN_is_zero(&point
->Z
);
1299 int ec_GFp_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
, BN_CTX
*ctx
)
1301 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1302 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1304 BN_CTX
*new_ctx
= NULL
;
1305 BIGNUM
*rh
, *tmp
, *Z4
, *Z6
;
1308 if (EC_POINT_is_at_infinity(group
, point
))
1311 field_mul
= group
->meth
->field_mul
;
1312 field_sqr
= group
->meth
->field_sqr
;
1317 ctx
= new_ctx
= BN_CTX_new();
1323 rh
= BN_CTX_get(ctx
);
1324 tmp
= BN_CTX_get(ctx
);
1325 Z4
= BN_CTX_get(ctx
);
1326 Z6
= BN_CTX_get(ctx
);
1327 if (Z6
== NULL
) goto err
;
1329 /* We have a curve defined by a Weierstrass equation
1330 * y^2 = x^3 + a*x + b.
1331 * The point to consider is given in Jacobian projective coordinates
1332 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1333 * Substituting this and multiplying by Z^6 transforms the above equation into
1334 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1335 * To test this, we add up the right-hand side in 'rh'.
1339 if (!field_sqr(group
, rh
, &point
->X
, ctx
)) goto err
;
1341 if (!point
->Z_is_one
)
1343 if (!field_sqr(group
, tmp
, &point
->Z
, ctx
)) goto err
;
1344 if (!field_sqr(group
, Z4
, tmp
, ctx
)) goto err
;
1345 if (!field_mul(group
, Z6
, Z4
, tmp
, ctx
)) goto err
;
1347 /* rh := (rh + a*Z^4)*X */
1348 if (group
->a_is_minus3
)
1350 if (!BN_mod_lshift1_quick(tmp
, Z4
, p
)) goto err
;
1351 if (!BN_mod_add_quick(tmp
, tmp
, Z4
, p
)) goto err
;
1352 if (!BN_mod_sub_quick(rh
, rh
, tmp
, p
)) goto err
;
1353 if (!field_mul(group
, rh
, rh
, &point
->X
, ctx
)) goto err
;
1357 if (!field_mul(group
, tmp
, Z4
, &group
->a
, ctx
)) goto err
;
1358 if (!BN_mod_add_quick(rh
, rh
, tmp
, p
)) goto err
;
1359 if (!field_mul(group
, rh
, rh
, &point
->X
, ctx
)) goto err
;
1362 /* rh := rh + b*Z^6 */
1363 if (!field_mul(group
, tmp
, &group
->b
, Z6
, ctx
)) goto err
;
1364 if (!BN_mod_add_quick(rh
, rh
, tmp
, p
)) goto err
;
1368 /* point->Z_is_one */
1370 /* rh := (rh + a)*X */
1371 if (!BN_mod_add_quick(rh
, rh
, &group
->a
, p
)) goto err
;
1372 if (!field_mul(group
, rh
, rh
, &point
->X
, ctx
)) goto err
;
1374 if (!BN_mod_add_quick(rh
, rh
, &group
->b
, p
)) goto err
;
1378 if (!field_sqr(group
, tmp
, &point
->Y
, ctx
)) goto err
;
1380 ret
= (0 == BN_ucmp(tmp
, rh
));
1384 if (new_ctx
!= NULL
)
1385 BN_CTX_free(new_ctx
);
1390 int ec_GFp_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
1394 * 0 equal (in affine coordinates)
1398 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1399 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1400 BN_CTX
*new_ctx
= NULL
;
1401 BIGNUM
*tmp1
, *tmp2
, *Za23
, *Zb23
;
1402 const BIGNUM
*tmp1_
, *tmp2_
;
1405 if (EC_POINT_is_at_infinity(group
, a
))
1407 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
1410 if (a
->Z_is_one
&& b
->Z_is_one
)
1412 return ((BN_cmp(&a
->X
, &b
->X
) == 0) && BN_cmp(&a
->Y
, &b
->Y
) == 0) ? 0 : 1;
1415 field_mul
= group
->meth
->field_mul
;
1416 field_sqr
= group
->meth
->field_sqr
;
1420 ctx
= new_ctx
= BN_CTX_new();
1426 tmp1
= BN_CTX_get(ctx
);
1427 tmp2
= BN_CTX_get(ctx
);
1428 Za23
= BN_CTX_get(ctx
);
1429 Zb23
= BN_CTX_get(ctx
);
1430 if (Zb23
== NULL
) goto end
;
1432 /* We have to decide whether
1433 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1434 * or equivalently, whether
1435 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1440 if (!field_sqr(group
, Zb23
, &b
->Z
, ctx
)) goto end
;
1441 if (!field_mul(group
, tmp1
, &a
->X
, Zb23
, ctx
)) goto end
;
1448 if (!field_sqr(group
, Za23
, &a
->Z
, ctx
)) goto end
;
1449 if (!field_mul(group
, tmp2
, &b
->X
, Za23
, ctx
)) goto end
;
1455 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1456 if (BN_cmp(tmp1_
, tmp2_
) != 0)
1458 ret
= 1; /* points differ */
1465 if (!field_mul(group
, Zb23
, Zb23
, &b
->Z
, ctx
)) goto end
;
1466 if (!field_mul(group
, tmp1
, &a
->Y
, Zb23
, ctx
)) goto end
;
1473 if (!field_mul(group
, Za23
, Za23
, &a
->Z
, ctx
)) goto end
;
1474 if (!field_mul(group
, tmp2
, &b
->Y
, Za23
, ctx
)) goto end
;
1480 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1481 if (BN_cmp(tmp1_
, tmp2_
) != 0)
1483 ret
= 1; /* points differ */
1487 /* points are equal */
1492 if (new_ctx
!= NULL
)
1493 BN_CTX_free(new_ctx
);
1498 int ec_GFp_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
1500 BN_CTX
*new_ctx
= NULL
;
1504 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
1509 ctx
= new_ctx
= BN_CTX_new();
1515 x
= BN_CTX_get(ctx
);
1516 y
= BN_CTX_get(ctx
);
1517 if (y
== NULL
) goto err
;
1519 if (!EC_POINT_get_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
1520 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
1521 if (!point
->Z_is_one
)
1523 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE
, ERR_R_INTERNAL_ERROR
);
1531 if (new_ctx
!= NULL
)
1532 BN_CTX_free(new_ctx
);
1537 int ec_GFp_simple_points_make_affine(const EC_GROUP
*group
, size_t num
, EC_POINT
*points
[], BN_CTX
*ctx
)
1539 BN_CTX
*new_ctx
= NULL
;
1540 BIGNUM
*tmp0
, *tmp1
;
1542 BIGNUM
**heap
= NULL
;
1551 ctx
= new_ctx
= BN_CTX_new();
1557 tmp0
= BN_CTX_get(ctx
);
1558 tmp1
= BN_CTX_get(ctx
);
1559 if (tmp0
== NULL
|| tmp1
== NULL
) goto err
;
1561 /* Before converting the individual points, compute inverses of all Z values.
1562 * Modular inversion is rather slow, but luckily we can do with a single
1563 * explicit inversion, plus about 3 multiplications per input value.
1569 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1570 * We need twice that. */
1573 heap
= OPENSSL_malloc(pow2
* sizeof heap
[0]);
1574 if (heap
== NULL
) goto err
;
1576 /* The array is used as a binary tree, exactly as in heapsort:
1580 * heap[4] heap[5] heap[6] heap[7]
1581 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1583 * We put the Z's in the last line;
1584 * then we set each other node to the product of its two child-nodes (where
1585 * empty or 0 entries are treated as ones);
1586 * then we invert heap[1];
1587 * then we invert each other node by replacing it by the product of its
1588 * parent (after inversion) and its sibling (before inversion).
1591 for (i
= pow2
/2 - 1; i
> 0; i
--)
1593 for (i
= 0; i
< num
; i
++)
1594 heap
[pow2
/2 + i
] = &points
[i
]->Z
;
1595 for (i
= pow2
/2 + num
; i
< pow2
; i
++)
1598 /* set each node to the product of its children */
1599 for (i
= pow2
/2 - 1; i
> 0; i
--)
1602 if (heap
[i
] == NULL
) goto err
;
1604 if (heap
[2*i
] != NULL
)
1606 if ((heap
[2*i
+ 1] == NULL
) || BN_is_zero(heap
[2*i
+ 1]))
1608 if (!BN_copy(heap
[i
], heap
[2*i
])) goto err
;
1612 if (BN_is_zero(heap
[2*i
]))
1614 if (!BN_copy(heap
[i
], heap
[2*i
+ 1])) goto err
;
1618 if (!group
->meth
->field_mul(group
, heap
[i
],
1619 heap
[2*i
], heap
[2*i
+ 1], ctx
)) goto err
;
1625 /* invert heap[1] */
1626 if (!BN_is_zero(heap
[1]))
1628 if (!BN_mod_inverse(heap
[1], heap
[1], &group
->field
, ctx
))
1630 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE
, ERR_R_BN_LIB
);
1634 if (group
->meth
->field_encode
!= 0)
1636 /* in the Montgomery case, we just turned R*H (representing H)
1637 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1638 * i.e. we have need to multiply by the Montgomery factor twice */
1639 if (!group
->meth
->field_encode(group
, heap
[1], heap
[1], ctx
)) goto err
;
1640 if (!group
->meth
->field_encode(group
, heap
[1], heap
[1], ctx
)) goto err
;
1643 /* set other heap[i]'s to their inverses */
1644 for (i
= 2; i
< pow2
/2 + num
; i
+= 2)
1647 if ((heap
[i
+ 1] != NULL
) && !BN_is_zero(heap
[i
+ 1]))
1649 if (!group
->meth
->field_mul(group
, tmp0
, heap
[i
/2], heap
[i
+ 1], ctx
)) goto err
;
1650 if (!group
->meth
->field_mul(group
, tmp1
, heap
[i
/2], heap
[i
], ctx
)) goto err
;
1651 if (!BN_copy(heap
[i
], tmp0
)) goto err
;
1652 if (!BN_copy(heap
[i
+ 1], tmp1
)) goto err
;
1656 if (!BN_copy(heap
[i
], heap
[i
/2])) goto err
;
1660 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1661 for (i
= 0; i
< num
; i
++)
1663 EC_POINT
*p
= points
[i
];
1665 if (!BN_is_zero(&p
->Z
))
1667 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1669 if (!group
->meth
->field_sqr(group
, tmp1
, &p
->Z
, ctx
)) goto err
;
1670 if (!group
->meth
->field_mul(group
, &p
->X
, &p
->X
, tmp1
, ctx
)) goto err
;
1672 if (!group
->meth
->field_mul(group
, tmp1
, tmp1
, &p
->Z
, ctx
)) goto err
;
1673 if (!group
->meth
->field_mul(group
, &p
->Y
, &p
->Y
, tmp1
, ctx
)) goto err
;
1675 if (group
->meth
->field_set_to_one
!= 0)
1677 if (!group
->meth
->field_set_to_one(group
, &p
->Z
, ctx
)) goto err
;
1681 if (!BN_one(&p
->Z
)) goto err
;
1691 if (new_ctx
!= NULL
)
1692 BN_CTX_free(new_ctx
);
1695 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1696 for (i
= pow2
/2 - 1; i
> 0; i
--)
1698 if (heap
[i
] != NULL
)
1699 BN_clear_free(heap
[i
]);
1707 int ec_GFp_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
1709 return BN_mod_mul(r
, a
, b
, &group
->field
, ctx
);
1713 int ec_GFp_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*ctx
)
1715 return BN_mod_sqr(r
, a
, &group
->field
, ctx
);