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 /* ====================================================================
5 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
33 * 6. Redistributions of any form whatsoever must retain the following
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
58 #include <openssl/err.h>
63 const EC_METHOD
*EC_GFp_simple_method(void)
65 static const EC_METHOD ret
= {
66 ec_GFp_simple_group_init
,
67 ec_GFp_simple_group_finish
,
68 ec_GFp_simple_group_clear_finish
,
69 ec_GFp_simple_group_copy
,
70 ec_GFp_simple_group_set_curve_GFp
,
71 ec_GFp_simple_group_get_curve_GFp
,
72 ec_GFp_simple_group_set_generator
,
73 ec_GFp_simple_group_get0_generator
,
74 ec_GFp_simple_group_get_order
,
75 ec_GFp_simple_group_get_cofactor
,
76 ec_GFp_simple_point_init
,
77 ec_GFp_simple_point_finish
,
78 ec_GFp_simple_point_clear_finish
,
79 ec_GFp_simple_point_copy
,
80 ec_GFp_simple_point_set_to_infinity
,
81 ec_GFp_simple_set_Jprojective_coordinates_GFp
,
82 ec_GFp_simple_get_Jprojective_coordinates_GFp
,
83 ec_GFp_simple_point_set_affine_coordinates_GFp
,
84 ec_GFp_simple_point_get_affine_coordinates_GFp
,
85 ec_GFp_simple_set_compressed_coordinates_GFp
,
86 ec_GFp_simple_point2oct
,
87 ec_GFp_simple_oct2point
,
91 ec_GFp_simple_is_at_infinity
,
92 ec_GFp_simple_is_on_curve
,
94 ec_GFp_simple_make_affine
,
95 ec_GFp_simple_points_make_affine
,
96 ec_GFp_simple_field_mul
,
97 ec_GFp_simple_field_sqr
,
100 0 /* field_set_to_one */ };
106 int ec_GFp_simple_group_init(EC_GROUP
*group
)
108 BN_init(&group
->field
);
111 group
->a_is_minus3
= 0;
112 group
->generator
= NULL
;
113 BN_init(&group
->order
);
114 BN_init(&group
->cofactor
);
119 void ec_GFp_simple_group_finish(EC_GROUP
*group
)
121 BN_free(&group
->field
);
124 if (group
->generator
!= NULL
)
125 EC_POINT_free(group
->generator
);
126 BN_free(&group
->order
);
127 BN_free(&group
->cofactor
);
131 void ec_GFp_simple_group_clear_finish(EC_GROUP
*group
)
133 BN_clear_free(&group
->field
);
134 BN_clear_free(&group
->a
);
135 BN_clear_free(&group
->b
);
136 if (group
->generator
!= NULL
)
138 EC_POINT_clear_free(group
->generator
);
139 group
->generator
= NULL
;
141 BN_clear_free(&group
->order
);
142 BN_clear_free(&group
->cofactor
);
146 int ec_GFp_simple_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
)
148 if (!BN_copy(&dest
->field
, &src
->field
)) return 0;
149 if (!BN_copy(&dest
->a
, &src
->a
)) return 0;
150 if (!BN_copy(&dest
->b
, &src
->b
)) return 0;
152 dest
->a_is_minus3
= src
->a_is_minus3
;
154 if (src
->generator
!= NULL
)
156 if (dest
->generator
== NULL
)
158 dest
->generator
= EC_POINT_new(dest
);
159 if (dest
->generator
== NULL
) return 0;
161 if (!EC_POINT_copy(dest
->generator
, src
->generator
)) return 0;
165 /* src->generator == NULL */
166 if (dest
->generator
!= NULL
)
168 EC_POINT_clear_free(dest
->generator
);
169 dest
->generator
= NULL
;
173 if (!BN_copy(&dest
->order
, &src
->order
)) return 0;
174 if (!BN_copy(&dest
->cofactor
, &src
->cofactor
)) return 0;
180 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP
*group
,
181 const BIGNUM
*p
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
184 BN_CTX
*new_ctx
= NULL
;
187 /* p must be a prime > 3 */
188 if (BN_num_bits(p
) <= 2 || !BN_is_odd(p
))
190 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP
, EC_R_INVALID_FIELD
);
196 ctx
= new_ctx
= BN_CTX_new();
202 tmp_a
= BN_CTX_get(ctx
);
203 if (tmp_a
== NULL
) goto err
;
206 if (!BN_copy(&group
->field
, p
)) goto err
;
207 group
->field
.neg
= 0;
210 if (!BN_nnmod(tmp_a
, a
, p
, ctx
)) goto err
;
211 if (group
->meth
->field_encode
)
212 { if (!group
->meth
->field_encode(group
, &group
->a
, tmp_a
, ctx
)) goto err
; }
214 if (!BN_copy(&group
->a
, tmp_a
)) goto err
;
217 if (!BN_nnmod(&group
->b
, b
, p
, ctx
)) goto err
;
218 if (group
->meth
->field_encode
)
219 if (!group
->meth
->field_encode(group
, &group
->b
, &group
->b
, ctx
)) goto err
;
221 /* group->a_is_minus3 */
222 if (!BN_add_word(tmp_a
, 3)) goto err
;
223 group
->a_is_minus3
= (0 == BN_cmp(tmp_a
, &group
->field
));
230 BN_CTX_free(new_ctx
);
235 int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP
*group
, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
)
238 BN_CTX
*new_ctx
= NULL
;
242 if (!BN_copy(p
, &group
->field
)) return 0;
245 if (a
!= NULL
|| b
!= NULL
)
247 if (group
->meth
->field_decode
)
251 ctx
= new_ctx
= BN_CTX_new();
257 if (!group
->meth
->field_decode(group
, a
, &group
->a
, ctx
)) goto err
;
261 if (!group
->meth
->field_decode(group
, b
, &group
->b
, ctx
)) goto err
;
268 if (!BN_copy(a
, &group
->a
)) goto err
;
272 if (!BN_copy(b
, &group
->b
)) goto err
;
281 BN_CTX_free(new_ctx
);
287 int ec_GFp_simple_group_set_generator(EC_GROUP
*group
, const EC_POINT
*generator
,
288 const BIGNUM
*order
, const BIGNUM
*cofactor
)
290 if (generator
== NULL
)
292 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR
, ERR_R_PASSED_NULL_PARAMETER
);
296 if (group
->generator
== NULL
)
298 group
->generator
= EC_POINT_new(group
);
299 if (group
->generator
== NULL
) return 0;
301 if (!EC_POINT_copy(group
->generator
, generator
)) return 0;
304 { if (!BN_copy(&group
->order
, order
)) return 0; }
306 { if (!BN_zero(&group
->order
)) return 0; }
308 if (cofactor
!= NULL
)
309 { if (!BN_copy(&group
->cofactor
, cofactor
)) return 0; }
311 { if (!BN_zero(&group
->cofactor
)) return 0; }
317 EC_POINT
*ec_GFp_simple_group_get0_generator(const EC_GROUP
*group
)
319 return group
->generator
;
323 int ec_GFp_simple_group_get_order(const EC_GROUP
*group
, BIGNUM
*order
, BN_CTX
*ctx
)
325 if (!BN_copy(order
, &group
->order
))
328 return !BN_is_zero(&group
->order
);
332 int ec_GFp_simple_group_get_cofactor(const EC_GROUP
*group
, BIGNUM
*cofactor
, BN_CTX
*ctx
)
334 if (!BN_copy(cofactor
, &group
->cofactor
))
337 return !BN_is_zero(&group
->cofactor
);
341 int ec_GFp_simple_point_init(EC_POINT
*point
)
352 void ec_GFp_simple_point_finish(EC_POINT
*point
)
360 void ec_GFp_simple_point_clear_finish(EC_POINT
*point
)
362 BN_clear_free(&point
->X
);
363 BN_clear_free(&point
->Y
);
364 BN_clear_free(&point
->Z
);
369 int ec_GFp_simple_point_copy(EC_POINT
*dest
, const EC_POINT
*src
)
371 if (!BN_copy(&dest
->X
, &src
->X
)) return 0;
372 if (!BN_copy(&dest
->Y
, &src
->Y
)) return 0;
373 if (!BN_copy(&dest
->Z
, &src
->Z
)) return 0;
374 dest
->Z_is_one
= src
->Z_is_one
;
380 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP
*group
, EC_POINT
*point
)
383 return (BN_zero(&point
->Z
));
387 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP
*group
, EC_POINT
*point
,
388 const BIGNUM
*x
, const BIGNUM
*y
, const BIGNUM
*z
, BN_CTX
*ctx
)
390 BN_CTX
*new_ctx
= NULL
;
395 ctx
= new_ctx
= BN_CTX_new();
402 if (!BN_nnmod(&point
->X
, x
, &group
->field
, ctx
)) goto err
;
403 if (group
->meth
->field_encode
)
405 if (!group
->meth
->field_encode(group
, &point
->X
, &point
->X
, ctx
)) goto err
;
411 if (!BN_nnmod(&point
->Y
, y
, &group
->field
, ctx
)) goto err
;
412 if (group
->meth
->field_encode
)
414 if (!group
->meth
->field_encode(group
, &point
->Y
, &point
->Y
, ctx
)) goto err
;
422 if (!BN_nnmod(&point
->Z
, z
, &group
->field
, ctx
)) goto err
;
423 Z_is_one
= BN_is_one(&point
->Z
);
424 if (group
->meth
->field_encode
)
426 if (Z_is_one
&& (group
->meth
->field_set_to_one
!= 0))
428 if (!group
->meth
->field_set_to_one(group
, &point
->Z
, ctx
)) goto err
;
432 if (!group
->meth
->field_encode(group
, &point
->Z
, &point
->Z
, ctx
)) goto err
;
435 point
->Z_is_one
= Z_is_one
;
442 BN_CTX_free(new_ctx
);
447 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP
*group
, const EC_POINT
*point
,
448 BIGNUM
*x
, BIGNUM
*y
, BIGNUM
*z
, BN_CTX
*ctx
)
450 BN_CTX
*new_ctx
= NULL
;
453 if (group
->meth
->field_decode
!= 0)
457 ctx
= new_ctx
= BN_CTX_new();
464 if (!group
->meth
->field_decode(group
, x
, &point
->X
, ctx
)) goto err
;
468 if (!group
->meth
->field_decode(group
, y
, &point
->Y
, ctx
)) goto err
;
472 if (!group
->meth
->field_decode(group
, z
, &point
->Z
, ctx
)) goto err
;
479 if (!BN_copy(x
, &point
->X
)) goto err
;
483 if (!BN_copy(y
, &point
->Y
)) goto err
;
487 if (!BN_copy(z
, &point
->Z
)) goto err
;
495 BN_CTX_free(new_ctx
);
500 int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP
*group
, EC_POINT
*point
,
501 const BIGNUM
*x
, const BIGNUM
*y
, BN_CTX
*ctx
)
503 if (x
== NULL
|| y
== NULL
)
505 /* unlike for projective coordinates, we do not tolerate this */
506 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP
, ERR_R_PASSED_NULL_PARAMETER
);
510 return EC_POINT_set_Jprojective_coordinates_GFp(group
, point
, x
, y
, BN_value_one(), ctx
);
514 int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP
*group
, const EC_POINT
*point
,
515 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*ctx
)
517 BN_CTX
*new_ctx
= NULL
;
518 BIGNUM
*X
, *Y
, *Z
, *Z_1
, *Z_2
, *Z_3
;
519 const BIGNUM
*X_
, *Y_
, *Z_
;
522 if (EC_POINT_is_at_infinity(group
, point
))
524 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP
, EC_R_POINT_AT_INFINITY
);
530 ctx
= new_ctx
= BN_CTX_new();
539 Z_1
= BN_CTX_get(ctx
);
540 Z_2
= BN_CTX_get(ctx
);
541 Z_3
= BN_CTX_get(ctx
);
542 if (Z_3
== NULL
) goto err
;
544 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
546 if (group
->meth
->field_decode
)
548 if (!group
->meth
->field_decode(group
, X
, &point
->X
, ctx
)) goto err
;
549 if (!group
->meth
->field_decode(group
, Y
, &point
->Y
, ctx
)) goto err
;
550 if (!group
->meth
->field_decode(group
, Z
, &point
->Z
, ctx
)) goto err
;
551 X_
= X
; Y_
= Y
; Z_
= Z
;
564 if (!BN_copy(x
, X_
)) goto err
;
568 if (!BN_copy(y
, Y_
)) goto err
;
573 if (!BN_mod_inverse(Z_1
, Z_
, &group
->field
, ctx
))
575 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP
, ERR_R_BN_LIB
);
579 if (group
->meth
->field_encode
== 0)
581 /* field_sqr works on standard representation */
582 if (!group
->meth
->field_sqr(group
, Z_2
, Z_1
, ctx
)) goto err
;
586 if (!BN_mod_sqr(Z_2
, Z_1
, &group
->field
, ctx
)) goto err
;
591 if (group
->meth
->field_encode
== 0)
593 /* field_mul works on standard representation */
594 if (!group
->meth
->field_mul(group
, x
, X_
, Z_2
, ctx
)) goto err
;
598 if (!BN_mod_mul(x
, X_
, Z_2
, &group
->field
, ctx
)) goto err
;
604 if (group
->meth
->field_encode
== 0)
606 /* field_mul works on standard representation */
607 if (!group
->meth
->field_mul(group
, Z_3
, Z_2
, Z_1
, ctx
)) goto err
;
608 if (!group
->meth
->field_mul(group
, y
, Y_
, Z_3
, ctx
)) goto err
;
613 if (!BN_mod_mul(Z_3
, Z_2
, Z_1
, &group
->field
, ctx
)) goto err
;
614 if (!BN_mod_mul(y
, Y_
, Z_3
, &group
->field
, ctx
)) goto err
;
624 BN_CTX_free(new_ctx
);
629 int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP
*group
, EC_POINT
*point
,
630 const BIGNUM
*x_
, int y_bit
, BN_CTX
*ctx
)
632 BN_CTX
*new_ctx
= NULL
;
633 BIGNUM
*tmp1
, *tmp2
, *x
, *y
;
638 ctx
= new_ctx
= BN_CTX_new();
643 y_bit
= (y_bit
!= 0);
646 tmp1
= BN_CTX_get(ctx
);
647 tmp2
= BN_CTX_get(ctx
);
650 if (y
== NULL
) goto err
;
652 /* Recover y. We have a Weierstrass equation
653 * y^2 = x^3 + a*x + b,
654 * so y is one of the square roots of x^3 + a*x + b.
658 if (!BN_nnmod(x
, x_
, &group
->field
,ctx
)) goto err
;
659 if (group
->meth
->field_decode
== 0)
661 /* field_{sqr,mul} work on standard representation */
662 if (!group
->meth
->field_sqr(group
, tmp2
, x_
, ctx
)) goto err
;
663 if (!group
->meth
->field_mul(group
, tmp1
, tmp2
, x_
, ctx
)) goto err
;
667 if (!BN_mod_sqr(tmp2
, x_
, &group
->field
, ctx
)) goto err
;
668 if (!BN_mod_mul(tmp1
, tmp2
, x_
, &group
->field
, ctx
)) goto err
;
671 /* tmp1 := tmp1 + a*x */
672 if (group
->a_is_minus3
)
674 if (!BN_mod_lshift1_quick(tmp2
, x
, &group
->field
)) goto err
;
675 if (!BN_mod_add_quick(tmp2
, tmp2
, x
, &group
->field
)) goto err
;
676 if (!BN_mod_sub_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
680 if (group
->meth
->field_decode
)
682 if (!group
->meth
->field_decode(group
, tmp2
, &group
->a
, ctx
)) goto err
;
683 if (!BN_mod_mul(tmp2
, tmp2
, x
, &group
->field
, ctx
)) goto err
;
687 /* field_mul works on standard representation */
688 if (!group
->meth
->field_mul(group
, tmp2
, &group
->a
, x
, ctx
)) goto err
;
691 if (!BN_mod_add_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
694 /* tmp1 := tmp1 + b */
695 if (group
->meth
->field_decode
)
697 if (!group
->meth
->field_decode(group
, tmp2
, &group
->b
, ctx
)) goto err
;
698 if (!BN_mod_add_quick(tmp1
, tmp1
, tmp2
, &group
->field
)) goto err
;
702 if (!BN_mod_add_quick(tmp1
, tmp1
, &group
->b
, &group
->field
)) goto err
;
705 if (!BN_mod_sqrt(y
, tmp1
, &group
->field
, ctx
))
707 unsigned long err
= ERR_peek_error();
709 if (ERR_GET_LIB(err
) == ERR_LIB_BN
&& ERR_GET_REASON(err
) == BN_R_NOT_A_SQUARE
)
711 (void)ERR_get_error();
712 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
, EC_R_INVALID_COMPRESSED_POINT
);
715 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
, ERR_R_BN_LIB
);
718 /* If tmp1 is not a square (i.e. there is no point on the curve with
719 * our x), then y now is a nonsense value too */
721 if (y_bit
!= BN_is_odd(y
))
727 kron
= BN_kronecker(x
, &group
->field
, ctx
);
728 if (kron
== -2) goto err
;
731 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
, EC_R_INVALID_COMPRESSION_BIT
);
733 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
, EC_R_INVALID_COMPRESSED_POINT
);
736 if (!BN_usub(y
, &group
->field
, y
)) goto err
;
738 if (y_bit
!= BN_is_odd(y
))
740 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
, ERR_R_INTERNAL_ERROR
);
744 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
751 BN_CTX_free(new_ctx
);
756 size_t ec_GFp_simple_point2oct(const EC_GROUP
*group
, const EC_POINT
*point
, point_conversion_form_t form
,
757 unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
760 BN_CTX
*new_ctx
= NULL
;
763 size_t field_len
, i
, skip
;
765 if ((form
!= POINT_CONVERSION_COMPRESSED
)
766 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
767 && (form
!= POINT_CONVERSION_HYBRID
))
769 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_INVALID_FORM
);
773 if (EC_POINT_is_at_infinity(group
, point
))
775 /* encodes to a single 0 octet */
780 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
789 /* ret := required output buffer length */
790 field_len
= BN_num_bytes(&group
->field
);
791 ret
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
793 /* if 'buf' is NULL, just return required length */
798 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, EC_R_BUFFER_TOO_SMALL
);
804 ctx
= new_ctx
= BN_CTX_new();
813 if (y
== NULL
) goto err
;
815 if (!EC_POINT_get_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
817 if ((form
== POINT_CONVERSION_COMPRESSED
|| form
== POINT_CONVERSION_HYBRID
) && BN_is_odd(y
))
824 skip
= field_len
- BN_num_bytes(x
);
825 if (skip
> field_len
)
827 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
835 skip
= BN_bn2bin(x
, buf
+ i
);
837 if (i
!= 1 + field_len
)
839 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
843 if (form
== POINT_CONVERSION_UNCOMPRESSED
|| form
== POINT_CONVERSION_HYBRID
)
845 skip
= field_len
- BN_num_bytes(y
);
846 if (skip
> field_len
)
848 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
856 skip
= BN_bn2bin(y
, buf
+ i
);
862 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT
, ERR_R_INTERNAL_ERROR
);
870 BN_CTX_free(new_ctx
);
877 BN_CTX_free(new_ctx
);
882 int ec_GFp_simple_oct2point(const EC_GROUP
*group
, EC_POINT
*point
,
883 const unsigned char *buf
, size_t len
, BN_CTX
*ctx
)
885 point_conversion_form_t form
;
887 BN_CTX
*new_ctx
= NULL
;
889 size_t field_len
, enc_len
;
894 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_BUFFER_TOO_SMALL
);
900 if ((form
!= 0) && (form
!= POINT_CONVERSION_COMPRESSED
)
901 && (form
!= POINT_CONVERSION_UNCOMPRESSED
)
902 && (form
!= POINT_CONVERSION_HYBRID
))
904 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
907 if ((form
== 0 || form
== POINT_CONVERSION_UNCOMPRESSED
) && y_bit
)
909 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
917 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
921 return EC_POINT_set_to_infinity(group
, point
);
924 field_len
= BN_num_bytes(&group
->field
);
925 enc_len
= (form
== POINT_CONVERSION_COMPRESSED
) ? 1 + field_len
: 1 + 2*field_len
;
929 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
935 ctx
= new_ctx
= BN_CTX_new();
943 if (y
== NULL
) goto err
;
945 if (!BN_bin2bn(buf
+ 1, field_len
, x
)) goto err
;
946 if (BN_ucmp(x
, &group
->field
) >= 0)
948 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
952 if (form
== POINT_CONVERSION_COMPRESSED
)
954 if (!EC_POINT_set_compressed_coordinates_GFp(group
, point
, x
, y_bit
, ctx
)) goto err
;
958 if (!BN_bin2bn(buf
+ 1 + field_len
, field_len
, y
)) goto err
;
959 if (BN_ucmp(y
, &group
->field
) >= 0)
961 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
964 if (form
== POINT_CONVERSION_HYBRID
)
966 if (y_bit
!= BN_is_odd(y
))
968 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_INVALID_ENCODING
);
973 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
976 if (!EC_POINT_is_on_curve(group
, point
, ctx
)) /* test required by X9.62 */
978 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT
, EC_R_POINT_IS_NOT_ON_CURVE
);
987 BN_CTX_free(new_ctx
);
992 int ec_GFp_simple_add(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
994 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
995 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
997 BN_CTX
*new_ctx
= NULL
;
998 BIGNUM
*n0
, *n1
, *n2
, *n3
, *n4
, *n5
, *n6
;
1002 return EC_POINT_dbl(group
, r
, a
, ctx
);
1003 if (EC_POINT_is_at_infinity(group
, a
))
1004 return EC_POINT_copy(r
, b
);
1005 if (EC_POINT_is_at_infinity(group
, b
))
1006 return EC_POINT_copy(r
, a
);
1008 field_mul
= group
->meth
->field_mul
;
1009 field_sqr
= group
->meth
->field_sqr
;
1014 ctx
= new_ctx
= BN_CTX_new();
1020 n0
= BN_CTX_get(ctx
);
1021 n1
= BN_CTX_get(ctx
);
1022 n2
= BN_CTX_get(ctx
);
1023 n3
= BN_CTX_get(ctx
);
1024 n4
= BN_CTX_get(ctx
);
1025 n5
= BN_CTX_get(ctx
);
1026 n6
= BN_CTX_get(ctx
);
1027 if (n6
== NULL
) goto end
;
1029 /* Note that in this function we must not read components of 'a' or 'b'
1030 * once we have written the corresponding components of 'r'.
1031 * ('r' might be one of 'a' or 'b'.)
1037 if (!BN_copy(n1
, &a
->X
)) goto end
;
1038 if (!BN_copy(n2
, &a
->Y
)) goto end
;
1044 if (!field_sqr(group
, n0
, &b
->Z
, ctx
)) goto end
;
1045 if (!field_mul(group
, n1
, &a
->X
, n0
, ctx
)) goto end
;
1046 /* n1 = X_a * Z_b^2 */
1048 if (!field_mul(group
, n0
, n0
, &b
->Z
, ctx
)) goto end
;
1049 if (!field_mul(group
, n2
, &a
->Y
, n0
, ctx
)) goto end
;
1050 /* n2 = Y_a * Z_b^3 */
1056 if (!BN_copy(n3
, &b
->X
)) goto end
;
1057 if (!BN_copy(n4
, &b
->Y
)) goto end
;
1063 if (!field_sqr(group
, n0
, &a
->Z
, ctx
)) goto end
;
1064 if (!field_mul(group
, n3
, &b
->X
, n0
, ctx
)) goto end
;
1065 /* n3 = X_b * Z_a^2 */
1067 if (!field_mul(group
, n0
, n0
, &a
->Z
, ctx
)) goto end
;
1068 if (!field_mul(group
, n4
, &b
->Y
, n0
, ctx
)) goto end
;
1069 /* n4 = Y_b * Z_a^3 */
1073 if (!BN_mod_sub_quick(n5
, n1
, n3
, p
)) goto end
;
1074 if (!BN_mod_sub_quick(n6
, n2
, n4
, p
)) goto end
;
1082 /* a is the same point as b */
1084 ret
= EC_POINT_dbl(group
, r
, a
, ctx
);
1090 /* a is the inverse of b */
1091 if (!BN_zero(&r
->Z
)) goto end
;
1099 if (!BN_mod_add_quick(n1
, n1
, n3
, p
)) goto end
;
1100 if (!BN_mod_add_quick(n2
, n2
, n4
, p
)) goto end
;
1101 /* 'n7' = n1 + n3 */
1102 /* 'n8' = n2 + n4 */
1105 if (a
->Z_is_one
&& b
->Z_is_one
)
1107 if (!BN_copy(&r
->Z
, n5
)) goto end
;
1112 { if (!BN_copy(n0
, &b
->Z
)) goto end
; }
1113 else if (b
->Z_is_one
)
1114 { if (!BN_copy(n0
, &a
->Z
)) goto end
; }
1116 { if (!field_mul(group
, n0
, &a
->Z
, &b
->Z
, ctx
)) goto end
; }
1117 if (!field_mul(group
, &r
->Z
, n0
, n5
, ctx
)) goto end
;
1120 /* Z_r = Z_a * Z_b * n5 */
1123 if (!field_sqr(group
, n0
, n6
, ctx
)) goto end
;
1124 if (!field_sqr(group
, n4
, n5
, ctx
)) goto end
;
1125 if (!field_mul(group
, n3
, n1
, n4
, ctx
)) goto end
;
1126 if (!BN_mod_sub_quick(&r
->X
, n0
, n3
, p
)) goto end
;
1127 /* X_r = n6^2 - n5^2 * 'n7' */
1130 if (!BN_mod_lshift1_quick(n0
, &r
->X
, p
)) goto end
;
1131 if (!BN_mod_sub_quick(n0
, n3
, n0
, p
)) goto end
;
1132 /* n9 = n5^2 * 'n7' - 2 * X_r */
1135 if (!field_mul(group
, n0
, n0
, n6
, ctx
)) goto end
;
1136 if (!field_mul(group
, n5
, n4
, n5
, ctx
)) goto end
; /* now n5 is n5^3 */
1137 if (!field_mul(group
, n1
, n2
, n5
, ctx
)) goto end
;
1138 if (!BN_mod_sub_quick(n0
, n0
, n1
, p
)) goto end
;
1140 if (!BN_add(n0
, n0
, p
)) goto end
;
1141 /* now 0 <= n0 < 2*p, and n0 is even */
1142 if (!BN_rshift1(&r
->Y
, n0
)) goto end
;
1143 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1148 if (ctx
) /* otherwise we already called BN_CTX_end */
1150 if (new_ctx
!= NULL
)
1151 BN_CTX_free(new_ctx
);
1156 int ec_GFp_simple_dbl(const EC_GROUP
*group
, EC_POINT
*r
, const EC_POINT
*a
, BN_CTX
*ctx
)
1158 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1159 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1161 BN_CTX
*new_ctx
= NULL
;
1162 BIGNUM
*n0
, *n1
, *n2
, *n3
;
1165 if (EC_POINT_is_at_infinity(group
, a
))
1167 if (!BN_zero(&r
->Z
)) return 0;
1172 field_mul
= group
->meth
->field_mul
;
1173 field_sqr
= group
->meth
->field_sqr
;
1178 ctx
= new_ctx
= BN_CTX_new();
1184 n0
= BN_CTX_get(ctx
);
1185 n1
= BN_CTX_get(ctx
);
1186 n2
= BN_CTX_get(ctx
);
1187 n3
= BN_CTX_get(ctx
);
1188 if (n3
== NULL
) goto err
;
1190 /* Note that in this function we must not read components of 'a'
1191 * once we have written the corresponding components of 'r'.
1192 * ('r' might the same as 'a'.)
1198 if (!field_sqr(group
, n0
, &a
->X
, ctx
)) goto err
;
1199 if (!BN_mod_lshift1_quick(n1
, n0
, p
)) goto err
;
1200 if (!BN_mod_add_quick(n0
, n0
, n1
, p
)) goto err
;
1201 if (!BN_mod_add_quick(n1
, n0
, &group
->a
, p
)) goto err
;
1202 /* n1 = 3 * X_a^2 + a_curve */
1204 else if (group
->a_is_minus3
)
1206 if (!field_sqr(group
, n1
, &a
->Z
, ctx
)) goto err
;
1207 if (!BN_mod_add_quick(n0
, &a
->X
, n1
, p
)) goto err
;
1208 if (!BN_mod_sub_quick(n2
, &a
->X
, n1
, p
)) goto err
;
1209 if (!field_mul(group
, n1
, n0
, n2
, ctx
)) goto err
;
1210 if (!BN_mod_lshift1_quick(n0
, n1
, p
)) goto err
;
1211 if (!BN_mod_add_quick(n1
, n0
, n1
, p
)) goto err
;
1212 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1213 * = 3 * X_a^2 - 3 * Z_a^4 */
1217 if (!field_sqr(group
, n0
, &a
->X
, ctx
)) goto err
;
1218 if (!BN_mod_lshift1_quick(n1
, n0
, p
)) goto err
;
1219 if (!BN_mod_add_quick(n0
, n0
, n1
, p
)) goto err
;
1220 if (!field_sqr(group
, n1
, &a
->Z
, ctx
)) goto err
;
1221 if (!field_sqr(group
, n1
, n1
, ctx
)) goto err
;
1222 if (!field_mul(group
, n1
, n1
, &group
->a
, ctx
)) goto err
;
1223 if (!BN_mod_add_quick(n1
, n1
, n0
, p
)) goto err
;
1224 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1230 if (!BN_copy(n0
, &a
->Y
)) goto err
;
1234 if (!field_mul(group
, n0
, &a
->Y
, &a
->Z
, ctx
)) goto err
;
1236 if (!BN_mod_lshift1_quick(&r
->Z
, n0
, p
)) goto err
;
1238 /* Z_r = 2 * Y_a * Z_a */
1241 if (!field_sqr(group
, n3
, &a
->Y
, ctx
)) goto err
;
1242 if (!field_mul(group
, n2
, &a
->X
, n3
, ctx
)) goto err
;
1243 if (!BN_mod_lshift_quick(n2
, n2
, 2, p
)) goto err
;
1244 /* n2 = 4 * X_a * Y_a^2 */
1247 if (!BN_mod_lshift1_quick(n0
, n2
, p
)) goto err
;
1248 if (!field_sqr(group
, &r
->X
, n1
, ctx
)) goto err
;
1249 if (!BN_mod_sub_quick(&r
->X
, &r
->X
, n0
, p
)) goto err
;
1250 /* X_r = n1^2 - 2 * n2 */
1253 if (!field_sqr(group
, n0
, n3
, ctx
)) goto err
;
1254 if (!BN_mod_lshift_quick(n3
, n0
, 3, p
)) goto err
;
1255 /* n3 = 8 * Y_a^4 */
1258 if (!BN_mod_sub_quick(n0
, n2
, &r
->X
, p
)) goto err
;
1259 if (!field_mul(group
, n0
, n1
, n0
, ctx
)) goto err
;
1260 if (!BN_mod_sub_quick(&r
->Y
, n0
, n3
, p
)) goto err
;
1261 /* Y_r = n1 * (n2 - X_r) - n3 */
1267 if (new_ctx
!= NULL
)
1268 BN_CTX_free(new_ctx
);
1273 int ec_GFp_simple_invert(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
1275 if (EC_POINT_is_at_infinity(group
, point
) || BN_is_zero(&point
->Y
))
1276 /* point is its own inverse */
1279 return BN_usub(&point
->Y
, &group
->field
, &point
->Y
);
1283 int ec_GFp_simple_is_at_infinity(const EC_GROUP
*group
, const EC_POINT
*point
)
1285 return BN_is_zero(&point
->Z
);
1289 int ec_GFp_simple_is_on_curve(const EC_GROUP
*group
, const EC_POINT
*point
, BN_CTX
*ctx
)
1291 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1292 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1294 BN_CTX
*new_ctx
= NULL
;
1295 BIGNUM
*rh
, *tmp1
, *tmp2
, *Z4
, *Z6
;
1298 if (EC_POINT_is_at_infinity(group
, point
))
1301 field_mul
= group
->meth
->field_mul
;
1302 field_sqr
= group
->meth
->field_sqr
;
1307 ctx
= new_ctx
= BN_CTX_new();
1313 rh
= BN_CTX_get(ctx
);
1314 tmp1
= BN_CTX_get(ctx
);
1315 tmp2
= BN_CTX_get(ctx
);
1316 Z4
= BN_CTX_get(ctx
);
1317 Z6
= BN_CTX_get(ctx
);
1318 if (Z6
== NULL
) goto err
;
1320 /* We have a curve defined by a Weierstrass equation
1321 * y^2 = x^3 + a*x + b.
1322 * The point to consider is given in Jacobian projective coordinates
1323 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1324 * Substituting this and multiplying by Z^6 transforms the above equation into
1325 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1326 * To test this, we add up the right-hand side in 'rh'.
1330 if (!field_sqr(group
, rh
, &point
->X
, ctx
)) goto err
;
1331 if (!field_mul(group
, rh
, rh
, &point
->X
, ctx
)) goto err
;
1333 if (!point
->Z_is_one
)
1335 if (!field_sqr(group
, tmp1
, &point
->Z
, ctx
)) goto err
;
1336 if (!field_sqr(group
, Z4
, tmp1
, ctx
)) goto err
;
1337 if (!field_mul(group
, Z6
, Z4
, tmp1
, ctx
)) goto err
;
1339 /* rh := rh + a*X*Z^4 */
1340 if (!field_mul(group
, tmp1
, &point
->X
, Z4
, ctx
)) goto err
;
1341 if (group
->a_is_minus3
)
1343 if (!BN_mod_lshift1_quick(tmp2
, tmp1
, p
)) goto err
;
1344 if (!BN_mod_add_quick(tmp2
, tmp2
, tmp1
, p
)) goto err
;
1345 if (!BN_mod_sub_quick(rh
, rh
, tmp2
, p
)) goto err
;
1349 if (!field_mul(group
, tmp2
, tmp1
, &group
->a
, ctx
)) goto err
;
1350 if (!BN_mod_add_quick(rh
, rh
, tmp2
, p
)) goto err
;
1353 /* rh := rh + b*Z^6 */
1354 if (!field_mul(group
, tmp1
, &group
->b
, Z6
, ctx
)) goto err
;
1355 if (!BN_mod_add_quick(rh
, rh
, tmp1
, p
)) goto err
;
1359 /* point->Z_is_one */
1361 /* rh := rh + a*X */
1362 if (group
->a_is_minus3
)
1364 if (!BN_mod_lshift1_quick(tmp2
, &point
->X
, p
)) goto err
;
1365 if (!BN_mod_add_quick(tmp2
, tmp2
, &point
->X
, p
)) goto err
;
1366 if (!BN_mod_sub_quick(rh
, rh
, tmp2
, p
)) goto err
;
1370 if (!field_mul(group
, tmp2
, &point
->X
, &group
->a
, ctx
)) goto err
;
1371 if (!BN_mod_add_quick(rh
, rh
, tmp2
, p
)) goto err
;
1375 if (!BN_mod_add_quick(rh
, rh
, &group
->b
, p
)) goto err
;
1379 if (!field_sqr(group
, tmp1
, &point
->Y
, ctx
)) goto err
;
1381 ret
= (0 == BN_cmp(tmp1
, rh
));
1385 if (new_ctx
!= NULL
)
1386 BN_CTX_free(new_ctx
);
1391 int ec_GFp_simple_cmp(const EC_GROUP
*group
, const EC_POINT
*a
, const EC_POINT
*b
, BN_CTX
*ctx
)
1395 * 0 equal (in affine coordinates)
1399 int (*field_mul
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1400 int (*field_sqr
)(const EC_GROUP
*, BIGNUM
*, const BIGNUM
*, BN_CTX
*);
1401 BN_CTX
*new_ctx
= NULL
;
1402 BIGNUM
*tmp1
, *tmp2
, *Za23
, *Zb23
;
1403 const BIGNUM
*tmp1_
, *tmp2_
;
1406 if (EC_POINT_is_at_infinity(group
, a
))
1408 return EC_POINT_is_at_infinity(group
, b
) ? 0 : 1;
1411 if (a
->Z_is_one
&& b
->Z_is_one
)
1413 return ((BN_cmp(&a
->X
, &b
->X
) == 0) && BN_cmp(&a
->Y
, &b
->Y
) == 0) ? 0 : 1;
1416 field_mul
= group
->meth
->field_mul
;
1417 field_sqr
= group
->meth
->field_sqr
;
1421 ctx
= new_ctx
= BN_CTX_new();
1427 tmp1
= BN_CTX_get(ctx
);
1428 tmp2
= BN_CTX_get(ctx
);
1429 Za23
= BN_CTX_get(ctx
);
1430 Zb23
= BN_CTX_get(ctx
);
1431 if (Zb23
== NULL
) goto end
;
1433 /* We have to decide whether
1434 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1435 * or equivalently, whether
1436 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1441 if (!field_sqr(group
, Zb23
, &b
->Z
, ctx
)) goto end
;
1442 if (!field_mul(group
, tmp1
, &a
->X
, Zb23
, ctx
)) goto end
;
1449 if (!field_sqr(group
, Za23
, &a
->Z
, ctx
)) goto end
;
1450 if (!field_mul(group
, tmp2
, &b
->X
, Za23
, ctx
)) goto end
;
1456 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1457 if (BN_cmp(tmp1_
, tmp2_
) != 0)
1459 ret
= 1; /* points differ */
1466 if (!field_mul(group
, Zb23
, Zb23
, &b
->Z
, ctx
)) goto end
;
1467 if (!field_mul(group
, tmp1
, &a
->Y
, Zb23
, ctx
)) goto end
;
1474 if (!field_mul(group
, Za23
, Za23
, &a
->Z
, ctx
)) goto end
;
1475 if (!field_mul(group
, tmp2
, &b
->Y
, Za23
, ctx
)) goto end
;
1481 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1482 if (BN_cmp(tmp1_
, tmp2_
) != 0)
1484 ret
= 1; /* points differ */
1488 /* points are equal */
1493 if (new_ctx
!= NULL
)
1494 BN_CTX_free(new_ctx
);
1499 int ec_GFp_simple_make_affine(const EC_GROUP
*group
, EC_POINT
*point
, BN_CTX
*ctx
)
1501 BN_CTX
*new_ctx
= NULL
;
1505 if (point
->Z_is_one
|| EC_POINT_is_at_infinity(group
, point
))
1510 ctx
= new_ctx
= BN_CTX_new();
1516 x
= BN_CTX_get(ctx
);
1517 y
= BN_CTX_get(ctx
);
1518 if (y
== NULL
) goto err
;
1520 if (!EC_POINT_get_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
1521 if (!EC_POINT_set_affine_coordinates_GFp(group
, point
, x
, y
, ctx
)) goto err
;
1522 if (!point
->Z_is_one
)
1524 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE
, ERR_R_INTERNAL_ERROR
);
1532 if (new_ctx
!= NULL
)
1533 BN_CTX_free(new_ctx
);
1538 int ec_GFp_simple_points_make_affine(const EC_GROUP
*group
, size_t num
, EC_POINT
*points
[], BN_CTX
*ctx
)
1540 BN_CTX
*new_ctx
= NULL
;
1541 BIGNUM
*tmp0
, *tmp1
;
1543 BIGNUM
**heap
= NULL
;
1552 ctx
= new_ctx
= BN_CTX_new();
1558 tmp0
= BN_CTX_get(ctx
);
1559 tmp1
= BN_CTX_get(ctx
);
1560 if (tmp0
== NULL
|| tmp1
== NULL
) goto err
;
1562 /* Before converting the individual points, compute inverses of all Z values.
1563 * Modular inversion is rather slow, but luckily we can do with a single
1564 * explicit inversion, plus about 3 multiplications per input value.
1570 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1571 * We need twice that. */
1574 heap
= OPENSSL_malloc(pow2
* sizeof heap
[0]);
1575 if (heap
== NULL
) goto err
;
1577 /* The array is used as a binary tree, exactly as in heapsort:
1581 * heap[4] heap[5] heap[6] heap[7]
1582 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1584 * We put the Z's in the last line;
1585 * then we set each other node to the product of its two child-nodes (where
1586 * empty or 0 entries are treated as ones);
1587 * then we invert heap[1];
1588 * then we invert each other node by replacing it by the product of its
1589 * parent (after inversion) and its sibling (before inversion).
1592 for (i
= pow2
/2 - 1; i
> 0; i
--)
1594 for (i
= 0; i
< num
; i
++)
1595 heap
[pow2
/2 + i
] = &points
[i
]->Z
;
1596 for (i
= pow2
/2 + num
; i
< pow2
; i
++)
1599 /* set each node to the product of its children */
1600 for (i
= pow2
/2 - 1; i
> 0; i
--)
1603 if (heap
[i
] == NULL
) goto err
;
1605 if (heap
[2*i
] != NULL
)
1607 if ((heap
[2*i
+ 1] == NULL
) || BN_is_zero(heap
[2*i
+ 1]))
1609 if (!BN_copy(heap
[i
], heap
[2*i
])) goto err
;
1613 if (BN_is_zero(heap
[2*i
]))
1615 if (!BN_copy(heap
[i
], heap
[2*i
+ 1])) goto err
;
1619 if (!group
->meth
->field_mul(group
, heap
[i
],
1620 heap
[2*i
], heap
[2*i
+ 1], ctx
)) goto err
;
1626 /* invert heap[1] */
1627 if (!BN_is_zero(heap
[1]))
1629 if (!BN_mod_inverse(heap
[1], heap
[1], &group
->field
, ctx
))
1631 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE
, ERR_R_BN_LIB
);
1635 if (group
->meth
->field_encode
!= 0)
1637 /* in the Montgomery case, we just turned R*H (representing H)
1638 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1639 * i.e. we have need to multiply by the Montgomery factor twice */
1640 if (!group
->meth
->field_encode(group
, heap
[1], heap
[1], ctx
)) goto err
;
1641 if (!group
->meth
->field_encode(group
, heap
[1], heap
[1], ctx
)) goto err
;
1644 /* set other heap[i]'s to their inverses */
1645 for (i
= 2; i
< pow2
/2 + num
; i
+= 2)
1648 if ((heap
[i
+ 1] != NULL
) && !BN_is_zero(heap
[i
+ 1]))
1650 if (!group
->meth
->field_mul(group
, tmp0
, heap
[i
/2], heap
[i
+ 1], ctx
)) goto err
;
1651 if (!group
->meth
->field_mul(group
, tmp1
, heap
[i
/2], heap
[i
], ctx
)) goto err
;
1652 if (!BN_copy(heap
[i
], tmp0
)) goto err
;
1653 if (!BN_copy(heap
[i
+ 1], tmp1
)) goto err
;
1657 if (!BN_copy(heap
[i
], heap
[i
/2])) goto err
;
1661 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1662 for (i
= 0; i
< num
; i
++)
1664 EC_POINT
*p
= points
[i
];
1666 if (!BN_is_zero(&p
->Z
))
1668 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1670 if (!group
->meth
->field_sqr(group
, tmp1
, &p
->Z
, ctx
)) goto err
;
1671 if (!group
->meth
->field_mul(group
, &p
->X
, &p
->X
, tmp1
, ctx
)) goto err
;
1673 if (!group
->meth
->field_mul(group
, tmp1
, tmp1
, &p
->Z
, ctx
)) goto err
;
1674 if (!group
->meth
->field_mul(group
, &p
->Y
, &p
->Y
, tmp1
, ctx
)) goto err
;
1676 if (group
->meth
->field_set_to_one
!= 0)
1678 if (!group
->meth
->field_set_to_one(group
, &p
->Z
, ctx
)) goto err
;
1682 if (!BN_one(&p
->Z
)) goto err
;
1692 if (new_ctx
!= NULL
)
1693 BN_CTX_free(new_ctx
);
1696 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1697 for (i
= pow2
/2 - 1; i
> 0; i
--)
1699 if (heap
[i
] != NULL
)
1700 BN_clear_free(heap
[i
]);
1708 int ec_GFp_simple_field_mul(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
1710 return BN_mod_mul(r
, a
, b
, &group
->field
, ctx
);
1714 int ec_GFp_simple_field_sqr(const EC_GROUP
*group
, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*ctx
)
1716 return BN_mod_sqr(r
, a
, &group
->field
, ctx
);