394 lines
18 KiB
C
394 lines
18 KiB
C
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/* crypto/ec/ec_lcl.h */
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/*
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* Originally written by Bodo Moeller for the OpenSSL project.
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*/
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/* ====================================================================
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* Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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*
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* Portions of the attached software ("Contribution") are developed by
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* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
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*
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* The Contribution is licensed pursuant to the OpenSSL open source
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* license provided above.
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*
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* The elliptic curve binary polynomial software is originally written by
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* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
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*
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*/
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#include <stdlib.h>
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#include <openssl/obj_mac.h>
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#include <openssl/ec.h>
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#include <openssl/bn.h>
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#if defined(__SUNPRO_C)
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# if __SUNPRO_C >= 0x520
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# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
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# endif
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#endif
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/* Structure details are not part of the exported interface,
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* so all this may change in future versions. */
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struct ec_method_st {
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/* used by EC_METHOD_get_field_type: */
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int field_type; /* a NID */
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/* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
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int (*group_init)(EC_GROUP *);
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void (*group_finish)(EC_GROUP *);
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void (*group_clear_finish)(EC_GROUP *);
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int (*group_copy)(EC_GROUP *, const EC_GROUP *);
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/* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
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/* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
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int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
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int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
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/* used by EC_GROUP_get_degree: */
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int (*group_get_degree)(const EC_GROUP *);
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/* used by EC_GROUP_check: */
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int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
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/* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
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int (*point_init)(EC_POINT *);
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void (*point_finish)(EC_POINT *);
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void (*point_clear_finish)(EC_POINT *);
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int (*point_copy)(EC_POINT *, const EC_POINT *);
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/* used by EC_POINT_set_to_infinity,
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* EC_POINT_set_Jprojective_coordinates_GFp,
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* EC_POINT_get_Jprojective_coordinates_GFp,
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* EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
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* EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
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* EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
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*/
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int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
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int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
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int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
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BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
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int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, const BIGNUM *y, BN_CTX *);
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int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
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BIGNUM *x, BIGNUM *y, BN_CTX *);
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int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, int y_bit, BN_CTX *);
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/* used by EC_POINT_point2oct, EC_POINT_oct2point: */
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size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
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unsigned char *buf, size_t len, BN_CTX *);
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int (*oct2point)(const EC_GROUP *, EC_POINT *,
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const unsigned char *buf, size_t len, BN_CTX *);
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/* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
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int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
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int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
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int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
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/* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
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int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
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int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
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int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
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/* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
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int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
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int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
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/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
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* (default implementations are used if the 'mul' pointer is 0): */
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int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
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int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
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int (*have_precompute_mult)(const EC_GROUP *group);
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/* internal functions */
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/* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
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* the same implementations of point operations can be used with different
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* optimized implementations of expensive field operations: */
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int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
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int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
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int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
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int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
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int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
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int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
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} /* EC_METHOD */;
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typedef struct ec_extra_data_st {
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struct ec_extra_data_st *next;
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void *data;
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void *(*dup_func)(void *);
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void (*free_func)(void *);
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void (*clear_free_func)(void *);
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} EC_EXTRA_DATA; /* used in EC_GROUP */
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struct ec_group_st {
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const EC_METHOD *meth;
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EC_POINT *generator; /* optional */
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BIGNUM order, cofactor;
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int curve_name;/* optional NID for named curve */
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int asn1_flag; /* flag to control the asn1 encoding */
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point_conversion_form_t asn1_form;
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unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
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size_t seed_len;
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EC_EXTRA_DATA *extra_data; /* linked list */
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/* The following members are handled by the method functions,
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* even if they appear generic */
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BIGNUM field; /* Field specification.
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* For curves over GF(p), this is the modulus;
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* for curves over GF(2^m), this is the
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* irreducible polynomial defining the field.
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*/
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int poly[6]; /* Field specification for curves over GF(2^m).
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* The irreducible f(t) is then of the form:
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* t^poly[0] + t^poly[1] + ... + t^poly[k]
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* where m = poly[0] > poly[1] > ... > poly[k] = 0.
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* The array is terminated with poly[k+1]=-1.
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* All elliptic curve irreducibles have at most 5
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* non-zero terms.
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*/
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BIGNUM a, b; /* Curve coefficients.
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* (Here the assumption is that BIGNUMs can be used
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* or abused for all kinds of fields, not just GF(p).)
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* For characteristic > 3, the curve is defined
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* by a Weierstrass equation of the form
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* y^2 = x^3 + a*x + b.
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* For characteristic 2, the curve is defined by
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* an equation of the form
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* y^2 + x*y = x^3 + a*x^2 + b.
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*/
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int a_is_minus3; /* enable optimized point arithmetics for special case */
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void *field_data1; /* method-specific (e.g., Montgomery structure) */
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void *field_data2; /* method-specific */
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int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
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} /* EC_GROUP */;
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struct ec_key_st {
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int version;
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EC_GROUP *group;
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EC_POINT *pub_key;
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BIGNUM *priv_key;
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unsigned int enc_flag;
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point_conversion_form_t conv_form;
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int references;
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EC_EXTRA_DATA *method_data;
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} /* EC_KEY */;
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/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
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* (with visibility limited to 'package' level for now).
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* We use the function pointers as index for retrieval; this obviates
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* global ex_data-style index tables.
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*/
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int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
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void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
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void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
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void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
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void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
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void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
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struct ec_point_st {
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const EC_METHOD *meth;
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/* All members except 'meth' are handled by the method functions,
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* even if they appear generic */
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BIGNUM X;
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BIGNUM Y;
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BIGNUM Z; /* Jacobian projective coordinates:
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* (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
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int Z_is_one; /* enable optimized point arithmetics for special case */
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} /* EC_POINT */;
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/* method functions in ec_mult.c
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* (ec_lib.c uses these as defaults if group->method->mul is 0) */
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int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
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int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
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int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
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/* method functions in ecp_smpl.c */
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int ec_GFp_simple_group_init(EC_GROUP *);
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void ec_GFp_simple_group_finish(EC_GROUP *);
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void ec_GFp_simple_group_clear_finish(EC_GROUP *);
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int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
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int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
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int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
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int ec_GFp_simple_group_get_degree(const EC_GROUP *);
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int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
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int ec_GFp_simple_point_init(EC_POINT *);
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void ec_GFp_simple_point_finish(EC_POINT *);
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void ec_GFp_simple_point_clear_finish(EC_POINT *);
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int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
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int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
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int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
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int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
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BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
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int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
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const BIGNUM *x, const BIGNUM *y, BN_CTX *);
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int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
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|
|
BIGNUM *x, BIGNUM *y, BN_CTX *);
|
||
|
|
int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
|
||
|
|
const BIGNUM *x, int y_bit, BN_CTX *);
|
||
|
|
size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
|
||
|
|
unsigned char *buf, size_t len, BN_CTX *);
|
||
|
|
int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
|
||
|
|
const unsigned char *buf, size_t len, BN_CTX *);
|
||
|
|
int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
|
||
|
|
int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
|
||
|
|
int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
|
||
|
|
int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
|
||
|
|
int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
|
||
|
|
int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
|
||
|
|
|
||
|
|
/* method functions in ecp_mont.c */
|
||
|
|
int ec_GFp_mont_group_init(EC_GROUP *);
|
||
|
|
int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
void ec_GFp_mont_group_finish(EC_GROUP *);
|
||
|
|
void ec_GFp_mont_group_clear_finish(EC_GROUP *);
|
||
|
|
int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
|
||
|
|
int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
|
||
|
|
|
||
|
|
|
||
|
|
/* method functions in ecp_nist.c */
|
||
|
|
int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
|
||
|
|
int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
|
||
|
|
|
||
|
|
/* method functions in ec2_smpl.c */
|
||
|
|
int ec_GF2m_simple_group_init(EC_GROUP *);
|
||
|
|
void ec_GF2m_simple_group_finish(EC_GROUP *);
|
||
|
|
void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
|
||
|
|
int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
|
||
|
|
int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
|
||
|
|
int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_point_init(EC_POINT *);
|
||
|
|
void ec_GF2m_simple_point_finish(EC_POINT *);
|
||
|
|
void ec_GF2m_simple_point_clear_finish(EC_POINT *);
|
||
|
|
int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
|
||
|
|
int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
|
||
|
|
int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
|
||
|
|
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
|
||
|
|
BIGNUM *x, BIGNUM *y, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
|
||
|
|
const BIGNUM *x, int y_bit, BN_CTX *);
|
||
|
|
size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
|
||
|
|
unsigned char *buf, size_t len, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
|
||
|
|
const unsigned char *buf, size_t len, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
|
||
|
|
int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
|
||
|
|
int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
|
||
|
|
int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
|
||
|
|
|
||
|
|
|
||
|
|
/* method functions in ec2_mult.c */
|
||
|
|
int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
|
||
|
|
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
|
||
|
|
int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
|
||
|
|
int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
|