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/* crypto/ec/ec_lcl.h */
/* ====================================================================
* Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include <stdlib.h>
#include <openssl/ec.h>
/* Structure details are not part of the exported interface,
* so all this may change in future versions. */
struct ec_method_st {
/* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
int (*group_init)(EC_GROUP *);
void (*group_finish)(EC_GROUP *);
void (*group_clear_finish)(EC_GROUP *);
int (*group_copy)(EC_GROUP *, const EC_GROUP *);
/* used by EC_GROUP_set_curve_GFp and EC_GROUP_get_curve_GFp: */
int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*group_get_curve_GFp)(EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
/* used by EC_GROUP_set_generator, EC_group_get0_generator,
* EC_GROUP_get_order, EC_GROUP_get_cofactor:
*/
int (*group_set_generator)(EC_GROUP *, const EC_POINT *generator,
const BIGNUM *order, const BIGNUM *cofactor);
EC_POINT *(*group_get0_generator)(EC_GROUP *);
int (*group_get_order)(EC_GROUP *, BIGNUM *order, BN_CTX *);
int (*group_get_cofactor)(EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
/* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
int (*point_init)(EC_POINT *);
void (*point_finish)(EC_POINT *);
void (*point_clear_finish)(EC_POINT *);
int (*point_copy)(EC_POINT *, const EC_POINT *);
/* used by EC_POINT_set_to_infinity,
* EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_get_Jprojective_coordinates_GFp,
* EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp,
* EC_POINT_set_compressed_coordinates_GFp:
*/
int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
int (*point_set_affine_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int (*point_get_affine_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int (*point_set_compressed_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
/* used by EC_POINT_point2oct, EC_POINT_oct2point: */
size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *);
int (*oct2point)(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
/* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
/* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
/* used by EC_POINT_make_affine: */
int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
/* internal functions */
/* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that
* the same implementations of point operations can be used with different
* optimized implementations of expensive field operations: */
int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
} /* EC_METHOD */;
struct ec_group_st {
const EC_METHOD *meth;
void *extra_data;
void *(*extra_data_dup_func)(void *);
void (*extra_data_free_func)(void *);
void (*extra_data_clear_free_func)(void *);
/* All members except 'meth' and 'extra_data...' are handled by
* the method functions, even if they appear generic */
BIGNUM field; /* Field specification.
* For curves over GF(p), this is the modulus. */
BIGNUM a, b; /* Curve coefficients.
* (Here the assumption is that BIGNUMs can be used
* or abused for all kinds of fields, not just GF(p).)
* For characteristic > 3, the curve is defined
* by a Weierstrass equation of the form
* y^2 = x^3 + a*x + b.
*/
int a_is_minus3; /* enable optimized point arithmetics for special case */
EC_POINT *generator; /* optional */
BIGNUM order, cofactor;
void *field_data; /* method-specific (e.g., Montgomery structure) */
} /* EC_GROUP */;
/* Basically a 'mixin' for extra data, but available for EC_GROUPs only
* (with visibility limited to 'package' level for now).
* We use the function pointers as index for retrieval; this obviates
* global ex_data-style index tables.
* (Currently, we have one slot only, but is is possible to extend this
* if necessary.) */
int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
void *EC_GROUP_get_extra_data(EC_GROUP *, void *(*extra_data_dup_func)(void *),
void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
void EC_GROUP_free_extra_data(EC_GROUP *);
void EC_GROUP_clear_free_extra_data(EC_GROUP *);
struct ec_point_st {
const EC_METHOD *meth;
/* All members except 'meth' are handled by the method functions,
* even if they appear generic */
BIGNUM X;
BIGNUM Y;
BIGNUM Z; /* Jacobian projective coordinates:
* (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
int Z_is_one; /* enable optimized point arithmetics for special case */
} /* EC_POINT */;
/* method functions in ecp_smpl.c */
int ec_GFp_simple_group_init(EC_GROUP *);
void ec_GFp_simple_group_finish(EC_GROUP *);
void ec_GFp_simple_group_clear_finish(EC_GROUP *);
int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_curve_GFp(EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_set_generator(EC_GROUP *, const EC_POINT *generator,
const BIGNUM *order, const BIGNUM *cofactor);
EC_POINT *ec_GFp_simple_group_get0_generator(EC_GROUP *);
int ec_GFp_simple_group_get_order(EC_GROUP *, BIGNUM *order, BN_CTX *);
int ec_GFp_simple_group_get_cofactor(EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
int ec_GFp_simple_point_init(EC_POINT *);
void ec_GFp_simple_point_finish(EC_POINT *);
void ec_GFp_simple_point_clear_finish(EC_POINT *);
int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int ec_GFp_simple_set_compressed_coordinates_GFp(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_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_GFp(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 *);
/* method functions in ecp_recp.c */
int ec_GFp_recp_group_init(EC_GROUP *);
int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
void ec_GFp_recp_group_finish(EC_GROUP *);
void ec_GFp_recp_group_clear_finish(EC_GROUP *);
int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
/* method functions in ecp_nist.c */
int ec_GFp_nist_group_init(EC_GROUP *);
int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
void ec_GFp_nist_group_finish(EC_GROUP *);
void ec_GFp_nist_group_clear_finish(EC_GROUP *);
int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
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 *);
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