/* crypto/ec/ec_lcl.h */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2010 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).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
#include <stdlib.h>
#include <openssl/obj_mac.h>
#include <openssl/ec.h>
#include <openssl/bn.h>
#if defined(__SUNPRO_C)
# if __SUNPRO_C >= 0x520
# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
# endif
#endif
/* Use default functions for poin2oct, oct2point and compressed coordinates */
#define EC_FLAGS_DEFAULT_OCT 0x1
/* Structure details are not part of the exported interface,
* so all this may change in future versions. */
struct ec_method_st {
/* Various method flags */
int flags;
/* used by EC_METHOD_get_field_type: */
int field_type; /* a NID */
/* 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, EC_GROUP_get_curve_GFp, */
/* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
/* used by EC_GROUP_get_degree: */
int (*group_get_degree)(const EC_GROUP *);
/* used by EC_GROUP_check: */
int (*group_check_discriminant)(const EC_GROUP *, 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, ..._GF2m,
* EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
* EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
*/
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)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int (*point_set_compressed_coordinates)(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, EC_POINTs_make_affine: */
int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
* (default implementations are used if the 'mul' pointer is 0): */
int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
int (*have_precompute_mult)(const EC_GROUP *group);
/* internal functions */
/* 'field_mul', 'field_sqr', and 'field_div' 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_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 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 */
int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
} /* EC_METHOD */;
typedef struct ec_extra_data_st {
struct ec_extra_data_st *next;
void *data;
void *(*dup_func)(void *);
void (*free_func)(void *);
void (*clear_free_func)(void *);
} EC_EXTRA_DATA; /* used in EC_GROUP */
struct ec_group_st {
const EC_METHOD *meth;
EC_POINT *generator; /* optional */
BIGNUM order, cofactor;
int curve_name;/* optional NID for named curve */
int asn1_flag; /* flag to control the asn1 encoding */
point_conversion_form_t asn1_form;
unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
size_t seed_len;
EC_EXTRA_DATA *extra_data; /* linked list */
/* The following members are handled by the method functions,
* even if they appear generic */
BIGNUM field; /* Field specification.
* For curves over GF(p), this is the modulus;
* for curves over GF(2^m), this is the
* irreducible polynomial defining the field.
*/
int poly[6]; /* Field specification for curves over GF(2^m).
* The irreducible f(t) is then of the form:
* t^poly[0] + t^poly[1] + ... + t^poly[k]
* where m = poly[0] > poly[1] > ... > poly[k] = 0.
* The array is terminated with poly[k+1]=-1.
* All elliptic curve irreducibles have at most 5
* non-zero terms.
*/
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.
* For characteristic 2, the curve is defined by
* an equation of the form
* y^2 + x*y = x^3 + a*x^2 + b.
*/
int a_is_minus3; /* enable optimized point arithmetics for special case */
void *field_data1; /* method-specific (e.g., Montgomery structure) */
void *field_data2; /* method-specific */
int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
} /* EC_GROUP */;
struct ec_key_st {
int version;
EC_GROUP *group;
EC_POINT *pub_key;
BIGNUM *priv_key;
unsigned int enc_flag;
point_conversion_form_t conv_form;
int references;
int flags;
EC_EXTRA_DATA *method_data;
} /* EC_KEY */;
/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs 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.
*/
int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
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 ec_mult.c
* (ec_lib.c uses these as defaults if group->method->mul is 0) */
int ec_wNAF_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_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
/* 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(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_degree(const EC_GROUP *);
int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, 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(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
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);
/* 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);
#ifndef OPENSSL_EC_NISTP_64_GCC_128
/* method functions in ecp_nistp224.c */
int ec_GFp_nistp224_group_init(EC_GROUP *group);
int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp224_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_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
/* method functions in ecp_nistp256.c */
int ec_GFp_nistp256_group_init(EC_GROUP *group);
int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp256_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_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
/* method functions in ecp_nistp521.c */
int ec_GFp_nistp521_group_init(EC_GROUP *group);
int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp521_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_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
/* utility functions in ecp_nistputil.c */
void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
size_t felem_size, void *tmp_felems,
void (*felem_one)(void *out),
int (*felem_is_zero)(const void *in),
void (*felem_assign)(void *out, const void *in),
void (*felem_square)(void *out, const void *in),
void (*felem_mul)(void *out, const void *in1, const void *in2),
void (*felem_inv)(void *out, const void *in),
void (*felem_contract)(void *out, const void *in));
void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
#endif