ec.h

/* crypto/ec/ec.h */
/*
 * Originally written by Bodo Moeller for the OpenSSL project.
 */
/**
 * \file crypto/ec/ec.h Include file for the OpenSSL EC functions
 * \author Originally written by Bodo Moeller for the OpenSSL project
 */
/* ====================================================================
 * Copyright (c) 1998-2005 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.
 *
 */

#ifndef HEADER_EC_H
#define HEADER_EC_H

#include <openssl/opensslconf.h>

#ifdef OPENSSL_NO_EC
#error EC is disabled.
#endif

#include <openssl/asn1.h>
#include <openssl/symhacks.h>
#ifndef OPENSSL_NO_DEPRECATED
#include <openssl/bn.h>
#endif

#ifdef  __cplusplus
extern "C" {
#elif defined(__SUNPRO_C)
# if __SUNPRO_C >= 0x520
# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
# endif
#endif

  
#ifndef OPENSSL_ECC_MAX_FIELD_BITS
# define OPENSSL_ECC_MAX_FIELD_BITS 661
#endif

/** Enum for the point conversion form as defined in X9.62 (ECDSA)
 *  for the encoding of a elliptic curve point (x,y) */
typedef enum {
	/** the point is encoded as z||x, where the octet z specifies 
	 *  which solution of the quadratic equation y is  */
	POINT_CONVERSION_COMPRESSED = 2,
	/** the point is encoded as z||x||y, where z is the octet 0x02  */
	POINT_CONVERSION_UNCOMPRESSED = 4,
	/** the point is encoded as z||x||y, where the octet z specifies
         *  which solution of the quadratic equation y is  */
	POINT_CONVERSION_HYBRID = 6
} point_conversion_form_t;


typedef struct ec_method_st EC_METHOD;

typedef struct ec_group_st
	/*
	 EC_METHOD *meth;
	 -- field definition
	 -- curve coefficients
	 -- optional generator with associated information (order, cofactor)
	 -- optional extra data (precomputed table for fast computation of multiples of generator)
	 -- ASN1 stuff
	*/
	EC_GROUP;

typedef struct ec_point_st EC_POINT;


/********************************************************************/
/*               EC_METHODs for curves over GF(p)                   */       
/********************************************************************/

/** Returns the basic GFp ec methods which provides the basis for the
 *  optimized methods. 
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_simple_method(void);

/** Returns GFp methods using montgomery multiplication.
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_mont_method(void);

/** Returns GFp methods using optimized methods for NIST recommended curves
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_nist_method(void);

#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
/** Returns 64-bit optimized methods for nistp224
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_nistp224_method(void);

/** Returns 64-bit optimized methods for nistp256
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_nistp256_method(void);

/** Returns 64-bit optimized methods for nistp521
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GFp_nistp521_method(void);
#endif

#ifndef OPENSSL_NO_EC2M
/********************************************************************/ 
/*           EC_METHOD for curves over GF(2^m)                      */
/********************************************************************/

/** Returns the basic GF2m ec method 
 *  \return  EC_METHOD object
 */
const EC_METHOD *EC_GF2m_simple_method(void);

#endif


/********************************************************************/
/*                   EC_GROUP functions                             */
/********************************************************************/

/** Creates a new EC_GROUP object
 *  \param   meth  EC_METHOD to use
 *  \return  newly created EC_GROUP object or NULL in case of an error.
 */
EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);

/** Frees a EC_GROUP object
 *  \param  group  EC_GROUP object to be freed.
 */
void EC_GROUP_free(EC_GROUP *group);

/** Clears and frees a EC_GROUP object
 *  \param  group  EC_GROUP object to be cleared and freed.
 */
void EC_GROUP_clear_free(EC_GROUP *group);

/** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
 *  \param  dst  destination EC_GROUP object
 *  \param  src  source EC_GROUP object
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);

/** Creates a new EC_GROUP object and copies the copies the content
 *  form src to the newly created EC_KEY object
 *  \param  src  source EC_GROUP object
 *  \return newly created EC_GROUP object or NULL in case of an error.
 */
EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);

/** Returns the EC_METHOD of the EC_GROUP object.
 *  \param  group  EC_GROUP object 
 *  \return EC_METHOD used in this EC_GROUP object.
 */
const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);

/** Returns the field type of the EC_METHOD.
 *  \param  meth  EC_METHOD object
 *  \return NID of the underlying field type OID.
 */
int EC_METHOD_get_field_type(const EC_METHOD *meth);

/** Sets the generator and it's order/cofactor of a EC_GROUP object.
 *  \param  group      EC_GROUP object 
 *  \param  generator  EC_POINT object with the generator.
 *  \param  order      the order of the group generated by the generator.
 *  \param  cofactor   the index of the sub-group generated by the generator
 *                     in the group of all points on the elliptic curve.
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);

/** Returns the generator of a EC_GROUP object.
 *  \param  group  EC_GROUP object
 *  \return the currently used generator (possibly NULL).
 */
const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);

/** Gets the order of a EC_GROUP
 *  \param  group  EC_GROUP object
 *  \param  order  BIGNUM to which the order is copied
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);

/** Gets the cofactor of a EC_GROUP
 *  \param  group     EC_GROUP object
 *  \param  cofactor  BIGNUM to which the cofactor is copied
 *  \param  ctx       BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);

/** Sets the name of a EC_GROUP object
 *  \param  group  EC_GROUP object
 *  \param  nid    NID of the curve name OID
 */
void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);

/** Returns the curve name of a EC_GROUP object
 *  \param  group  EC_GROUP object
 *  \return NID of the curve name OID or 0 if not set.
 */
int EC_GROUP_get_curve_name(const EC_GROUP *group);

void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);

unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
size_t EC_GROUP_get_seed_len(const EC_GROUP *);
size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);

/** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b
 *  \param  group  EC_GROUP object
 *  \param  p      BIGNUM with the prime number
 *  \param  a      BIGNUM with parameter a of the equation
 *  \param  b      BIGNUM with parameter b of the equation
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

/** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b
 *  \param  group  EC_GROUP object
 *  \param  p      BIGNUM for the prime number
 *  \param  a      BIGNUM for parameter a of the equation
 *  \param  b      BIGNUM for parameter b of the equation
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

#ifndef OPENSSL_NO_EC2M
/** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
 *  \param  group  EC_GROUP object
 *  \param  p      BIGNUM with the polynomial defining the underlying field
 *  \param  a      BIGNUM with parameter a of the equation
 *  \param  b      BIGNUM with parameter b of the equation
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

/** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b
 *  \param  group  EC_GROUP object
 *  \param  p      BIGNUM for the polynomial defining the underlying field
 *  \param  a      BIGNUM for parameter a of the equation
 *  \param  b      BIGNUM for parameter b of the equation
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
#endif
/** Returns the number of bits needed to represent a field element 
 *  \param  group  EC_GROUP object
 *  \return number of bits needed to represent a field element
 */
int EC_GROUP_get_degree(const EC_GROUP *group);

/** Checks whether the parameter in the EC_GROUP define a valid ec group
 *  \param  group  EC_GROUP object
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 if group is a valid ec group and 0 otherwise
 */
int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);

/** Checks whether the discriminant of the elliptic curve is zero or not
 *  \param  group  EC_GROUP object
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 if the discriminant is not zero and 0 otherwise
 */
int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);

/** Compares two EC_GROUP objects
 *  \param  a    first EC_GROUP object
 *  \param  b    second EC_GROUP object
 *  \param  ctx  BN_CTX object (optional)
 *  \return 0 if both groups are equal and 1 otherwise
 */
int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);

/* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*()
 * after choosing an appropriate EC_METHOD */

/** Creates a new EC_GROUP object with the specified parameters defined
 *  over GFp (defined by the equation y^2 = x^3 + a*x + b)
 *  \param  p    BIGNUM with the prime number
 *  \param  a    BIGNUM with the parameter a of the equation
 *  \param  b    BIGNUM with the parameter b of the equation
 *  \param  ctx  BN_CTX object (optional)
 *  \return newly created EC_GROUP object with the specified parameters
 */
EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
#ifndef OPENSSL_NO_EC2M
/** Creates a new EC_GROUP object with the specified parameters defined
 *  over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
 *  \param  p    BIGNUM with the polynomial defining the underlying field
 *  \param  a    BIGNUM with the parameter a of the equation
 *  \param  b    BIGNUM with the parameter b of the equation
 *  \param  ctx  BN_CTX object (optional)
 *  \return newly created EC_GROUP object with the specified parameters
 */
EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
#endif
/** Creates a EC_GROUP object with a curve specified by a NID
 *  \param  nid  NID of the OID of the curve name
 *  \return newly created EC_GROUP object with specified curve or NULL
 *          if an error occurred
 */
EC_GROUP *EC_GROUP_new_by_curve_name(int nid);


/********************************************************************/
/*               handling of internal curves                        */
/********************************************************************/

typedef struct { 
	int nid;
	const char *comment;
	} EC_builtin_curve;

/* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number 
 * of all available curves or zero if a error occurred. 
 * In case r ist not zero nitems EC_builtin_curve structures 
 * are filled with the data of the first nitems internal groups */
size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);


/********************************************************************/
/*                    EC_POINT functions                            */
/********************************************************************/

/** Creates a new EC_POINT object for the specified EC_GROUP
 *  \param  group  EC_GROUP the underlying EC_GROUP object
 *  \return newly created EC_POINT object or NULL if an error occurred
 */
EC_POINT *EC_POINT_new(const EC_GROUP *group);

/** Frees a EC_POINT object
 *  \param  point  EC_POINT object to be freed
 */
void EC_POINT_free(EC_POINT *point);

/** Clears and frees a EC_POINT object
 *  \param  point  EC_POINT object to be cleared and freed
 */
void EC_POINT_clear_free(EC_POINT *point);

/** Copies EC_POINT object
 *  \param  dst  destination EC_POINT object
 *  \param  src  source EC_POINT object
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);

/** Creates a new EC_POINT object and copies the content of the supplied
 *  EC_POINT
 *  \param  src    source EC_POINT object
 *  \param  group  underlying the EC_GROUP object
 *  \return newly created EC_POINT object or NULL if an error occurred 
 */
EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
 
/** Returns the EC_METHOD used in EC_POINT object 
 *  \param  point  EC_POINT object
 *  \return the EC_METHOD used
 */
const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);

/** Sets a point to infinity (neutral element)
 *  \param  group  underlying EC_GROUP object
 *  \param  point  EC_POINT to set to infinity
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);

/** Sets the jacobian projective coordinates of a EC_POINT over GFp
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM with the x-coordinate
 *  \param  y      BIGNUM with the y-coordinate
 *  \param  z      BIGNUM with the z-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
	const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);

/** Gets the jacobian projective coordinates of a EC_POINT over GFp
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM for the x-coordinate
 *  \param  y      BIGNUM for the y-coordinate
 *  \param  z      BIGNUM for the z-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
	const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);

/** Sets the affine coordinates of a EC_POINT over GFp
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM with the x-coordinate
 *  \param  y      BIGNUM with the y-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);

/** Gets the affine coordinates of a EC_POINT over GFp
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM for the x-coordinate
 *  \param  y      BIGNUM for the y-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
	const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);

/** Sets the x9.62 compressed coordinates of a EC_POINT over GFp
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM with x-coordinate
 *  \param  y_bit  integer with the y-Bit (either 0 or 1)
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
	const BIGNUM *x, int y_bit, BN_CTX *ctx);
#ifndef OPENSSL_NO_EC2M
/** Sets the affine coordinates of a EC_POINT over GF2m
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM with the x-coordinate
 *  \param  y      BIGNUM with the y-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);

/** Gets the affine coordinates of a EC_POINT over GF2m
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM for the x-coordinate
 *  \param  y      BIGNUM for the y-coordinate
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
	const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);

/** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  x      BIGNUM with x-coordinate
 *  \param  y_bit  integer with the y-Bit (either 0 or 1)
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
	const BIGNUM *x, int y_bit, BN_CTX *ctx);
#endif
/** Encodes a EC_POINT object to a octet string
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  form   point conversion form
 *  \param  buf    memory buffer for the result. If NULL the function returns
 *                 required buffer size.
 *  \param  len    length of the memory buffer
 *  \param  ctx    BN_CTX object (optional)
 *  \return the length of the encoded octet string or 0 if an error occurred
 */
size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
	point_conversion_form_t form,
        unsigned char *buf, size_t len, BN_CTX *ctx);

/** Decodes a EC_POINT from a octet string
 *  \param  group  underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \param  buf    memory buffer with the encoded ec point
 *  \param  len    length of the encoded ec point
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
        const unsigned char *buf, size_t len, BN_CTX *ctx);

/* other interfaces to point2oct/oct2point: */
BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
	point_conversion_form_t form, BIGNUM *, BN_CTX *);
EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
	EC_POINT *, BN_CTX *);
char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
	point_conversion_form_t form, BN_CTX *);
EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
	EC_POINT *, BN_CTX *);


/********************************************************************/
/*         functions for doing EC_POINT arithmetic                  */
/********************************************************************/

/** Computes the sum of two EC_POINT 
 *  \param  group  underlying EC_GROUP object
 *  \param  r      EC_POINT object for the result (r = a + b)
 *  \param  a      EC_POINT object with the first summand
 *  \param  b      EC_POINT object with the second summand
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);

/** Computes the double of a EC_POINT
 *  \param  group  underlying EC_GROUP object
 *  \param  r      EC_POINT object for the result (r = 2 * a)
 *  \param  a      EC_POINT object 
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);

/** Computes the inverse of a EC_POINT
 *  \param  group  underlying EC_GROUP object
 *  \param  a      EC_POINT object to be inverted (it's used for the result as well)
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);

/** Checks whether the point is the neutral element of the group
 *  \param  group  the underlying EC_GROUP object
 *  \param  p      EC_POINT object
 *  \return 1 if the point is the neutral element and 0 otherwise
 */
int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);

/** Checks whether the point is on the curve 
 *  \param  group  underlying EC_GROUP object
 *  \param  point  EC_POINT object to check
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 if point if on the curve and 0 otherwise
 */
int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);

/** Compares two EC_POINTs 
 *  \param  group  underlying EC_GROUP object
 *  \param  a      first EC_POINT object
 *  \param  b      second EC_POINT object
 *  \param  ctx    BN_CTX object (optional)
 *  \return 0 if both points are equal and a value != 0 otherwise
 */
int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);

int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx);

/** Computes r = generator * n sum_{i=0}^{num-1} p[i] * m[i]
 *  \param  group  underlying EC_GROUP object
 *  \param  r      EC_POINT object for the result
 *  \param  n      BIGNUM with the multiplier for the group generator (optional)
 *  \param  num    number futher summands
 *  \param  p      array of size num of EC_POINT objects
 *  \param  m      array of size num of BIGNUM objects
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);

/** Computes r = generator * n + q * m
 *  \param  group  underlying EC_GROUP object
 *  \param  r      EC_POINT object for the result
 *  \param  n      BIGNUM with the multiplier for the group generator (optional)
 *  \param  q      EC_POINT object with the first factor of the second summand
 *  \param  m      BIGNUM with the second factor of the second summand
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);

/** Stores multiples of generator for faster point multiplication
 *  \param  group  EC_GROUP object
 *  \param  ctx    BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occured
 */
int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);

/** Reports whether a precomputation has been done
 *  \param  group  EC_GROUP object
 *  \return 1 if a pre-computation has been done and 0 otherwise
 */
int EC_GROUP_have_precompute_mult(const EC_GROUP *group);


/********************************************************************/
/*                       ASN1 stuff                                 */
/********************************************************************/

/* EC_GROUP_get_basis_type() returns the NID of the basis type
 * used to represent the field elements */
int EC_GROUP_get_basis_type(const EC_GROUP *);
#ifndef OPENSSL_NO_EC2M
int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, 
	unsigned int *k2, unsigned int *k3);
#endif

#define OPENSSL_EC_NAMED_CURVE	0x001

typedef struct ecpk_parameters_st ECPKPARAMETERS;

EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);

#define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
#define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
#define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
                (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
#define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
		(unsigned char *)(x))

#ifndef OPENSSL_NO_BIO
int     ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
#endif
#ifndef OPENSSL_NO_FP_API
int     ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
#endif


/********************************************************************/
/*                      EC_KEY functions                            */
/********************************************************************/

typedef struct ec_key_st EC_KEY;

/* some values for the encoding_flag */
#define EC_PKEY_NO_PARAMETERS	0x001
#define EC_PKEY_NO_PUBKEY	0x002

/* some values for the flags field */
#define EC_FLAG_NON_FIPS_ALLOW	0x1
#define EC_FLAG_FIPS_CHECKED	0x2

/** Creates a new EC_KEY object.
 *  \return EC_KEY object or NULL if an error occurred.
 */
EC_KEY *EC_KEY_new(void);

int EC_KEY_get_flags(const EC_KEY *key);

void EC_KEY_set_flags(EC_KEY *key, int flags);

void EC_KEY_clear_flags(EC_KEY *key, int flags);

/** Creates a new EC_KEY object using a named curve as underlying
 *  EC_GROUP object.
 *  \param  nid  NID of the named curve.
 *  \return EC_KEY object or NULL if an error occurred. 
 */
EC_KEY *EC_KEY_new_by_curve_name(int nid);

/** Frees a EC_KEY object.
 *  \param  key  EC_KEY object to be freed.
 */
void EC_KEY_free(EC_KEY *key);

/** Copies a EC_KEY object.
 *  \param  dst  destination EC_KEY object
 *  \param  src  src EC_KEY object
 *  \return dst or NULL if an error occurred.
 */
EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);

/** Creates a new EC_KEY object and copies the content from src to it.
 *  \param  src  the source EC_KEY object
 *  \return newly created EC_KEY object or NULL if an error occurred.
 */
EC_KEY *EC_KEY_dup(const EC_KEY *src);

/** Increases the internal reference count of a EC_KEY object.
 *  \param  key  EC_KEY object
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_up_ref(EC_KEY *key);

/** Returns the EC_GROUP object of a EC_KEY object
 *  \param  key  EC_KEY object
 *  \return the EC_GROUP object (possibly NULL).
 */
const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);

/** Sets the EC_GROUP of a EC_KEY object.
 *  \param  key    EC_KEY object
 *  \param  group  EC_GROUP to use in the EC_KEY object (note: the EC_KEY
 *                 object will use an own copy of the EC_GROUP).
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);

/** Returns the private key of a EC_KEY object.
 *  \param  key  EC_KEY object
 *  \return a BIGNUM with the private key (possibly NULL).
 */
const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);

/** Sets the private key of a EC_KEY object.
 *  \param  key  EC_KEY object
 *  \param  prv  BIGNUM with the private key (note: the EC_KEY object
 *               will use an own copy of the BIGNUM).
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);

/** Returns the public key of a EC_KEY object.
 *  \param  key  the EC_KEY object
 *  \return a EC_POINT object with the public key (possibly NULL)
 */
const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);

/** Sets the public key of a EC_KEY object.
 *  \param  key  EC_KEY object
 *  \param  pub  EC_POINT object with the public key (note: the EC_KEY object
 *               will use an own copy of the EC_POINT object).
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);

unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
/* functions to set/get method specific data  */
void *EC_KEY_get_key_method_data(EC_KEY *key, 
	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
/** Sets the key method data of an EC_KEY object, if none has yet been set.
 *  \param  key              EC_KEY object
 *  \param  data             opaque data to install.
 *  \param  dup_func         a function that duplicates |data|.
 *  \param  free_func        a function that frees |data|.
 *  \param  clear_free_func  a function that wipes and frees |data|.
 *  \return the previously set data pointer, or NULL if |data| was inserted.
 */
void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
/* wrapper functions for the underlying EC_GROUP object */
void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);

/** Creates a table of pre-computed multiples of the generator to 
 *  accelerate further EC_KEY operations.
 *  \param  key  EC_KEY object
 *  \param  ctx  BN_CTX object (optional)
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);

/** Creates a new ec private (and optional a new public) key.
 *  \param  key  EC_KEY object
 *  \return 1 on success and 0 if an error occurred.
 */
int EC_KEY_generate_key(EC_KEY *key);

/** Verifies that a private and/or public key is valid.
 *  \param  key  the EC_KEY object
 *  \return 1 on success and 0 otherwise.
 */
int EC_KEY_check_key(const EC_KEY *key);

/** Sets a public key from affine coordindates performing
 *  neccessary NIST PKV tests.
 *  \param  key  the EC_KEY object
 *  \param  x    public key x coordinate
 *  \param  y    public key y coordinate
 *  \return 1 on success and 0 otherwise.
 */
int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y);


/********************************************************************/
/*        de- and encoding functions for SEC1 ECPrivateKey          */
/********************************************************************/

/** Decodes a private key from a memory buffer.
 *  \param  key  a pointer to a EC_KEY object which should be used (or NULL)
 *  \param  in   pointer to memory with the DER encoded private key
 *  \param  len  length of the DER encoded private key
 *  \return the decoded private key or NULL if an error occurred.
 */
EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);

/** Encodes a private key object and stores the result in a buffer.
 *  \param  key  the EC_KEY object to encode
 *  \param  out  the buffer for the result (if NULL the function returns number
 *               of bytes needed).
 *  \return 1 on success and 0 if an error occurred.
 */
int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);


/********************************************************************/
/*        de- and encoding functions for EC parameters              */
/********************************************************************/

/** Decodes ec parameter from a memory buffer.
 *  \param  key  a pointer to a EC_KEY object which should be used (or NULL)
 *  \param  in   pointer to memory with the DER encoded ec parameters
 *  \param  len  length of the DER encoded ec parameters
 *  \return a EC_KEY object with the decoded parameters or NULL if an error
 *          occurred.
 */
EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);

/** Encodes ec parameter and stores the result in a buffer.
 *  \param  key  the EC_KEY object with ec paramters to encode
 *  \param  out  the buffer for the result (if NULL the function returns number
 *               of bytes needed).
 *  \return 1 on success and 0 if an error occurred.
 */
int i2d_ECParameters(EC_KEY *key, unsigned char **out);


/********************************************************************/
/*         de- and encoding functions for EC public key             */
/*         (octet string, not DER -- hence 'o2i' and 'i2o')         */
/********************************************************************/

/** Decodes a ec public key from a octet string.
 *  \param  key  a pointer to a EC_KEY object which should be used
 *  \param  in   memory buffer with the encoded public key
 *  \param  len  length of the encoded public key
 *  \return EC_KEY object with decoded public key or NULL if an error
 *          occurred.
 */
EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);

/** Encodes a ec public key in an octet string.
 *  \param  key  the EC_KEY object with the public key
 *  \param  out  the buffer for the result (if NULL the function returns number
 *               of bytes needed).
 *  \return 1 on success and 0 if an error occurred
 */
int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);

#ifndef OPENSSL_NO_BIO
/** Prints out the ec parameters on human readable form.
 *  \param  bp   BIO object to which the information is printed
 *  \param  key  EC_KEY object
 *  \return 1 on success and 0 if an error occurred
 */
int	ECParameters_print(BIO *bp, const EC_KEY *key);

/** Prints out the contents of a EC_KEY object
 *  \param  bp   BIO object to which the information is printed
 *  \param  key  EC_KEY object
 *  \param  off  line offset 
 *  \return 1 on success and 0 if an error occurred
 */
int	EC_KEY_print(BIO *bp, const EC_KEY *key, int off);

#endif
#ifndef OPENSSL_NO_FP_API
/** Prints out the ec parameters on human readable form.
 *  \param  fp   file descriptor to which the information is printed
 *  \param  key  EC_KEY object
 *  \return 1 on success and 0 if an error occurred
 */
int	ECParameters_print_fp(FILE *fp, const EC_KEY *key);

/** Prints out the contents of a EC_KEY object
 *  \param  fp   file descriptor to which the information is printed
 *  \param  key  EC_KEY object
 *  \param  off  line offset 
 *  \return 1 on success and 0 if an error occurred
 */
int	EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);

#endif

#define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)

#ifndef __cplusplus
#if defined(__SUNPRO_C)
#  if __SUNPRO_C >= 0x520
# pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
#  endif
# endif
#endif

#define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
	EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \
				EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)


#define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID		(EVP_PKEY_ALG_CTRL + 1)

/* BEGIN ERROR CODES */
/* The following lines are auto generated by the script mkerr.pl. Any changes
 * made after this point may be overwritten when the script is next run.
 */
void ERR_load_EC_strings(void);

/* Error codes for the EC functions. */

/* Function codes. */
#define EC_F_BN_TO_FELEM				 224
#define EC_F_COMPUTE_WNAF				 143
#define EC_F_D2I_ECPARAMETERS				 144
#define EC_F_D2I_ECPKPARAMETERS				 145
#define EC_F_D2I_ECPRIVATEKEY				 146
#define EC_F_DO_EC_KEY_PRINT				 221
#define EC_F_ECKEY_PARAM2TYPE				 223
#define EC_F_ECKEY_PARAM_DECODE				 212
#define EC_F_ECKEY_PRIV_DECODE				 213
#define EC_F_ECKEY_PRIV_ENCODE				 214
#define EC_F_ECKEY_PUB_DECODE				 215
#define EC_F_ECKEY_PUB_ENCODE				 216
#define EC_F_ECKEY_TYPE2PARAM				 220
#define EC_F_ECPARAMETERS_PRINT				 147
#define EC_F_ECPARAMETERS_PRINT_FP			 148
#define EC_F_ECPKPARAMETERS_PRINT			 149
#define EC_F_ECPKPARAMETERS_PRINT_FP			 150
#define EC_F_ECP_NIST_MOD_192				 203
#define EC_F_ECP_NIST_MOD_224				 204
#define EC_F_ECP_NIST_MOD_256				 205
#define EC_F_ECP_NIST_MOD_521				 206
#define EC_F_EC_ASN1_GROUP2CURVE			 153
#define EC_F_EC_ASN1_GROUP2FIELDID			 154