mbedtls/include/polarssl/ecp.h

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/**
* \file ecp.h
*
* \brief Elliptic curves over GF(p)
*
* Copyright (C) 2012, Brainspark B.V.
*
* This file is part of PolarSSL (http://www.polarssl.org)
* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
*
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#ifndef POLARSSL_ECP_H
#define POLARSSL_ECP_H
#include "bignum.h"
/*
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* ECP error codes
*
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* (Only one error code available...)
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*/
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#define POLARSSL_ERR_ECP_GENERIC -0x007E /**< Generic ECP error */
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/**
* \brief ECP point structure (jacobian coordinates)
*
* \note All functions expect and return points satisfying
* the following condition: Z == 0 or Z == 1. (Other
* values of Z are used by internal functions only.)
* The point is zero, or "at infinity", if Z == 0.
* Otherwise, X and Y are its standard (affine) coordinates.
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*/
typedef struct
{
mpi X; /*!< the point's X coordinate */
mpi Y; /*!< the point's Y coordinate */
mpi Z; /*!< the point's Z coordinate */
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}
ecp_point;
/**
* \brief ECP group structure
*
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* The curves we consider are defined by y^2 = x^3 - 3x + B mod P,
* and a generator for a large subgroup of order N is fixed.
*
* pbits and nbits must be the size of P and N in bits.
*
* If modp is NULL, reduction modulo P is done using a generic
* algorithm. Otherwise, it must point to a function that takes an mpi
* in the range 0..2^(2*pbits) and transforms it in-place in an integer
* of little more than pbits, so that the integer may be efficiently
* brought in the 0..P range by a few additions or substractions. It
* must return 0 on success and a POLARSSL_ERR_ECP_XXX error on failure.
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*/
typedef struct
{
mpi P; /*!< prime modulus of the base field */
mpi B; /*!< constant term in the equation */
ecp_point G; /*!< generator of the subgroup used */
mpi N; /*!< the order of G */
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size_t pbits; /*!< number of bits in P */
size_t nbits; /*!< number of bits in N */
int (*modp)(mpi *); /*!< function for fast reduction mod P */
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}
ecp_group;
/**
* RFC 5114 defines a number of standardized ECP groups for use with TLS.
*
* These also are the NIST-recommended ECP groups, are the random ECP groups
* recommended by SECG, and include the two groups used by NSA Suite B.
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* There are known as secpLLLr1 with LLL = 192, 224, 256, 384, 521.
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*
* \warning This library does not support validation of arbitrary domain
* parameters. Therefore, only well-known domain parameters from trusted
* sources should be used. See ecp_use_known_dp().
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*/
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#define POLARSSL_ECP_DP_SECP192R1 0
#define POLARSSL_ECP_DP_SECP224R1 1
#define POLARSSL_ECP_DP_SECP256R1 2
#define POLARSSL_ECP_DP_SECP384R1 3
#define POLARSSL_ECP_DP_SECP521R1 4
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#ifdef __cplusplus
extern "C" {
#endif
/**
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* \brief Initialize a point (as zero)
*/
void ecp_point_init( ecp_point *pt );
/**
* \brief Initialize a group (to something meaningless)
*/
void ecp_group_init( ecp_group *grp );
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/**
* \brief Free the components of a point
*/
void ecp_point_free( ecp_point *pt );
/**
* \brief Free the components of an ECP group
*/
void ecp_group_free( ecp_group *grp );
/**
* \brief Set a point to zero
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int ecp_set_zero( ecp_point *pt );
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/**
* \brief Copy the contents of point Q into P
*
* \param P Destination point
* \param Q Source point
*
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* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
int ecp_copy( ecp_point *P, const ecp_point *Q );
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/**
* \brief Import a non-zero point from two ASCII strings
*
* \param P Destination point
* \param radix Input numeric base
* \param x First affine coordinate as a null-terminated string
* \param y Second affine coordinate as a null-terminated string
*
* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
*/
int ecp_point_read_string( ecp_point *P, int radix,
const char *x, const char *y );
/**
* \brief Import an ECP group from null-terminated ASCII strings
*
* \param grp Destination group
* \param radix Input numeric base
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* \param p Prime modulus of the base field
* \param b Constant term in the equation
* \param gx The generator's X coordinate
* \param gy The generator's Y coordinate
* \param n The generator's order
*
* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
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*
* \note Sets all fields except modp.
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*/
int ecp_group_read_string( ecp_group *grp, int radix,
const char *p, const char *b,
const char *gx, const char *gy, const char *n);
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/**
* \brief Set a group using well-known domain parameters
*
* \param grp Destination group
* \param index Index in the list of well-known domain parameters
*
* \return O if successful,
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* POLARSSL_ERR_MPI_XXX if initialization failed
* POLARSSL_ERR_ECP_GENERIC if index is out of range
*
* \note Index should be a POLARSSL_ECP_DP_XXX macro.
*/
int ecp_use_known_dp( ecp_group *grp, size_t index );
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/**
* \brief Addition: R = P + Q
*
* \param grp ECP group
* \param R Destination point
* \param P Left-hand point
* \param Q Right-hand point
*
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* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
int ecp_add( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q );
/**
* \brief Multiplication by an integer: R = m * P
*
* \param grp ECP group
* \param R Destination point
* \param m Integer by which to multiply
* \param P Point to multiply
*
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* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
* POLARSSL_ERR_ECP_GENERIC if m < 0
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*/
int ecp_mul( const ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P );
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/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int ecp_self_test( int verbose );
#ifdef __cplusplus
}
#endif
#endif