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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"
/*
* ECP error codes
*
* (Only one error code available...)
*/
#define POLARSSL_ERR_ECP_GENERIC -0x007E /**< Generic ECP error */
/**
* \brief ECP point structure (affine coordinates)
*
* Note: if the point is zero, X and Y are irrelevant and should be freed.
*/
typedef struct
{
char is_zero; /*!< true if point at infinity */
mpi X; /*!< the point's X coordinate */
mpi Y; /*!< the point's Y coordinate */
}
ecp_point;
/**
* \brief ECP group structure
*
* The curves we consider are defined by y^2 = x^3 - 3x + b mod p,
* and a generator for a large subgroup is fixed.
*/
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 */
}
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.
* There are known as secpLLLr1 with LLL = 192, 224, 256, 384, 521.
*
* \warning This library does not support validation of arbitrary domain
* parameters. Therefore, only well-known domain parameters from trusted
* sources (such as the ones below) should be used.
*/
#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
#define POLARSSL_ECP_SECP192R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"
#define POLARSSL_ECP_SECP192R1_B \
"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
#define POLARSSL_ECP_SECP192R1_GX \
"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
#define POLARSSL_ECP_SECP192R1_GY \
"07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
#define POLARSSL_ECP_SECP192R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"
#define POLARSSL_ECP_SECP224R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"
#define POLARSSL_ECP_SECP224R1_B \
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
#define POLARSSL_ECP_SECP224R1_GX \
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
#define POLARSSL_ECP_SECP224R1_GY \
"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
#define POLARSSL_ECP_SECP224R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"
#define POLARSSL_ECP_SECP256R1_P \
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"
#define POLARSSL_ECP_SECP256R1_B \
"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"
#define POLARSSL_ECP_SECP256R1_GX \
"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
#define POLARSSL_ECP_SECP256R1_GY \
"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"
#define POLARSSL_ECP_SECP256R1_N \
"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"
#define POLARSSL_ECP_SECP384R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"
#define POLARSSL_ECP_SECP384R1_B \
"B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \
"0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"
#define POLARSSL_ECP_SECP384R1_GX \
"AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \
"59F741E082542A385502F25DBF55296C3A545E3872760AB7"
#define POLARSSL_ECP_SECP384R1_GY \
"3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \
"E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"
#define POLARSSL_ECP_SECP384R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"
#define POLARSSL_ECP_SECP521R1_P \
"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
#define POLARSSL_ECP_SECP521R1_B \
"00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \
"99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \
"3BB1BF073573DF883D2C34F1EF451FD46B503F00"
#define POLARSSL_ECP_SECP521R1_GX \
"000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \
"053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \
"A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
#define POLARSSL_ECP_SECP521R1_GY \
"0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \
"579B446817AFBD17273E662C97EE72995EF42640C550B901" \
"3FAD0761353C7086A272C24088BE94769FD16650"
#define POLARSSL_ECP_SECP521R1_N \
"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \
"F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
#ifdef __cplusplus
extern "C" {
#endif
/**
* \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 );
/**
* \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
*/
void ecp_set_zero( ecp_point *pt );
/**
* \brief Copy the contents of point Q into P
*
* \param P Destination point
* \param Q Source point
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int ecp_copy( ecp_point *P, const ecp_point *Q );
/**
* \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
* \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
*/
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);
/**
* \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 successul,
* 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 );
/**
* \brief Addition: R = P + Q
*
* \param grp ECP group
* \param R Destination point
* \param P Left-hand point
* \param Q Right-hand point
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO (shouldn't happen)
* (temporary, a faster version not using division will be
* used in the future)
*/
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
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO (shouldn't happen)
* (temporary, a faster version not using division will be
* used in the future)
*/
int ecp_mul( const ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P );
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int ecp_self_test( int verbose );
#ifdef __cplusplus
}
#endif
#endif