350 lines
12 KiB
C
350 lines
12 KiB
C
/**
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* \file ecp.h
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*
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* \brief Elliptic curves over GF(p)
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*
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* Copyright (C) 2006-2013, Brainspark B.V.
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*
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* This file is part of PolarSSL (http://www.polarssl.org)
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* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
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*
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* All rights reserved.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#ifndef POLARSSL_ECP_H
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#define POLARSSL_ECP_H
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#include "polarssl/bignum.h"
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/*
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* ECP error codes
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*/
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#define POLARSSL_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */
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#define POLARSSL_ERR_ECP_GENERIC -0x4F00 /**< Generic ECP error */
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/**
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* \brief ECP point structure (jacobian coordinates)
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*
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* \note All functions expect and return points satisfying
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* the following condition: Z == 0 or Z == 1. (Other
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* values of Z are used by internal functions only.)
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* The point is zero, or "at infinity", if Z == 0.
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* Otherwise, X and Y are its standard (affine) coordinates.
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*/
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typedef struct
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{
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mpi X; /*!< the point's X coordinate */
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mpi Y; /*!< the point's Y coordinate */
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mpi Z; /*!< the point's Z coordinate */
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}
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ecp_point;
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/**
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* \brief ECP group structure
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*
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* The curves we consider are defined by y^2 = x^3 - 3x + B mod P,
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* and a generator for a large subgroup of order N is fixed.
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*
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* pbits and nbits must be the size of P and N in bits.
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*
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* If modp is NULL, reduction modulo P is done using a generic
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* algorithm. Otherwise, it must point to a function that takes an mpi
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* in the range 0..2^(2*pbits) and transforms it in-place in an integer
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* of little more than pbits, so that the integer may be efficiently
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* brought in the 0..P range by a few additions or substractions. It
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* must return 0 on success and a POLARSSL_ERR_ECP_XXX error on failure.
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*/
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typedef struct
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{
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mpi P; /*!< prime modulus of the base field */
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mpi B; /*!< constant term in the equation */
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ecp_point G; /*!< generator of the subgroup used */
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mpi N; /*!< the order of G */
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size_t pbits; /*!< number of bits in P */
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size_t nbits; /*!< number of bits in N */
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int (*modp)(mpi *); /*!< function for fast reduction mod P */
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}
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ecp_group;
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/**
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* RFC 5114 defines a number of standardized ECP groups for use with TLS.
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*
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* These also are the NIST-recommended ECP groups, are the random ECP groups
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* 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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*
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* \warning This library does not support validation of arbitrary domain
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* parameters. Therefore, only well-known domain parameters from trusted
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* sources should be used. See ecp_use_known_dp().
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*/
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#define POLARSSL_ECP_DP_SECP192R1 0
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#define POLARSSL_ECP_DP_SECP224R1 1
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#define POLARSSL_ECP_DP_SECP256R1 2
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#define POLARSSL_ECP_DP_SECP384R1 3
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#define POLARSSL_ECP_DP_SECP521R1 4
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/**
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* Maximum bit size of the groups (that is, of N)
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*/
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#define POLARSSL_ECP_MAX_N_BITS 521
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/*
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* Maximum window size (actually, NAF width) used for point multipliation.
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* Default: 7.
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* Minimum value: 2. Maximum value: 8.
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*
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* Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) )
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* points used for point multiplication, so at most 64 by default.
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* In practice, most curves will use less precomputed points.
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*
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* Reduction in size may reduce speed for big curves.
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*/
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#define POLARSSL_ECP_WINDOW_SIZE 7 /**< Maximum NAF width used. */
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/*
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* Point formats
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*/
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#define POLARSSL_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format */
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#define POLARSSL_ECP_PF_COMPRESSED 1 /**< Compressed point format */
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#ifdef __cplusplus
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extern "C" {
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#endif
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/**
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* \brief Initialize a point (as zero)
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*/
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void ecp_point_init( ecp_point *pt );
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/**
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* \brief Initialize a group (to something meaningless)
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*/
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void ecp_group_init( ecp_group *grp );
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/**
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* \brief Free the components of a point
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*/
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void ecp_point_free( ecp_point *pt );
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/**
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* \brief Free the components of an ECP group
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*/
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void ecp_group_free( ecp_group *grp );
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/**
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* \brief Set a point to zero
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*
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* \param pt Destination point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
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int ecp_set_zero( ecp_point *pt );
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/**
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* \brief Tell if a point is zero
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*
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* \param pt Point to test
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*
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* \return 1 if point is zero, 0 otherwise
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*/
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int ecp_is_zero( ecp_point *pt );
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/**
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* \brief Copy the contents of point Q into P
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*
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* \param P Destination point
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* \param Q Source point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
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int ecp_copy( ecp_point *P, const ecp_point *Q );
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/**
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* \brief Check that a point is a valid public key on this curve
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*
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* \param grp Curve/group the point should belong to
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* \param pt Point to check
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*
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* \return 0 if point is a valid public key,
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* POLARSSL_ERR_ECP_GENERIC otherwise.
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*
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* \note This function only checks the point is non-zero, has valid
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* coordinates and lies on the curve, but not that it is
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* indeed a multiple of G. This is additional check is more
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* expensive, isn't required by standards, and shouldn't be
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* necessary if the group used has a small cofactor. In
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* particular, it is useless for the NIST groups which all
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* have a cofactor of 1.
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*/
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int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt );
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/**
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* \brief Import a non-zero point from two ASCII strings
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*
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* \param P Destination point
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* \param radix Input numeric base
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* \param x First affine coordinate as a null-terminated string
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* \param y Second affine coordinate as a null-terminated string
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*
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* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
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*/
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int ecp_point_read_string( ecp_point *P, int radix,
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const char *x, const char *y );
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/**
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* \brief Import an ECP group from null-terminated ASCII strings
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*
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* \param grp Destination group
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* \param radix Input numeric base
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* \param p Prime modulus of the base field
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* \param b Constant term in the equation
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* \param gx The generator's X coordinate
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* \param gy The generator's Y coordinate
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* \param n The generator's order
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*
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* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
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*
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* \note Sets all fields except modp.
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*/
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int ecp_group_read_string( ecp_group *grp, int radix,
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const char *p, const char *b,
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const char *gx, const char *gy, const char *n);
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/**
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* \brief Export a point into unsigned binary data
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*
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* \param grp Group to which the point should belong
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* \param P Point to export
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* \param format Point format, should be a POLARSSL_ECP_PF_XXX macro
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* \param olen Length of the actual ouput
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* \param buf Output buffer
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* \param buflen Length of the output buffer
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*
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* \return 0 if successful, or POLARSSL_ERR_ECP_GENERIC
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*/
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int ecp_write_binary( const ecp_group *grp, const ecp_point *P, int format,
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size_t *olen, unsigned char *buf, size_t buflen );
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/**
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* \brief Import a point from unsigned binary data
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*
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* \param grp Group to which the point should belong
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* \param P Point to import
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* \param format Point format, must be POLARSSL_ECP_PF_UNCOMPRESSED for now
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* \param buf Input buffer
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* \param ilen Actual length of input
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*
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* \return 0 if successful,
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* POLARSSL_ERR_ECP_GENERIC if input is invalid
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*
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* \note This function does NOT check that the point actually
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* belongs to the given group, see ecp_check_pubkey() for
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* that.
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*/
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int ecp_read_binary( const ecp_group *grp, ecp_point *P, int format,
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const unsigned char *buf, size_t ilen );
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/**
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* \brief Set a group using well-known domain parameters
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*
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* \param grp Destination group
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* \param index Index in the list of well-known domain parameters
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*
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* \return O if successful,
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* POLARSSL_ERR_MPI_XXX if initialization failed
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* POLARSSL_ERR_ECP_GENERIC if index is out of range
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*
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* \note Index should be a POLARSSL_ECP_DP_XXX macro.
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*/
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int ecp_use_known_dp( ecp_group *grp, size_t index );
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/**
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* \brief Addition: R = P + Q
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*
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* \param grp ECP group
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* \param R Destination point
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* \param P Left-hand point
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* \param Q Right-hand point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
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int ecp_add( const ecp_group *grp, ecp_point *R,
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const ecp_point *P, const ecp_point *Q );
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/**
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* \brief Subtraction: R = P - Q
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*
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* \param grp ECP group
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* \param R Destination point
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* \param P Left-hand point
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* \param Q Right-hand point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
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int ecp_sub( const ecp_group *grp, ecp_point *R,
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const ecp_point *P, const ecp_point *Q );
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/**
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* \brief Multiplication by an integer: R = m * P
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*
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* \param grp ECP group
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* \param R Destination point
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* \param m Integer by which to multiply
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* \param P Point to multiply
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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* POLARSSL_ERR_ECP_GENERIC if m < 0 of m has greater bit
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* length than N, the number of points in the group.
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*
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* \note This function executes a constant number of operations
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* for random m in the allowed range.
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*/
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int ecp_mul( const ecp_group *grp, ecp_point *R,
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const mpi *m, const ecp_point *P );
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/**
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* \brief Generate a keypair
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*
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* \param grp ECP group
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* \param d Destination MPI (secret part)
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* \param Q Destination point (public part)
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* \param f_rng RNG function
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* \param p_rng RNG parameter
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*
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* \return 0 if successful,
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* or a POLARSSL_ERR_ECP_XXX or POLARSSL_MPI_XXX error code
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*/
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int ecp_gen_keypair( const ecp_group *grp, mpi *d, ecp_point *Q,
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int (*f_rng)(void *, unsigned char *, size_t),
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void *p_rng );
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/**
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* \brief Checkup routine
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*
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* \return 0 if successful, or 1 if the test failed
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*/
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int ecp_self_test( int verbose );
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#ifdef __cplusplus
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}
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#endif
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#endif
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