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685 lines
21 KiB
C
685 lines
21 KiB
C
/**
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* \file bignum.h
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*
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* \brief Multi-precision integer library
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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_BIGNUM_H
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#define POLARSSL_BIGNUM_H
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#include <stdio.h>
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#include <string.h>
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#include "polarssl_config.h"
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#ifdef _MSC_VER
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#include <basetsd.h>
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#if (_MSC_VER <= 1200)
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typedef signed short int16_t;
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typedef unsigned short uint16_t;
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#else
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typedef INT16 int16_t;
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typedef UINT16 uint16_t;
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#endif
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typedef INT32 int32_t;
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typedef INT64 int64_t;
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typedef UINT32 uint32_t;
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typedef UINT64 uint64_t;
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#else
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#include <inttypes.h>
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#endif
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#define POLARSSL_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
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#define POLARSSL_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
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#define POLARSSL_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
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#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
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#define POLARSSL_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
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#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
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#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
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#define POLARSSL_ERR_MPI_MALLOC_FAILED -0x0010 /**< Memory allocation failed. */
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#define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup
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/*
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* Maximum size MPIs are allowed to grow to in number of limbs.
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*/
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#define POLARSSL_MPI_MAX_LIMBS 10000
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#if !defined(POLARSSL_CONFIG_OPTIONS)
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/*
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* Maximum window size used for modular exponentiation. Default: 6
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* Minimum value: 1. Maximum value: 6.
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*
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* Result is an array of ( 2 << POLARSSL_MPI_WINDOW_SIZE ) MPIs used
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* for the sliding window calculation. (So 64 by default)
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*
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* Reduction in size, reduces speed.
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*/
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#define POLARSSL_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
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/*
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* Maximum size of MPIs allowed in bits and bytes for user-MPIs.
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* ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
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*
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* Note: Calculations can results temporarily in larger MPIs. So the number
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* of limbs required (POLARSSL_MPI_MAX_LIMBS) is higher.
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*/
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#define POLARSSL_MPI_MAX_SIZE 512 /**< Maximum number of bytes for usable MPIs. */
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#endif /* !POLARSSL_CONFIG_OPTIONS */
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#define POLARSSL_MPI_MAX_BITS ( 8 * POLARSSL_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
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/*
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* When reading from files with mpi_read_file() and writing to files with
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* mpi_write_file() the buffer should have space
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* for a (short) label, the MPI (in the provided radix), the newline
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* characters and the '\0'.
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*
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* By default we assume at least a 10 char label, a minimum radix of 10
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* (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
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* Autosized at compile time for at least a 10 char label, a minimum radix
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* of 10 (decimal) for a number of POLARSSL_MPI_MAX_BITS size.
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*
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* This used to be statically sized to 1250 for a maximum of 4096 bit
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* numbers (1234 decimal chars).
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*
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* Calculate using the formula:
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* POLARSSL_MPI_RW_BUFFER_SIZE = ceil(POLARSSL_MPI_MAX_BITS / ln(10) * ln(2)) +
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* LabelSize + 6
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*/
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#define POLARSSL_MPI_MAX_BITS_SCALE100 ( 100 * POLARSSL_MPI_MAX_BITS )
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#define LN_2_DIV_LN_10_SCALE100 332
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#define POLARSSL_MPI_RW_BUFFER_SIZE ( ((POLARSSL_MPI_MAX_BITS_SCALE100 + LN_2_DIV_LN_10_SCALE100 - 1) / LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
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/*
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* Define the base integer type, architecture-wise
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*/
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#if defined(POLARSSL_HAVE_INT8)
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typedef signed char t_sint;
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typedef unsigned char t_uint;
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typedef uint16_t t_udbl;
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#define POLARSSL_HAVE_UDBL
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#else
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#if defined(POLARSSL_HAVE_INT16)
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typedef int16_t t_sint;
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typedef uint16_t t_uint;
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typedef uint32_t t_udbl;
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#define POLARSSL_HAVE_UDBL
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#else
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#if ( defined(_MSC_VER) && defined(_M_AMD64) )
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typedef int64_t t_sint;
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typedef uint64_t t_uint;
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#else
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#if ( defined(__GNUC__) && ( \
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defined(__amd64__) || defined(__x86_64__) || \
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defined(__ppc64__) || defined(__powerpc64__) || \
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defined(__ia64__) || defined(__alpha__) || \
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(defined(__sparc__) && defined(__arch64__)) || \
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defined(__s390x__) ) )
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typedef int64_t t_sint;
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typedef uint64_t t_uint;
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typedef unsigned int t_udbl __attribute__((mode(TI)));
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#define POLARSSL_HAVE_UDBL
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#else
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typedef int32_t t_sint;
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typedef uint32_t t_uint;
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#if ( defined(_MSC_VER) && defined(_M_IX86) )
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typedef uint64_t t_udbl;
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#define POLARSSL_HAVE_UDBL
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#else
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#if defined( POLARSSL_HAVE_LONGLONG )
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typedef unsigned long long t_udbl;
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#define POLARSSL_HAVE_UDBL
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#endif
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#endif
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#endif
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#endif
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#endif /* POLARSSL_HAVE_INT16 */
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#endif /* POLARSSL_HAVE_INT8 */
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/**
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* \brief MPI structure
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*/
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typedef struct
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{
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int s; /*!< integer sign */
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size_t n; /*!< total # of limbs */
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t_uint *p; /*!< pointer to limbs */
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}
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mpi;
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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 one MPI
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*
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* \param X One MPI to initialize.
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*/
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void mpi_init( mpi *X );
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/**
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* \brief Unallocate one MPI
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*
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* \param X One MPI to unallocate.
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*/
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void mpi_free( mpi *X );
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/**
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* \brief Enlarge to the specified number of limbs
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*
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* \param X MPI to grow
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* \param nblimbs The target number of limbs
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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 mpi_grow( mpi *X, size_t nblimbs );
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/**
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* \brief Copy the contents of Y into X
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*
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* \param X Destination MPI
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* \param Y Source MPI
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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 mpi_copy( mpi *X, const mpi *Y );
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/**
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* \brief Swap the contents of X and Y
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*
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* \param X First MPI value
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* \param Y Second MPI value
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*/
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void mpi_swap( mpi *X, mpi *Y );
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/**
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* \brief Set value from integer
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*
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* \param X MPI to set
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* \param z Value to use
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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 mpi_lset( mpi *X, t_sint z );
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/**
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* \brief Get a specific bit from X
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*
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* \param X MPI to use
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* \param pos Zero-based index of the bit in X
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*
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* \return Either a 0 or a 1
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*/
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int mpi_get_bit( const mpi *X, size_t pos );
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/**
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* \brief Set a bit of X to a specific value of 0 or 1
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*
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* \note Will grow X if necessary to set a bit to 1 in a not yet
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* existing limb. Will not grow if bit should be set to 0
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*
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* \param X MPI to use
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* \param pos Zero-based index of the bit in X
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* \param val The value to set the bit to (0 or 1)
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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_MPI_BAD_INPUT_DATA if val is not 0 or 1
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*/
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int mpi_set_bit( mpi *X, size_t pos, unsigned char val );
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/**
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* \brief Return the number of zero-bits before the least significant
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* '1' bit
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*
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* Note: Thus also the zero-based index of the least significant '1' bit
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*
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* \param X MPI to use
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*/
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size_t mpi_lsb( const mpi *X );
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/**
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* \brief Return the number of bits up to and including the most
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* significant '1' bit'
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*
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* Note: Thus also the one-based index of the most significant '1' bit
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*
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* \param X MPI to use
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*/
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size_t mpi_msb( const mpi *X );
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/**
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* \brief Return the total size in bytes
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*
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* \param X MPI to use
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*/
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size_t mpi_size( const mpi *X );
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/**
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* \brief Import from an ASCII string
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*
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* \param X Destination MPI
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* \param radix Input numeric base
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* \param s Null-terminated string buffer
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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 mpi_read_string( mpi *X, int radix, const char *s );
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/**
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* \brief Export into an ASCII string
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*
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* \param X Source MPI
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* \param radix Output numeric base
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* \param s String buffer
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* \param slen String buffer size
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*
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* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code.
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* *slen is always updated to reflect the amount
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* of data that has (or would have) been written.
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*
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* \note Call this function with *slen = 0 to obtain the
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* minimum required buffer size in *slen.
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*/
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int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen );
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#if defined(POLARSSL_FS_IO)
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/**
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* \brief Read X from an opened file
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*
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* \param X Destination MPI
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* \param radix Input numeric base
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* \param fin Input file handle
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*
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* \return 0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if
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* the file read buffer is too small or a
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* POLARSSL_ERR_MPI_XXX error code
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*/
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int mpi_read_file( mpi *X, int radix, FILE *fin );
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/**
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* \brief Write X into an opened file, or stdout if fout is NULL
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*
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* \param p Prefix, can be NULL
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* \param X Source MPI
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* \param radix Output numeric base
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* \param fout Output file handle (can be NULL)
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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 Set fout == NULL to print X on the console.
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*/
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int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout );
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#endif /* POLARSSL_FS_IO */
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/**
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* \brief Import X from unsigned binary data, big endian
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*
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* \param X Destination MPI
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* \param buf Input buffer
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* \param buflen Input buffer size
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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 mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen );
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/**
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* \brief Export X into unsigned binary data, big endian
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*
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* \param X Source MPI
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* \param buf Output buffer
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* \param buflen Output buffer size
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
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*/
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int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen );
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/**
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* \brief Left-shift: X <<= count
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*
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* \param X MPI to shift
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* \param count Amount to shift
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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 mpi_shift_l( mpi *X, size_t count );
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/**
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* \brief Right-shift: X >>= count
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*
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* \param X MPI to shift
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* \param count Amount to shift
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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 mpi_shift_r( mpi *X, size_t count );
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/**
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* \brief Compare unsigned values
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*
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* \param X Left-hand MPI
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* \param Y Right-hand MPI
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*
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* \return 1 if |X| is greater than |Y|,
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* -1 if |X| is lesser than |Y| or
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* 0 if |X| is equal to |Y|
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*/
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int mpi_cmp_abs( const mpi *X, const mpi *Y );
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/**
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* \brief Compare signed values
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*
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* \param X Left-hand MPI
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* \param Y Right-hand MPI
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*
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* \return 1 if X is greater than Y,
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* -1 if X is lesser than Y or
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* 0 if X is equal to Y
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*/
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int mpi_cmp_mpi( const mpi *X, const mpi *Y );
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/**
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* \brief Compare signed values
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*
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* \param X Left-hand MPI
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* \param z The integer value to compare to
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*
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* \return 1 if X is greater than z,
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* -1 if X is lesser than z or
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* 0 if X is equal to z
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*/
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int mpi_cmp_int( const mpi *X, t_sint z );
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/**
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* \brief Unsigned addition: X = |A| + |B|
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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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 mpi_add_abs( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Unsigned substraction: X = |A| - |B|
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A
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*/
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int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed addition: X = A + B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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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 mpi_add_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed substraction: X = A - B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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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 mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed addition: X = A + b
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param b The integer value to add
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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 mpi_add_int( mpi *X, const mpi *A, t_sint b );
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/**
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* \brief Signed substraction: X = A - b
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param b The integer value to subtract
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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 mpi_sub_int( mpi *X, const mpi *A, t_sint b );
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/**
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* \brief Baseline multiplication: X = A * B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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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 mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Baseline multiplication: X = A * b
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* Note: b is an unsigned integer type, thus
|
|
* Negative values of b are ignored.
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|
*
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|
* \param X Destination MPI
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|
* \param A Left-hand MPI
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|
* \param b The integer value to multiply with
|
|
*
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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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int mpi_mul_int( mpi *X, const mpi *A, t_sint b );
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|
|
|
/**
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|
* \brief Division by mpi: A = Q * B + R
|
|
*
|
|
* \param Q Destination MPI for the quotient
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|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
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|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
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|
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0
|
|
*
|
|
* \note Either Q or R can be NULL.
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|
*/
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|
int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B );
|
|
|
|
/**
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|
* \brief Division by int: A = Q * b + R
|
|
*
|
|
* \param Q Destination MPI for the quotient
|
|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
|
|
* \param b Integer to divide by
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0
|
|
*
|
|
* \note Either Q or R can be NULL.
|
|
*/
|
|
int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b );
|
|
|
|
/**
|
|
* \brief Modulo: R = A mod B
|
|
*
|
|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0,
|
|
* POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0
|
|
*/
|
|
int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B );
|
|
|
|
/**
|
|
* \brief Modulo: r = A mod b
|
|
*
|
|
* \param r Destination t_uint
|
|
* \param A Left-hand MPI
|
|
* \param b Integer to divide by
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0,
|
|
* POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0
|
|
*/
|
|
int mpi_mod_int( t_uint *r, const mpi *A, t_sint b );
|
|
|
|
/**
|
|
* \brief Sliding-window exponentiation: X = A^E mod N
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param E Exponent MPI
|
|
* \param N Modular MPI
|
|
* \param _RR Speed-up MPI used for recalculations
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even or if
|
|
* E is negative
|
|
*
|
|
* \note _RR is used to avoid re-computing R*R mod N across
|
|
* multiple calls, which speeds up things a bit. It can
|
|
* be set to NULL if the extra performance is unneeded.
|
|
*/
|
|
int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR );
|
|
|
|
/**
|
|
* \brief Fill an MPI X with size bytes of random
|
|
*
|
|
* \param X Destination MPI
|
|
* \param size Size in bytes
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mpi_fill_random( mpi *X, size_t size,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Greatest common divisor: G = gcd(A, B)
|
|
*
|
|
* \param G Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mpi_gcd( mpi *G, const mpi *A, const mpi *B );
|
|
|
|
/**
|
|
* \brief Modular inverse: X = A^-1 mod N
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param N Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
|
|
POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
|
|
*/
|
|
int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N );
|
|
|
|
/**
|
|
* \brief Miller-Rabin primality test
|
|
*
|
|
* \param X MPI to check
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime
|
|
*/
|
|
int mpi_is_prime( mpi *X,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Prime number generation
|
|
*
|
|
* \param X Destination MPI
|
|
* \param nbits Required size of X in bits ( 3 <= nbits <= POLARSSL_MPI_MAX_BITS )
|
|
* \param dh_flag If 1, then (X-1)/2 will be prime too
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
|
|
* POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
|
|
*/
|
|
int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Checkup routine
|
|
*
|
|
* \return 0 if successful, or 1 if the test failed
|
|
*/
|
|
int mpi_self_test( int verbose );
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif /* bignum.h */
|