536 lines
15 KiB
C
536 lines
15 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) 2006-2010, 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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#define POLARSSL_ERR_MPI_FILE_IO_ERROR 0x0002
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#define POLARSSL_ERR_MPI_BAD_INPUT_DATA 0x0004
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#define POLARSSL_ERR_MPI_INVALID_CHARACTER 0x0006
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#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL 0x0008
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#define POLARSSL_ERR_MPI_NEGATIVE_VALUE 0x000A
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#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO 0x000C
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#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE 0x000E
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#define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup
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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 unsigned char t_int;
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typedef unsigned short t_dbl;
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#else
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#if defined(POLARSSL_HAVE_INT16)
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typedef unsigned short t_int;
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typedef unsigned long t_dbl;
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#else
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typedef unsigned long t_int;
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#if defined(_MSC_VER) && defined(_M_IX86)
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typedef unsigned __int64 t_dbl;
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#else
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#if 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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typedef unsigned int t_dbl __attribute__((mode(TI)));
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#else
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#if defined(POLARSSL_HAVE_LONGLONG)
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typedef unsigned long long t_dbl;
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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
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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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int n; /*!< total # of limbs */
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t_int *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 or more mpi
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*/
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void mpi_init( mpi *X, ... );
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/**
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* \brief Unallocate one or more mpi
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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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* 1 if memory allocation failed
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*/
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int mpi_grow( mpi *X, int 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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* 1 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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* 1 if memory allocation failed
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*/
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int mpi_lset( mpi *X, int z );
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/**
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* \brief Return the number of least significant bits
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*
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* \param X MPI to use
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*/
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int mpi_lsb( const mpi *X );
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/**
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* \brief Return the number of most significant bits
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*
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* \param X MPI to use
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*/
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int 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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int 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 an 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 an 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, int *slen );
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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, or an 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 an 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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/**
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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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* 1 if memory allocation failed
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*/
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int mpi_read_binary( mpi *X, const unsigned char *buf, int 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, int 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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* 1 if memory allocation failed
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*/
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int mpi_shift_l( mpi *X, int 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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* 1 if memory allocation failed
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*/
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int mpi_shift_r( mpi *X, int 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, int 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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* 1 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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* 1 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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* 1 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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* 1 if memory allocation failed
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*/
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int mpi_add_int( mpi *X, const mpi *A, int 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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* 1 if memory allocation failed
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*/
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int mpi_sub_int( mpi *X, const mpi *A, int 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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* 1 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
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* 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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*
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* \return 0 if successful,
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* 1 if memory allocation failed
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*/
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int mpi_mul_int( mpi *X, const mpi *A, t_int b );
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/**
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* \brief Division by mpi: A = Q * B + R
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*
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* \param Q Destination MPI for the quotient
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* \param R Destination MPI for the rest value
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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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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0
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*
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* \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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/**
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* \brief Division by int: A = Q * b + R
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*
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* \param Q Destination MPI for the quotient
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* \param R Destination MPI for the rest value
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* \param A Left-hand MPI
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* \param b Integer to divide by
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*
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* \return 0 if successful,
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0
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*
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* \note Either Q or R can be NULL.
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*/
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int mpi_div_int( mpi *Q, mpi *R, const mpi *A, int b );
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/**
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* \brief Modulo: R = A mod B
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*
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* \param R Destination MPI for the rest value
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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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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0,
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* POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0
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*/
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int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B );
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/**
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* \brief Modulo: r = A mod b
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*
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* \param r Destination t_int
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* \param A Left-hand MPI
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* \param b Integer to divide by
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*
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* \return 0 if successful,
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0,
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* POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0
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*/
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int mpi_mod_int( t_int *r, const mpi *A, int b );
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/**
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* \brief Sliding-window exponentiation: X = A^E mod N
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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 E Exponent MPI
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* \param N Modular MPI
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* \param _RR Speed-up MPI used for recalculations
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*
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* \return 0 if successful,
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even
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*
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* \note _RR is used to avoid re-computing R*R mod N across
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* multiple calls, which speeds up things a bit. It can
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* be set to NULL if the extra performance is unneeded.
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*/
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int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR );
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/**
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* \brief Greatest common divisor: G = gcd(A, B)
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*
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* \param G 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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* 1 if memory allocation failed
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*/
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int mpi_gcd( mpi *G, const mpi *A, const mpi *B );
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/**
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* \brief Modular inverse: X = A^-1 mod N
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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 N Right-hand MPI
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*
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* \return 0 if successful,
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
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POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
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*/
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int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N );
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/**
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* \brief Miller-Rabin primality test
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*
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* \param X MPI to check
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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 (probably prime),
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime
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*/
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int mpi_is_prime( mpi *X, int (*f_rng)(void *), void *p_rng );
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/**
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* \brief Prime number generation
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*
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* \param X Destination MPI
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* \param nbits Required size of X in bits
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* \param dh_flag If 1, then (X-1)/2 will be prime too
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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 (probably prime),
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* 1 if memory allocation failed,
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* POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
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*/
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int mpi_gen_prime( mpi *X, int nbits, int dh_flag,
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int (*f_rng)(void *), 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 mpi_self_test( int verbose );
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#ifdef __cplusplus
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}
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#endif
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#endif /* bignum.h */
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