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mbedtls/include/polarssl/bignum.h

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/**
* \file bignum.h
*
* \brief Multi-precision integer library
*
* Copyright (C) 2006-2010, Brainspark B.V.
*
* This file is part of PolarSSL (http://www.polarssl.org)
* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
*
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#ifndef POLARSSL_BIGNUM_H
#define POLARSSL_BIGNUM_H
#include <stdio.h>
#include <string.h>
#include "config.h"
#ifdef _MSC_VER
#include <basetsd.h>
#if (_MSC_VER <= 1200)
typedef signed short int16_t;
typedef unsigned short uint16_t;
#else
typedef INT16 int16_t;
typedef UINT16 uint16_t;
#endif
typedef INT32 int32_t;
typedef UINT32 uint32_t;
typedef UINT64 uint64_t;
#else
#include <inttypes.h>
#endif
#define POLARSSL_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
#define POLARSSL_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
#define POLARSSL_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
#define POLARSSL_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
#define POLARSSL_ERR_MPI_MALLOC_FAILED -0x0010 /**< Memory allocation failed. */
#define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup
/*
* Maximum size MPIs are allowed to grow to in number of limbs.
*/
#define POLARSSL_MPI_MAX_LIMBS 10000
/*
* Maximum window size used for modular exponentiation. Default: 6
* Minimum value: 1. Maximum value: 6.
*
* Result is an array of ( 2 << POLARSSL_MPI_WINDOW_SIZE ) MPIs used
* for the sliding window calculation. (So 64 by default)
*
* Reduction in size, reduces speed.
*/
#define POLARSSL_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
/*
* Maximum size of MPIs allowed in bits and bytes for user-MPIs.
* ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
*
* Note: Calculations can results temporarily in larger MPIs. So the number
* of limbs required (POLARSSL_MPI_MAX_LIMBS) is higher.
*/
#define POLARSSL_MPI_MAX_SIZE 512 /**< Maximum number of bytes for usable MPIs. */
#define POLARSSL_MPI_MAX_BITS ( 8 * POLARSSL_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
/*
* When reading from files with mpi_read_file() and writing to files with
* mpi_write_file() the buffer should have space
* for a (short) label, the MPI (in the provided radix), the newline
* characters and the '\0'.
*
* By default we assume at least a 10 char label, a minimum radix of 10
* (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
* Autosized at compile time for at least a 10 char label, a minimum radix
* of 10 (decimal) for a number of POLARSSL_MPI_MAX_BITS size.
*
* This used to be statically sized to 1250 for a maximum of 4096 bit
* numbers (1234 decimal chars).
*
* Calculate using the formula:
* POLARSSL_MPI_RW_BUFFER_SIZE = ceil(POLARSSL_MPI_MAX_BITS / ln(10) * ln(2)) +
* LabelSize + 6
*/
#define POLARSSL_MPI_MAX_BITS_SCALE100 ( 100 * POLARSSL_MPI_MAX_BITS )
#define LN_2_DIV_LN_10_SCALE100 332
#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 )
/*
* Define the base integer type, architecture-wise
*/
#if defined(POLARSSL_HAVE_INT8)
typedef signed char t_sint;
typedef unsigned char t_uint;
typedef uint16_t t_udbl;
#define POLARSSL_HAVE_UDBL
#else
#if defined(POLARSSL_HAVE_INT16)
typedef int16_t t_sint;
typedef uint16_t t_uint;
typedef uint32_t t_udbl;
#define POLARSSL_HAVE_UDBL
#else
#if ( defined(__MSC_VER) && defined(_M_AMD64) )
typedef int64_t t_sint;
typedef uint64_t t_uint;
#else
#if ( defined(__GNUC__) && ( \
defined(__amd64__) || defined(__x86_64__) || \
defined(__ppc64__) || defined(__powerpc64__) || \
defined(__ia64__) || defined(__alpha__) || \
(defined(__sparc__) && defined(__arch64__)) || \
defined(__s390x__) ) )
typedef int64_t t_sint;
typedef uint64_t t_uint;
typedef unsigned int t_udbl __attribute__((mode(TI)));
#define POLARSSL_HAVE_UDBL
#else
typedef int32_t t_sint;
typedef uint32_t t_uint;
#if ( defined(_MSC_VER) && defined(_M_IX86) )
typedef uint64_t t_udbl;
#define POLARSSL_HAVE_UDBL
#else
#if defined( POLARSSL_HAVE_LONGLONG )
typedef unsigned long long t_udbl;
#define POLARSSL_HAVE_UDBL
#endif
#endif
#endif
#endif
#endif /* POLARSSL_HAVE_INT16 */
#endif /* POLARSSL_HAVE_INT8 */
/**
* \brief MPI structure
*/
typedef struct
{
int s; /*!< integer sign */
size_t n; /*!< total # of limbs */
t_uint *p; /*!< pointer to limbs */
}
mpi;
#ifdef __cplusplus
extern "C" {
#endif
/**
* \brief Initialize one MPI
*
* \param X One MPI to initialize.
*/
void mpi_init( mpi *X );
/**
* \brief Unallocate one MPI
*
* \param X One MPI to unallocate.
*/
void mpi_free( mpi *X );
/**
* \brief Enlarge to the specified number of limbs
*
* \param X MPI to grow
* \param nblimbs The target number of limbs
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_grow( mpi *X, size_t nblimbs );
/**
* \brief Copy the contents of Y into X
*
* \param X Destination MPI
* \param Y Source MPI
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_copy( mpi *X, const mpi *Y );
/**
* \brief Swap the contents of X and Y
*
* \param X First MPI value
* \param Y Second MPI value
*/
void mpi_swap( mpi *X, mpi *Y );
/**
* \brief Set value from integer
*
* \param X MPI to set
* \param z Value to use
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_lset( mpi *X, t_sint z );
/**
* \brief Get a specific bit from X
*
* \param X MPI to use
* \param pos Zero-based index of the bit in X
*
* \return Either a 0 or a 1
*/
int mpi_get_bit( const mpi *X, size_t pos );
/**
* \brief Set a bit of X to a specific value of 0 or 1
*
* \note Will grow X if necessary to set a bit to 1 in a not yet
* existing limb. Will not grow if bit should be set to 0
*
* \param X MPI to use
* \param pos Zero-based index of the bit in X
* \param val The value to set the bit to (0 or 1)
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
* POLARSSL_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
*/
int mpi_set_bit( mpi *X, size_t pos, unsigned char val );
/**
* \brief Return the number of zero-bits before the least significant
* '1' bit
*
* Note: Thus also the zero-based index of the least significant '1' bit
*
* \param X MPI to use
*/
size_t mpi_lsb( const mpi *X );
/**
* \brief Return the number of bits up to and including the most
* significant '1' bit'
*
* Note: Thus also the one-based index of the most significant '1' bit
*
* \param X MPI to use
*/
size_t mpi_msb( const mpi *X );
/**
* \brief Return the total size in bytes
*
* \param X MPI to use
*/
size_t mpi_size( const mpi *X );
/**
* \brief Import from an ASCII string
*
* \param X Destination MPI
* \param radix Input numeric base
* \param s Null-terminated string buffer
*
* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
*/
int mpi_read_string( mpi *X, int radix, const char *s );
/**
* \brief Export into an ASCII string
*
* \param X Source MPI
* \param radix Output numeric base
* \param s String buffer
* \param slen String buffer size
*
* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code.
* *slen is always updated to reflect the amount
* of data that has (or would have) been written.
*
* \note Call this function with *slen = 0 to obtain the
* minimum required buffer size in *slen.
*/
int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen );
#if defined(POLARSSL_FS_IO)
/**
* \brief Read X from an opened file
*
* \param X Destination MPI
* \param radix Input numeric base
* \param fin Input file handle
*
* \return 0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if
* the file read buffer is too small or a
* POLARSSL_ERR_MPI_XXX error code
*/
int mpi_read_file( mpi *X, int radix, FILE *fin );
/**
* \brief Write X into an opened file, or stdout if fout is NULL
*
* \param p Prefix, can be NULL
* \param X Source MPI
* \param radix Output numeric base
* \param fout Output file handle (can be NULL)
*
* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
*
* \note Set fout == NULL to print X on the console.
*/
int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout );
#endif /* POLARSSL_FS_IO */
/**
* \brief Import X from unsigned binary data, big endian
*
* \param X Destination MPI
* \param buf Input buffer
* \param buflen Input buffer size
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen );
/**
* \brief Export X into unsigned binary data, big endian
*
* \param X Source MPI
* \param buf Output buffer
* \param buflen Output buffer size
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
*/
int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen );
/**
* \brief Left-shift: X <<= count
*
* \param X MPI to shift
* \param count Amount to shift
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_shift_l( mpi *X, size_t count );
/**
* \brief Right-shift: X >>= count
*
* \param X MPI to shift
* \param count Amount to shift
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_shift_r( mpi *X, size_t count );
/**
* \brief Compare unsigned values
*
* \param X Left-hand MPI
* \param Y Right-hand MPI
*
* \return 1 if |X| is greater than |Y|,
* -1 if |X| is lesser than |Y| or
* 0 if |X| is equal to |Y|
*/
int mpi_cmp_abs( const mpi *X, const mpi *Y );
/**
* \brief Compare signed values
*
* \param X Left-hand MPI
* \param Y Right-hand MPI
*
* \return 1 if X is greater than Y,
* -1 if X is lesser than Y or
* 0 if X is equal to Y
*/
int mpi_cmp_mpi( const mpi *X, const mpi *Y );
/**
* \brief Compare signed values
*
* \param X Left-hand MPI
* \param z The integer value to compare to
*
* \return 1 if X is greater than z,
* -1 if X is lesser than z or
* 0 if X is equal to z
*/
int mpi_cmp_int( const mpi *X, t_sint z );
/**
* \brief Unsigned addition: X = |A| + |B|
*
* \param X 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_add_abs( mpi *X, const mpi *A, const mpi *B );
/**
* \brief Unsigned substraction: X = |A| - |B|
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param B Right-hand MPI
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A
*/
int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B );
/**
* \brief Signed addition: X = A + B
*
* \param X 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_add_mpi( mpi *X, const mpi *A, const mpi *B );
/**
* \brief Signed substraction: X = A - B
*
* \param X 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_sub_mpi( mpi *X, const mpi *A, const mpi *B );
/**
* \brief Signed addition: X = A + b
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The integer value to add
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_add_int( mpi *X, const mpi *A, t_sint b );
/**
* \brief Signed substraction: X = A - b
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The integer value to subtract
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_sub_int( mpi *X, const mpi *A, t_sint b );
/**
* \brief Baseline multiplication: X = A * B
*
* \param X 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_mul_mpi( mpi *X, const mpi *A, const mpi *B );
/**
* \brief Baseline multiplication: X = A * b
* Note: b is an unsigned integer type, thus
* Negative values of b are ignored.
*
* \param X Destination MPI
* \param A Left-hand MPI
* \param b The integer value to multiply with
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int mpi_mul_int( mpi *X, const mpi *A, t_sint b );
/**
* \brief Division by mpi: 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 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
*
* \note Either Q or R can be NULL.
*/
int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B );
/**
* \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 */
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