| /** |
| * \file bignum.h |
| * |
| * \brief Multi-precision integer library |
| * |
| * Copyright (C) 2006-2014, 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> |
| |
| #if !defined(POLARSSL_CONFIG_FILE) |
| #include "config.h" |
| #else |
| #include POLARSSL_CONFIG_FILE |
| #endif |
| |
| #if defined(_MSC_VER) && !defined(EFIX64) && !defined(EFI32) |
| #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 INT64 int64_t; |
| typedef UINT32 uint32_t; |
| typedef UINT64 uint64_t; |
| #else |
| #include <inttypes.h> |
| #endif /* _MSC_VER && !EFIX64 && !EFI32 */ |
| |
| #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) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 ) |
| |
| /* |
| * Maximum size MPIs are allowed to grow to in number of limbs. |
| */ |
| #define POLARSSL_MPI_MAX_LIMBS 10000 |
| |
| #if !defined(POLARSSL_MPI_WINDOW_SIZE) |
| /* |
| * 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. */ |
| #endif /* !POLARSSL_MPI_WINDOW_SIZE */ |
| |
| #if !defined(POLARSSL_MPI_MAX_SIZE) |
| /* |
| * 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. */ |
| #endif /* !POLARSSL_MPI_MAX_SIZE */ |
| |
| #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 |
| /* |
| * 32-bit integers can be forced on 64-bit arches (eg. for testing purposes) |
| * by defining POLARSSL_HAVE_INT32 and undefining POLARSSL_HAVE_ASM |
| */ |
| #if ( ! defined(POLARSSL_HAVE_INT32) && \ |
| defined(_MSC_VER) && defined(_M_AMD64) ) |
| #define POLARSSL_HAVE_INT64 |
| typedef int64_t t_sint; |
| typedef uint64_t t_uint; |
| #else |
| #if ( ! defined(POLARSSL_HAVE_INT32) && \ |
| defined(__GNUC__) && ( \ |
| defined(__amd64__) || defined(__x86_64__) || \ |
| defined(__ppc64__) || defined(__powerpc64__) || \ |
| defined(__ia64__) || defined(__alpha__) || \ |
| (defined(__sparc__) && defined(__arch64__)) || \ |
| defined(__s390x__) ) ) |
| #define POLARSSL_HAVE_INT64 |
| typedef int64_t t_sint; |
| typedef uint64_t t_uint; |
| typedef unsigned int t_udbl __attribute__((mode(TI))); |
| #define POLARSSL_HAVE_UDBL |
| #else |
| #define POLARSSL_HAVE_INT32 |
| 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 /* !POLARSSL_HAVE_INT32 && __GNUC__ && 64-bit platform */ |
| #endif /* !POLARSSL_HAVE_INT32 && _MSC_VER && _M_AMD64 */ |
| #endif /* POLARSSL_HAVE_INT16 */ |
| #endif /* POLARSSL_HAVE_INT8 */ |
| |
| #ifdef __cplusplus |
| extern "C" { |
| #endif |
| |
| /** |
| * \brief MPI structure |
| */ |
| typedef struct |
| { |
| int s; /*!< integer sign */ |
| size_t n; /*!< total # of limbs */ |
| t_uint *p; /*!< pointer to limbs */ |
| } |
| mpi; |
| |
| /** |
| * \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 Resize down, keeping at least the specified number of limbs |
| * |
| * \param X MPI to shrink |
| * \param nblimbs The minimum number of limbs to keep |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| */ |
| int mpi_shrink( 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 Safe conditional assignement X = Y if assign is 1 |
| * |
| * \param X MPI to conditionally assign to |
| * \param Y Value to be assigned |
| * \param assign 1: perform the assignment, 0: keep X's original value |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, |
| * |
| * \note This function is equivalent to |
| * if( assign ) mpi_copy( X, Y ); |
| * except that it avoids leaking any information about whether |
| * the assignment was done or not (the above code may leak |
| * information through branch prediction and/or memory access |
| * patterns analysis). |
| */ |
| int mpi_safe_cond_assign( mpi *X, const mpi *Y, unsigned char assign ); |
| |
| /** |
| * \brief Safe conditional swap X <-> Y if swap is 1 |
| * |
| * \param X First mpi value |
| * \param Y Second mpi value |
| * \param assign 1: perform the swap, 0: keep X and Y's original values |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, |
| * |
| * \note This function is equivalent to |
| * if( assign ) mpi_swap( X, Y ); |
| * except that it avoids leaking any information about whether |
| * the assignment was done or not (the above code may leak |
| * information through branch prediction and/or memory access |
| * patterns analysis). |
| */ |
| int mpi_safe_cond_swap( mpi *X, mpi *Y, unsigned char assign ); |
| |
| /** |
| * \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 subtraction: 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 subtraction: 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 subtraction: 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: despite the functon signature, b is treated as a |
| * t_uint. Negative values of b are treated as large positive |
| * values. |
| * |
| * \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 */ |
