Diff: SSL/include/polarssl/bignum.h

Revision:

0:796d0f61a05b

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SSL/include/polarssl/bignum.h	Thu Sep 27 06:34:22 2018 +0000
@@ -0,0 +1,751 @@
+/**
+ * \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_CONFIG_OPTIONS)
+/*
+ * 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. */
+
+#endif /* !POLARSSL_CONFIG_OPTIONS */
+
+#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 POARSSL_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
+  #endif
+#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 */
+
+