Diff: mbedtls/mbedtls/bignum.h

Revision:

11:cada08fc8a70

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mbedtls/mbedtls/bignum.h	Thu Jun 09 17:08:36 2016 +0000
@@ -0,0 +1,716 @@
+/**
+ * \file bignum.h
+ *
+ * \brief  Multi-precision integer library
+ *
+ *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
+ *  SPDX-License-Identifier: Apache-2.0
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License"); you may
+ *  not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+ *  This file is part of mbed TLS (https://tls.mbed.org)
+ */
+#ifndef MBEDTLS_BIGNUM_H
+#define MBEDTLS_BIGNUM_H
+
+#if !defined(MBEDTLS_CONFIG_FILE)
+#include "config.h"
+#else
+#include MBEDTLS_CONFIG_FILE
+#endif
+
+#include <stddef.h>
+#include <stdint.h>
+
+#if defined(MBEDTLS_FS_IO)
+#include <stdio.h>
+#endif
+
+#define MBEDTLS_ERR_MPI_FILE_IO_ERROR                     -0x0002  /**< An error occurred while reading from or writing to a file. */
+#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA                    -0x0004  /**< Bad input parameters to function. */
+#define MBEDTLS_ERR_MPI_INVALID_CHARACTER                 -0x0006  /**< There is an invalid character in the digit string. */
+#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008  /**< The buffer is too small to write to. */
+#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE                    -0x000A  /**< The input arguments are negative or result in illegal output. */
+#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO                  -0x000C  /**< The input argument for division is zero, which is not allowed. */
+#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE                    -0x000E  /**< The input arguments are not acceptable. */
+#define MBEDTLS_ERR_MPI_ALLOC_FAILED                      -0x0010  /**< Memory allocation failed. */
+
+#define MBEDTLS_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 MBEDTLS_MPI_MAX_LIMBS                             10000
+
+#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
+/*
+ * Maximum window size used for modular exponentiation. Default: 6
+ * Minimum value: 1. Maximum value: 6.
+ *
+ * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
+ * for the sliding window calculation. (So 64 by default)
+ *
+ * Reduction in size, reduces speed.
+ */
+#define MBEDTLS_MPI_WINDOW_SIZE                           6        /**< Maximum windows size used. */
+#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
+
+#if !defined(MBEDTLS_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 (MBEDTLS_MPI_MAX_LIMBS) is higher.
+ */
+#define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */
+#endif /* !MBEDTLS_MPI_MAX_SIZE */
+
+#define MBEDTLS_MPI_MAX_BITS                              ( 8 * MBEDTLS_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */
+
+/*
+ * When reading from files with mbedtls_mpi_read_file() and writing to files with
+ * mbedtls_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 MBEDTLS_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:
+ *  MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
+ *                                LabelSize + 6
+ */
+#define MBEDTLS_MPI_MAX_BITS_SCALE100          ( 100 * MBEDTLS_MPI_MAX_BITS )
+#define MBEDTLS_LN_2_DIV_LN_10_SCALE100                 332
+#define MBEDTLS_MPI_RW_BUFFER_SIZE             ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
+
+/*
+ * Define the base integer type, architecture-wise.
+ *
+ * 32-bit integers can be forced on 64-bit arches (eg. for testing purposes)
+ * by defining MBEDTLS_HAVE_INT32 and undefining MBEDTLS_HAVE_ASM
+ */
+#if ( ! defined(MBEDTLS_HAVE_INT32) && \
+        defined(_MSC_VER) && defined(_M_AMD64) )
+  #define MBEDTLS_HAVE_INT64
+  typedef  int64_t mbedtls_mpi_sint;
+  typedef uint64_t mbedtls_mpi_uint;
+#else
+  #if ( ! defined(MBEDTLS_HAVE_INT32) &&               \
+        defined(__GNUC__) && (                          \
+        defined(__amd64__) || defined(__x86_64__)    || \
+        defined(__ppc64__) || defined(__powerpc64__) || \
+        defined(__ia64__)  || defined(__alpha__)     || \
+        (defined(__sparc__) && defined(__arch64__))  || \
+        defined(__s390x__) || defined(__mips64) ) )
+     #define MBEDTLS_HAVE_INT64
+     typedef  int64_t mbedtls_mpi_sint;
+     typedef uint64_t mbedtls_mpi_uint;
+     typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
+     #define MBEDTLS_HAVE_UDBL
+  #else
+     #define MBEDTLS_HAVE_INT32
+     typedef  int32_t mbedtls_mpi_sint;
+     typedef uint32_t mbedtls_mpi_uint;
+     typedef uint64_t mbedtls_t_udbl;
+     #define MBEDTLS_HAVE_UDBL
+  #endif /* !MBEDTLS_HAVE_INT32 && __GNUC__ && 64-bit platform */
+#endif /* !MBEDTLS_HAVE_INT32 && _MSC_VER && _M_AMD64 */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * \brief          MPI structure
+ */
+typedef struct
+{
+    int s;              /*!<  integer sign      */
+    size_t n;           /*!<  total # of limbs  */
+    mbedtls_mpi_uint *p;          /*!<  pointer to limbs  */
+}
+mbedtls_mpi;
+
+/**
+ * \brief           Initialize one MPI (make internal references valid)
+ *                  This just makes it ready to be set or freed,
+ *                  but does not define a value for the MPI.
+ *
+ * \param X         One MPI to initialize.
+ */
+void mbedtls_mpi_init( mbedtls_mpi *X );
+
+/**
+ * \brief          Unallocate one MPI
+ *
+ * \param X        One MPI to unallocate.
+ */
+void mbedtls_mpi_free( mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_grow( mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_shrink( mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
+
+/**
+ * \brief          Swap the contents of X and Y
+ *
+ * \param X        First MPI value
+ * \param Y        Second MPI value
+ */
+void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *
+ * \note           This function is equivalent to
+ *                      if( assign ) mbedtls_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 mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
+
+/**
+ * \brief          Safe conditional swap X <-> Y if swap is 1
+ *
+ * \param X        First mbedtls_mpi value
+ * \param Y        Second mbedtls_mpi value
+ * \param assign   1: perform the swap, 0: keep X and Y's original values
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *
+ * \note           This function is equivalent to
+ *                      if( assign ) mbedtls_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 mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
+
+/**
+ * \brief          Set value from integer
+ *
+ * \param X        MPI to set
+ * \param z        Value to use
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_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 mbedtls_mpi_get_bit( const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
+ */
+int mbedtls_mpi_set_bit( mbedtls_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 mbedtls_mpi_lsb( const mbedtls_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 mbedtls_mpi_bitlen( const mbedtls_mpi *X );
+
+/**
+ * \brief          Return the total size in bytes
+ *
+ * \param X        MPI to use
+ */
+size_t mbedtls_mpi_size( const mbedtls_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 MBEDTLS_ERR_MPI_XXX error code
+ */
+int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
+
+/**
+ * \brief          Export into an ASCII string
+ *
+ * \param X        Source MPI
+ * \param radix    Output numeric base
+ * \param buf      Buffer to write the string to
+ * \param buflen   Length of buf
+ * \param olen     Length of the string written, including final NUL byte
+ *
+ * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
+ *                 *olen is always updated to reflect the amount
+ *                 of data that has (or would have) been written.
+ *
+ * \note           Call this function with buflen = 0 to obtain the
+ *                 minimum required buffer size in *olen.
+ */
+int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
+                              char *buf, size_t buflen, size_t *olen );
+
+#if defined(MBEDTLS_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, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
+ *                 the file read buffer is too small or a
+ *                 MBEDTLS_ERR_MPI_XXX error code
+ */
+int mbedtls_mpi_read_file( mbedtls_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 MBEDTLS_ERR_MPI_XXX error code
+ *
+ * \note           Set fout == NULL to print X on the console.
+ */
+int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
+#endif /* MBEDTLS_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
+
+/**
+ * \brief          Export X into unsigned binary data, big endian.
+ *                 Always fills the whole buffer, which will start with zeros
+ *                 if the number is smaller.
+ *
+ * \param X        Source MPI
+ * \param buf      Output buffer
+ * \param buflen   Output buffer size
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
+ */
+int mbedtls_mpi_write_binary( const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
+
+/**
+ * \brief          Right-shift: X >>= count
+ *
+ * \param X        MPI to shift
+ * \param count    Amount to shift
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_shift_r( mbedtls_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 mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_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 mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_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 mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
+ */
+int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
+
+/**
+ * \brief          Baseline multiplication: X = A * b
+ *
+ * \param X        Destination MPI
+ * \param A        Left-hand MPI
+ * \param b        The unsigned integer value to multiply with
+ *
+ * \note           b is unsigned
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
+
+/**
+ * \brief          Division by mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
+ *
+ * \note           Either Q or R can be NULL.
+ */
+int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
+ *
+ * \note           Either Q or R can be NULL.
+ */
+int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
+ *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
+ */
+int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
+
+/**
+ * \brief          Modulo: r = A mod b
+ *
+ * \param r        Destination mbedtls_mpi_uint
+ * \param A        Left-hand MPI
+ * \param b        Integer to divide by
+ *
+ * \return         0 if successful,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
+ *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
+ */
+int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_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 mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_fill_random( mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ */
+int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_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,
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
+                   MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
+ */
+int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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),
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
+ */
+int mbedtls_mpi_is_prime( const mbedtls_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 <= MBEDTLS_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),
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
+ */
+int mbedtls_mpi_gen_prime( mbedtls_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 mbedtls_mpi_self_test( int verbose );
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* bignum.h */