backports: add signature verification code

Uh, this was awful. Because the crypto/ things are completely
impossible to backport, I've actually implemented this by using
mbedtls and embedding the relevant functions it has...

The mbedtls code is taken from mbedtls version 2.6.0 and only
minimally modified (mostly to remove <string.h> and similar).

Signed-off-by: Johannes Berg <johannes.berg@intel.com>

1 files changed, 760 insertions, 0 deletions

diff --git a/backport/compat/verification/mbedtls/bignum.h b/backport/compat/verification/mbedtls/bignum.h
new file mode 100644
index 00000000..69f8e2d9
--- /dev/null
+++ b/backport/compat/verification/mbedtls/bignum.h
@@ -0,0 +1,760 @@
+/**
+ * \file bignum.h
+ *
+ * \brief  Multi-precision integer library
+ *
+ *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
+ *  SPDX-License-Identifier: GPL-2.0
+ *
+ *  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.
+ *
+ *  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
+
+#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 or 64-bit integer types can be forced regardless of the underlying
+ * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
+ * respectively and undefining MBEDTLS_HAVE_ASM.
+ *
+ * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
+ * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
+ */
+#if !defined(MBEDTLS_HAVE_INT32)
+    #if defined(_MSC_VER) && defined(_M_AMD64)
+        /* Always choose 64-bit when using MSC */
+        #if !defined(MBEDTLS_HAVE_INT64)
+            #define MBEDTLS_HAVE_INT64
+        #endif /* !MBEDTLS_HAVE_INT64 */
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+    #elif defined(__GNUC__) && (                         \
+        defined(__amd64__) || defined(__x86_64__)     || \
+        defined(__ppc64__) || defined(__powerpc64__)  || \
+        defined(__ia64__)  || defined(__alpha__)      || \
+        ( defined(__sparc__) && defined(__arch64__) ) || \
+        defined(__s390x__) || defined(__mips64) )
+        #if !defined(MBEDTLS_HAVE_INT64)
+            #define MBEDTLS_HAVE_INT64
+        #endif /* MBEDTLS_HAVE_INT64 */
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+        #if !defined(MBEDTLS_NO_UDBL_DIVISION)
+            /* mbedtls_t_udbl defined as 128-bit unsigned int */
+            typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
+            #define MBEDTLS_HAVE_UDBL
+        #endif /* !MBEDTLS_NO_UDBL_DIVISION */
+    #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
+        /*
+         * __ARMCC_VERSION is defined for both armcc and armclang and
+         * __aarch64__ is only defined by armclang when compiling 64-bit code
+         */
+        #if !defined(MBEDTLS_HAVE_INT64)
+            #define MBEDTLS_HAVE_INT64
+        #endif /* !MBEDTLS_HAVE_INT64 */
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+        #if !defined(MBEDTLS_NO_UDBL_DIVISION)
+            /* mbedtls_t_udbl defined as 128-bit unsigned int */
+            typedef __uint128_t mbedtls_t_udbl;
+            #define MBEDTLS_HAVE_UDBL
+        #endif /* !MBEDTLS_NO_UDBL_DIVISION */
+    #elif defined(MBEDTLS_HAVE_INT64)
+        /* Force 64-bit integers with unknown compiler */
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+    #endif
+#endif /* !MBEDTLS_HAVE_INT32 */
+
+#if !defined(MBEDTLS_HAVE_INT64)
+    /* Default to 32-bit compilation */
+    #if !defined(MBEDTLS_HAVE_INT32)
+        #define MBEDTLS_HAVE_INT32
+    #endif /* !MBEDTLS_HAVE_INT32 */
+    typedef  int32_t mbedtls_mpi_sint;
+    typedef uint32_t mbedtls_mpi_uint;
+    #if !defined(MBEDTLS_NO_UDBL_DIVISION)
+        typedef uint64_t mbedtls_t_udbl;
+        #define MBEDTLS_HAVE_UDBL
+    #endif /* !MBEDTLS_NO_UDBL_DIVISION */
+#endif /* !MBEDTLS_HAVE_INT64 */
+
+#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 MPI from a line in 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
+ *
+ * \note           On success, this function advances the file stream
+ *                 to the end of the current line or to EOF.
+ *
+ *                 The function returns 0 on an empty line.
+ *
+ *                 Leading whitespaces are ignored, as is a
+ *                 '0x' prefix for radix 16.
+ *
+ */
+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 <= 1,
+                   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 */