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, 2447 insertions, 0 deletions

diff --git a/backport/compat/verification/bignum.c b/backport/compat/verification/bignum.c
new file mode 100644
index 00000000..7edfb083
--- /dev/null
+++ b/backport/compat/verification/bignum.c
@@ -0,0 +1,2447 @@
+/*
+ *  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)
+ */
+
+/*
+ *  The following sources were referenced in the design of this Multi-precision
+ *  Integer library:
+ *
+ *  [1] Handbook of Applied Cryptography - 1997
+ *      Menezes, van Oorschot and Vanstone
+ *
+ *  [2] Multi-Precision Math
+ *      Tom St Denis
+ *      https://github.com/libtom/libtommath/blob/develop/tommath.pdf
+ *
+ *  [3] GNU Multi-Precision Arithmetic Library
+ *      https://gmplib.org/manual/index.html
+ *
+ */
+
+#if !defined(MBEDTLS_CONFIG_FILE)
+#include "mbedtls/config.h"
+#else
+#include MBEDTLS_CONFIG_FILE
+#endif
+
+#if defined(MBEDTLS_BIGNUM_C)
+
+#include "mbedtls/bignum.h"
+#include "mbedtls/bn_mul.h"
+
+#if defined(MBEDTLS_PLATFORM_C)
+#include "mbedtls/platform.h"
+#else
+#include <stdio.h>
+#include <stdlib.h>
+#define mbedtls_printf     printf
+#define mbedtls_calloc    calloc
+#define mbedtls_free       free
+#endif
+
+/* Implementation that should never be optimized out by the compiler */
+static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n ) {
+    volatile mbedtls_mpi_uint *p = v; while( n-- ) *p++ = 0;
+}
+
+#define ciL    (sizeof(mbedtls_mpi_uint))         /* chars in limb  */
+#define biL    (ciL << 3)               /* bits  in limb  */
+#define biH    (ciL << 2)               /* half limb size */
+
+#define MPI_SIZE_T_MAX  ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
+
+/*
+ * Convert between bits/chars and number of limbs
+ * Divide first in order to avoid potential overflows
+ */
+#define BITS_TO_LIMBS(i)  ( (i) / biL + ( (i) % biL != 0 ) )
+#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
+
+/*
+ * Initialize one MPI
+ */
+void mbedtls_mpi_init( mbedtls_mpi *X )
+{
+    if( X == NULL )
+        return;
+
+    X->s = 1;
+    X->n = 0;
+    X->p = NULL;
+}
+
+/*
+ * Unallocate one MPI
+ */
+void mbedtls_mpi_free( mbedtls_mpi *X )
+{
+    if( X == NULL )
+        return;
+
+    if( X->p != NULL )
+    {
+        mbedtls_mpi_zeroize( X->p, X->n );
+        mbedtls_free( X->p );
+    }
+
+    X->s = 1;
+    X->n = 0;
+    X->p = NULL;
+}
+
+/*
+ * Enlarge to the specified number of limbs
+ */
+int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs )
+{
+    mbedtls_mpi_uint *p;
+
+    if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
+        return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
+
+    if( X->n < nblimbs )
+    {
+        if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( nblimbs, ciL ) ) == NULL )
+            return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
+
+        if( X->p != NULL )
+        {
+            memcpy( p, X->p, X->n * ciL );
+            mbedtls_mpi_zeroize( X->p, X->n );
+            mbedtls_free( X->p );
+        }
+
+        X->n = nblimbs;
+        X->p = p;
+    }
+
+    return( 0 );
+}
+
+/*
+ * Resize down as much as possible,
+ * while keeping at least the specified number of limbs
+ */
+int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs )
+{
+    mbedtls_mpi_uint *p;
+    size_t i;
+
+    /* Actually resize up in this case */
+    if( X->n <= nblimbs )
+        return( mbedtls_mpi_grow( X, nblimbs ) );
+
+    for( i = X->n - 1; i > 0; i-- )
+        if( X->p[i] != 0 )
+            break;
+    i++;
+
+    if( i < nblimbs )
+        i = nblimbs;
+
+    if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL )
+        return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
+
+    if( X->p != NULL )
+    {
+        memcpy( p, X->p, i * ciL );
+        mbedtls_mpi_zeroize( X->p, X->n );
+        mbedtls_free( X->p );
+    }
+
+    X->n = i;
+    X->p = p;
+
+    return( 0 );
+}
+
+/*
+ * Copy the contents of Y into X
+ */
+int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
+{
+    int ret;
+    size_t i;
+
+    if( X == Y )
+        return( 0 );
+
+    if( Y->p == NULL )
+    {
+        mbedtls_mpi_free( X );
+        return( 0 );
+    }
+
+    for( i = Y->n - 1; i > 0; i-- )
+        if( Y->p[i] != 0 )
+            break;
+    i++;
+
+    X->s = Y->s;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
+
+    memset( X->p, 0, X->n * ciL );
+    memcpy( X->p, Y->p, i * ciL );
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Swap the contents of X and Y
+ */
+void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
+{
+    mbedtls_mpi T;
+
+    memcpy( &T,  X, sizeof( mbedtls_mpi ) );
+    memcpy(  X,  Y, sizeof( mbedtls_mpi ) );
+    memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
+}
+
+/*
+ * Conditionally assign X = Y, without leaking information
+ * about whether the assignment was made or not.
+ * (Leaking information about the respective sizes of X and Y is ok however.)
+ */
+int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign )
+{
+    int ret = 0;
+    size_t i;
+
+    /* make sure assign is 0 or 1 in a time-constant manner */
+    assign = (assign | (unsigned char)-assign) >> 7;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
+
+    X->s = X->s * ( 1 - assign ) + Y->s * assign;
+
+    for( i = 0; i < Y->n; i++ )
+        X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
+
+    for( ; i < X->n; i++ )
+        X->p[i] *= ( 1 - assign );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Conditionally swap X and Y, without leaking information
+ * about whether the swap was made or not.
+ * Here it is not ok to simply swap the pointers, which whould lead to
+ * different memory access patterns when X and Y are used afterwards.
+ */
+int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
+{
+    int ret, s;
+    size_t i;
+    mbedtls_mpi_uint tmp;
+
+    if( X == Y )
+        return( 0 );
+
+    /* make sure swap is 0 or 1 in a time-constant manner */
+    swap = (swap | (unsigned char)-swap) >> 7;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
+
+    s = X->s;
+    X->s = X->s * ( 1 - swap ) + Y->s * swap;
+    Y->s = Y->s * ( 1 - swap ) +    s * swap;
+
+
+    for( i = 0; i < X->n; i++ )
+    {
+        tmp = X->p[i];
+        X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
+        Y->p[i] = Y->p[i] * ( 1 - swap ) +     tmp * swap;
+    }
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Set value from integer
+ */
+int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
+{
+    int ret;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
+    memset( X->p, 0, X->n * ciL );
+
+    X->p[0] = ( z < 0 ) ? -z : z;
+    X->s    = ( z < 0 ) ? -1 : 1;
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Get a specific bit
+ */
+int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos )
+{
+    if( X->n * biL <= pos )
+        return( 0 );
+
+    return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
+}
+
+/*
+ * Set a bit to a specific value of 0 or 1
+ */
+int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val )
+{
+    int ret = 0;
+    size_t off = pos / biL;
+    size_t idx = pos % biL;
+
+    if( val != 0 && val != 1 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    if( X->n * biL <= pos )
+    {
+        if( val == 0 )
+            return( 0 );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) );
+    }
+
+    X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx );
+    X->p[off] |= (mbedtls_mpi_uint) val << idx;
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Return the number of less significant zero-bits
+ */
+size_t mbedtls_mpi_lsb( const mbedtls_mpi *X )
+{
+    size_t i, j, count = 0;
+
+    for( i = 0; i < X->n; i++ )
+        for( j = 0; j < biL; j++, count++ )
+            if( ( ( X->p[i] >> j ) & 1 ) != 0 )
+                return( count );
+
+    return( 0 );
+}
+
+/*
+ * Count leading zero bits in a given integer
+ */
+static size_t mbedtls_clz( const mbedtls_mpi_uint x )
+{
+    size_t j;
+    mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
+
+    for( j = 0; j < biL; j++ )
+    {
+        if( x & mask ) break;
+
+        mask >>= 1;
+    }
+
+    return j;
+}
+
+/*
+ * Return the number of bits
+ */
+size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X )
+{
+    size_t i, j;
+
+    if( X->n == 0 )
+        return( 0 );
+
+    for( i = X->n - 1; i > 0; i-- )
+        if( X->p[i] != 0 )
+            break;
+
+    j = biL - mbedtls_clz( X->p[i] );
+
+    return( ( i * biL ) + j );
+}
+
+/*
+ * Return the total size in bytes
+ */
+size_t mbedtls_mpi_size( const mbedtls_mpi *X )
+{
+    return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 );
+}
+
+/*
+ * Convert an ASCII character to digit value
+ */
+static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c )
+{
+    *d = 255;
+
+    if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
+    if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
+    if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
+
+    if( *d >= (mbedtls_mpi_uint) radix )
+        return( MBEDTLS_ERR_MPI_INVALID_CHARACTER );
+
+    return( 0 );
+}
+
+/*
+ * Import from an ASCII string
+ */
+int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
+{
+    int ret;
+    size_t i, j, slen, n;
+    mbedtls_mpi_uint d;
+    mbedtls_mpi T;
+
+    if( radix < 2 || radix > 16 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    mbedtls_mpi_init( &T );
+
+    slen = strlen( s );
+
+    if( radix == 16 )
+    {
+        if( slen > MPI_SIZE_T_MAX >> 2 )
+            return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+        n = BITS_TO_LIMBS( slen << 2 );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
+
+        for( i = slen, j = 0; i > 0; i--, j++ )
+        {
+            if( i == 1 && s[i - 1] == '-' )
+            {
+                X->s = -1;
+                break;
+            }
+
+            MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
+            X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
+        }
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
+
+        for( i = 0; i < slen; i++ )
+        {
+            if( i == 0 && s[i] == '-' )
+            {
+                X->s = -1;
+                continue;
+            }
+
+            MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
+
+            if( X->s == 1 )
+            {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
+            }
+            else
+            {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
+            }
+        }
+    }
+
+cleanup:
+
+    mbedtls_mpi_free( &T );
+
+    return( ret );
+}
+
+/*
+ * Helper to write the digits high-order first
+ */
+static int mpi_write_hlp( mbedtls_mpi *X, int radix, char **p )
+{
+    int ret;
+    mbedtls_mpi_uint r;
+
+    if( radix < 2 || radix > 16 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
+
+    if( mbedtls_mpi_cmp_int( X, 0 ) != 0 )
+        MBEDTLS_MPI_CHK( mpi_write_hlp( X, radix, p ) );
+
+    if( r < 10 )
+        *(*p)++ = (char)( r + 0x30 );
+    else
+        *(*p)++ = (char)( r + 0x37 );
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Export into an ASCII string
+ */
+int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
+                              char *buf, size_t buflen, size_t *olen )
+{
+    int ret = 0;
+    size_t n;
+    char *p;
+    mbedtls_mpi T;
+
+    if( radix < 2 || radix > 16 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    n = mbedtls_mpi_bitlen( X );
+    if( radix >=  4 ) n >>= 1;
+    if( radix >= 16 ) n >>= 1;
+    /*
+     * Round up the buffer length to an even value to ensure that there is
+     * enough room for hexadecimal values that can be represented in an odd
+     * number of digits.
+     */
+    n += 3 + ( ( n + 1 ) & 1 );
+
+    if( buflen < n )
+    {
+        *olen = n;
+        return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
+    }
+
+    p = buf;
+    mbedtls_mpi_init( &T );
+
+    if( X->s == -1 )
+        *p++ = '-';
+
+    if( radix == 16 )
+    {
+        int c;
+        size_t i, j, k;
+
+        for( i = X->n, k = 0; i > 0; i-- )
+        {
+            for( j = ciL; j > 0; j-- )
+            {
+                c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
+
+                if( c == 0 && k == 0 && ( i + j ) != 2 )
+                    continue;
+
+                *(p++) = "0123456789ABCDEF" [c / 16];
+                *(p++) = "0123456789ABCDEF" [c % 16];
+                k = 1;
+            }
+        }
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) );
+
+        if( T.s == -1 )
+            T.s = 1;
+
+        MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
+    }
+
+    *p++ = '\0';
+    *olen = p - buf;
+
+cleanup:
+
+    mbedtls_mpi_free( &T );
+
+    return( ret );
+}
+
+#if defined(MBEDTLS_FS_IO)
+/*
+ * Read X from an opened file
+ */
+int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin )
+{
+    mbedtls_mpi_uint d;
+    size_t slen;
+    char *p;
+    /*
+     * Buffer should have space for (short) label and decimal formatted MPI,
+     * newline characters and '\0'
+     */
+    char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
+
+    memset( s, 0, sizeof( s ) );
+    if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
+        return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
+
+    slen = strlen( s );
+    if( slen == sizeof( s ) - 2 )
+        return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
+
+    if( slen > 0 && s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
+    if( slen > 0 && s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
+
+    p = s + slen;
+    while( p-- > s )
+        if( mpi_get_digit( &d, radix, *p ) != 0 )
+            break;
+
+    return( mbedtls_mpi_read_string( X, radix, p + 1 ) );
+}
+
+/*
+ * Write X into an opened file (or stdout if fout == NULL)
+ */
+int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout )
+{
+    int ret;
+    size_t n, slen, plen;
+    /*
+     * Buffer should have space for (short) label and decimal formatted MPI,
+     * newline characters and '\0'
+     */
+    char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
+
+    memset( s, 0, sizeof( s ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) );
+
+    if( p == NULL ) p = "";
+
+    plen = strlen( p );
+    slen = strlen( s );
+    s[slen++] = '\r';
+    s[slen++] = '\n';
+
+    if( fout != NULL )
+    {
+        if( fwrite( p, 1, plen, fout ) != plen ||
+            fwrite( s, 1, slen, fout ) != slen )
+            return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
+    }
+    else
+        mbedtls_printf( "%s%s", p, s );
+
+cleanup:
+
+    return( ret );
+}
+#endif /* MBEDTLS_FS_IO */
+
+/*
+ * Import X from unsigned binary data, big endian
+ */
+int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
+{
+    int ret;
+    size_t i, j, n;
+
+    for( n = 0; n < buflen; n++ )
+        if( buf[n] != 0 )
+            break;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
+
+    for( i = buflen, j = 0; i > n; i--, j++ )
+        X->p[j / ciL] |= ((mbedtls_mpi_uint) buf[i - 1]) << ((j % ciL) << 3);
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Export X into unsigned binary data, big endian
+ */
+int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen )
+{
+    size_t i, j, n;
+
+    n = mbedtls_mpi_size( X );
+
+    if( buflen < n )
+        return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
+
+    memset( buf, 0, buflen );
+
+    for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- )
+        buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) );
+
+    return( 0 );
+}
+
+/*
+ * Left-shift: X <<= count
+ */
+int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count )
+{
+    int ret;
+    size_t i, v0, t1;
+    mbedtls_mpi_uint r0 = 0, r1;
+
+    v0 = count / (biL    );
+    t1 = count & (biL - 1);
+
+    i = mbedtls_mpi_bitlen( X ) + count;
+
+    if( X->n * biL < i )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) );
+
+    ret = 0;
+
+    /*
+     * shift by count / limb_size
+     */
+    if( v0 > 0 )
+    {
+        for( i = X->n; i > v0; i-- )
+            X->p[i - 1] = X->p[i - v0 - 1];
+
+        for( ; i > 0; i-- )
+            X->p[i - 1] = 0;
+    }
+
+    /*
+     * shift by count % limb_size
+     */
+    if( t1 > 0 )
+    {
+        for( i = v0; i < X->n; i++ )
+        {
+            r1 = X->p[i] >> (biL - t1);
+            X->p[i] <<= t1;
+            X->p[i] |= r0;
+            r0 = r1;
+        }
+    }
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Right-shift: X >>= count
+ */
+int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count )
+{
+    size_t i, v0, v1;
+    mbedtls_mpi_uint r0 = 0, r1;
+
+    v0 = count /  biL;
+    v1 = count & (biL - 1);
+
+    if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
+        return mbedtls_mpi_lset( X, 0 );
+
+    /*
+     * shift by count / limb_size
+     */
+    if( v0 > 0 )
+    {
+        for( i = 0; i < X->n - v0; i++ )
+            X->p[i] = X->p[i + v0];
+
+        for( ; i < X->n; i++ )
+            X->p[i] = 0;
+    }
+
+    /*
+     * shift by count % limb_size
+     */
+    if( v1 > 0 )
+    {
+        for( i = X->n; i > 0; i-- )
+        {
+            r1 = X->p[i - 1] << (biL - v1);
+            X->p[i - 1] >>= v1;
+            X->p[i - 1] |= r0;
+            r0 = r1;
+        }
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare unsigned values
+ */
+int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y )
+{
+    size_t i, j;
+
+    for( i = X->n; i > 0; i-- )
+        if( X->p[i - 1] != 0 )
+            break;
+
+    for( j = Y->n; j > 0; j-- )
+        if( Y->p[j - 1] != 0 )
+            break;
+
+    if( i == 0 && j == 0 )
+        return( 0 );
+
+    if( i > j ) return(  1 );
+    if( j > i ) return( -1 );
+
+    for( ; i > 0; i-- )
+    {
+        if( X->p[i - 1] > Y->p[i - 1] ) return(  1 );
+        if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
+{
+    size_t i, j;
+
+    for( i = X->n; i > 0; i-- )
+        if( X->p[i - 1] != 0 )
+            break;
+
+    for( j = Y->n; j > 0; j-- )
+        if( Y->p[j - 1] != 0 )
+            break;
+
+    if( i == 0 && j == 0 )
+        return( 0 );
+
+    if( i > j ) return(  X->s );
+    if( j > i ) return( -Y->s );
+
+    if( X->s > 0 && Y->s < 0 ) return(  1 );
+    if( Y->s > 0 && X->s < 0 ) return( -1 );
+
+    for( ; i > 0; i-- )
+    {
+        if( X->p[i - 1] > Y->p[i - 1] ) return(  X->s );
+        if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
+{
+    mbedtls_mpi Y;
+    mbedtls_mpi_uint p[1];
+
+    *p  = ( z < 0 ) ? -z : z;
+    Y.s = ( z < 0 ) ? -1 : 1;
+    Y.n = 1;
+    Y.p = p;
+
+    return( mbedtls_mpi_cmp_mpi( X, &Y ) );
+}
+
+/*
+ * Unsigned addition: X = |A| + |B|  (HAC 14.7)
+ */
+int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret;
+    size_t i, j;
+    mbedtls_mpi_uint *o, *p, c, tmp;
+
+    if( X == B )
+    {
+        const mbedtls_mpi *T = A; A = X; B = T;
+    }
+
+    if( X != A )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
+
+    /*
+     * X should always be positive as a result of unsigned additions.
+     */
+    X->s = 1;
+
+    for( j = B->n; j > 0; j-- )
+        if( B->p[j - 1] != 0 )
+            break;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
+
+    o = B->p; p = X->p; c = 0;
+
+    /*
+     * tmp is used because it might happen that p == o
+     */
+    for( i = 0; i < j; i++, o++, p++ )
+    {
+        tmp= *o;
+        *p +=  c; c  = ( *p <  c );
+        *p += tmp; c += ( *p < tmp );
+    }
+
+    while( c != 0 )
+    {
+        if( i >= X->n )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
+            p = X->p + i;
+        }
+
+        *p += c; c = ( *p < c ); i++; p++;
+    }
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Helper for mbedtls_mpi subtraction
+ */
+static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
+{
+    size_t i;
+    mbedtls_mpi_uint c, z;
+
+    for( i = c = 0; i < n; i++, s++, d++ )
+    {
+        z = ( *d <  c );     *d -=  c;
+        c = ( *d < *s ) + z; *d -= *s;
+    }
+
+    while( c != 0 )
+    {
+        z = ( *d < c ); *d -= c;
+        c = z; i++; d++;
+    }
+}
+
+/*
+ * Unsigned subtraction: X = |A| - |B|  (HAC 14.9)
+ */
+int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    mbedtls_mpi TB;
+    int ret;
+    size_t n;
+
+    if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
+        return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
+
+    mbedtls_mpi_init( &TB );
+
+    if( X == B )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
+        B = &TB;
+    }
+
+    if( X != A )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
+
+    /*
+     * X should always be positive as a result of unsigned subtractions.
+     */
+    X->s = 1;
+
+    ret = 0;
+
+    for( n = B->n; n > 0; n-- )
+        if( B->p[n - 1] != 0 )
+            break;
+
+    mpi_sub_hlp( n, B->p, X->p );
+
+cleanup:
+
+    mbedtls_mpi_free( &TB );
+
+    return( ret );
+}
+
+/*
+ * Signed addition: X = A + B
+ */
+int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret, s = A->s;
+
+    if( A->s * B->s < 0 )
+    {
+        if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
+            X->s =  s;
+        }
+        else
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
+            X->s = -s;
+        }
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
+        X->s = s;
+    }
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Signed subtraction: X = A - B
+ */
+int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret, s = A->s;
+
+    if( A->s * B->s > 0 )
+    {
+        if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
+            X->s =  s;
+        }
+        else
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
+            X->s = -s;
+        }
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
+        X->s = s;
+    }
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Signed addition: X = A + b
+ */
+int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
+{
+    mbedtls_mpi _B;
+    mbedtls_mpi_uint p[1];
+
+    p[0] = ( b < 0 ) ? -b : b;
+    _B.s = ( b < 0 ) ? -1 : 1;
+    _B.n = 1;
+    _B.p = p;
+
+    return( mbedtls_mpi_add_mpi( X, A, &_B ) );
+}
+
+/*
+ * Signed subtraction: X = A - b
+ */
+int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
+{
+    mbedtls_mpi _B;
+    mbedtls_mpi_uint p[1];
+
+    p[0] = ( b < 0 ) ? -b : b;
+    _B.s = ( b < 0 ) ? -1 : 1;
+    _B.n = 1;
+    _B.p = p;
+
+    return( mbedtls_mpi_sub_mpi( X, A, &_B ) );
+}
+
+/*
+ * Helper for mbedtls_mpi multiplication
+ */
+static
+#if defined(__APPLE__) && defined(__arm__)
+/*
+ * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
+ * appears to need this to prevent bad ARM code generation at -O3.
+ */
+__attribute__ ((noinline))
+#endif
+void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
+{
+    mbedtls_mpi_uint c = 0, t = 0;
+
+#if defined(MULADDC_HUIT)
+    for( ; i >= 8; i -= 8 )
+    {
+        MULADDC_INIT
+        MULADDC_HUIT
+        MULADDC_STOP
+    }
+
+    for( ; i > 0; i-- )
+    {
+        MULADDC_INIT
+        MULADDC_CORE
+        MULADDC_STOP
+    }
+#else /* MULADDC_HUIT */
+    for( ; i >= 16; i -= 16 )
+    {
+        MULADDC_INIT
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_STOP
+    }
+
+    for( ; i >= 8; i -= 8 )
+    {
+        MULADDC_INIT
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_CORE   MULADDC_CORE
+        MULADDC_STOP
+    }
+
+    for( ; i > 0; i-- )
+    {
+        MULADDC_INIT
+        MULADDC_CORE
+        MULADDC_STOP
+    }
+#endif /* MULADDC_HUIT */
+
+    t++;
+
+    do {
+        *d += c; c = ( *d < c ); d++;
+    }
+    while( c != 0 );
+}
+
+/*
+ * Baseline multiplication: X = A * B  (HAC 14.12)
+ */
+int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret;
+    size_t i, j;
+    mbedtls_mpi TA, TB;
+
+    mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
+
+    if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
+    if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
+
+    for( i = A->n; i > 0; i-- )
+        if( A->p[i - 1] != 0 )
+            break;
+
+    for( j = B->n; j > 0; j-- )
+        if( B->p[j - 1] != 0 )
+            break;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
+
+    for( i++; j > 0; j-- )
+        mpi_mul_hlp( i - 1, A->p, X->p + j - 1, B->p[j - 1] );
+
+    X->s = A->s * B->s;
+
+cleanup:
+
+    mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
+
+    return( ret );
+}
+
+/*
+ * Baseline multiplication: X = A * b
+ */
+int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
+{
+    mbedtls_mpi _B;
+    mbedtls_mpi_uint p[1];
+
+    _B.s = 1;
+    _B.n = 1;
+    _B.p = p;
+    p[0] = b;
+
+    return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
+}
+
+/*
+ * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
+ * mbedtls_mpi_uint divisor, d
+ */
+static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1,
+            mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r )
+{
+#if defined(MBEDTLS_HAVE_UDBL)
+    mbedtls_t_udbl dividend, quotient;
+#else
+    const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
+    const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1;
+    mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
+    mbedtls_mpi_uint u0_msw, u0_lsw;
+    size_t s;
+#endif
+
+    /*
+     * Check for overflow
+     */
+    if( 0 == d || u1 >= d )
+    {
+        if (r != NULL) *r = ~0;
+
+        return ( ~0 );
+    }
+
+#if defined(MBEDTLS_HAVE_UDBL)
+    dividend  = (mbedtls_t_udbl) u1 << biL;
+    dividend |= (mbedtls_t_udbl) u0;
+    quotient = dividend / d;
+    if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
+        quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1;
+
+    if( r != NULL )
+        *r = (mbedtls_mpi_uint)( dividend - (quotient * d ) );
+
+    return (mbedtls_mpi_uint) quotient;
+#else
+
+    /*
+     * Algorithm D, Section 4.3.1 - The Art of Computer Programming
+     *   Vol. 2 - Seminumerical Algorithms, Knuth
+     */
+
+    /*
+     * Normalize the divisor, d, and dividend, u0, u1
+     */
+    s = mbedtls_clz( d );
+    d = d << s;
+
+    u1 = u1 << s;
+    u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) );
+    u0 =  u0 << s;
+
+    d1 = d >> biH;
+    d0 = d & uint_halfword_mask;
+
+    u0_msw = u0 >> biH;
+    u0_lsw = u0 & uint_halfword_mask;
+
+    /*
+     * Find the first quotient and remainder
+     */
+    q1 = u1 / d1;
+    r0 = u1 - d1 * q1;
+
+    while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
+    {
+        q1 -= 1;
+        r0 += d1;
+
+        if ( r0 >= radix ) break;
+    }
+
+    rAX = ( u1 * radix ) + ( u0_msw - q1 * d );
+    q0 = rAX / d1;
+    r0 = rAX - q0 * d1;
+
+    while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
+    {
+        q0 -= 1;
+        r0 += d1;
+
+        if ( r0 >= radix ) break;
+    }
+
+    if (r != NULL)
+        *r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
+
+    quotient = q1 * radix + q0;
+
+    return quotient;
+#endif
+}
+
+/*
+ * Division by mbedtls_mpi: A = Q * B + R  (HAC 14.20)
+ */
+int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret;
+    size_t i, n, t, k;
+    mbedtls_mpi X, Y, Z, T1, T2;
+
+    if( mbedtls_mpi_cmp_int( B, 0 ) == 0 )
+        return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
+
+    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
+    mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
+
+    if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
+    {
+        if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
+        if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) );
+        return( 0 );
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) );
+    X.s = Y.s = 1;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z,  0 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, 2 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) );
+
+    k = mbedtls_mpi_bitlen( &Y ) % biL;
+    if( k < biL - 1 )
+    {
+        k = biL - 1 - k;
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) );
+    }
+    else k = 0;
+
+    n = X.n - 1;
+    t = Y.n - 1;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) );
+
+    while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 )
+    {
+        Z.p[n - t]++;
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
+    }
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) );
+
+    for( i = n; i > t ; i-- )
+    {
+        if( X.p[i] >= Y.p[t] )
+            Z.p[i - t - 1] = ~0;
+        else
+        {
+            Z.p[i - t - 1] = mbedtls_int_div_int( X.p[i], X.p[i - 1],
+                                                            Y.p[t], NULL);
+        }
+
+        Z.p[i - t - 1]++;
+        do
+        {
+            Z.p[i - t - 1]--;
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
+            T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
+            T1.p[1] = Y.p[t];
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) );
+            T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2];
+            T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1];
+            T2.p[2] = X.p[i];
+        }
+        while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1,  biL * ( i - t - 1 ) ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) );
+
+        if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) );
+            Z.p[i - t - 1]--;
+        }
+    }
+
+    if( Q != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
+        Q->s = A->s * B->s;
+    }
+
+    if( R != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
+        X.s = A->s;
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
+
+        if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
+            R->s = 1;
+    }
+
+cleanup:
+
+    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
+    mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
+
+    return( ret );
+}
+
+/*
+ * Division by int: A = Q * b + R
+ */
+int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b )
+{
+    mbedtls_mpi _B;
+    mbedtls_mpi_uint p[1];
+
+    p[0] = ( b < 0 ) ? -b : b;
+    _B.s = ( b < 0 ) ? -1 : 1;
+    _B.n = 1;
+    _B.p = p;
+
+    return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) );
+}
+
+/*
+ * Modulo: R = A mod B
+ */
+int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret;
+
+    if( mbedtls_mpi_cmp_int( B, 0 ) < 0 )
+        return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) );
+
+    while( mbedtls_mpi_cmp_int( R, 0 ) < 0 )
+      MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) );
+
+    while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 )
+      MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) );
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Modulo: r = A mod b
+ */
+int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b )
+{
+    size_t i;
+    mbedtls_mpi_uint x, y, z;
+
+    if( b == 0 )
+        return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
+
+    if( b < 0 )
+        return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
+
+    /*
+     * handle trivial cases
+     */
+    if( b == 1 )
+    {
+        *r = 0;
+        return( 0 );
+    }
+
+    if( b == 2 )
+    {
+        *r = A->p[0] & 1;
+        return( 0 );
+    }
+
+    /*
+     * general case
+     */
+    for( i = A->n, y = 0; i > 0; i-- )
+    {
+        x  = A->p[i - 1];
+        y  = ( y << biH ) | ( x >> biH );
+        z  = y / b;
+        y -= z * b;
+
+        x <<= biH;
+        y  = ( y << biH ) | ( x >> biH );
+        z  = y / b;
+        y -= z * b;
+    }
+
+    /*
+     * If A is negative, then the current y represents a negative value.
+     * Flipping it to the positive side.
+     */
+    if( A->s < 0 && y != 0 )
+        y = b - y;
+
+    *r = y;
+
+    return( 0 );
+}
+
+/*
+ * Fast Montgomery initialization (thanks to Tom St Denis)
+ */
+static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
+{
+    mbedtls_mpi_uint x, m0 = N->p[0];
+    unsigned int i;
+
+    x  = m0;
+    x += ( ( m0 + 2 ) & 4 ) << 1;
+
+    for( i = biL; i >= 8; i /= 2 )
+        x *= ( 2 - ( m0 * x ) );
+
+    *mm = ~x + 1;
+}
+
+/*
+ * Montgomery multiplication: A = A * B * R^-1 mod N  (HAC 14.36)
+ */
+static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
+                         const mbedtls_mpi *T )
+{
+    size_t i, n, m;
+    mbedtls_mpi_uint u0, u1, *d;
+
+    if( T->n < N->n + 1 || T->p == NULL )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    memset( T->p, 0, T->n * ciL );
+
+    d = T->p;
+    n = N->n;
+    m = ( B->n < n ) ? B->n : n;
+
+    for( i = 0; i < n; i++ )
+    {
+        /*
+         * T = (T + u0*B + u1*N) / 2^biL
+         */
+        u0 = A->p[i];
+        u1 = ( d[0] + u0 * B->p[0] ) * mm;
+
+        mpi_mul_hlp( m, B->p, d, u0 );
+        mpi_mul_hlp( n, N->p, d, u1 );
+
+        *d++ = u0; d[n + 1] = 0;
+    }
+
+    memcpy( A->p, d, ( n + 1 ) * ciL );
+
+    if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
+        mpi_sub_hlp( n, N->p, A->p );
+    else
+        /* prevent timing attacks */
+        mpi_sub_hlp( n, A->p, T->p );
+
+    return( 0 );
+}
+
+/*
+ * Montgomery reduction: A = A * R^-1 mod N
+ */
+static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T )
+{
+    mbedtls_mpi_uint z = 1;
+    mbedtls_mpi U;
+
+    U.n = U.s = (int) z;
+    U.p = &z;
+
+    return( mpi_montmul( A, &U, N, mm, T ) );
+}
+
+/*
+ * Sliding-window exponentiation: X = A^E mod N  (HAC 14.85)
+ */
+int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR )
+{
+    int ret;
+    size_t wbits, wsize, one = 1;
+    size_t i, j, nblimbs;
+    size_t bufsize, nbits;
+    mbedtls_mpi_uint ei, mm, state;
+    mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
+    int neg;
+
+    if( mbedtls_mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    /*
+     * Init temps and window size
+     */
+    mpi_montg_init( &mm, N );
+    mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
+    mbedtls_mpi_init( &Apos );
+    memset( W, 0, sizeof( W ) );
+
+    i = mbedtls_mpi_bitlen( E );
+
+    wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
+            ( i >  79 ) ? 4 : ( i >  23 ) ? 3 : 1;
+
+    if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
+        wsize = MBEDTLS_MPI_WINDOW_SIZE;
+
+    j = N->n + 1;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1],  j ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
+
+    /*
+     * Compensate for negative A (and correct at the end)
+     */
+    neg = ( A->s == -1 );
+    if( neg )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
+        Apos.s = 1;
+        A = &Apos;
+    }
+
+    /*
+     * If 1st call, pre-compute R^2 mod N
+     */
+    if( _RR == NULL || _RR->p == NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
+
+        if( _RR != NULL )
+            memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
+    }
+    else
+        memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
+
+    /*
+     * W[1] = A * R^2 * R^-1 mod N = A * R mod N
+     */
+    if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
+    else
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
+
+    MBEDTLS_MPI_CHK( mpi_montmul( &W[1], &RR, N, mm, &T ) );
+
+    /*
+     * X = R^2 * R^-1 mod N = R mod N
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
+    MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
+
+    if( wsize > 1 )
+    {
+        /*
+         * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
+         */
+        j =  one << ( wsize - 1 );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1]    ) );
+
+        for( i = 0; i < wsize - 1; i++ )
+            MBEDTLS_MPI_CHK( mpi_montmul( &W[j], &W[j], N, mm, &T ) );
+
+        /*
+         * W[i] = W[i - 1] * W[1]
+         */
+        for( i = j + 1; i < ( one << wsize ); i++ )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
+
+            MBEDTLS_MPI_CHK( mpi_montmul( &W[i], &W[1], N, mm, &T ) );
+        }
+    }
+
+    nblimbs = E->n;
+    bufsize = 0;
+    nbits   = 0;
+    wbits   = 0;
+    state   = 0;
+
+    while( 1 )
+    {
+        if( bufsize == 0 )
+        {
+            if( nblimbs == 0 )
+                break;
+
+            nblimbs--;
+
+            bufsize = sizeof( mbedtls_mpi_uint ) << 3;
+        }
+
+        bufsize--;
+
+        ei = (E->p[nblimbs] >> bufsize) & 1;
+
+        /*
+         * skip leading 0s
+         */
+        if( ei == 0 && state == 0 )
+            continue;
+
+        if( ei == 0 && state == 1 )
+        {
+            /*
+             * out of window, square X
+             */
+            MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
+            continue;
+        }
+
+        /*
+         * add ei to current window
+         */
+        state = 2;
+
+        nbits++;
+        wbits |= ( ei << ( wsize - nbits ) );
+
+        if( nbits == wsize )
+        {
+            /*
+             * X = X^wsize R^-1 mod N
+             */
+            for( i = 0; i < wsize; i++ )
+                MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
+
+            /*
+             * X = X * W[wbits] R^-1 mod N
+             */
+            MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) );
+
+            state--;
+            nbits = 0;
+            wbits = 0;
+        }
+    }
+
+    /*
+     * process the remaining bits
+     */
+    for( i = 0; i < nbits; i++ )
+    {
+        MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
+
+        wbits <<= 1;
+
+        if( ( wbits & ( one << wsize ) ) != 0 )
+            MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) );
+    }
+
+    /*
+     * X = A^E * R * R^-1 mod N = A^E mod N
+     */
+    MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
+
+    if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
+    {
+        X->s = -1;
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
+    }
+
+cleanup:
+
+    for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
+        mbedtls_mpi_free( &W[i] );
+
+    mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
+
+    if( _RR == NULL || _RR->p == NULL )
+        mbedtls_mpi_free( &RR );
+
+    return( ret );
+}
+
+/*
+ * Greatest common divisor: G = gcd(A, B)  (HAC 14.54)
+ */
+int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
+{
+    int ret;
+    size_t lz, lzt;
+    mbedtls_mpi TG, TA, TB;
+
+    mbedtls_mpi_init( &TG ); mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
+
+    lz = mbedtls_mpi_lsb( &TA );
+    lzt = mbedtls_mpi_lsb( &TB );
+
+    if( lzt < lz )
+        lz = lzt;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
+
+    TA.s = TB.s = 1;
+
+    while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
+
+        if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
+        }
+        else
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
+        }
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
+
+cleanup:
+
+    mbedtls_mpi_free( &TG ); mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
+
+    return( ret );
+}
+
+/*
+ * Fill X with size bytes of random.
+ *
+ * Use a temporary bytes representation to make sure the result is the same
+ * regardless of the platform endianness (useful when f_rng is actually
+ * deterministic, eg for tests).
+ */
+int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
+                     int (*f_rng)(void *, unsigned char *, size_t),
+                     void *p_rng )
+{
+    int ret;
+    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];
+
+    if( size > MBEDTLS_MPI_MAX_SIZE )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    MBEDTLS_MPI_CHK( f_rng( p_rng, buf, size ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( X, buf, size ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Modular inverse: X = A^-1 mod N  (HAC 14.61 / 14.64)
+ */
+int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
+{
+    int ret;
+    mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
+
+    if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
+    mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV );
+    mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) );
+
+    if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
+    {
+        ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+        goto cleanup;
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) );
+
+    do
+    {
+        while( ( TU.p[0] & 1 ) == 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 1 ) );
+
+            if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
+            {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) );
+                MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) );
+            }
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) );
+        }
+
+        while( ( TV.p[0] & 1 ) == 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 1 ) );
+
+            if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
+            {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) );
+                MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) );
+            }
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 1 ) );
+        }
+
+        if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 )
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) );
+        }
+        else
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) );
+        }
+    }
+    while( mbedtls_mpi_cmp_int( &TU, 0 ) != 0 );
+
+    while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) );
+
+    while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) );
+
+cleanup:
+
+    mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 );
+    mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV );
+    mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 );
+
+    return( ret );
+}
+
+#if defined(MBEDTLS_GENPRIME)
+
+static const int small_prime[] =
+{
+        3,    5,    7,   11,   13,   17,   19,   23,
+       29,   31,   37,   41,   43,   47,   53,   59,
+       61,   67,   71,   73,   79,   83,   89,   97,
+      101,  103,  107,  109,  113,  127,  131,  137,
+      139,  149,  151,  157,  163,  167,  173,  179,
+      181,  191,  193,  197,  199,  211,  223,  227,
+      229,  233,  239,  241,  251,  257,  263,  269,
+      271,  277,  281,  283,  293,  307,  311,  313,
+      317,  331,  337,  347,  349,  353,  359,  367,
+      373,  379,  383,  389,  397,  401,  409,  419,
+      421,  431,  433,  439,  443,  449,  457,  461,
+      463,  467,  479,  487,  491,  499,  503,  509,
+      521,  523,  541,  547,  557,  563,  569,  571,
+      577,  587,  593,  599,  601,  607,  613,  617,
+      619,  631,  641,  643,  647,  653,  659,  661,
+      673,  677,  683,  691,  701,  709,  719,  727,
+      733,  739,  743,  751,  757,  761,  769,  773,
+      787,  797,  809,  811,  821,  823,  827,  829,
+      839,  853,  857,  859,  863,  877,  881,  883,
+      887,  907,  911,  919,  929,  937,  941,  947,
+      953,  967,  971,  977,  983,  991,  997, -103
+};
+
+/*
+ * Small divisors test (X must be positive)
+ *
+ * Return values:
+ * 0: no small factor (possible prime, more tests needed)
+ * 1: certain prime
+ * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
+ * other negative: error
+ */
+static int mpi_check_small_factors( const mbedtls_mpi *X )
+{
+    int ret = 0;
+    size_t i;
+    mbedtls_mpi_uint r;
+
+    if( ( X->p[0] & 1 ) == 0 )
+        return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
+
+    for( i = 0; small_prime[i] > 0; i++ )
+    {
+        if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 )
+            return( 1 );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) );
+
+        if( r == 0 )
+            return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
+    }
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Miller-Rabin pseudo-primality test  (HAC 4.24)
+ */
+static int mpi_miller_rabin( const mbedtls_mpi *X,
+                             int (*f_rng)(void *, unsigned char *, size_t),
+                             void *p_rng )
+{
+    int ret, count;
+    size_t i, j, k, n, s;
+    mbedtls_mpi W, R, T, A, RR;
+
+    mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
+    mbedtls_mpi_init( &RR );
+
+    /*
+     * W = |X| - 1
+     * R = W >> lsb( W )
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) );
+    s = mbedtls_mpi_lsb( &W );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
+
+    i = mbedtls_mpi_bitlen( X );
+    /*
+     * HAC, table 4.4
+     */
+    n = ( ( i >= 1300 ) ?  2 : ( i >=  850 ) ?  3 :
+          ( i >=  650 ) ?  4 : ( i >=  350 ) ?  8 :
+          ( i >=  250 ) ? 12 : ( i >=  150 ) ? 18 : 27 );
+
+    for( i = 0; i < n; i++ )
+    {
+        /*
+         * pick a random A, 1 < A < |X| - 1
+         */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
+
+        if( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 )
+        {
+            j = mbedtls_mpi_bitlen( &A ) - mbedtls_mpi_bitlen( &W );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j + 1 ) );
+        }
+        A.p[0] |= 3;
+
+        count = 0;
+        do {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
+
+            j = mbedtls_mpi_bitlen( &A );
+            k = mbedtls_mpi_bitlen( &W );
+            if (j > k) {
+                MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j - k ) );
+            }
+
+            if (count++ > 30) {
+                return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+            }
+
+        } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
+                  mbedtls_mpi_cmp_int( &A, 1 )  <= 0    );
+
+        /*
+         * A = A^R mod |X|
+         */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) );
+
+        if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 ||
+            mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
+            continue;
+
+        j = 1;
+        while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 )
+        {
+            /*
+             * A = A * A mod |X|
+             */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X  ) );
+
+            if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
+                break;
+
+            j++;
+        }
+
+        /*
+         * not prime if A != |X| - 1 or A == 1
+         */
+        if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ||
+            mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
+        {
+            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+            break;
+        }
+    }
+
+cleanup:
+    mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A );
+    mbedtls_mpi_free( &RR );
+
+    return( ret );
+}
+
+/*
+ * Pseudo-primality test: small factors, then Miller-Rabin
+ */
+int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
+                  int (*f_rng)(void *, unsigned char *, size_t),
+                  void *p_rng )
+{
+    int ret;
+    mbedtls_mpi XX;
+
+    XX.s = 1;
+    XX.n = X->n;
+    XX.p = X->p;
+
+    if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 ||
+        mbedtls_mpi_cmp_int( &XX, 1 ) == 0 )
+        return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
+
+    if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 )
+        return( 0 );
+
+    if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
+    {
+        if( ret == 1 )
+            return( 0 );
+
+        return( ret );
+    }
+
+    return( mpi_miller_rabin( &XX, f_rng, p_rng ) );
+}
+
+/*
+ * Prime number generation
+ */
+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 )
+{
+    int ret;
+    size_t k, n;
+    mbedtls_mpi_uint r;
+    mbedtls_mpi Y;
+
+    if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    mbedtls_mpi_init( &Y );
+
+    n = BITS_TO_LIMBS( nbits );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
+
+    k = mbedtls_mpi_bitlen( X );
+    if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits + 1 ) );
+
+    mbedtls_mpi_set_bit( X, nbits-1, 1 );
+
+    X->p[0] |= 1;
+
+    if( dh_flag == 0 )
+    {
+        while( ( ret = mbedtls_mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
+        {
+            if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
+                goto cleanup;
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 2 ) );
+        }
+    }
+    else
+    {
+        /*
+         * An necessary condition for Y and X = 2Y + 1 to be prime
+         * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
+         * Make sure it is satisfied, while keeping X = 3 mod 4
+         */
+
+        X->p[0] |= 2;
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
+        if( r == 0 )
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
+        else if( r == 1 )
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) );
+
+        /* Set Y = (X-1) / 2, which is X / 2 because X is odd */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 1 ) );
+
+        while( 1 )
+        {
+            /*
+             * First, check small factors for X and Y
+             * before doing Miller-Rabin on any of them
+             */
+            if( ( ret = mpi_check_small_factors(  X         ) ) == 0 &&
+                ( ret = mpi_check_small_factors( &Y         ) ) == 0 &&
+                ( ret = mpi_miller_rabin(  X, f_rng, p_rng  ) ) == 0 &&
+                ( ret = mpi_miller_rabin( &Y, f_rng, p_rng  ) ) == 0 )
+            {
+                break;
+            }
+
+            if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
+                goto cleanup;
+
+            /*
+             * Next candidates. We want to preserve Y = (X-1) / 2 and
+             * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
+             * so up Y by 6 and X by 12.
+             */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int(  X,  X, 12 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6  ) );
+        }
+    }
+
+cleanup:
+
+    mbedtls_mpi_free( &Y );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_GENPRIME */
+
+#if defined(MBEDTLS_SELF_TEST)
+
+#define GCD_PAIR_COUNT  3
+
+static const int gcd_pairs[GCD_PAIR_COUNT][3] =
+{
+    { 693, 609, 21 },
+    { 1764, 868, 28 },
+    { 768454923, 542167814, 1 }
+};
+
+/*
+ * Checkup routine
+ */
+int mbedtls_mpi_self_test( int verbose )
+{
+    int ret, i;
+    mbedtls_mpi A, E, N, X, Y, U, V;
+
+    mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X );
+    mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16,
+        "EFE021C2645FD1DC586E69184AF4A31E" \
+        "D5F53E93B5F123FA41680867BA110131" \
+        "944FE7952E2517337780CB0DB80E61AA" \
+        "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16,
+        "B2E7EFD37075B9F03FF989C7C5051C20" \
+        "34D2A323810251127E7BF8625A4F49A5" \
+        "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
+        "5B5C25763222FEFCCFC38B832366C29E" ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16,
+        "0066A198186C18C10B2F5ED9B522752A" \
+        "9830B69916E535C8F047518A889A43A5" \
+        "94B6BED27A168D31D4A52F88925AA8F5" ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
+        "602AB7ECA597A3D6B56FF9829A5E8B85" \
+        "9E857EA95A03512E2BAE7391688D264A" \
+        "A5663B0341DB9CCFD2C4C5F421FEC814" \
+        "8001B72E848A38CAE1C65F78E56ABDEF" \
+        "E12D3C039B8A02D6BE593F0BBBDA56F1" \
+        "ECF677152EF804370C1A305CAF3B5BF1" \
+        "30879B56C61DE584A0F53A2447A51E" ) );
+
+    if( verbose != 0 )
+        mbedtls_printf( "  MPI test #1 (mul_mpi): " );
+
+    if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
+    {
+        if( verbose != 0 )
+            mbedtls_printf( "failed\n" );
+
+        ret = 1;
+        goto cleanup;
+    }
+
+    if( verbose != 0 )
+        mbedtls_printf( "passed\n" );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
+        "256567336059E52CAE22925474705F39A94" ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16,
+        "6613F26162223DF488E9CD48CC132C7A" \
+        "0AC93C701B001B092E4E5B9F73BCD27B" \
+        "9EE50D0657C77F374E903CDFA4C642" ) );
+
+    if( verbose != 0 )
+        mbedtls_printf( "  MPI test #2 (div_mpi): " );
+
+    if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ||
+        mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 )
+    {
+        if( verbose != 0 )
+            mbedtls_printf( "failed\n" );
+
+        ret = 1;
+        goto cleanup;
+    }
+
+    if( verbose != 0 )
+        mbedtls_printf( "passed\n" );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
+        "36E139AEA55215609D2816998ED020BB" \
+        "BD96C37890F65171D948E9BC7CBAA4D9" \
+        "325D24D6A3C12710F10A09FA08AB87" ) );
+
+    if( verbose != 0 )
+        mbedtls_printf( "  MPI test #3 (exp_mod): " );
+
+    if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
+    {
+        if( verbose != 0 )
+            mbedtls_printf( "failed\n" );
+
+        ret = 1;
+        goto cleanup;
+    }
+
+    if( verbose != 0 )
+        mbedtls_printf( "passed\n" );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
+        "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
+        "C3DBA76456363A10869622EAC2DD84EC" \
+        "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
+
+    if( verbose != 0 )
+        mbedtls_printf( "  MPI test #4 (inv_mod): " );
+
+    if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
+    {
+        if( verbose != 0 )
+            mbedtls_printf( "failed\n" );
+
+        ret = 1;
+        goto cleanup;
+    }
+
+    if( verbose != 0 )
+        mbedtls_printf( "passed\n" );
+
+    if( verbose != 0 )
+        mbedtls_printf( "  MPI test #5 (simple gcd): " );
+
+    for( i = 0; i < GCD_PAIR_COUNT; i++ )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) );
+
+        if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
+        {
+            if( verbose != 0 )
+                mbedtls_printf( "failed at %d\n", i );
+
+            ret = 1;
+            goto cleanup;
+        }
+    }
+
+    if( verbose != 0 )
+        mbedtls_printf( "passed\n" );
+
+cleanup:
+
+    if( ret != 0 && verbose != 0 )
+        mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
+
+    mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X );
+    mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V );
+
+    if( verbose != 0 )
+        mbedtls_printf( "\n" );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_SELF_TEST */
+
+#endif /* MBEDTLS_BIGNUM_C */