Add mbedTLS lib. Version 2.7.0, license Apache 2.0

1 files changed, 2457 insertions, 0 deletions

diff --git a/thirdparty/mbedtls/library/bignum.c b/thirdparty/mbedtls/library/bignum.c
new file mode 100644
index 0000000000..d27c130bcb
--- /dev/null
+++ b/thirdparty/mbedtls/library/bignum.c
@@ -0,0 +1,2457 @@
+/*
+ *  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)
+ */
+
+/*
+ *  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"
+
+#include <string.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;
+}
+
+/* Implementation that should never be optimized out by the compiler */
+static void mbedtls_zeroize( void *v, size_t n ) {
+    volatile unsigned char *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;
+    size_t const limbs = CHARS_TO_LIMBS( buflen );
+
+    /* Ensure that target MPI has exactly the necessary number of limbs */
+    if( X->n != limbs )
+    {
+        mbedtls_mpi_free( X );
+        mbedtls_mpi_init( X );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
+
+    for( i = buflen, j = 0; i > 0; 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:
+    mbedtls_zeroize( buf, sizeof( buf ) );
+    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 */