Removed old mbedtls, replacing with submodule.

1 files changed, 0 insertions, 3384 deletions

diff --git a/lib/mbedtls-2.27.0/library/bignum.c b/lib/mbedtls-2.27.0/library/bignum.c
deleted file mode 100644
index 20afa22..0000000
--- a/lib/mbedtls-2.27.0/library/bignum.c
+++ /dev/null
@@ -1,3384 +0,0 @@
-/*
- *  Multi-precision integer library
- *
- *  Copyright The Mbed TLS Contributors
- *  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.
- */
-
-/*
- *  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
- *
- */
-
-#include "common.h"
-
-#if defined(MBEDTLS_BIGNUM_C)
-
-#include "mbedtls/bignum.h"
-#include "mbedtls/bn_mul.h"
-#include "mbedtls/platform_util.h"
-#include "mbedtls/error.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
-
-#define MPI_VALIDATE_RET( cond )                                       \
-    MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA )
-#define MPI_VALIDATE( cond )                                           \
-    MBEDTLS_INTERNAL_VALIDATE( cond )
-
-#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 ) )
-
-/* Implementation that should never be optimized out by the compiler */
-static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n )
-{
-    mbedtls_platform_zeroize( v, ciL * n );
-}
-
-/*
- * Initialize one MPI
- */
-void mbedtls_mpi_init( mbedtls_mpi *X )
-{
-    MPI_VALIDATE( X != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-
-    if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
-        return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
-
-    /* Actually resize up if there are currently fewer than nblimbs limbs. */
-    if( X->n <= nblimbs )
-        return( mbedtls_mpi_grow( X, nblimbs ) );
-    /* After this point, then X->n > nblimbs and in particular X->n > 0. */
-
-    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 );
-}
-
-/* Resize X to have exactly n limbs and set it to 0. */
-static int mbedtls_mpi_resize_clear( mbedtls_mpi *X, size_t limbs )
-{
-    if( limbs == 0 )
-    {
-        mbedtls_mpi_free( X );
-        return( 0 );
-    }
-    else if( X->n == limbs )
-    {
-        memset( X->p, 0, limbs * ciL );
-        X->s = 1;
-        return( 0 );
-    }
-    else
-    {
-        mbedtls_mpi_free( X );
-        return( mbedtls_mpi_grow( X, limbs ) );
-    }
-}
-
-/*
- * Copy the contents of Y into X.
- *
- * This function is not constant-time. Leading zeros in Y may be removed.
- *
- * Ensure that X does not shrink. This is not guaranteed by the public API,
- * but some code in the bignum module relies on this property, for example
- * in mbedtls_mpi_exp_mod().
- */
-int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
-{
-    int ret = 0;
-    size_t i;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-
-    if( X == Y )
-        return( 0 );
-
-    if( Y->n == 0 )
-    {
-        if( X->n != 0 )
-        {
-            X->s = 1;
-            memset( X->p, 0, X->n * ciL );
-        }
-        return( 0 );
-    }
-
-    for( i = Y->n - 1; i > 0; i-- )
-        if( Y->p[i] != 0 )
-            break;
-    i++;
-
-    X->s = Y->s;
-
-    if( X->n < i )
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
-    }
-    else
-    {
-        memset( X->p + i, 0, ( X->n - i ) * 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;
-    MPI_VALIDATE( X != NULL );
-    MPI_VALIDATE( Y != NULL );
-
-    memcpy( &T,  X, sizeof( mbedtls_mpi ) );
-    memcpy(  X,  Y, sizeof( mbedtls_mpi ) );
-    memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
-}
-
-/**
- * Select between two sign values in constant-time.
- *
- * This is functionally equivalent to second ? a : b but uses only bit
- * operations in order to avoid branches.
- *
- * \param[in] a         The first sign; must be either +1 or -1.
- * \param[in] b         The second sign; must be either +1 or -1.
- * \param[in] second    Must be either 1 (return b) or 0 (return a).
- *
- * \return The selected sign value.
- */
-static int mpi_safe_cond_select_sign( int a, int b, unsigned char second )
-{
-    /* In order to avoid questions about what we can reasonnably assume about
-     * the representations of signed integers, move everything to unsigned
-     * by taking advantage of the fact that a and b are either +1 or -1. */
-    unsigned ua = a + 1;
-    unsigned ub = b + 1;
-
-    /* second was 0 or 1, mask is 0 or 2 as are ua and ub */
-    const unsigned mask = second << 1;
-
-    /* select ua or ub */
-    unsigned ur = ( ua & ~mask ) | ( ub & mask );
-
-    /* ur is now 0 or 2, convert back to -1 or +1 */
-    return( (int) ur - 1 );
-}
-
-/*
- * Conditionally assign dest = src, without leaking information
- * about whether the assignment was made or not.
- * dest and src must be arrays of limbs of size n.
- * assign must be 0 or 1.
- */
-static void mpi_safe_cond_assign( size_t n,
-                                  mbedtls_mpi_uint *dest,
-                                  const mbedtls_mpi_uint *src,
-                                  unsigned char assign )
-{
-    size_t i;
-
-    /* MSVC has a warning about unary minus on unsigned integer types,
-     * but this is well-defined and precisely what we want to do here. */
-#if defined(_MSC_VER)
-#pragma warning( push )
-#pragma warning( disable : 4146 )
-#endif
-
-    /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */
-    const mbedtls_mpi_uint mask = -assign;
-
-#if defined(_MSC_VER)
-#pragma warning( pop )
-#endif
-
-    for( i = 0; i < n; i++ )
-        dest[i] = ( src[i] & mask ) | ( dest[i] & ~mask );
-}
-
-/*
- * 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;
-    mbedtls_mpi_uint limb_mask;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-
-    /* MSVC has a warning about unary minus on unsigned integer types,
-     * but this is well-defined and precisely what we want to do here. */
-#if defined(_MSC_VER)
-#pragma warning( push )
-#pragma warning( disable : 4146 )
-#endif
-
-    /* make sure assign is 0 or 1 in a time-constant manner */
-    assign = (assign | (unsigned char)-assign) >> (sizeof( assign ) * 8 - 1);
-    /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */
-    limb_mask = -assign;
-
-#if defined(_MSC_VER)
-#pragma warning( pop )
-#endif
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
-
-    X->s = mpi_safe_cond_select_sign( X->s, Y->s, assign );
-
-    mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );
-
-    for( i = Y->n; i < X->n; i++ )
-        X->p[i] &= ~limb_mask;
-
-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 limb_mask;
-    mbedtls_mpi_uint tmp;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-
-    if( X == Y )
-        return( 0 );
-
-    /* MSVC has a warning about unary minus on unsigned integer types,
-     * but this is well-defined and precisely what we want to do here. */
-#if defined(_MSC_VER)
-#pragma warning( push )
-#pragma warning( disable : 4146 )
-#endif
-
-    /* make sure swap is 0 or 1 in a time-constant manner */
-    swap = (swap | (unsigned char)-swap) >> (sizeof( swap ) * 8 - 1);
-    /* all-bits 1 if swap is 1, all-bits 0 if swap is 0 */
-    limb_mask = -swap;
-
-#if defined(_MSC_VER)
-#pragma warning( pop )
-#endif
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
-
-    s = X->s;
-    X->s = mpi_safe_cond_select_sign( X->s, Y->s, swap );
-    Y->s = mpi_safe_cond_select_sign( Y->s, s, swap );
-
-
-    for( i = 0; i < X->n; i++ )
-    {
-        tmp = X->p[i];
-        X->p[i] = ( X->p[i] & ~limb_mask ) | ( Y->p[i] & limb_mask );
-        Y->p[i] = ( Y->p[i] & ~limb_mask ) | (     tmp & limb_mask );
-    }
-
-cleanup:
-    return( ret );
-}
-
-/*
- * Set value from integer
- */
-int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    MPI_VALIDATE_RET( X != NULL );
-
-    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 )
-{
-    MPI_VALIDATE_RET( X != NULL );
-
-    if( X->n * biL <= pos )
-        return( 0 );
-
-    return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
-}
-
-/* Get a specific byte, without range checks. */
-#define GET_BYTE( X, i )                                \
-    ( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff )
-
-/*
- * 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;
-    MPI_VALIDATE_RET( X != NULL );
-
-    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;
-    MBEDTLS_INTERNAL_VALIDATE_RET( X != NULL, 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, j, slen, n;
-    int sign = 1;
-    mbedtls_mpi_uint d;
-    mbedtls_mpi T;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( s != NULL );
-
-    if( radix < 2 || radix > 16 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    mbedtls_mpi_init( &T );
-
-    if( s[0] == 0 )
-    {
-        mbedtls_mpi_free( X );
-        return( 0 );
-    }
-
-    if( s[0] == '-' )
-    {
-        ++s;
-        sign = -1;
-    }
-
-    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++ )
-        {
-            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++ )
-        {
-            MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
-            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
-            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
-        }
-    }
-
-    if( sign < 0 && mbedtls_mpi_bitlen( X ) != 0 )
-        X->s = -1;
-
-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, const size_t buflen )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    mbedtls_mpi_uint r;
-    size_t length = 0;
-    char *p_end = *p + buflen;
-
-    do
-    {
-        if( length >= buflen )
-        {
-            return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
-        }
-
-        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
-        /*
-         * Write the residue in the current position, as an ASCII character.
-         */
-        if( r < 0xA )
-            *(--p_end) = (char)( '0' + r );
-        else
-            *(--p_end) = (char)( 'A' + ( r - 0xA ) );
-
-        length++;
-    } while( mbedtls_mpi_cmp_int( X, 0 ) != 0 );
-
-    memmove( *p, p_end, length );
-    *p += length;
-
-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;
-    MPI_VALIDATE_RET( X    != NULL );
-    MPI_VALIDATE_RET( olen != NULL );
-    MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
-
-    if( radix < 2 || radix > 16 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    n = mbedtls_mpi_bitlen( X ); /* Number of bits necessary to present `n`. */
-    if( radix >=  4 ) n >>= 1;   /* Number of 4-adic digits necessary to present
-                                  * `n`. If radix > 4, this might be a strict
-                                  * overapproximation of the number of
-                                  * radix-adic digits needed to present `n`. */
-    if( radix >= 16 ) n >>= 1;   /* Number of hexadecimal digits necessary to
-                                  * present `n`. */
-
-    n += 1; /* Terminating null byte */
-    n += 1; /* Compensate for the divisions above, which round down `n`
-             * in case it's not even. */
-    n += 1; /* Potential '-'-sign. */
-    n += ( n & 1 ); /* Make n even to have enough space for hexadecimal writing,
-                     * which always uses an even number of hex-digits. */
-
-    if( buflen < n )
-    {
-        *olen = n;
-        return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
-    }
-
-    p = buf;
-    mbedtls_mpi_init( &T );
-
-    if( X->s == -1 )
-    {
-        *p++ = '-';
-        buflen--;
-    }
-
-    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, buflen ) );
-    }
-
-    *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 ];
-
-    MPI_VALIDATE_RET( X   != NULL );
-    MPI_VALIDATE_RET( fin != NULL );
-
-    if( radix < 2 || radix > 16 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    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 ];
-    MPI_VALIDATE_RET( X != NULL );
-
-    if( radix < 2 || radix > 16 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    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 */
-
-
-/* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
- * into the storage form used by mbedtls_mpi. */
-
-static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c( mbedtls_mpi_uint x )
-{
-    uint8_t i;
-    unsigned char *x_ptr;
-    mbedtls_mpi_uint tmp = 0;
-
-    for( i = 0, x_ptr = (unsigned char*) &x; i < ciL; i++, x_ptr++ )
-    {
-        tmp <<= CHAR_BIT;
-        tmp |= (mbedtls_mpi_uint) *x_ptr;
-    }
-
-    return( tmp );
-}
-
-static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x )
-{
-#if defined(__BYTE_ORDER__)
-
-/* Nothing to do on bigendian systems. */
-#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
-    return( x );
-#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
-
-#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
-
-/* For GCC and Clang, have builtins for byte swapping. */
-#if defined(__GNUC__) && defined(__GNUC_PREREQ)
-#if __GNUC_PREREQ(4,3)
-#define have_bswap
-#endif
-#endif
-
-#if defined(__clang__) && defined(__has_builtin)
-#if __has_builtin(__builtin_bswap32)  &&                 \
-    __has_builtin(__builtin_bswap64)
-#define have_bswap
-#endif
-#endif
-
-#if defined(have_bswap)
-    /* The compiler is hopefully able to statically evaluate this! */
-    switch( sizeof(mbedtls_mpi_uint) )
-    {
-        case 4:
-            return( __builtin_bswap32(x) );
-        case 8:
-            return( __builtin_bswap64(x) );
-    }
-#endif
-#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
-#endif /* __BYTE_ORDER__ */
-
-    /* Fall back to C-based reordering if we don't know the byte order
-     * or we couldn't use a compiler-specific builtin. */
-    return( mpi_uint_bigendian_to_host_c( x ) );
-}
-
-static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs )
-{
-    mbedtls_mpi_uint *cur_limb_left;
-    mbedtls_mpi_uint *cur_limb_right;
-    if( limbs == 0 )
-        return;
-
-    /*
-     * Traverse limbs and
-     * - adapt byte-order in each limb
-     * - swap the limbs themselves.
-     * For that, simultaneously traverse the limbs from left to right
-     * and from right to left, as long as the left index is not bigger
-     * than the right index (it's not a problem if limbs is odd and the
-     * indices coincide in the last iteration).
-     */
-    for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 );
-         cur_limb_left <= cur_limb_right;
-         cur_limb_left++, cur_limb_right-- )
-    {
-        mbedtls_mpi_uint tmp;
-        /* Note that if cur_limb_left == cur_limb_right,
-         * this code effectively swaps the bytes only once. */
-        tmp             = mpi_uint_bigendian_to_host( *cur_limb_left  );
-        *cur_limb_left  = mpi_uint_bigendian_to_host( *cur_limb_right );
-        *cur_limb_right = tmp;
-    }
-}
-
-/*
- * Import X from unsigned binary data, little endian
- */
-int mbedtls_mpi_read_binary_le( mbedtls_mpi *X,
-                                const unsigned char *buf, size_t buflen )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i;
-    size_t const limbs = CHARS_TO_LIMBS( buflen );
-
-    /* Ensure that target MPI has exactly the necessary number of limbs */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) );
-
-    for( i = 0; i < buflen; i++ )
-        X->p[i / ciL] |= ((mbedtls_mpi_uint) buf[i]) << ((i % ciL) << 3);
-
-cleanup:
-
-    /*
-     * This function is also used to import keys. However, wiping the buffers
-     * upon failure is not necessary because failure only can happen before any
-     * input is copied.
-     */
-    return( ret );
-}
-
-/*
- * 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t const limbs    = CHARS_TO_LIMBS( buflen );
-    size_t const overhead = ( limbs * ciL ) - buflen;
-    unsigned char *Xp;
-
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
-
-    /* Ensure that target MPI has exactly the necessary number of limbs */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) );
-
-    /* Avoid calling `memcpy` with NULL source or destination argument,
-     * even if buflen is 0. */
-    if( buflen != 0 )
-    {
-        Xp = (unsigned char*) X->p;
-        memcpy( Xp + overhead, buf, buflen );
-
-        mpi_bigendian_to_host( X->p, limbs );
-    }
-
-cleanup:
-
-    /*
-     * This function is also used to import keys. However, wiping the buffers
-     * upon failure is not necessary because failure only can happen before any
-     * input is copied.
-     */
-    return( ret );
-}
-
-/*
- * Export X into unsigned binary data, little endian
- */
-int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X,
-                                 unsigned char *buf, size_t buflen )
-{
-    size_t stored_bytes = X->n * ciL;
-    size_t bytes_to_copy;
-    size_t i;
-
-    if( stored_bytes < buflen )
-    {
-        bytes_to_copy = stored_bytes;
-    }
-    else
-    {
-        bytes_to_copy = buflen;
-
-        /* The output buffer is smaller than the allocated size of X.
-         * However X may fit if its leading bytes are zero. */
-        for( i = bytes_to_copy; i < stored_bytes; i++ )
-        {
-            if( GET_BYTE( X, i ) != 0 )
-                return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
-        }
-    }
-
-    for( i = 0; i < bytes_to_copy; i++ )
-        buf[i] = GET_BYTE( X, i );
-
-    if( stored_bytes < buflen )
-    {
-        /* Write trailing 0 bytes */
-        memset( buf + stored_bytes, 0, buflen - stored_bytes );
-    }
-
-    return( 0 );
-}
-
-/*
- * 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 stored_bytes;
-    size_t bytes_to_copy;
-    unsigned char *p;
-    size_t i;
-
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
-
-    stored_bytes = X->n * ciL;
-
-    if( stored_bytes < buflen )
-    {
-        /* There is enough space in the output buffer. Write initial
-         * null bytes and record the position at which to start
-         * writing the significant bytes. In this case, the execution
-         * trace of this function does not depend on the value of the
-         * number. */
-        bytes_to_copy = stored_bytes;
-        p = buf + buflen - stored_bytes;
-        memset( buf, 0, buflen - stored_bytes );
-    }
-    else
-    {
-        /* The output buffer is smaller than the allocated size of X.
-         * However X may fit if its leading bytes are zero. */
-        bytes_to_copy = buflen;
-        p = buf;
-        for( i = bytes_to_copy; i < stored_bytes; i++ )
-        {
-            if( GET_BYTE( X, i ) != 0 )
-                return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
-        }
-    }
-
-    for( i = 0; i < bytes_to_copy; i++ )
-        p[bytes_to_copy - i - 1] = GET_BYTE( X, i );
-
-    return( 0 );
-}
-
-/*
- * Left-shift: X <<= count
- */
-int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, v0, t1;
-    mbedtls_mpi_uint r0 = 0, r1;
-    MPI_VALIDATE_RET( X != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-
-    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 );
-}
-
-/** Decide if an integer is less than the other, without branches.
- *
- * \param x         First integer.
- * \param y         Second integer.
- *
- * \return          1 if \p x is less than \p y, 0 otherwise
- */
-static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x,
-        const mbedtls_mpi_uint y )
-{
-    mbedtls_mpi_uint ret;
-    mbedtls_mpi_uint cond;
-
-    /*
-     * Check if the most significant bits (MSB) of the operands are different.
-     */
-    cond = ( x ^ y );
-    /*
-     * If the MSB are the same then the difference x-y will be negative (and
-     * have its MSB set to 1 during conversion to unsigned) if and only if x<y.
-     */
-    ret = ( x - y ) & ~cond;
-    /*
-     * If the MSB are different, then the operand with the MSB of 1 is the
-     * bigger. (That is if y has MSB of 1, then x<y is true and it is false if
-     * the MSB of y is 0.)
-     */
-    ret |= y & cond;
-
-
-    ret = ret >> ( biL - 1 );
-
-    return (unsigned) ret;
-}
-
-/*
- * Compare signed values in constant time
- */
-int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
-        unsigned *ret )
-{
-    size_t i;
-    /* The value of any of these variables is either 0 or 1 at all times. */
-    unsigned cond, done, X_is_negative, Y_is_negative;
-
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( Y != NULL );
-    MPI_VALIDATE_RET( ret != NULL );
-
-    if( X->n != Y->n )
-        return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
-
-    /*
-     * Set sign_N to 1 if N >= 0, 0 if N < 0.
-     * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
-     */
-    X_is_negative = ( X->s & 2 ) >> 1;
-    Y_is_negative = ( Y->s & 2 ) >> 1;
-
-    /*
-     * If the signs are different, then the positive operand is the bigger.
-     * That is if X is negative (X_is_negative == 1), then X < Y is true and it
-     * is false if X is positive (X_is_negative == 0).
-     */
-    cond = ( X_is_negative ^ Y_is_negative );
-    *ret = cond & X_is_negative;
-
-    /*
-     * This is a constant-time function. We might have the result, but we still
-     * need to go through the loop. Record if we have the result already.
-     */
-    done = cond;
-
-    for( i = X->n; i > 0; i-- )
-    {
-        /*
-         * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
-         * X and Y are negative.
-         *
-         * Again even if we can make a decision, we just mark the result and
-         * the fact that we are done and continue looping.
-         */
-        cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] );
-        *ret |= cond & ( 1 - done ) & X_is_negative;
-        done |= cond;
-
-        /*
-         * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
-         * X and Y are positive.
-         *
-         * Again even if we can make a decision, we just mark the result and
-         * the fact that we are done and continue looping.
-         */
-        cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] );
-        *ret |= cond & ( 1 - done ) & ( 1 - X_is_negative );
-        done |= cond;
-    }
-
-    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];
-    MPI_VALIDATE_RET( X != NULL );
-
-    *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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, j;
-    mbedtls_mpi_uint *o, *p, c, tmp;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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.
- *
- * Calculate l - r where l and r have the same size.
- * This function operates modulo (2^ciL)^n and returns the carry
- * (1 if there was a wraparound, i.e. if `l < r`, and 0 otherwise).
- *
- * d may be aliased to l or r.
- *
- * \param n             Number of limbs of \p d, \p l and \p r.
- * \param[out] d        The result of the subtraction.
- * \param[in] l         The left operand.
- * \param[in] r         The right operand.
- *
- * \return              1 if `l < r`.
- *                      0 if `l >= r`.
- */
-static mbedtls_mpi_uint mpi_sub_hlp( size_t n,
-                                     mbedtls_mpi_uint *d,
-                                     const mbedtls_mpi_uint *l,
-                                     const mbedtls_mpi_uint *r )
-{
-    size_t i;
-    mbedtls_mpi_uint c = 0, t, z;
-
-    for( i = 0; i < n; i++ )
-    {
-        z = ( l[i] <  c );    t = l[i] - c;
-        c = ( t < r[i] ) + z; d[i] = t - r[i];
-    }
-
-    return( c );
-}
-
-/*
- * Unsigned subtraction: X = |A| - |B|  (HAC 14.9, 14.10)
- */
-int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t n;
-    mbedtls_mpi_uint carry;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    for( n = B->n; n > 0; n-- )
-        if( B->p[n - 1] != 0 )
-            break;
-    if( n > A->n )
-    {
-        /* B >= (2^ciL)^n > A */
-        ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
-        goto cleanup;
-    }
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, A->n ) );
-
-    /* Set the high limbs of X to match A. Don't touch the lower limbs
-     * because X might be aliased to B, and we must not overwrite the
-     * significant digits of B. */
-    if( A->n > n )
-        memcpy( X->p + n, A->p + n, ( A->n - n ) * ciL );
-    if( X->n > A->n )
-        memset( X->p + A->n, 0, ( X->n - A->n ) * ciL );
-
-    carry = mpi_sub_hlp( n, X->p, A->p, B->p );
-    if( carry != 0 )
-    {
-        /* Propagate the carry to the first nonzero limb of X. */
-        for( ; n < X->n && X->p[n] == 0; n++ )
-            --X->p[n];
-        /* If we ran out of space for the carry, it means that the result
-         * is negative. */
-        if( n == X->n )
-        {
-            ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
-            goto cleanup;
-        }
-        --X->p[n];
-    }
-
-    /* X should always be positive as a result of unsigned subtractions. */
-    X->s = 1;
-
-cleanup:
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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];
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-
-    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];
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-
-    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.
- *
- * Add \p b * \p s to \p d.
- *
- * \param i             The number of limbs of \p s.
- * \param[in] s         A bignum to multiply, of size \p i.
- *                      It may overlap with \p d, but only if
- *                      \p d <= \p s.
- *                      Its leading limb must not be \c 0.
- * \param[in,out] d     The bignum to add to.
- *                      It must be sufficiently large to store the
- *                      result of the multiplication. This means
- *                      \p i + 1 limbs if \p d[\p i - 1] started as 0 and \p b
- *                      is not known a priori.
- * \param b             A scalar to multiply.
- */
-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,
-                  const 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++;
-
-    while( c != 0 )
-    {
-        *d += c; c = ( *d < c ); d++;
-    }
-}
-
-/*
- * 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, j;
-    mbedtls_mpi TA, TB;
-    int result_is_zero = 0;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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;
-    if( i == 0 )
-        result_is_zero = 1;
-
-    for( j = B->n; j > 0; j-- )
-        if( B->p[j - 1] != 0 )
-            break;
-    if( j == 0 )
-        result_is_zero = 1;
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
-
-    for( ; j > 0; j-- )
-        mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
-
-    /* If the result is 0, we don't shortcut the operation, which reduces
-     * but does not eliminate side channels leaking the zero-ness. We do
-     * need to take care to set the sign bit properly since the library does
-     * not fully support an MPI object with a value of 0 and s == -1. */
-    if( result_is_zero )
-        X->s = 1;
-    else
-        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 )
-{
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-
-    /* mpi_mul_hlp can't deal with a leading 0. */
-    size_t n = A->n;
-    while( n > 0 && A->p[n - 1] == 0 )
-        --n;
-
-    /* The general method below doesn't work if n==0 or b==0. By chance
-     * calculating the result is trivial in those cases. */
-    if( b == 0 || n == 0 )
-    {
-        return( mbedtls_mpi_lset( X, 0 ) );
-    }
-
-    /* Calculate A*b as A + A*(b-1) to take advantage of mpi_mul_hlp */
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    /* In general, A * b requires 1 limb more than b. If
-     * A->p[n - 1] * b / b == A->p[n - 1], then A * b fits in the same
-     * number of limbs as A and the call to grow() is not required since
-     * copy() will take care of the growth if needed. However, experimentally,
-     * making the call to grow() unconditional causes slightly fewer
-     * calls to calloc() in ECP code, presumably because it reuses the
-     * same mpi for a while and this way the mpi is more likely to directly
-     * grow to its final size. */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n + 1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
-    mpi_mul_hlp( n, A->p, X->p, b - 1 );
-
-cleanup:
-    return( ret );
-}
-
-/*
- * 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, n, t, k;
-    mbedtls_mpi X, Y, Z, T1, T2;
-    mbedtls_mpi_uint TP2[3];
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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 );
-    /*
-     * Avoid dynamic memory allocations for constant-size T2.
-     *
-     * T2 is used for comparison only and the 3 limbs are assigned explicitly,
-     * so nobody increase the size of the MPI and we're safe to use an on-stack
-     * buffer.
-     */
-    T2.s = 1;
-    T2.n = sizeof( TP2 ) / sizeof( *TP2 );
-    T2.p = TP2;
-
-    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, A->n + 2 ) );
-
-    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);
-        }
-
-        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];
-
-        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] ) );
-        }
-        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_platform_zeroize( TP2, sizeof( TP2 ) );
-
-    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];
-    MPI_VALIDATE_RET( A != NULL );
-
-    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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    MPI_VALIDATE_RET( R != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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;
-    MPI_VALIDATE_RET( r != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-
-    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)
- *
- * \param[in,out]   A   One of the numbers to multiply.
- *                      It must have at least as many limbs as N
- *                      (A->n >= N->n), and any limbs beyond n are ignored.
- *                      On successful completion, A contains the result of
- *                      the multiplication A * B * R^-1 mod N where
- *                      R = (2^ciL)^n.
- * \param[in]       B   One of the numbers to multiply.
- *                      It must be nonzero and must not have more limbs than N
- *                      (B->n <= N->n).
- * \param[in]       N   The modulo. N must be odd.
- * \param           mm  The value calculated by `mpi_montg_init(&mm, N)`.
- *                      This is -N^-1 mod 2^ciL.
- * \param[in,out]   T   A bignum for temporary storage.
- *                      It must be at least twice the limb size of N plus 2
- *                      (T->n >= 2 * (N->n + 1)).
- *                      Its initial content is unused and
- *                      its final content is indeterminate.
- *                      Note that unlike the usual convention in the library
- *                      for `const mbedtls_mpi*`, the content of T can change.
- */
-static void 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;
-
-    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;
-    }
-
-    /* At this point, d is either the desired result or the desired result
-     * plus N. We now potentially subtract N, avoiding leaking whether the
-     * subtraction is performed through side channels. */
-
-    /* Copy the n least significant limbs of d to A, so that
-     * A = d if d < N (recall that N has n limbs). */
-    memcpy( A->p, d, n * ciL );
-    /* If d >= N then we want to set A to d - N. To prevent timing attacks,
-     * do the calculation without using conditional tests. */
-    /* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */
-    d[n] += 1;
-    d[n] -= mpi_sub_hlp( n, d, d, N->p );
-    /* If d0 < N then d < (2^biL)^n
-     * so d[n] == 0 and we want to keep A as it is.
-     * If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n
-     * so d[n] == 1 and we want to set A to the result of the subtraction
-     * which is d - (2^biL)^n, i.e. the n least significant limbs of d.
-     * This exactly corresponds to a conditional assignment. */
-    mpi_safe_cond_assign( n, A->p, d, (unsigned char) d[n] );
-}
-
-/*
- * Montgomery reduction: A = A * R^-1 mod N
- *
- * See mpi_montmul() regarding constraints and guarantees on the parameters.
- */
-static void 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;
-
-    mpi_montmul( A, &U, N, mm, T );
-}
-
-/*
- * Constant-flow boolean "equal" comparison:
- * return x == y
- *
- * This function can be used to write constant-time code by replacing branches
- * with bit operations - it can be used in conjunction with
- * mbedtls_ssl_cf_mask_from_bit().
- *
- * This function is implemented without using comparison operators, as those
- * might be translated to branches by some compilers on some platforms.
- */
-static size_t mbedtls_mpi_cf_bool_eq( size_t x, size_t y )
-{
-    /* diff = 0 if x == y, non-zero otherwise */
-    const size_t diff = x ^ y;
-
-    /* MSVC has a warning about unary minus on unsigned integer types,
-     * but this is well-defined and precisely what we want to do here. */
-#if defined(_MSC_VER)
-#pragma warning( push )
-#pragma warning( disable : 4146 )
-#endif
-
-    /* diff_msb's most significant bit is equal to x != y */
-    const size_t diff_msb = ( diff | (size_t) -diff );
-
-#if defined(_MSC_VER)
-#pragma warning( pop )
-#endif
-
-    /* diff1 = (x != y) ? 1 : 0 */
-    const size_t diff1 = diff_msb >> ( sizeof( diff_msb ) * 8 - 1 );
-
-    return( 1 ^ diff1 );
-}
-
-/**
- * Select an MPI from a table without leaking the index.
- *
- * This is functionally equivalent to mbedtls_mpi_copy(R, T[idx]) except it
- * reads the entire table in order to avoid leaking the value of idx to an
- * attacker able to observe memory access patterns.
- *
- * \param[out] R        Where to write the selected MPI.
- * \param[in] T         The table to read from.
- * \param[in] T_size    The number of elements in the table.
- * \param[in] idx       The index of the element to select;
- *                      this must satisfy 0 <= idx < T_size.
- *
- * \return \c 0 on success, or a negative error code.
- */
-static int mpi_select( mbedtls_mpi *R, const mbedtls_mpi *T, size_t T_size, size_t idx )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-
-    for( size_t i = 0; i < T_size; i++ )
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( R, &T[i],
-                        (unsigned char) mbedtls_mpi_cf_bool_eq( i, idx ) ) );
-    }
-
-cleanup:
-    return( ret );
-}
-
-/*
- * 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    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[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos;
-    int neg;
-
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( E != NULL );
-    MPI_VALIDATE_RET( N != NULL );
-
-    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 );
-
-    if( mbedtls_mpi_bitlen( E ) > MBEDTLS_MPI_MAX_BITS ||
-        mbedtls_mpi_bitlen( N ) > MBEDTLS_MPI_MAX_BITS )
-        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 );
-    mbedtls_mpi_init( &WW );
-    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( MBEDTLS_MPI_WINDOW_SIZE < 6 )
-    if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
-        wsize = MBEDTLS_MPI_WINDOW_SIZE;
-#endif
-
-    j = N->n + 1;
-    /* All W[i] and X must have at least N->n limbs for the mpi_montmul()
-     * and mpi_montred() calls later. Here we ensure that W[1] and X are
-     * large enough, and later we'll grow other W[i] to the same length.
-     * They must not be shrunk midway through this function!
-     */
-    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 ) );
-        /* This should be a no-op because W[1] is already that large before
-         * mbedtls_mpi_mod_mpi(), but it's necessary to avoid an overflow
-         * in mpi_montmul() below, so let's make sure. */
-        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], N->n + 1 ) );
-    }
-    else
-        MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
-
-    /* Note that this is safe because W[1] always has at least N->n limbs
-     * (it grew above and was preserved by mbedtls_mpi_copy()). */
-    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 ) );
-    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++ )
-            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] ) );
-
-            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
-             */
-            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++ )
-                mpi_montmul( X, X, N, mm, &T );
-
-            /*
-             * X = X * W[wbits] R^-1 mod N
-             */
-            MBEDTLS_MPI_CHK( mpi_select( &WW, W, (size_t) 1 << wsize, wbits ) );
-            mpi_montmul( X, &WW, N, mm, &T );
-
-            state--;
-            nbits = 0;
-            wbits = 0;
-        }
-    }
-
-    /*
-     * process the remaining bits
-     */
-    for( i = 0; i < nbits; i++ )
-    {
-        mpi_montmul( X, X, N, mm, &T );
-
-        wbits <<= 1;
-
-        if( ( wbits & ( one << wsize ) ) != 0 )
-            mpi_montmul( X, &W[1], N, mm, &T );
-    }
-
-    /*
-     * X = A^E * R * R^-1 mod N = A^E mod N
-     */
-    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 );
-    mbedtls_mpi_free( &WW );
-
-    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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t lz, lzt;
-    mbedtls_mpi TA, TB;
-
-    MPI_VALIDATE_RET( G != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( B != NULL );
-
-    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 );
-
-    /* The loop below gives the correct result when A==0 but not when B==0.
-     * So have a special case for B==0. Leverage the fact that we just
-     * calculated the lsb and lsb(B)==0 iff B is odd or 0 to make the test
-     * slightly more efficient than cmp_int(). */
-    if( lzt == 0 && mbedtls_mpi_get_bit( &TB, 0 ) == 0 )
-    {
-        ret = mbedtls_mpi_copy( G, A );
-        goto cleanup;
-    }
-
-    if( lzt < lz )
-        lz = lzt;
-
-    TA.s = TB.s = 1;
-
-    /* We mostly follow the procedure described in HAC 14.54, but with some
-     * minor differences:
-     * - Sequences of multiplications or divisions by 2 are grouped into a
-     *   single shift operation.
-     * - The procedure in HAC assumes that 0 < TB <= TA.
-     *     - The condition TB <= TA is not actually necessary for correctness.
-     *       TA and TB have symmetric roles except for the loop termination
-     *       condition, and the shifts at the beginning of the loop body
-     *       remove any significance from the ordering of TA vs TB before
-     *       the shifts.
-     *     - If TA = 0, the loop goes through 0 iterations and the result is
-     *       correctly TB.
-     *     - The case TB = 0 was short-circuited above.
-     *
-     * For the correctness proof below, decompose the original values of
-     * A and B as
-     *   A = sa * 2^a * A' with A'=0 or A' odd, and sa = +-1
-     *   B = sb * 2^b * B' with B'=0 or B' odd, and sb = +-1
-     * Then gcd(A, B) = 2^{min(a,b)} * gcd(A',B'),
-     * and gcd(A',B') is odd or 0.
-     *
-     * At the beginning, we have TA = |A| and TB = |B| so gcd(A,B) = gcd(TA,TB).
-     * The code maintains the following invariant:
-     *     gcd(A,B) = 2^k * gcd(TA,TB) for some k   (I)
-     */
-
-    /* Proof that the loop terminates:
-     * At each iteration, either the right-shift by 1 is made on a nonzero
-     * value and the nonnegative integer bitlen(TA) + bitlen(TB) decreases
-     * by at least 1, or the right-shift by 1 is made on zero and then
-     * TA becomes 0 which ends the loop (TB cannot be 0 if it is right-shifted
-     * since in that case TB is calculated from TB-TA with the condition TB>TA).
-     */
-    while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
-    {
-        /* Divisions by 2 preserve the invariant (I). */
-        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
-
-        /* Set either TA or TB to |TA-TB|/2. Since TA and TB are both odd,
-         * TA-TB is even so the division by 2 has an integer result.
-         * Invariant (I) is preserved since any odd divisor of both TA and TB
-         * also divides |TA-TB|/2, and any odd divisor of both TA and |TA-TB|/2
-         * also divides TB, and any odd divisior of both TB and |TA-TB|/2 also
-         * divides TA.
-         */
-        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 ) );
-        }
-        /* Note that one of TA or TB is still odd. */
-    }
-
-    /* By invariant (I), gcd(A,B) = 2^k * gcd(TA,TB) for some k.
-     * At the loop exit, TA = 0, so gcd(TA,TB) = TB.
-     * - If there was at least one loop iteration, then one of TA or TB is odd,
-     *   and TA = 0, so TB is odd and gcd(TA,TB) = gcd(A',B'). In this case,
-     *   lz = min(a,b) so gcd(A,B) = 2^lz * TB.
-     * - If there was no loop iteration, then A was 0, and gcd(A,B) = B.
-     *   In this case, lz = 0 and B = TB so gcd(A,B) = B = 2^lz * TB as well.
-     */
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
-
-cleanup:
-
-    mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
-
-    return( ret );
-}
-
-/* Fill X with n_bytes random bytes.
- * X must already have room for those bytes.
- * The ordering of the bytes returned from the RNG is suitable for
- * deterministic ECDSA (see RFC 6979 §3.3 and mbedtls_mpi_random()).
- * The size and sign of X are unchanged.
- * n_bytes must not be 0.
- */
-static int mpi_fill_random_internal(
-    mbedtls_mpi *X, size_t n_bytes,
-    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    const size_t limbs = CHARS_TO_LIMBS( n_bytes );
-    const size_t overhead = ( limbs * ciL ) - n_bytes;
-
-    if( X->n < limbs )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    memset( X->p, 0, overhead );
-    memset( (unsigned char *) X->p + limbs * ciL, 0, ( X->n - limbs ) * ciL );
-    MBEDTLS_MPI_CHK( f_rng( p_rng, (unsigned char *) X->p + overhead, n_bytes ) );
-    mpi_bigendian_to_host( X->p, limbs );
-
-cleanup:
-    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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t const limbs = CHARS_TO_LIMBS( size );
-
-    MPI_VALIDATE_RET( X     != NULL );
-    MPI_VALIDATE_RET( f_rng != NULL );
-
-    /* Ensure that target MPI has exactly the necessary number of limbs */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) );
-    if( size == 0 )
-        return( 0 );
-
-    ret = mpi_fill_random_internal( X, size, f_rng, p_rng );
-
-cleanup:
-    return( ret );
-}
-
-int mbedtls_mpi_random( mbedtls_mpi *X,
-                        mbedtls_mpi_sint min,
-                        const mbedtls_mpi *N,
-                        int (*f_rng)(void *, unsigned char *, size_t),
-                        void *p_rng )
-{
-    int ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
-    int count;
-    unsigned lt_lower = 1, lt_upper = 0;
-    size_t n_bits = mbedtls_mpi_bitlen( N );
-    size_t n_bytes = ( n_bits + 7 ) / 8;
-    mbedtls_mpi lower_bound;
-
-    if( min < 0 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-    if( mbedtls_mpi_cmp_int( N, min ) <= 0 )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    /*
-     * When min == 0, each try has at worst a probability 1/2 of failing
-     * (the msb has a probability 1/2 of being 0, and then the result will
-     * be < N), so after 30 tries failure probability is a most 2**(-30).
-     *
-     * When N is just below a power of 2, as is the case when generating
-     * a random scalar on most elliptic curves, 1 try is enough with
-     * overwhelming probability. When N is just above a power of 2,
-     * as when generating a random scalar on secp224k1, each try has
-     * a probability of failing that is almost 1/2.
-     *
-     * The probabilities are almost the same if min is nonzero but negligible
-     * compared to N. This is always the case when N is crypto-sized, but
-     * it's convenient to support small N for testing purposes. When N
-     * is small, use a higher repeat count, otherwise the probability of
-     * failure is macroscopic.
-     */
-    count = ( n_bytes > 4 ? 30 : 250 );
-
-    mbedtls_mpi_init( &lower_bound );
-
-    /* Ensure that target MPI has exactly the same number of limbs
-     * as the upper bound, even if the upper bound has leading zeros.
-     * This is necessary for the mbedtls_mpi_lt_mpi_ct() check. */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, N->n ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &lower_bound, N->n ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &lower_bound, min ) );
-
-    /*
-     * Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
-     * when f_rng is a suitably parametrized instance of HMAC_DRBG:
-     * - use the same byte ordering;
-     * - keep the leftmost n_bits bits of the generated octet string;
-     * - try until result is in the desired range.
-     * This also avoids any bias, which is especially important for ECDSA.
-     */
-    do
-    {
-        MBEDTLS_MPI_CHK( mpi_fill_random_internal( X, n_bytes, f_rng, p_rng ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, 8 * n_bytes - n_bits ) );
-
-        if( --count == 0 )
-        {
-            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
-            goto cleanup;
-        }
-
-        MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, &lower_bound, &lt_lower ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, N, &lt_upper ) );
-    }
-    while( lt_lower != 0 || lt_upper == 0 );
-
-cleanup:
-    mbedtls_mpi_free( &lower_bound );
-    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_ERR_ERROR_CORRUPTION_DETECTED;
-    mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
-    MPI_VALIDATE_RET( X != NULL );
-    MPI_VALIDATE_RET( A != NULL );
-    MPI_VALIDATE_RET( N != NULL );
-
-    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, size_t rounds,
-                             int (*f_rng)(void *, unsigned char *, size_t),
-                             void *p_rng )
-{
-    int ret, count;
-    size_t i, j, k, s;
-    mbedtls_mpi W, R, T, A, RR;
-
-    MPI_VALIDATE_RET( X     != NULL );
-    MPI_VALIDATE_RET( f_rng != NULL );
-
-    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 ) );
-
-    for( i = 0; i < rounds; i++ )
-    {
-        /*
-         * pick a random A, 1 < A < |X| - 1
-         */
-        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) {
-                A.p[A.n - 1] &= ( (mbedtls_mpi_uint) 1 << ( k - ( A.n - 1 ) * biL - 1 ) ) - 1;
-            }
-
-            if (count++ > 30) {
-                ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
-                goto cleanup;
-            }
-
-        } 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_ext( const mbedtls_mpi *X, int rounds,
-                              int (*f_rng)(void *, unsigned char *, size_t),
-                              void *p_rng )
-{
-    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    mbedtls_mpi XX;
-    MPI_VALIDATE_RET( X     != NULL );
-    MPI_VALIDATE_RET( f_rng != NULL );
-
-    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, rounds, f_rng, p_rng ) );
-}
-
-#if !defined(MBEDTLS_DEPRECATED_REMOVED)
-/*
- * Pseudo-primality test, error probability 2^-80
- */
-int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
-                  int (*f_rng)(void *, unsigned char *, size_t),
-                  void *p_rng )
-{
-    MPI_VALIDATE_RET( X     != NULL );
-    MPI_VALIDATE_RET( f_rng != NULL );
-
-    /*
-     * In the past our key generation aimed for an error rate of at most
-     * 2^-80. Since this function is deprecated, aim for the same certainty
-     * here as well.
-     */
-    return( mbedtls_mpi_is_prime_ext( X, 40, f_rng, p_rng ) );
-}
-#endif
-
-/*
- * Prime number generation
- *
- * To generate an RSA key in a way recommended by FIPS 186-4, both primes must
- * be either 1024 bits or 1536 bits long, and flags must contain
- * MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR.
- */
-int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
-                   int (*f_rng)(void *, unsigned char *, size_t),
-                   void *p_rng )
-{
-#ifdef MBEDTLS_HAVE_INT64
-// ceil(2^63.5)
-#define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL
-#else
-// ceil(2^31.5)
-#define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U
-#endif
-    int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
-    size_t k, n;
-    int rounds;
-    mbedtls_mpi_uint r;
-    mbedtls_mpi Y;
-
-    MPI_VALIDATE_RET( X     != NULL );
-    MPI_VALIDATE_RET( f_rng != NULL );
-
-    if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
-    mbedtls_mpi_init( &Y );
-
-    n = BITS_TO_LIMBS( nbits );
-
-    if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR ) == 0 )
-    {
-        /*
-         * 2^-80 error probability, number of rounds chosen per HAC, table 4.4
-         */
-        rounds = ( ( nbits >= 1300 ) ?  2 : ( nbits >=  850 ) ?  3 :
-                   ( nbits >=  650 ) ?  4 : ( nbits >=  350 ) ?  8 :
-                   ( nbits >=  250 ) ? 12 : ( nbits >=  150 ) ? 18 : 27 );
-    }
-    else
-    {
-        /*
-         * 2^-100 error probability, number of rounds computed based on HAC,
-         * fact 4.48
-         */
-        rounds = ( ( nbits >= 1450 ) ?  4 : ( nbits >=  1150 ) ?  5 :
-                   ( nbits >= 1000 ) ?  6 : ( nbits >=   850 ) ?  7 :
-                   ( nbits >=  750 ) ?  8 : ( nbits >=   500 ) ? 13 :
-                   ( nbits >=  250 ) ? 28 : ( nbits >=   150 ) ? 40 : 51 );
-    }
-
-    while( 1 )
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
-        /* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */
-        if( X->p[n-1] < CEIL_MAXUINT_DIV_SQRT2 ) continue;
-
-        k = n * biL;
-        if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) );
-        X->p[0] |= 1;
-
-        if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 )
-        {
-            ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng );
-
-            if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
-                goto cleanup;
-        }
-        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, rounds, f_rng, p_rng  ) )
-                                                                    == 0 &&
-                    ( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng  ) )
-                                                                    == 0 )
-                    goto cleanup;
-
-                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", (unsigned int) 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 */