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8fd95c6757
mbedtls/library/bignum.c
Gilles Peskine 8fd95c6757 Perform mbedtls_mpi_mul_int in place if possible 
Rewrite mbedtls_mpi_mul_int to call mpi_mul_hlp directly rather than
create a temporary mpi object. This has the benefit of not performing
an allocation when the multiplication is in place (mpi operand aliased
with the result) and the result mpi is large enough.

This saves about 40% of the calloc() calls in test_suite_ecp. There is
no measurable performance difference on my Linux PC.

The cost is a few bytes in bignum.o.

When there is no aliasing, or when there is aliasing but the mpi
object needs to be enlarged, the performance difference is negligible.

Signed-off-by: Gilles Peskine <Gilles.Peskine@arm.com>
2020-12-07 22:51:25 +01:00

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/*
* 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 );
}
/*
* Copy the contents of Y into X
*/
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 )
{
mbedtls_mpi_free( X );
return( 0 );
}
for( i = Y->n - 1; i > 0; i-- )
if( Y->p[i] != 0 )
break;
i++;
X->s = Y->s;
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 ) );
}
/*
* 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;
for( i = 0; i < n; i++ )
dest[i] = dest[i] * ( 1 - assign ) + src[i] * assign;
}
/*
* 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;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( Y != NULL );
/* make sure assign is 0 or 1 in a time-constant manner */
assign = (assign | (unsigned char)-assign) >> 7;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
X->s = X->s * ( 1 - assign ) + Y->s * assign;
mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );
for( i = Y->n; i < X->n; i++ )
X->p[i] *= ( 1 - assign );
cleanup:
return( ret );
}
/*
* Conditionally swap X and Y, without leaking information
* about whether the swap was made or not.
* Here it is not ok to simply swap the pointers, which whould lead to
* different memory access patterns when X and Y are used afterwards.
*/
int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
{
int ret, s;
size_t i;
mbedtls_mpi_uint tmp;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( Y != NULL );
if( X == Y )
return( 0 );
/* make sure swap is 0 or 1 in a time-constant manner */
swap = (swap | (unsigned char)-swap) >> 7;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
s = X->s;
X->s = X->s * ( 1 - swap ) + Y->s * swap;
Y->s = Y->s * ( 1 - swap ) + s * swap;
for( i = 0; i < X->n; i++ )
{
tmp = X->p[i];
X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
Y->p[i] = Y->p[i] * ( 1 - swap ) + tmp * swap;
}
cleanup:
return( ret );
}
/*
* Set value from integer
*/
int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
{
int ret = MBEDTLS_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;
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 );
slen = strlen( s );
if( radix == 16 )
{
if( slen > MPI_SIZE_T_MAX >> 2 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
n = BITS_TO_LIMBS( slen << 2 );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = slen, j = 0; i > 0; i--, j++ )
{
if( i == 1 && s[i - 1] == '-' )
{
X->s = -1;
break;
}
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
}
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = 0; i < slen; i++ )
{
if( i == 0 && s[i] == '-' )
{
X->s = -1;
continue;
}
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
if( X->s == 1 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
}
}
}
cleanup:
mbedtls_mpi_free( &T );
return( ret );
}
/*
* Helper to write the digits high-order first.
*/
static int mpi_write_hlp( mbedtls_mpi *X, int radix,
char **p, 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 */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = 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 */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
/* Avoid calling `memcpy` with NULL source argument,
* even if buflen is 0. */
if( buf != NULL )
{
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;
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++;
do {
*d += c; c = ( *d < c ); d++;
}
while( c != 0 );
}
/*
* Baseline multiplication: X = A * B (HAC 14.12)
*/
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, j;
mbedtls_mpi TA, TB;
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;
for( j = B->n; j > 0; j-- )
if( B->p[j - 1] != 0 )
break;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( ; j > 0; j-- )
mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
X->s = A->s * B->s;
cleanup:
mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
return( ret );
}
/*
* Baseline multiplication: X = A * b
*/
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
{
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 )
{
mbedtls_mpi_lset( X, 0 );
return( 0 );
}
/* Calculate X*b as A + A*(b-1) to take advantage of mpi_mul_hlp */
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
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, 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 );
}
/*
* 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 ], 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 );
/*
* Init temps and window size
*/
mpi_montg_init( &mm, N );
mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
mbedtls_mpi_init( &Apos );
memset( W, 0, sizeof( W ) );
i = mbedtls_mpi_bitlen( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
#if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
wsize = MBEDTLS_MPI_WINDOW_SIZE;
#endif
j = N->n + 1;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
/*
* Compensate for negative A (and correct at the end)
*/
neg = ( A->s == -1 );
if( neg )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
Apos.s = 1;
A = &Apos;
}
/*
* If 1st call, pre-compute R^2 mod N
*/
if( _RR == NULL || _RR->p == NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
if( _RR != NULL )
memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
}
else
memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
/*
* W[1] = A * R^2 * R^-1 mod N = A * R mod N
*/
if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
else
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
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
*/
mpi_montmul( X, &W[wbits], 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 );
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 );
if( lzt < lz )
lz = lzt;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
TA.s = TB.s = 1;
while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
}
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
cleanup:
mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
return( ret );
}
/*
* Fill X with size bytes of random.
*
* Use a temporary bytes representation to make sure the result is the same
* regardless of the platform endianness (useful when f_rng is actually
* deterministic, eg for tests).
*/
int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t const limbs = CHARS_TO_LIMBS( size );
size_t const overhead = ( limbs * ciL ) - size;
unsigned char *Xp;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( f_rng != NULL );
/* Ensure that target MPI has exactly the necessary number of limbs */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
Xp = (unsigned char*) X->p;
f_rng( p_rng, Xp + overhead, size );
mpi_bigendian_to_host( X->p, limbs );
cleanup:
return( ret );
}
/*
* Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
*/
int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
{
int ret = MBEDTLS_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 */
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