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bd87a59007
mbedtls/library/bignum.c
Janos Follath bd87a59007 mbedtls_mpi_lt_mpi_ct: Improve documentation
2019-11-11 12:32:12 +00:00

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/*
* Multi-precision integer library
*
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* This file is part of mbed TLS (https://tls.mbed.org)
*/
/*
* The following sources were referenced in the design of this Multi-precision
* Integer library:
*
* [1] Handbook of Applied Cryptography - 1997
* Menezes, van Oorschot and Vanstone
*
* [2] Multi-Precision Math
* Tom St Denis
* https://github.com/libtom/libtommath/blob/develop/tommath.pdf
*
* [3] GNU Multi-Precision Arithmetic Library
* https://gmplib.org/manual/index.html
*
*/
#if !defined(MBEDTLS_CONFIG_FILE)
#include "mbedtls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif
#if defined(MBEDTLS_BIGNUM_C)
#include "mbedtls/bignum.h"
#include "mbedtls/bn_mul.h"
#include "mbedtls/platform_util.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 in this case */
if( X->n <= nblimbs )
return( mbedtls_mpi_grow( X, nblimbs ) );
for( i = X->n - 1; i > 0; i-- )
if( X->p[i] != 0 )
break;
i++;
if( i < nblimbs )
i = nblimbs;
if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL )
return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
if( X->p != NULL )
{
memcpy( p, X->p, i * ciL );
mbedtls_mpi_zeroize( X->p, X->n );
mbedtls_free( X->p );
}
X->n = i;
X->p = p;
return( 0 );
}
/*
* Copy the contents of Y into X
*/
int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
{
int ret = 0;
size_t i;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( Y != NULL );
if( X == Y )
return( 0 );
if( Y->p == NULL )
{
mbedtls_mpi_free( X );
return( 0 );
}
for( i = Y->n - 1; i > 0; i-- )
if( Y->p[i] != 0 )
break;
i++;
X->s = Y->s;
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 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;
for( i = 0; i < Y->n; i++ )
X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
for( ; i < X->n; i++ )
X->p[i] *= ( 1 - assign );
cleanup:
return( ret );
}
/*
* Conditionally swap X and Y, without leaking information
* about whether the swap was made or not.
* Here it is not ok to simply swap the pointers, which whould lead to
* different memory access patterns when X and Y are used afterwards.
*/
int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
{
int ret, s;
size_t i;
mbedtls_mpi_uint tmp;
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;
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;
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_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;
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, big endian
*/
int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
{
int ret;
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:
return( ret );
}
/*
* Export X into unsigned binary data, big endian
*/
int mbedtls_mpi_write_binary( const mbedtls_mpi *X,
unsigned char *buf, size_t buflen )
{
size_t 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;
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 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, sign_X, sign_Y;
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.
*/
sign_X = ( X->s & 2 ) >> 1;
sign_Y = ( Y->s & 2 ) >> 1;
/*
* If the signs are different, then the positive operand is the bigger.
* That is if X is negative (sign_X == 1), then X < Y is true and it is
* false if X is positive (sign_X == 0).
*/
cond = ( sign_X ^ sign_Y );
*ret = cond & sign_X;
/*
* 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] and both X and Y are negative, then
* X < Y.
*
* 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] ) & sign_X;
*ret |= cond & ( 1 - done );
done |= cond & ( 1 - done );
/*
* If X->p[i - 1] < Y->p[i - 1] and both X and Y are positive, then
* X < Y.
*
* 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] ) & ( 1 - sign_X );
*ret |= cond & ( 1 - done );
done |= cond & ( 1 - done );
}
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;
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
*/
static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
{
size_t i;
mbedtls_mpi_uint c, z;
for( i = c = 0; i < n; i++, s++, d++ )
{
z = ( *d < c ); *d -= c;
c = ( *d < *s ) + z; *d -= *s;
}
while( c != 0 )
{
z = ( *d < c ); *d -= c;
c = z; d++;
}
}
/*
* Unsigned subtraction: X = |A| - |B| (HAC 14.9)
*/
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
mbedtls_mpi TB;
int ret;
size_t n;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
mbedtls_mpi_init( &TB );
if( X == B )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
B = &TB;
}
if( X != A )
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
/*
* X should always be positive as a result of unsigned subtractions.
*/
X->s = 1;
ret = 0;
for( n = B->n; n > 0; n-- )
if( B->p[n - 1] != 0 )
break;
mpi_sub_hlp( n, B->p, X->p );
cleanup:
mbedtls_mpi_free( &TB );
return( ret );
}
/*
* Signed addition: X = A + B
*/
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret, s;
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
*/
static
#if defined(__APPLE__) && defined(__arm__)
/*
* Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
* appears to need this to prevent bad ARM code generation at -O3.
*/
__attribute__ ((noinline))
#endif
void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
{
mbedtls_mpi_uint c = 0, t = 0;
#if defined(MULADDC_HUIT)
for( ; i >= 8; i -= 8 )
{
MULADDC_INIT
MULADDC_HUIT
MULADDC_STOP
}
for( ; i > 0; i-- )
{
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#else /* MULADDC_HUIT */
for( ; i >= 16; i -= 16 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i >= 8; i -= 8 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i > 0; i-- )
{
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#endif /* MULADDC_HUIT */
t++;
do {
*d += c; c = ( *d < c ); d++;
}
while( c != 0 );
}
/*
* Baseline multiplication: X = A * B (HAC 14.12)
*/
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret;
size_t i, j;
mbedtls_mpi TA, TB;
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 )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
_B.s = 1;
_B.n = 1;
_B.p = p;
p[0] = b;
return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
}
/*
* Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
* mbedtls_mpi_uint divisor, d
*/
static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1,
mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r )
{
#if defined(MBEDTLS_HAVE_UDBL)
mbedtls_t_udbl dividend, quotient;
#else
const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1;
mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
mbedtls_mpi_uint u0_msw, u0_lsw;
size_t s;
#endif
/*
* Check for overflow
*/
if( 0 == d || u1 >= d )
{
if (r != NULL) *r = ~0;
return ( ~0 );
}
#if defined(MBEDTLS_HAVE_UDBL)
dividend = (mbedtls_t_udbl) u1 << biL;
dividend |= (mbedtls_t_udbl) u0;
quotient = dividend / d;
if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1;
if( r != NULL )
*r = (mbedtls_mpi_uint)( dividend - (quotient * d ) );
return (mbedtls_mpi_uint) quotient;
#else
/*
* Algorithm D, Section 4.3.1 - The Art of Computer Programming
* Vol. 2 - Seminumerical Algorithms, Knuth
*/
/*
* Normalize the divisor, d, and dividend, u0, u1
*/
s = mbedtls_clz( d );
d = d << s;
u1 = u1 << s;
u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) );
u0 = u0 << s;
d1 = d >> biH;
d0 = d & uint_halfword_mask;
u0_msw = u0 >> biH;
u0_lsw = u0 & uint_halfword_mask;
/*
* Find the first quotient and remainder
*/
q1 = u1 / d1;
r0 = u1 - d1 * q1;
while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
{
q1 -= 1;
r0 += d1;
if ( r0 >= radix ) break;
}
rAX = ( u1 * radix ) + ( u0_msw - q1 * d );
q0 = rAX / d1;
r0 = rAX - q0 * d1;
while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
{
q0 -= 1;
r0 += d1;
if ( r0 >= radix ) break;
}
if (r != NULL)
*r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
quotient = q1 * radix + q0;
return quotient;
#endif
}
/*
* Division by mbedtls_mpi: A = Q * B + R (HAC 14.20)
*/
int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
const mbedtls_mpi *B )
{
int ret;
size_t i, n, t, k;
mbedtls_mpi X, Y, Z, T1, T2;
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 ); mbedtls_mpi_init( &T2 );
if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
{
if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) );
return( 0 );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) );
X.s = Y.s = 1;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z, 0 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, 2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) );
k = mbedtls_mpi_bitlen( &Y ) % biL;
if( k < biL - 1 )
{
k = biL - 1 - k;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) );
}
else k = 0;
n = X.n - 1;
t = Y.n - 1;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) );
while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 )
{
Z.p[n - t]++;
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) );
for( i = n; i > t ; i-- )
{
if( X.p[i] >= Y.p[t] )
Z.p[i - t - 1] = ~0;
else
{
Z.p[i - t - 1] = mbedtls_int_div_int( X.p[i], X.p[i - 1],
Y.p[t], NULL);
}
Z.p[i - t - 1]++;
do
{
Z.p[i - t - 1]--;
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
T1.p[1] = Y.p[t];
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) );
T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2];
T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1];
T2.p[2] = X.p[i];
}
while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) );
if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) );
Z.p[i - t - 1]--;
}
}
if( Q != NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
Q->s = A->s * B->s;
}
if( R != NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
X.s = A->s;
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
R->s = 1;
}
cleanup:
mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
return( ret );
}
/*
* Division by int: A = Q * b + R
*/
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R,
const mbedtls_mpi *A,
mbedtls_mpi_sint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
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;
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)
*/
static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
const mbedtls_mpi *T )
{
size_t i, n, m;
mbedtls_mpi_uint u0, u1, *d;
if( T->n < N->n + 1 || T->p == NULL )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
memset( T->p, 0, T->n * ciL );
d = T->p;
n = N->n;
m = ( B->n < n ) ? B->n : n;
for( i = 0; i < n; i++ )
{
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = A->p[i];
u1 = ( d[0] + u0 * B->p[0] ) * mm;
mpi_mul_hlp( m, B->p, d, u0 );
mpi_mul_hlp( n, N->p, d, u1 );
*d++ = u0; d[n + 1] = 0;
}
memcpy( A->p, d, ( n + 1 ) * ciL );
if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
mpi_sub_hlp( n, N->p, A->p );
else
/* prevent timing attacks */
mpi_sub_hlp( n, A->p, T->p );
return( 0 );
}
/*
* Montgomery reduction: A = A * R^-1 mod N
*/
static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T )
{
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;
U.n = U.s = (int) z;
U.p = &z;
return( mpi_montmul( A, &U, N, mm, T ) );
}
/*
* Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
*/
int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *E, const mbedtls_mpi *N,
mbedtls_mpi *_RR )
{
int ret;
size_t wbits, wsize, one = 1;
size_t i, j, nblimbs;
size_t bufsize, nbits;
mbedtls_mpi_uint ei, mm, state;
mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
int neg;
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 ) );
MBEDTLS_MPI_CHK( mpi_montmul( &W[1], &RR, N, mm, &T ) );
/*
* X = R^2 * R^-1 mod N = R mod N
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
if( wsize > 1 )
{
/*
* W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
*/
j = one << ( wsize - 1 );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) );
for( i = 0; i < wsize - 1; i++ )
MBEDTLS_MPI_CHK( mpi_montmul( &W[j], &W[j], N, mm, &T ) );
/*
* W[i] = W[i - 1] * W[1]
*/
for( i = j + 1; i < ( one << wsize ); i++ )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
MBEDTLS_MPI_CHK( mpi_montmul( &W[i], &W[1], N, mm, &T ) );
}
}
nblimbs = E->n;
bufsize = 0;
nbits = 0;
wbits = 0;
state = 0;
while( 1 )
{
if( bufsize == 0 )
{
if( nblimbs == 0 )
break;
nblimbs--;
bufsize = sizeof( mbedtls_mpi_uint ) << 3;
}
bufsize--;
ei = (E->p[nblimbs] >> bufsize) & 1;
/*
* skip leading 0s
*/
if( ei == 0 && state == 0 )
continue;
if( ei == 0 && state == 1 )
{
/*
* out of window, square X
*/
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
continue;
}
/*
* add ei to current window
*/
state = 2;
nbits++;
wbits |= ( ei << ( wsize - nbits ) );
if( nbits == wsize )
{
/*
* X = X^wsize R^-1 mod N
*/
for( i = 0; i < wsize; i++ )
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
/*
* X = X * W[wbits] R^-1 mod N
*/
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) );
state--;
nbits = 0;
wbits = 0;
}
}
/*
* process the remaining bits
*/
for( i = 0; i < nbits; i++ )
{
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
wbits <<= 1;
if( ( wbits & ( one << wsize ) ) != 0 )
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) );
}
/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
{
X->s = -1;
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
}
cleanup:
for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
mbedtls_mpi_free( &W[i] );
mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
if( _RR == NULL || _RR->p == NULL )
mbedtls_mpi_free( &RR );
return( ret );
}
/*
* Greatest common divisor: G = gcd(A, B) (HAC 14.54)
*/
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret;
size_t lz, lzt;
mbedtls_mpi TG, TA, TB;
MPI_VALIDATE_RET( G != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
mbedtls_mpi_init( &TG ); mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
lz = mbedtls_mpi_lsb( &TA );
lzt = mbedtls_mpi_lsb( &TB );
if( lzt < lz )
lz = lzt;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
TA.s = TB.s = 1;
while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
}
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
cleanup:
mbedtls_mpi_free( &TG ); mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
return( ret );
}
/*
* Fill X with size bytes of random.
*
* Use a temporary bytes representation to make sure the result is the same
* regardless of the platform endianness (useful when f_rng is actually
* deterministic, eg for tests).
*/
int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
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_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_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", 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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