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mbedtls/library/bignum.c
Manuel Pégourié-Gonnard 59efb6a1b9 Fix potential buffer overflow in mpi_read_string() 
Found by Guido Vranken.

Two possible integer overflows (during << 2 or addition in BITS_TO_LIMB())
could result in far too few memory to be allocated, then overflowing the
buffer in the subsequent for loop.

Both integer overflows happen when slen is close to or greater than
SIZE_T_MAX >> 2 (ie 2^30 on a 32 bit system).

Note: one could also avoid those overflows by changing BITS_TO_LIMB(s << 2) to
CHARS_TO_LIMB(s >> 1) but the solution implemented looks more robust with
respect to future code changes.
2015-09-30 16:50:31 +02:00

2359 lines
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/*
* Multi-precision integer library
*
* Copyright (C) 2006-2014, ARM Limited, All Rights Reserved
*
* This file is part of mbed TLS (https://tls.mbed.org)
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
/*
* This MPI implementation is based on:
*
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
* http://www.stillhq.com/extracted/gnupg-api/mpi/
* http://math.libtomcrypt.com/files/tommath.pdf
*/
#if !defined(POLARSSL_CONFIG_FILE)
#include "polarssl/config.h"
#else
#include POLARSSL_CONFIG_FILE
#endif
#if defined(POLARSSL_BIGNUM_C)
#include "polarssl/bignum.h"
#include "polarssl/bn_mul.h"
#include <string.h>
#include <limits.h>
#if defined(POLARSSL_PLATFORM_C)
#include "polarssl/platform.h"
#else
#include <stdio.h>
#include <stdlib.h>
#define polarssl_printf printf
#define polarssl_malloc malloc
#define polarssl_free free
#endif
/* Implementation that should never be optimized out by the compiler */
static void polarssl_zeroize( void *v, size_t n ) {
volatile unsigned char *p = v; while( n-- ) *p++ = 0;
}
#define ciL (sizeof(t_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
#define biH (ciL << 2) /* half limb size */
/*
* Convert between bits/chars and number of limbs
* Divide first in order to avoid potential overflows
*/
#define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) )
#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
/*
* Initialize one MPI
*/
void mpi_init( mpi *X )
{
if( X == NULL )
return;
X->s = 1;
X->n = 0;
X->p = NULL;
}
/*
* Unallocate one MPI
*/
void mpi_free( mpi *X )
{
if( X == NULL )
return;
if( X->p != NULL )
{
polarssl_zeroize( X->p, X->n * ciL );
polarssl_free( X->p );
}
X->s = 1;
X->n = 0;
X->p = NULL;
}
/*
* Enlarge to the specified number of limbs
*/
int mpi_grow( mpi *X, size_t nblimbs )
{
t_uint *p;
if( nblimbs > POLARSSL_MPI_MAX_LIMBS )
return( POLARSSL_ERR_MPI_MALLOC_FAILED );
if( X->n < nblimbs )
{
if( ( p = polarssl_malloc( nblimbs * ciL ) ) == NULL )
return( POLARSSL_ERR_MPI_MALLOC_FAILED );
memset( p, 0, nblimbs * ciL );
if( X->p != NULL )
{
memcpy( p, X->p, X->n * ciL );
polarssl_zeroize( X->p, X->n * ciL );
polarssl_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 mpi_shrink( mpi *X, size_t nblimbs )
{
t_uint *p;
size_t i;
/* Actually resize up in this case */
if( X->n <= nblimbs )
return( 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 = polarssl_malloc( i * ciL ) ) == NULL )
return( POLARSSL_ERR_MPI_MALLOC_FAILED );
memset( p, 0, i * ciL );
if( X->p != NULL )
{
memcpy( p, X->p, i * ciL );
polarssl_zeroize( X->p, X->n * ciL );
polarssl_free( X->p );
}
X->n = i;
X->p = p;
return( 0 );
}
/*
* Copy the contents of Y into X
*/
int mpi_copy( mpi *X, const mpi *Y )
{
int ret;
size_t i;
if( X == Y )
return( 0 );
if( Y->p == NULL )
{
mpi_free( X );
return( 0 );
}
for( i = Y->n - 1; i > 0; i-- )
if( Y->p[i] != 0 )
break;
i++;
X->s = Y->s;
MPI_CHK( mpi_grow( X, i ) );
memset( X->p, 0, X->n * ciL );
memcpy( X->p, Y->p, i * ciL );
cleanup:
return( ret );
}
/*
* Swap the contents of X and Y
*/
void mpi_swap( mpi *X, mpi *Y )
{
mpi T;
memcpy( &T, X, sizeof( mpi ) );
memcpy( X, Y, sizeof( mpi ) );
memcpy( Y, &T, sizeof( 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 mpi_safe_cond_assign( mpi *X, const mpi *Y, unsigned char assign )
{
int ret = 0;
size_t i;
/* make sure assign is 0 or 1 in a time-constant manner */
assign = (assign | (unsigned char)-assign) >> 7;
MPI_CHK( 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 mpi_safe_cond_swap( mpi *X, mpi *Y, unsigned char swap )
{
int ret, s;
size_t i;
t_uint tmp;
if( X == Y )
return( 0 );
/* make sure swap is 0 or 1 in a time-constant manner */
swap = (swap | (unsigned char)-swap) >> 7;
MPI_CHK( mpi_grow( X, Y->n ) );
MPI_CHK( 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 mpi_lset( mpi *X, t_sint z )
{
int ret;
MPI_CHK( 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 mpi_get_bit( const mpi *X, size_t pos )
{
if( X->n * biL <= pos )
return( 0 );
return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
}
/*
* Set a bit to a specific value of 0 or 1
*/
int mpi_set_bit( mpi *X, size_t pos, unsigned char val )
{
int ret = 0;
size_t off = pos / biL;
size_t idx = pos % biL;
if( val != 0 && val != 1 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
if( X->n * biL <= pos )
{
if( val == 0 )
return( 0 );
MPI_CHK( mpi_grow( X, off + 1 ) );
}
X->p[off] &= ~( (t_uint) 0x01 << idx );
X->p[off] |= (t_uint) val << idx;
cleanup:
return( ret );
}
/*
* Return the number of least significant bits
*/
size_t mpi_lsb( const mpi *X )
{
size_t i, j, count = 0;
for( i = 0; i < X->n; i++ )
for( j = 0; j < biL; j++, count++ )
if( ( ( X->p[i] >> j ) & 1 ) != 0 )
return( count );
return( 0 );
}
/*
* Return the number of most significant bits
*/
size_t mpi_msb( const 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;
for( j = biL; j > 0; j-- )
if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
break;
return( ( i * biL ) + j );
}
/*
* Return the total size in bytes
*/
size_t mpi_size( const mpi *X )
{
return( ( mpi_msb( X ) + 7 ) >> 3 );
}
/*
* Convert an ASCII character to digit value
*/
static int mpi_get_digit( t_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 >= (t_uint) radix )
return( POLARSSL_ERR_MPI_INVALID_CHARACTER );
return( 0 );
}
/*
* Import from an ASCII string
*/
int mpi_read_string( mpi *X, int radix, const char *s )
{
int ret;
size_t i, j, slen, n;
t_uint d;
mpi T;
if( radix < 2 || radix > 16 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
mpi_init( &T );
slen = strlen( s );
if( radix == 16 )
{
if( slen > SIZE_T_MAX >> 2 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
n = BITS_TO_LIMBS( slen << 2 );
MPI_CHK( mpi_grow( X, n ) );
MPI_CHK( mpi_lset( X, 0 ) );
for( i = slen, j = 0; i > 0; i--, j++ )
{
if( i == 1 && s[i - 1] == '-' )
{
X->s = -1;
break;
}
MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
}
}
else
{
MPI_CHK( mpi_lset( X, 0 ) );
for( i = 0; i < slen; i++ )
{
if( i == 0 && s[i] == '-' )
{
X->s = -1;
continue;
}
MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
MPI_CHK( mpi_mul_int( &T, X, radix ) );
if( X->s == 1 )
{
MPI_CHK( mpi_add_int( X, &T, d ) );
}
else
{
MPI_CHK( mpi_sub_int( X, &T, d ) );
}
}
}
cleanup:
mpi_free( &T );
return( ret );
}
/*
* Helper to write the digits high-order first
*/
static int mpi_write_hlp( mpi *X, int radix, char **p )
{
int ret;
t_uint r;
if( radix < 2 || radix > 16 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
MPI_CHK( mpi_mod_int( &r, X, radix ) );
MPI_CHK( mpi_div_int( X, NULL, X, radix ) );
if( mpi_cmp_int( X, 0 ) != 0 )
MPI_CHK( mpi_write_hlp( X, radix, p ) );
if( r < 10 )
*(*p)++ = (char)( r + 0x30 );
else
*(*p)++ = (char)( r + 0x37 );
cleanup:
return( ret );
}
/*
* Export into an ASCII string
*/
int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen )
{
int ret = 0;
size_t n;
char *p;
mpi T;
if( radix < 2 || radix > 16 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
n = mpi_msb( X );
if( radix >= 4 ) n >>= 1;
if( radix >= 16 ) n >>= 1;
n += 3;
if( *slen < n )
{
*slen = n;
return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
}
p = s;
mpi_init( &T );
if( X->s == -1 )
*p++ = '-';
if( radix == 16 )
{
int c;
size_t i, j, k;
for( i = X->n, k = 0; i > 0; i-- )
{
for( j = ciL; j > 0; j-- )
{
c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
if( c == 0 && k == 0 && ( i + j ) != 2 )
continue;
*(p++) = "0123456789ABCDEF" [c / 16];
*(p++) = "0123456789ABCDEF" [c % 16];
k = 1;
}
}
}
else
{
MPI_CHK( mpi_copy( &T, X ) );
if( T.s == -1 )
T.s = 1;
MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
}
*p++ = '\0';
*slen = p - s;
cleanup:
mpi_free( &T );
return( ret );
}
#if defined(POLARSSL_FS_IO)
/*
* Read X from an opened file
*/
int mpi_read_file( mpi *X, int radix, FILE *fin )
{
t_uint d;
size_t slen;
char *p;
/*
* Buffer should have space for (short) label and decimal formatted MPI,
* newline characters and '\0'
*/
char s[ POLARSSL_MPI_RW_BUFFER_SIZE ];
memset( s, 0, sizeof( s ) );
if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
slen = strlen( s );
if( slen == sizeof( s ) - 2 )
return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
p = s + slen;
while( --p >= s )
if( mpi_get_digit( &d, radix, *p ) != 0 )
break;
return( mpi_read_string( X, radix, p + 1 ) );
}
/*
* Write X into an opened file (or stdout if fout == NULL)
*/
int mpi_write_file( const char *p, const 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[ POLARSSL_MPI_RW_BUFFER_SIZE ];
n = sizeof( s );
memset( s, 0, n );
n -= 2;
MPI_CHK( mpi_write_string( X, radix, s, (size_t *) &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( POLARSSL_ERR_MPI_FILE_IO_ERROR );
}
else
polarssl_printf( "%s%s", p, s );
cleanup:
return( ret );
}
#endif /* POLARSSL_FS_IO */
/*
* Import X from unsigned binary data, big endian
*/
int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen )
{
int ret;
size_t i, j, n;
for( n = 0; n < buflen; n++ )
if( buf[n] != 0 )
break;
MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) );
MPI_CHK( mpi_lset( X, 0 ) );
for( i = buflen, j = 0; i > n; i--, j++ )
X->p[j / ciL] |= ((t_uint) buf[i - 1]) << ((j % ciL) << 3);
cleanup:
return( ret );
}
/*
* Export X into unsigned binary data, big endian
*/
int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen )
{
size_t i, j, n;
n = mpi_size( X );
if( buflen < n )
return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
memset( buf, 0, buflen );
for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- )
buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) );
return( 0 );
}
/*
* Left-shift: X <<= count
*/
int mpi_shift_l( mpi *X, size_t count )
{
int ret;
size_t i, v0, t1;
t_uint r0 = 0, r1;
v0 = count / (biL );
t1 = count & (biL - 1);
i = mpi_msb( X ) + count;
if( X->n * biL < i )
MPI_CHK( 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 mpi_shift_r( mpi *X, size_t count )
{
size_t i, v0, v1;
t_uint r0 = 0, r1;
v0 = count / biL;
v1 = count & (biL - 1);
if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
return 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 mpi_cmp_abs( const mpi *X, const mpi *Y )
{
size_t i, j;
for( i = X->n; i > 0; i-- )
if( X->p[i - 1] != 0 )
break;
for( j = Y->n; j > 0; j-- )
if( Y->p[j - 1] != 0 )
break;
if( i == 0 && j == 0 )
return( 0 );
if( i > j ) return( 1 );
if( j > i ) return( -1 );
for( ; i > 0; i-- )
{
if( X->p[i - 1] > Y->p[i - 1] ) return( 1 );
if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
}
return( 0 );
}
/*
* Compare signed values
*/
int mpi_cmp_mpi( const mpi *X, const mpi *Y )
{
size_t i, j;
for( i = X->n; i > 0; i-- )
if( X->p[i - 1] != 0 )
break;
for( j = Y->n; j > 0; j-- )
if( Y->p[j - 1] != 0 )
break;
if( i == 0 && j == 0 )
return( 0 );
if( i > j ) return( X->s );
if( j > i ) return( -Y->s );
if( X->s > 0 && Y->s < 0 ) return( 1 );
if( Y->s > 0 && X->s < 0 ) return( -1 );
for( ; i > 0; i-- )
{
if( X->p[i - 1] > Y->p[i - 1] ) return( X->s );
if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
}
return( 0 );
}
/*
* Compare signed values
*/
int mpi_cmp_int( const mpi *X, t_sint z )
{
mpi Y;
t_uint p[1];
*p = ( z < 0 ) ? -z : z;
Y.s = ( z < 0 ) ? -1 : 1;
Y.n = 1;
Y.p = p;
return( mpi_cmp_mpi( X, &Y ) );
}
/*
* Unsigned addition: X = |A| + |B| (HAC 14.7)
*/
int mpi_add_abs( mpi *X, const mpi *A, const mpi *B )
{
int ret;
size_t i, j;
t_uint *o, *p, c;
if( X == B )
{
const mpi *T = A; A = X; B = T;
}
if( X != A )
MPI_CHK( 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;
MPI_CHK( mpi_grow( X, j ) );
o = B->p; p = X->p; c = 0;
for( i = 0; i < j; i++, o++, p++ )
{
*p += c; c = ( *p < c );
*p += *o; c += ( *p < *o );
}
while( c != 0 )
{
if( i >= X->n )
{
MPI_CHK( mpi_grow( X, i + 1 ) );
p = X->p + i;
}
*p += c; c = ( *p < c ); i++; p++;
}
cleanup:
return( ret );
}
/*
* Helper for mpi subtraction
*/
static void mpi_sub_hlp( size_t n, t_uint *s, t_uint *d )
{
size_t i;
t_uint c, z;
for( i = c = 0; i < n; i++, s++, d++ )
{
z = ( *d < c ); *d -= c;
c = ( *d < *s ) + z; *d -= *s;
}
while( c != 0 )
{
z = ( *d < c ); *d -= c;
c = z; i++; d++;
}
}
/*
* Unsigned subtraction: X = |A| - |B| (HAC 14.9)
*/
int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B )
{
mpi TB;
int ret;
size_t n;
if( mpi_cmp_abs( A, B ) < 0 )
return( POLARSSL_ERR_MPI_NEGATIVE_VALUE );
mpi_init( &TB );
if( X == B )
{
MPI_CHK( mpi_copy( &TB, B ) );
B = &TB;
}
if( X != A )
MPI_CHK( 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:
mpi_free( &TB );
return( ret );
}
/*
* Signed addition: X = A + B
*/
int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B )
{
int ret, s = A->s;
if( A->s * B->s < 0 )
{
if( mpi_cmp_abs( A, B ) >= 0 )
{
MPI_CHK( mpi_sub_abs( X, A, B ) );
X->s = s;
}
else
{
MPI_CHK( mpi_sub_abs( X, B, A ) );
X->s = -s;
}
}
else
{
MPI_CHK( mpi_add_abs( X, A, B ) );
X->s = s;
}
cleanup:
return( ret );
}
/*
* Signed subtraction: X = A - B
*/
int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B )
{
int ret, s = A->s;
if( A->s * B->s > 0 )
{
if( mpi_cmp_abs( A, B ) >= 0 )
{
MPI_CHK( mpi_sub_abs( X, A, B ) );
X->s = s;
}
else
{
MPI_CHK( mpi_sub_abs( X, B, A ) );
X->s = -s;
}
}
else
{
MPI_CHK( mpi_add_abs( X, A, B ) );
X->s = s;
}
cleanup:
return( ret );
}
/*
* Signed addition: X = A + b
*/
int mpi_add_int( mpi *X, const mpi *A, t_sint b )
{
mpi _B;
t_uint p[1];
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mpi_add_mpi( X, A, &_B ) );
}
/*
* Signed subtraction: X = A - b
*/
int mpi_sub_int( mpi *X, const mpi *A, t_sint b )
{
mpi _B;
t_uint p[1];
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mpi_sub_mpi( X, A, &_B ) );
}
/*
* Helper for 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, t_uint *s, t_uint *d, t_uint b )
{
t_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 mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B )
{
int ret;
size_t i, j;
mpi TA, TB;
mpi_init( &TA ); mpi_init( &TB );
if( X == A ) { MPI_CHK( mpi_copy( &TA, A ) ); A = &TA; }
if( X == B ) { MPI_CHK( 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;
MPI_CHK( mpi_grow( X, i + j ) );
MPI_CHK( mpi_lset( X, 0 ) );
for( i++; j > 0; j-- )
mpi_mul_hlp( i - 1, A->p, X->p + j - 1, B->p[j - 1] );
X->s = A->s * B->s;
cleanup:
mpi_free( &TB ); mpi_free( &TA );
return( ret );
}
/*
* Baseline multiplication: X = A * b
*/
int mpi_mul_int( mpi *X, const mpi *A, t_sint b )
{
mpi _B;
t_uint p[1];
_B.s = 1;
_B.n = 1;
_B.p = p;
p[0] = b;
return( mpi_mul_mpi( X, A, &_B ) );
}
/*
* Division by mpi: A = Q * B + R (HAC 14.20)
*/
int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B )
{
int ret;
size_t i, n, t, k;
mpi X, Y, Z, T1, T2;
if( mpi_cmp_int( B, 0 ) == 0 )
return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
mpi_init( &T1 ); mpi_init( &T2 );
if( mpi_cmp_abs( A, B ) < 0 )
{
if( Q != NULL ) MPI_CHK( mpi_lset( Q, 0 ) );
if( R != NULL ) MPI_CHK( mpi_copy( R, A ) );
return( 0 );
}
MPI_CHK( mpi_copy( &X, A ) );
MPI_CHK( mpi_copy( &Y, B ) );
X.s = Y.s = 1;
MPI_CHK( mpi_grow( &Z, A->n + 2 ) );
MPI_CHK( mpi_lset( &Z, 0 ) );
MPI_CHK( mpi_grow( &T1, 2 ) );
MPI_CHK( mpi_grow( &T2, 3 ) );
k = mpi_msb( &Y ) % biL;
if( k < biL - 1 )
{
k = biL - 1 - k;
MPI_CHK( mpi_shift_l( &X, k ) );
MPI_CHK( mpi_shift_l( &Y, k ) );
}
else k = 0;
n = X.n - 1;
t = Y.n - 1;
MPI_CHK( mpi_shift_l( &Y, biL * ( n - t ) ) );
while( mpi_cmp_mpi( &X, &Y ) >= 0 )
{
Z.p[n - t]++;
MPI_CHK( mpi_sub_mpi( &X, &X, &Y ) );
}
MPI_CHK( 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
{
#if defined(POLARSSL_HAVE_UDBL)
t_udbl r;
r = (t_udbl) X.p[i] << biL;
r |= (t_udbl) X.p[i - 1];
r /= Y.p[t];
if( r > ( (t_udbl) 1 << biL ) - 1 )
r = ( (t_udbl) 1 << biL ) - 1;
Z.p[i - t - 1] = (t_uint) r;
#else
/*
* __udiv_qrnnd_c, from gmp/longlong.h
*/
t_uint q0, q1, r0, r1;
t_uint d0, d1, d, m;
d = Y.p[t];
d0 = ( d << biH ) >> biH;
d1 = ( d >> biH );
q1 = X.p[i] / d1;
r1 = X.p[i] - d1 * q1;
r1 <<= biH;
r1 |= ( X.p[i - 1] >> biH );
m = q1 * d0;
if( r1 < m )
{
q1--, r1 += d;
while( r1 >= d && r1 < m )
q1--, r1 += d;
}
r1 -= m;
q0 = r1 / d1;
r0 = r1 - d1 * q0;
r0 <<= biH;
r0 |= ( X.p[i - 1] << biH ) >> biH;
m = q0 * d0;
if( r0 < m )
{
q0--, r0 += d;
while( r0 >= d && r0 < m )
q0--, r0 += d;
}
r0 -= m;
Z.p[i - t - 1] = ( q1 << biH ) | q0;
#endif /* POLARSSL_HAVE_UDBL && !64-bit Apple with Clang 5.0 */
}
Z.p[i - t - 1]++;
do
{
Z.p[i - t - 1]--;
MPI_CHK( mpi_lset( &T1, 0 ) );
T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
T1.p[1] = Y.p[t];
MPI_CHK( mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
MPI_CHK( 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( mpi_cmp_mpi( &T1, &T2 ) > 0 );
MPI_CHK( mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
MPI_CHK( mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) );
if( mpi_cmp_int( &X, 0 ) < 0 )
{
MPI_CHK( mpi_copy( &T1, &Y ) );
MPI_CHK( mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
MPI_CHK( mpi_add_mpi( &X, &X, &T1 ) );
Z.p[i - t - 1]--;
}
}
if( Q != NULL )
{
MPI_CHK( mpi_copy( Q, &Z ) );
Q->s = A->s * B->s;
}
if( R != NULL )
{
MPI_CHK( mpi_shift_r( &X, k ) );
X.s = A->s;
MPI_CHK( mpi_copy( R, &X ) );
if( mpi_cmp_int( R, 0 ) == 0 )
R->s = 1;
}
cleanup:
mpi_free( &X ); mpi_free( &Y ); mpi_free( &Z );
mpi_free( &T1 ); mpi_free( &T2 );
return( ret );
}
/*
* Division by int: A = Q * b + R
*/
int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b )
{
mpi _B;
t_uint p[1];
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mpi_div_mpi( Q, R, A, &_B ) );
}
/*
* Modulo: R = A mod B
*/
int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B )
{
int ret;
if( mpi_cmp_int( B, 0 ) < 0 )
return( POLARSSL_ERR_MPI_NEGATIVE_VALUE );
MPI_CHK( mpi_div_mpi( NULL, R, A, B ) );
while( mpi_cmp_int( R, 0 ) < 0 )
MPI_CHK( mpi_add_mpi( R, R, B ) );
while( mpi_cmp_mpi( R, B ) >= 0 )
MPI_CHK( mpi_sub_mpi( R, R, B ) );
cleanup:
return( ret );
}
/*
* Modulo: r = A mod b
*/
int mpi_mod_int( t_uint *r, const mpi *A, t_sint b )
{
size_t i;
t_uint x, y, z;
if( b == 0 )
return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
if( b < 0 )
return( POLARSSL_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( t_uint *mm, const mpi *N )
{
t_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 void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm,
const mpi *T )
{
size_t i, n, m;
t_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;
}
memcpy( A->p, d, ( n + 1 ) * ciL );
if( 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 );
}
/*
* Montgomery reduction: A = A * R^-1 mod N
*/
static void mpi_montred( mpi *A, const mpi *N, t_uint mm, const mpi *T )
{
t_uint z = 1;
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 mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
{
int ret;
size_t wbits, wsize, one = 1;
size_t i, j, nblimbs;
size_t bufsize, nbits;
t_uint ei, mm, state;
mpi RR, T, W[ 2 << POLARSSL_MPI_WINDOW_SIZE ], Apos;
int neg;
if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
if( mpi_cmp_int( E, 0 ) < 0 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
/*
* Init temps and window size
*/
mpi_montg_init( &mm, N );
mpi_init( &RR ); mpi_init( &T );
mpi_init( &Apos );
memset( W, 0, sizeof( W ) );
i = mpi_msb( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
if( wsize > POLARSSL_MPI_WINDOW_SIZE )
wsize = POLARSSL_MPI_WINDOW_SIZE;
j = N->n + 1;
MPI_CHK( mpi_grow( X, j ) );
MPI_CHK( mpi_grow( &W[1], j ) );
MPI_CHK( mpi_grow( &T, j * 2 ) );
/*
* Compensate for negative A (and correct at the end)
*/
neg = ( A->s == -1 );
if( neg )
{
MPI_CHK( mpi_copy( &Apos, A ) );
Apos.s = 1;
A = &Apos;
}
/*
* If 1st call, pre-compute R^2 mod N
*/
if( _RR == NULL || _RR->p == NULL )
{
MPI_CHK( mpi_lset( &RR, 1 ) );
MPI_CHK( mpi_shift_l( &RR, N->n * 2 * biL ) );
MPI_CHK( mpi_mod_mpi( &RR, &RR, N ) );
if( _RR != NULL )
memcpy( _RR, &RR, sizeof( mpi ) );
}
else
memcpy( &RR, _RR, sizeof( mpi ) );
/*
* W[1] = A * R^2 * R^-1 mod N = A * R mod N
*/
if( mpi_cmp_mpi( A, N ) >= 0 )
MPI_CHK( mpi_mod_mpi( &W[1], A, N ) );
else
MPI_CHK( mpi_copy( &W[1], A ) );
mpi_montmul( &W[1], &RR, N, mm, &T );
/*
* X = R^2 * R^-1 mod N = R mod N
*/
MPI_CHK( 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 );
MPI_CHK( mpi_grow( &W[j], N->n + 1 ) );
MPI_CHK( 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++ )
{
MPI_CHK( mpi_grow( &W[i], N->n + 1 ) );
MPI_CHK( 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( t_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 )
{
X->s = -1;
MPI_CHK( mpi_add_mpi( X, N, X ) );
}
cleanup:
for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
mpi_free( &W[i] );
mpi_free( &W[1] ); mpi_free( &T ); mpi_free( &Apos );
if( _RR == NULL || _RR->p == NULL )
mpi_free( &RR );
return( ret );
}
/*
* Greatest common divisor: G = gcd(A, B) (HAC 14.54)
*/
int mpi_gcd( mpi *G, const mpi *A, const mpi *B )
{
int ret;
size_t lz, lzt;
mpi TG, TA, TB;
mpi_init( &TG ); mpi_init( &TA ); mpi_init( &TB );
MPI_CHK( mpi_copy( &TA, A ) );
MPI_CHK( mpi_copy( &TB, B ) );
lz = mpi_lsb( &TA );
lzt = mpi_lsb( &TB );
if( lzt < lz )
lz = lzt;
MPI_CHK( mpi_shift_r( &TA, lz ) );
MPI_CHK( mpi_shift_r( &TB, lz ) );
TA.s = TB.s = 1;
while( mpi_cmp_int( &TA, 0 ) != 0 )
{
MPI_CHK( mpi_shift_r( &TA, mpi_lsb( &TA ) ) );
MPI_CHK( mpi_shift_r( &TB, mpi_lsb( &TB ) ) );
if( mpi_cmp_mpi( &TA, &TB ) >= 0 )
{
MPI_CHK( mpi_sub_abs( &TA, &TA, &TB ) );
MPI_CHK( mpi_shift_r( &TA, 1 ) );
}
else
{
MPI_CHK( mpi_sub_abs( &TB, &TB, &TA ) );
MPI_CHK( mpi_shift_r( &TB, 1 ) );
}
}
MPI_CHK( mpi_shift_l( &TB, lz ) );
MPI_CHK( mpi_copy( G, &TB ) );
cleanup:
mpi_free( &TG ); mpi_free( &TA ); 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 mpi_fill_random( mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
unsigned char buf[POLARSSL_MPI_MAX_SIZE];
if( size > POLARSSL_MPI_MAX_SIZE )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
MPI_CHK( f_rng( p_rng, buf, size ) );
MPI_CHK( mpi_read_binary( X, buf, size ) );
cleanup:
return( ret );
}
/*
* Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
*/
int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N )
{
int ret;
mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
if( mpi_cmp_int( N, 0 ) <= 0 )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
mpi_init( &TA ); mpi_init( &TU ); mpi_init( &U1 ); mpi_init( &U2 );
mpi_init( &G ); mpi_init( &TB ); mpi_init( &TV );
mpi_init( &V1 ); mpi_init( &V2 );
MPI_CHK( mpi_gcd( &G, A, N ) );
if( mpi_cmp_int( &G, 1 ) != 0 )
{
ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
goto cleanup;
}
MPI_CHK( mpi_mod_mpi( &TA, A, N ) );
MPI_CHK( mpi_copy( &TU, &TA ) );
MPI_CHK( mpi_copy( &TB, N ) );
MPI_CHK( mpi_copy( &TV, N ) );
MPI_CHK( mpi_lset( &U1, 1 ) );
MPI_CHK( mpi_lset( &U2, 0 ) );
MPI_CHK( mpi_lset( &V1, 0 ) );
MPI_CHK( mpi_lset( &V2, 1 ) );
do
{
while( ( TU.p[0] & 1 ) == 0 )
{
MPI_CHK( mpi_shift_r( &TU, 1 ) );
if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
{
MPI_CHK( mpi_add_mpi( &U1, &U1, &TB ) );
MPI_CHK( mpi_sub_mpi( &U2, &U2, &TA ) );
}
MPI_CHK( mpi_shift_r( &U1, 1 ) );
MPI_CHK( mpi_shift_r( &U2, 1 ) );
}
while( ( TV.p[0] & 1 ) == 0 )
{
MPI_CHK( mpi_shift_r( &TV, 1 ) );
if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
{
MPI_CHK( mpi_add_mpi( &V1, &V1, &TB ) );
MPI_CHK( mpi_sub_mpi( &V2, &V2, &TA ) );
}
MPI_CHK( mpi_shift_r( &V1, 1 ) );
MPI_CHK( mpi_shift_r( &V2, 1 ) );
}
if( mpi_cmp_mpi( &TU, &TV ) >= 0 )
{
MPI_CHK( mpi_sub_mpi( &TU, &TU, &TV ) );
MPI_CHK( mpi_sub_mpi( &U1, &U1, &V1 ) );
MPI_CHK( mpi_sub_mpi( &U2, &U2, &V2 ) );
}
else
{
MPI_CHK( mpi_sub_mpi( &TV, &TV, &TU ) );
MPI_CHK( mpi_sub_mpi( &V1, &V1, &U1 ) );
MPI_CHK( mpi_sub_mpi( &V2, &V2, &U2 ) );
}
}
while( mpi_cmp_int( &TU, 0 ) != 0 );
while( mpi_cmp_int( &V1, 0 ) < 0 )
MPI_CHK( mpi_add_mpi( &V1, &V1, N ) );
while( mpi_cmp_mpi( &V1, N ) >= 0 )
MPI_CHK( mpi_sub_mpi( &V1, &V1, N ) );
MPI_CHK( mpi_copy( X, &V1 ) );
cleanup:
mpi_free( &TA ); mpi_free( &TU ); mpi_free( &U1 ); mpi_free( &U2 );
mpi_free( &G ); mpi_free( &TB ); mpi_free( &TV );
mpi_free( &V1 ); mpi_free( &V2 );
return( ret );
}
#if defined(POLARSSL_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
* POLARSSL_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
* other negative: error
*/
static int mpi_check_small_factors( const mpi *X )
{
int ret = 0;
size_t i;
t_uint r;
if( ( X->p[0] & 1 ) == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
for( i = 0; small_prime[i] > 0; i++ )
{
if( mpi_cmp_int( X, small_prime[i] ) <= 0 )
return( 1 );
MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) );
if( r == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
}
cleanup:
return( ret );
}
/*
* Miller-Rabin pseudo-primality test (HAC 4.24)
*/
static int mpi_miller_rabin( const mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret, count;
size_t i, j, k, n, s;
mpi W, R, T, A, RR;
mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A );
mpi_init( &RR );
/*
* W = |X| - 1
* R = W >> lsb( W )
*/
MPI_CHK( mpi_sub_int( &W, X, 1 ) );
s = mpi_lsb( &W );
MPI_CHK( mpi_copy( &R, &W ) );
MPI_CHK( mpi_shift_r( &R, s ) );
i = mpi_msb( X );
/*
* HAC, table 4.4
*/
n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 :
( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 :
( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 );
for( i = 0; i < n; i++ )
{
/*
* pick a random A, 1 < A < |X| - 1
*/
count = 0;
do {
MPI_CHK( mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
j = mpi_msb( &A );
k = mpi_msb( &W );
if (j > k) {
MPI_CHK( mpi_shift_r( &A, j - k ) );
}
if (count++ > 30) {
return POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
}
} while ( (mpi_cmp_mpi( &A, &W ) >= 0) ||
(mpi_cmp_int( &A, 1 ) <= 0) );
/*
* A = A^R mod |X|
*/
MPI_CHK( mpi_exp_mod( &A, &A, &R, X, &RR ) );
if( mpi_cmp_mpi( &A, &W ) == 0 ||
mpi_cmp_int( &A, 1 ) == 0 )
continue;
j = 1;
while( j < s && mpi_cmp_mpi( &A, &W ) != 0 )
{
/*
* A = A * A mod |X|
*/
MPI_CHK( mpi_mul_mpi( &T, &A, &A ) );
MPI_CHK( mpi_mod_mpi( &A, &T, X ) );
if( mpi_cmp_int( &A, 1 ) == 0 )
break;
j++;
}
/*
* not prime if A != |X| - 1 or A == 1
*/
if( mpi_cmp_mpi( &A, &W ) != 0 ||
mpi_cmp_int( &A, 1 ) == 0 )
{
ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
break;
}
}
cleanup:
mpi_free( &W ); mpi_free( &R ); mpi_free( &T ); mpi_free( &A );
mpi_free( &RR );
return( ret );
}
/*
* Pseudo-primality test: small factors, then Miller-Rabin
*/
int mpi_is_prime( mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
mpi XX;
XX.s = 1;
XX.n = X->n;
XX.p = X->p;
if( mpi_cmp_int( &XX, 0 ) == 0 ||
mpi_cmp_int( &XX, 1 ) == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
if( mpi_cmp_int( &XX, 2 ) == 0 )
return( 0 );
if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
{
if( ret == 1 )
return( 0 );
return( ret );
}
return( mpi_miller_rabin( &XX, f_rng, p_rng ) );
}
/*
* Prime number generation
*/
int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
size_t k, n;
t_uint r;
mpi Y;
if( nbits < 3 || nbits > POLARSSL_MPI_MAX_BITS )
return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
mpi_init( &Y );
n = BITS_TO_LIMBS( nbits );
MPI_CHK( mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
k = mpi_msb( X );
if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits + 1 ) );
mpi_set_bit( X, nbits-1, 1 );
X->p[0] |= 1;
if( dh_flag == 0 )
{
while( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
{
if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
goto cleanup;
MPI_CHK( mpi_add_int( X, X, 2 ) );
}
}
else
{
/*
* An necessary condition for Y and X = 2Y + 1 to be prime
* is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
* Make sure it is satisfied, while keeping X = 3 mod 4
*/
X->p[0] |= 2;
MPI_CHK( mpi_mod_int( &r, X, 3 ) );
if( r == 0 )
MPI_CHK( mpi_add_int( X, X, 8 ) );
else if( r == 1 )
MPI_CHK( mpi_add_int( X, X, 4 ) );
/* Set Y = (X-1) / 2, which is X / 2 because X is odd */
MPI_CHK( mpi_copy( &Y, X ) );
MPI_CHK( mpi_shift_r( &Y, 1 ) );
while( 1 )
{
/*
* First, check small factors for X and Y
* before doing Miller-Rabin on any of them
*/
if( ( ret = mpi_check_small_factors( X ) ) == 0 &&
( ret = mpi_check_small_factors( &Y ) ) == 0 &&
( ret = mpi_miller_rabin( X, f_rng, p_rng ) ) == 0 &&
( ret = mpi_miller_rabin( &Y, f_rng, p_rng ) ) == 0 )
{
break;
}
if( ret != POLARSSL_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.
*/
MPI_CHK( mpi_add_int( X, X, 12 ) );
MPI_CHK( mpi_add_int( &Y, &Y, 6 ) );
}
}
cleanup:
mpi_free( &Y );
return( ret );
}
#endif /* POLARSSL_GENPRIME */
#if defined(POLARSSL_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 mpi_self_test( int verbose )
{
int ret, i;
mpi A, E, N, X, Y, U, V;
mpi_init( &A ); mpi_init( &E ); mpi_init( &N ); mpi_init( &X );
mpi_init( &Y ); mpi_init( &U ); mpi_init( &V );
MPI_CHK( mpi_read_string( &A, 16,
"EFE021C2645FD1DC586E69184AF4A31E" \
"D5F53E93B5F123FA41680867BA110131" \
"944FE7952E2517337780CB0DB80E61AA" \
"E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
MPI_CHK( mpi_read_string( &E, 16,
"B2E7EFD37075B9F03FF989C7C5051C20" \
"34D2A323810251127E7BF8625A4F49A5" \
"F3E27F4DA8BD59C47D6DAABA4C8127BD" \
"5B5C25763222FEFCCFC38B832366C29E" ) );
MPI_CHK( mpi_read_string( &N, 16,
"0066A198186C18C10B2F5ED9B522752A" \
"9830B69916E535C8F047518A889A43A5" \
"94B6BED27A168D31D4A52F88925AA8F5" ) );
MPI_CHK( mpi_mul_mpi( &X, &A, &N ) );
MPI_CHK( mpi_read_string( &U, 16,
"602AB7ECA597A3D6B56FF9829A5E8B85" \
"9E857EA95A03512E2BAE7391688D264A" \
"A5663B0341DB9CCFD2C4C5F421FEC814" \
"8001B72E848A38CAE1C65F78E56ABDEF" \
"E12D3C039B8A02D6BE593F0BBBDA56F1" \
"ECF677152EF804370C1A305CAF3B5BF1" \
"30879B56C61DE584A0F53A2447A51E" ) );
if( verbose != 0 )
polarssl_printf( " MPI test #1 (mul_mpi): " );
if( mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
polarssl_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
polarssl_printf( "passed\n" );
MPI_CHK( mpi_div_mpi( &X, &Y, &A, &N ) );
MPI_CHK( mpi_read_string( &U, 16,
"256567336059E52CAE22925474705F39A94" ) );
MPI_CHK( mpi_read_string( &V, 16,
"6613F26162223DF488E9CD48CC132C7A" \
"0AC93C701B001B092E4E5B9F73BCD27B" \
"9EE50D0657C77F374E903CDFA4C642" ) );
if( verbose != 0 )
polarssl_printf( " MPI test #2 (div_mpi): " );
if( mpi_cmp_mpi( &X, &U ) != 0 ||
mpi_cmp_mpi( &Y, &V ) != 0 )
{
if( verbose != 0 )
polarssl_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
polarssl_printf( "passed\n" );
MPI_CHK( mpi_exp_mod( &X, &A, &E, &N, NULL ) );
MPI_CHK( mpi_read_string( &U, 16,
"36E139AEA55215609D2816998ED020BB" \
"BD96C37890F65171D948E9BC7CBAA4D9" \
"325D24D6A3C12710F10A09FA08AB87" ) );
if( verbose != 0 )
polarssl_printf( " MPI test #3 (exp_mod): " );
if( mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
polarssl_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
polarssl_printf( "passed\n" );
MPI_CHK( mpi_inv_mod( &X, &A, &N ) );
MPI_CHK( mpi_read_string( &U, 16,
"003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
"C3DBA76456363A10869622EAC2DD84EC" \
"C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
if( verbose != 0 )
polarssl_printf( " MPI test #4 (inv_mod): " );
if( mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
polarssl_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
polarssl_printf( "passed\n" );
if( verbose != 0 )
polarssl_printf( " MPI test #5 (simple gcd): " );
for( i = 0; i < GCD_PAIR_COUNT; i++ )
{
MPI_CHK( mpi_lset( &X, gcd_pairs[i][0] ) );
MPI_CHK( mpi_lset( &Y, gcd_pairs[i][1] ) );
MPI_CHK( mpi_gcd( &A, &X, &Y ) );
if( mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
{
if( verbose != 0 )
polarssl_printf( "failed at %d\n", i );
ret = 1;
goto cleanup;
}
}
if( verbose != 0 )
polarssl_printf( "passed\n" );
cleanup:
if( ret != 0 && verbose != 0 )
polarssl_printf( "Unexpected error, return code = %08X\n", ret );
mpi_free( &A ); mpi_free( &E ); mpi_free( &N ); mpi_free( &X );
mpi_free( &Y ); mpi_free( &U ); mpi_free( &V );
if( verbose != 0 )
polarssl_printf( "\n" );
return( ret );
}
#endif /* POLARSSL_SELF_TEST */
#endif /* POLARSSL_BIGNUM_C */
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