| /* |
| * Multi-precision integer library |
| * |
| * Copyright (C) 2006-2010, Brainspark B.V. |
| * |
| * This file is part of PolarSSL (http://www.polarssl.org) |
| * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org> |
| * |
| * All rights reserved. |
| * |
| * 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 |
| */ |
| |
| #include "polarssl/config.h" |
| |
| #if defined(POLARSSL_BIGNUM_C) |
| |
| #include "polarssl/bignum.h" |
| #include "polarssl/bn_mul.h" |
| |
| #include <stdlib.h> |
| |
| #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 |
| */ |
| #define BITS_TO_LIMBS(i) (((i) + biL - 1) / biL) |
| #define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL) |
| |
| /* |
| * 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 ) |
| { |
| memset( X->p, 0, X->n * ciL ); |
| 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 = (t_uint *) 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 ); |
| memset( X->p, 0, X->n * ciL ); |
| free( X->p ); |
| } |
| |
| X->n = nblimbs; |
| 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 ); |
| |
| 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 ) ); |
| } |
| |
| /* |
| * 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] = ( X->p[off] & ~( 0x01 << idx ) ) | ( 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; |
| |
| 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 ) |
| { |
| 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 + 3 ) != 0 ) |
| continue; |
| |
| p += sprintf( p, "%02X", c ); |
| 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 |
| 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); |
| |
| /* |
| * 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 substraction |
| */ |
| 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 substraction: 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 substractions. |
| */ |
| 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 substraction: 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 substraction: 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 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 |
| 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 |
| |
| 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_sub_mpi( &X, &X, &Y ); |
| } |
| 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 |
| } |
| |
| 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_copy( Q, &Z ); |
| Q->s = A->s * B->s; |
| } |
| |
| if( R != NULL ) |
| { |
| mpi_shift_r( &X, k ); |
| mpi_copy( R, &X ); |
| |
| R->s = A->s; |
| 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 |
| * |
| * Returns 0 if successful |
| * 1 if memory allocation failed |
| * POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0 |
| */ |
| 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]; |
| |
| x = m0; |
| x += ( ( m0 + 2 ) & 4 ) << 1; |
| x *= ( 2 - ( m0 * x ) ); |
| |
| if( biL >= 16 ) x *= ( 2 - ( m0 * x ) ); |
| if( biL >= 32 ) x *= ( 2 - ( m0 * x ) ); |
| if( biL >= 64 ) 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 = 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 ); |
| 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 ); |
| |
| mpi_init( &Apos ); |
| 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_mod_mpi( &W[1], A, N ); |
| else 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; |
| |
| 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_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 ) |
| 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 ); |
| } |
| |
| int mpi_fill_random( mpi *X, size_t size, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ) |
| { |
| int ret; |
| |
| MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( size ) ) ); |
| MPI_CHK( mpi_lset( X, 0 ) ); |
| |
| MPI_CHK( f_rng( p_rng, (unsigned char *) X->p, size ) ); |
| |
| cleanup: |
| return( ret ); |
| } |
| |
| #if defined(POLARSSL_GENPRIME) |
| |
| /* |
| * 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 ); |
| } |
| |
| 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 |
| }; |
| |
| /* |
| * Miller-Rabin primality test (HAC 4.24) |
| */ |
| int mpi_is_prime( mpi *X, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ) |
| { |
| int ret, xs; |
| size_t i, j, n, s; |
| mpi W, R, T, A, RR; |
| |
| if( mpi_cmp_int( X, 0 ) == 0 || |
| mpi_cmp_int( X, 1 ) == 0 ) |
| return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| |
| if( mpi_cmp_int( X, 2 ) == 0 ) |
| return( 0 ); |
| |
| mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A ); |
| mpi_init( &RR ); |
| |
| xs = X->s; X->s = 1; |
| |
| /* |
| * test trivial factors first |
| */ |
| if( ( X->p[0] & 1 ) == 0 ) |
| return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| |
| for( i = 0; small_prime[i] > 0; i++ ) |
| { |
| t_uint r; |
| |
| if( mpi_cmp_int( X, small_prime[i] ) <= 0 ) |
| return( 0 ); |
| |
| MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) ); |
| |
| if( r == 0 ) |
| return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); |
| } |
| |
| /* |
| * 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 |
| */ |
| MPI_CHK( mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) ); |
| |
| if( mpi_cmp_mpi( &A, &W ) >= 0 ) |
| { |
| j = mpi_msb( &A ) - mpi_msb( &W ); |
| MPI_CHK( mpi_shift_r( &A, j + 1 ) ); |
| } |
| A.p[0] |= 3; |
| |
| /* |
| * 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: |
| |
| X->s = xs; |
| |
| mpi_free( &W ); mpi_free( &R ); mpi_free( &T ); mpi_free( &A ); |
| mpi_free( &RR ); |
| |
| return( ret ); |
| } |
| |
| /* |
| * 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; |
| 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_l( X, nbits - k ) ); |
| if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits ) ); |
| |
| X->p[0] |= 3; |
| |
| 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 |
| { |
| MPI_CHK( mpi_sub_int( &Y, X, 1 ) ); |
| MPI_CHK( mpi_shift_r( &Y, 1 ) ); |
| |
| while( 1 ) |
| { |
| if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 ) |
| { |
| if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 ) |
| break; |
| |
| if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) |
| goto cleanup; |
| } |
| |
| if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE ) |
| goto cleanup; |
| |
| MPI_CHK( mpi_add_int( &Y, X, 1 ) ); |
| MPI_CHK( mpi_add_int( X, X, 2 ) ); |
| MPI_CHK( mpi_shift_r( &Y, 1 ) ); |
| } |
| } |
| |
| cleanup: |
| |
| mpi_free( &Y ); |
| |
| return( ret ); |
| } |
| |
| #endif |
| |
| #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 ) |
| printf( " MPI test #1 (mul_mpi): " ); |
| |
| if( mpi_cmp_mpi( &X, &U ) != 0 ) |
| { |
| if( verbose != 0 ) |
| printf( "failed\n" ); |
| |
| return( 1 ); |
| } |
| |
| if( verbose != 0 ) |
| 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 ) |
| printf( " MPI test #2 (div_mpi): " ); |
| |
| if( mpi_cmp_mpi( &X, &U ) != 0 || |
| mpi_cmp_mpi( &Y, &V ) != 0 ) |
| { |
| if( verbose != 0 ) |
| printf( "failed\n" ); |
| |
| return( 1 ); |
| } |
| |
| if( verbose != 0 ) |
| 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 ) |
| printf( " MPI test #3 (exp_mod): " ); |
| |
| if( mpi_cmp_mpi( &X, &U ) != 0 ) |
| { |
| if( verbose != 0 ) |
| printf( "failed\n" ); |
| |
| return( 1 ); |
| } |
| |
| if( verbose != 0 ) |
| printf( "passed\n" ); |
| |
| #if defined(POLARSSL_GENPRIME) |
| MPI_CHK( mpi_inv_mod( &X, &A, &N ) ); |
| |
| MPI_CHK( mpi_read_string( &U, 16, |
| "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \ |
| "C3DBA76456363A10869622EAC2DD84EC" \ |
| "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) ); |
| |
| if( verbose != 0 ) |
| printf( " MPI test #4 (inv_mod): " ); |
| |
| if( mpi_cmp_mpi( &X, &U ) != 0 ) |
| { |
| if( verbose != 0 ) |
| printf( "failed\n" ); |
| |
| return( 1 ); |
| } |
| |
| if( verbose != 0 ) |
| printf( "passed\n" ); |
| #endif |
| |
| if( verbose != 0 ) |
| 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 ) |
| printf( "failed at %d\n", i ); |
| |
| return( 1 ); |
| } |
| } |
| |
| if( verbose != 0 ) |
| printf( "passed\n" ); |
| |
| cleanup: |
| |
| if( ret != 0 && verbose != 0 ) |
| 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 ) |
| printf( "\n" ); |
| |
| return( ret ); |
| } |
| |
| #endif |
| |
| #endif |