/* * 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 * * 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 #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++) = "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 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 */ static int mpi_cmp_abs_limbs (size_t n, const t_uint *p0, const t_uint *p1) { size_t i, j; p0 += n; for( i = n; i > 0; i-- ) if( *--p0 != 0 ) break; p1 += n; for( j = n; j > 0; j-- ) if( *--p1 != 0 ) break; if( i == 0 && j == 0 ) return( 0 ); if( i > j ) return( 1 ); if( j > i ) return( -1 ); for( ; i > 0; i-- ) { if( *p0 > *p1 ) return( 1 ); if( *p0 < *p1 ) return( -1 ); p0--; p1--; } 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 t_uint mpi_sub_hlp( size_t n, const 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; } return c; } /* * 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; t_uint *d; t_uint c, z; 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; c = mpi_sub_hlp( n, B->p, X->p ); d = X->p + n; while( c != 0 ) { z = ( *d < c ); *d -= c; c = z; d++; } 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 #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 t_uint mpi_mul_hlp( size_t i, const t_uint *s, t_uint *d, t_uint b ) { t_uint c = 0, t = 0; #if defined(MULADDC_1024_LOOP) MULADDC_1024_LOOP for( ; i > 0; i-- ) { MULADDC_INIT MULADDC_CORE MULADDC_STOP } #elif 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++; *d += c; c = ( *d < c ); return c; } /* * 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, k; 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(k = 0; k < j; k++ ) mpi_mul_hlp( i, A->p, X->p + k, B->p[k]); 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 ); X.s = A->s; 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]; 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) * A is placed at the upper half of D. */ static void mpi_montmul( size_t n, const t_uint *np, t_uint mm, t_uint *d, const t_uint *bp ) { size_t i; t_uint u0, u1, c = 0; for( i = 0; i < n; i++ ) { /* * T = (T + u0*B + u1*N) / 2^biL */ u0 = d[n]; d[n] = c; u1 = ( d[0] + u0 * bp[0] ) * mm; mpi_mul_hlp( n, bp, d, u0 ); c = mpi_mul_hlp( n, np, d, u1 ); d++; } /* prevent timing attacks */ if( ((mpi_cmp_abs_limbs ( n, d, np ) >= 0) | c) ) mpi_sub_hlp( n, np, d ); else mpi_sub_hlp( n, d - n, d - n); } /* * Montgomery reduction: A = A * R^-1 mod N * A is placed at the upper half of D. */ static void mpi_montred( size_t n, const t_uint *np, t_uint mm, t_uint *d ) { size_t i, j; t_uint u0, u1, c = 0; for( i = 0; i < n; i++ ) { /* * T = (T + u0 + u1*N) / 2^biL */ u0 = d[n]; d[n] = c; u1 = (d[0] + u0) * mm; d[0] += u0; c = (d[0] < u0); for (j = 1; j < n; j++) { d[j] += c; c = ( d[j] < c ); } c = mpi_mul_hlp( n, np, d, u1 ); d++; } /* prevent timing attacks */ if( ((mpi_cmp_abs_limbs ( n, d, np ) >= 0) | c) ) mpi_sub_hlp( n, np, d ); else mpi_sub_hlp( n, d - n, d - n); } /* * Montgomery square: A = A * A * R^-1 mod N * A is placed at the upper half of D. */ static void mpi_montsqr( size_t n, const t_uint *np, t_uint mm, t_uint *d ) { size_t i; register t_uint c = 0; for (i = 0; i < n; i++) { t_uint *wij = &d[i*2]; t_uint *xj = &d[i+n]; t_uint x_i; x_i = *xj; *xj++ = c; asm (/* (C,R4,R5) := w_i_i + x_i*x_i; w_i_i := R5; */ "mov %[c], #0\n\t" "ldr r5, [%[wij]]\n\t" /* R5 := w_i_i; */ "mov r4, %[c]\n\t" "umlal r5, r4, %[x_i], %[x_i]\n\t" "str r5, [%[wij]], #4\n\t" "cmp %[xj], %[x_max1]\n\t" "bhi 0f\n\t" "mov r9, %[c]\n\t" /* R9 := 0, the constant ZERO from here. */ "beq 1f\n" "2:\n\t" "ldmia %[xj]!, { r7, r8 }\n\t" "ldmia %[wij], { r5, r6 }\n\t" /* (C,R4,R5) := (C,R4) + w_i_j + 2*x_i*x_j; */ "umull r7, r12, %[x_i], r7\n\t" "adds r5, r5, r4\n\t" "adc r4, %[c], r9\n\t" "adds r5, r5, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], r9, r9\n\t" "adds r5, r5, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], %[c], r9\n\t" /* (C,R4,R6) := (C,R4) + w_i_j + 2*x_i*x_j; */ "adds r6, r6, r4\n\t" "adc r4, %[c], r9\n\t" "umull r7, r12, %[x_i], r8\n\t" "adds r6, r6, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], r9, r9\n\t" "adds r6, r6, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], %[c], r9\n\t" /**/ "stmia %[wij]!, { r5, r6 }\n\t" "cmp %[xj], %[x_max1]\n\t" "bcc 2b\n\t" "bne 0f\n" "1:\n\t" /* (C,R4,R5) := (C,R4) + w_i_j + 2*x_i*x_j; */ "ldr r5, [%[wij]]\n\t" "ldr r6, [%[xj]], #4\n\t" "adds r5, r5, r4\n\t" "adc r4, %[c], r9\n\t" "umull r7, r12, %[x_i], r6\n\t" "adds r5, r5, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], r9, r9\n\t" "adds r5, r5, r7\n\t" "adcs r4, r4, r12\n\t" "adc %[c], %[c], r9\n\t" "str r5, [%[wij]], #4\n" "0:\n\t" "ldr r5, [%[wij]]\n\t" "adds r4, r4, r5\n\t" "adc %[c], %[c], #0\n\t" "str r4, [%[wij]]" : [c] "=&r" (c), [wij] "=r" (wij), [xj] "=r" (xj) : [x_i] "r" (x_i), [x_max1] "r" (&d[n*2-1]), "[wij]" (wij), "[xj]" (xj) : "r4", "r5", "r6", "r7", "r8", "r9", "r12", "memory", "cc"); c += mpi_mul_hlp( n, np, &d[i], d[i] * mm ); } d += n; /* prevent timing attacks */ if( ((mpi_cmp_abs_limbs ( n, d, np ) >= 0) | c) ) mpi_sub_hlp( n, np, d ); else mpi_sub_hlp( n, d - n, d - n); } /* * 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 i = mpi_msb( E ); size_t wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; size_t wbits, one = 1; size_t nblimbs; size_t bufsize, nbits; t_uint ei, mm, state; mpi RR; t_uint d[N->n*2]; t_uint w1[N->n]; t_uint wn[(one << (wsize - 1))][N->n]; 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 ); if( A->s == -1 ) return( POLARSSL_ERR_MPI_BAD_INPUT_DATA ); /* * Init temps and window size */ mpi_montg_init( &mm, N ); MPI_CHK( mpi_grow( X, N->n ) ); /* * If 1st call, pre-compute R^2 mod N */ if( _RR == NULL || _RR->p == NULL ) { mpi T; mpi_init( &RR ); T.s = 1; T.n = N->n * 2; T.p = d; memset (d, 0, 2 * N->n * ciL); /* Set D zero. */ mpi_sub_hlp( N->n, N->p, d + N->n); MPI_CHK( mpi_mod_mpi( &RR, &T, N ) ); if( _RR != NULL ) memcpy( _RR, &RR, sizeof( mpi ) ); /* The condition of "the lower half of D is all zero" is kept. */ } else { memcpy( &RR, _RR, sizeof( mpi ) ); memset (d, 0, N->n * ciL); /* Set lower half of D zero. */ } /* * W[1] = A * R^2 * R^-1 mod N = A * R mod N */ if( mpi_cmp_mpi( A, N ) >= 0 ) { mpi W1; W1.s = 1; W1.n = N->n; W1.p = d + N->n; mpi_mod_mpi( &W1, A, N ); } else { memset (d + N->n, 0, N->n * ciL); memcpy (d + N->n, A->p, A->n * ciL); } mpi_montmul( N->n, N->p, mm, d, RR.p ); memcpy (w1, d + N->n, N->n * ciL); { /* * W[1 << (wsize - 1)] = W[1] ^ ( 2 ^ (wsize - 1) ) */ for( i = 0; i < wsize - 1; i++ ) mpi_montsqr( N->n, N->p, mm, d ); memcpy (wn[0], d + N->n, N->n * ciL); /* * W[i] = W[i - 1] * W[1] */ for( i = 1; i < (one << (wsize - 1)); i++ ) { mpi_montmul( N->n, N->p, mm, d, w1 ); memcpy (wn[i], d + N->n, N->n * ciL); } } /* * X = R^2 * R^-1 mod N = R mod N */ memcpy (d + N->n, RR.p, N->n * ciL); mpi_montred( N->n, N->p, mm, d ); 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_montsqr( N->n, N->p, mm, d ); 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_montsqr( N->n, N->p, mm, d ); /* * X = X * W[wbits] R^-1 mod N */ mpi_montmul( N->n, N->p, mm, d, wn[wbits - (one << (wsize - 1))]); state--; nbits = 0; wbits = 0; } } /* * process the remaining bits */ for( i = 0; i < nbits; i++ ) { mpi_montsqr( N->n, N->p, mm, d ); wbits <<= 1; if( (wbits & (one << wsize)) != 0 ) mpi_montmul( N->n, N->p, mm, d, w1); } /* * X = A^E * R * R^-1 mod N = A^E mod N */ mpi_montred( N->n, N->p, mm, d ); memcpy (X->p, d + N->n, N->n * ciL); cleanup: 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 ); } /* * 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[] = { #if 0 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, #else 97, #endif 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, #if 0 797, #endif 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, #if 1 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, #endif -103 }; /* * From Public domain code of JKISS RNG. * * Reference: David Jones, UCL Bioinformatics Group * Good Practice in (Pseudo) Random Number Generation for * Bioinformatics Applications * */ struct jkiss_state { uint32_t x, y, z, c; }; static struct jkiss_state jkiss_state_v; int prng_seed (int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) { int ret; struct jkiss_state *s = &jkiss_state_v; MPI_CHK ( f_rng (p_rng, (unsigned char *)s, sizeof (struct jkiss_state)) ); while (s->y == 0) MPI_CHK ( f_rng (p_rng, (unsigned char *)&s->y, sizeof (uint32_t)) ); s->z |= 1; /* avoiding z=c=0 */ cleanup: return ret; } static uint32_t jkiss (struct jkiss_state *s) { uint64_t t; s->x = 314527869 * s->x + 1234567; s->y ^= s->y << 5; s->y ^= s->y >> 7; s->y ^= s->y << 22; t = 4294584393ULL * s->z + s->c; s->c = (uint32_t)(t >> 32); s->z = (uint32_t)t; return s->x + s->y + s->z; } static int mpi_fill_pseudo_random ( mpi *X, size_t size) { int ret; uint32_t *p; MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( size ) ) ); MPI_CHK( mpi_lset( X, 0 ) ); /* Assume little endian. */ p = X->p; while (p < X->p + (size/ciL)) *p++ = jkiss (&jkiss_state_v); if ((size % ciL)) *p = jkiss (&jkiss_state_v) & ((1 << (8*(size % ciL))) - 1); cleanup: return ret; } /* * Miller-Rabin primality test (HAC 4.24) */ static int mpi_is_prime( mpi *X) { 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; ret = 0; #if 0 /* * test trivial factors first */ if( ( X->p[0] & 1 ) == 0 ) return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE ); #endif 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 ); /* Fermat primality test with 2. */ mpi_lset (&T, 2); MPI_CHK( mpi_exp_mod( &T, &T, &W, X, &RR ) ); if ( mpi_cmp_int (&T, 1) != 0) { ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE; goto cleanup; } /* * 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_pseudo_random( &A, X->n * ciL ) ); 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 ); } /* * Value M: multiply all primes up to 701 (except 97) and 797 * (so that MAX_A will be convenient value) */ #define M_LIMBS 31 #define M_SIZE 122 static const t_uint limbs_M[] = { /* Little endian */ 0x84EEB59E, 0x9344A6AB, 0xFF21529F, 0xEC855CDA, 0x009BAB38, 0x477E991E, 0x9F5B86F3, 0x2EEA2357, 0x41D6502F, 0xAC17D304, 0x0A468A6D, 0x38FF52B9, 0xFD42E5EF, 0x63630419, 0x91DB2572, 0x48CE17D0, 0xE3B57D0E, 0x708AB00A, 0xCD723598, 0xF8A9DE08, 0x4432C93B, 0x73141137, 0x2779FAB3, 0x554DF261, 0x953D2BA5, 0xDEEBDA58, 0x5F57D007, 0xD1D66F2F, 0xE84E9F2B, 0xB85C9607, 0x0000401D }; static const mpi M[1] = {{ 1, M_LIMBS, (t_uint *)limbs_M }}; /* * MAX_A : 2^1024 / M - 1 */ #define MAX_A_LIMBS 2 #define MAX_A_FILL_SIZE 6 static const t_uint limbs_MAX_A[] = { /* Little endian */ 0x56A2B35F, 0x0003FE25 }; static const mpi MAX_A[1] = {{ 1, MAX_A_LIMBS, (t_uint *)limbs_MAX_A }}; /* * Prime number generation * * Special version for 1024-bit only. Ignores DH_FLAG. */ 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; mpi B[1], G[1]; (void)dh_flag; if (nbits != 1024) return POLARSSL_ERR_MPI_BAD_INPUT_DATA; mpi_init ( B ); mpi_init ( G ); /* * Get random value 1 to M-1 avoiding bias, and proceed when it is * coprime to all small primes. */ do { MPI_CHK ( mpi_fill_random ( B, M_SIZE, f_rng, p_rng ) ); B->p[0] |= 0x1; B->p[M_LIMBS - 1] &= 0x00007FFF; if (mpi_cmp_abs (B, M) >= 0) continue; MPI_CHK ( mpi_gcd ( G, B, M ) ); } while (mpi_cmp_int ( G, 1 ) != 0); /* * Get random value avoiding bias, comput P with the value, * check if it's big enough, lastly, check if it's prime. */ while (1) { MPI_CHK( mpi_fill_random( X, MAX_A_FILL_SIZE, f_rng, p_rng ) ); MPI_CHK ( mpi_sub_abs (X, MAX_A, X) ); MPI_CHK ( mpi_mul_mpi ( X, X, M ) ); MPI_CHK ( mpi_add_abs ( X, X, B ) ); if (X->n <= 31 || (X->p[31] & 0xc0000000) == 0) continue; ret = mpi_is_prime ( X ); if (ret == 0 || ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE) break; } cleanup: mpi_free ( B ); mpi_free ( G ); 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