diff options
Diffstat (limited to 'library/bignum.c')
| -rw-r--r-- | library/bignum.c | 138 |
1 files changed, 102 insertions, 36 deletions
diff --git a/library/bignum.c b/library/bignum.c index a68957a53..65708c9f3 100644 --- a/library/bignum.c +++ b/library/bignum.c @@ -1590,11 +1590,11 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi *prec_RR ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; - size_t wbits, wsize, one = 1; + size_t window_bitsize; size_t i, j, nblimbs; size_t bufsize, nbits; mbedtls_mpi_uint ei, mm, state; - mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos; + mbedtls_mpi RR, T, W[ (size_t) 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos; int neg; MPI_VALIDATE_RET( X != NULL ); @@ -1623,21 +1623,59 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, i = mbedtls_mpi_bitlen( E ); - wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : + window_bitsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; #if( MBEDTLS_MPI_WINDOW_SIZE < 6 ) - if( wsize > MBEDTLS_MPI_WINDOW_SIZE ) - wsize = MBEDTLS_MPI_WINDOW_SIZE; + if( window_bitsize > MBEDTLS_MPI_WINDOW_SIZE ) + window_bitsize = MBEDTLS_MPI_WINDOW_SIZE; #endif + const size_t w_table_used_size = (size_t) 1 << window_bitsize; + + /* + * This function is not constant-trace: its memory accesses depend on the + * exponent value. To defend against timing attacks, callers (such as RSA + * and DHM) should use exponent blinding. However this is not enough if the + * adversary can find the exponent in a single trace, so this function + * takes extra precautions against adversaries who can observe memory + * access patterns. + * + * This function performs a series of multiplications by table elements and + * squarings, and we want the prevent the adversary from finding out which + * table element was used, and from distinguishing between multiplications + * and squarings. Firstly, when multiplying by an element of the window + * W[i], we do a constant-trace table lookup to obfuscate i. This leaves + * squarings as having a different memory access patterns from other + * multiplications. So secondly, we put the accumulator X in the table as + * well, and also do a constant-trace table lookup to multiply by X. + * + * This way, all multiplications take the form of a lookup-and-multiply. + * The number of lookup-and-multiply operations inside each iteration of + * the main loop still depends on the bits of the exponent, but since the + * other operations in the loop don't have an easily recognizable memory + * trace, an adversary is unlikely to be able to observe the exact + * patterns. + * + * An adversary may still be able to recover the exponent if they can + * observe both memory accesses and branches. However, branch prediction + * exploitation typically requires many traces of execution over the same + * data, which is defeated by randomized blinding. + * + * To achieve this, we make a copy of X and we use the table entry in each + * calculation from this point on. + */ + const size_t x_index = 0; + mbedtls_mpi_init( &W[x_index] ); + mbedtls_mpi_copy( &W[x_index], X ); + j = N->n + 1; /* All W[i] and X must have at least N->n limbs for the mpi_montmul() * and mpi_montred() calls later. Here we ensure that W[1] and X are * large enough, and later we'll grow other W[i] to the same length. * They must not be shrunk midway through this function! */ - MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[x_index], j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) ); @@ -1686,28 +1724,36 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, mpi_montmul( &W[1], &RR, N, mm, &T ); /* - * X = R^2 * R^-1 mod N = R mod N + * W[x_index] = R^2 * R^-1 mod N = R mod N */ - MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) ); - mpi_montred( X, N, mm, &T ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[x_index], &RR ) ); + mpi_montred( &W[x_index], N, mm, &T ); + - if( wsize > 1 ) + if( window_bitsize > 1 ) { /* - * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) + * W[i] = W[1] ^ i + * + * The first bit of the sliding window is always 1 and therefore we + * only need to store the second half of the table. + * + * (There are two special elements in the table: W[0] for the + * accumulator/result and W[1] for A in Montgomery form. Both of these + * are already set at this point.) */ - j = one << ( wsize - 1 ); + j = w_table_used_size / 2; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) ); - for( i = 0; i < wsize - 1; i++ ) + for( i = 0; i < window_bitsize - 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++ ) + for( i = j + 1; i < w_table_used_size; i++ ) { MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) ); @@ -1719,7 +1765,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, nblimbs = E->n; bufsize = 0; nbits = 0; - wbits = 0; + size_t exponent_bits_in_window = 0; state = 0; while( 1 ) @@ -1747,9 +1793,10 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, if( ei == 0 && state == 1 ) { /* - * out of window, square X + * out of window, square W[x_index] */ - mpi_montmul( X, X, N, mm, &T ); + MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, x_index ) ); + mpi_montmul( &W[x_index], &WW, N, mm, &T ); continue; } @@ -1759,25 +1806,30 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, state = 2; nbits++; - wbits |= ( ei << ( wsize - nbits ) ); + exponent_bits_in_window |= ( ei << ( window_bitsize - nbits ) ); - if( nbits == wsize ) + if( nbits == window_bitsize ) { /* - * X = X^wsize R^-1 mod N + * W[x_index] = W[x_index]^window_bitsize R^-1 mod N */ - for( i = 0; i < wsize; i++ ) - mpi_montmul( X, X, N, mm, &T ); + for( i = 0; i < window_bitsize; i++ ) + { + MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, + x_index ) ); + mpi_montmul( &W[x_index], &WW, N, mm, &T ); + } /* - * X = X * W[wbits] R^-1 mod N + * W[x_index] = W[x_index] * W[exponent_bits_in_window] R^-1 mod N */ - MBEDTLS_MPI_CHK( mpi_select( &WW, W, (size_t) 1 << wsize, wbits ) ); - mpi_montmul( X, &WW, N, mm, &T ); + MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, + exponent_bits_in_window ) ); + mpi_montmul( &W[x_index], &WW, N, mm, &T ); state--; nbits = 0; - wbits = 0; + exponent_bits_in_window = 0; } } @@ -1786,31 +1838,45 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, */ for( i = 0; i < nbits; i++ ) { - mpi_montmul( X, X, N, mm, &T ); + MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, x_index ) ); + mpi_montmul( &W[x_index], &WW, N, mm, &T ); - wbits <<= 1; + exponent_bits_in_window <<= 1; - if( ( wbits & ( one << wsize ) ) != 0 ) - mpi_montmul( X, &W[1], N, mm, &T ); + if( ( exponent_bits_in_window & ( (size_t) 1 << window_bitsize ) ) != 0 ) + { + MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, 1 ) ); + mpi_montmul( &W[x_index], &WW, N, mm, &T ); + } } /* - * X = A^E * R * R^-1 mod N = A^E mod N + * W[x_index] = A^E * R * R^-1 mod N = A^E mod N */ - mpi_montred( X, N, mm, &T ); + mpi_montred( &W[x_index], N, mm, &T ); if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 ) { - X->s = -1; - MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) ); + W[x_index].s = -1; + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &W[x_index], N, &W[x_index] ) ); } + /* + * Load the result in the output variable. + */ + mbedtls_mpi_copy( X, &W[x_index] ); + cleanup: - for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ ) + /* The first bit of the sliding window is always 1 and therefore the first + * half of the table was unused. */ + for( i = w_table_used_size/2; i < w_table_used_size; i++ ) mbedtls_mpi_free( &W[i] ); - mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos ); + mbedtls_mpi_free( &W[x_index] ); + mbedtls_mpi_free( &W[1] ); + mbedtls_mpi_free( &T ); + mbedtls_mpi_free( &Apos ); mbedtls_mpi_free( &WW ); if( prec_RR == NULL || prec_RR->p == NULL ) |