891 lines
26 KiB
C
891 lines
26 KiB
C
/*
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* Core bignum functions
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*
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* Copyright The Mbed TLS Contributors
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "common.h"
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#if defined(MBEDTLS_BIGNUM_C)
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#include <string.h>
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#include "mbedtls/error.h"
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#include "mbedtls/platform_util.h"
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#include "constant_time_internal.h"
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#include "mbedtls/platform.h"
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#include "bignum_core.h"
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#include "bn_mul.h"
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#include "constant_time_internal.h"
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size_t mbedtls_mpi_core_clz( mbedtls_mpi_uint a )
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{
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size_t j;
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mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
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for( j = 0; j < biL; j++ )
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{
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if( a & mask ) break;
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mask >>= 1;
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}
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return( j );
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}
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size_t mbedtls_mpi_core_bitlen( const mbedtls_mpi_uint *A, size_t A_limbs )
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{
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size_t i, j;
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if( A_limbs == 0 )
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return( 0 );
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for( i = A_limbs - 1; i > 0; i-- )
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if( A[i] != 0 )
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break;
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j = biL - mbedtls_mpi_core_clz( A[i] );
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return( ( i * biL ) + j );
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}
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/* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
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* into the storage form used by mbedtls_mpi. */
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static mbedtls_mpi_uint mpi_bigendian_to_host_c( mbedtls_mpi_uint a )
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{
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uint8_t i;
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unsigned char *a_ptr;
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mbedtls_mpi_uint tmp = 0;
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for( i = 0, a_ptr = (unsigned char *) &a; i < ciL; i++, a_ptr++ )
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{
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tmp <<= CHAR_BIT;
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tmp |= (mbedtls_mpi_uint) *a_ptr;
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}
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return( tmp );
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}
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static mbedtls_mpi_uint mpi_bigendian_to_host( mbedtls_mpi_uint a )
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{
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if ( MBEDTLS_IS_BIG_ENDIAN )
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{
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/* Nothing to do on bigendian systems. */
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return( a );
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}
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else
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{
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switch( sizeof(mbedtls_mpi_uint) )
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{
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case 4:
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return (mbedtls_mpi_uint) MBEDTLS_BSWAP32( (uint32_t)a );
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case 8:
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return (mbedtls_mpi_uint) MBEDTLS_BSWAP64( (uint64_t)a );
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}
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/* Fall back to C-based reordering if we don't know the byte order
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* or we couldn't use a compiler-specific builtin. */
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return( mpi_bigendian_to_host_c( a ) );
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}
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}
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void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint *A,
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size_t A_limbs )
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{
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mbedtls_mpi_uint *cur_limb_left;
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mbedtls_mpi_uint *cur_limb_right;
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if( A_limbs == 0 )
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return;
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/*
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* Traverse limbs and
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* - adapt byte-order in each limb
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* - swap the limbs themselves.
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* For that, simultaneously traverse the limbs from left to right
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* and from right to left, as long as the left index is not bigger
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* than the right index (it's not a problem if limbs is odd and the
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* indices coincide in the last iteration).
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*/
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for( cur_limb_left = A, cur_limb_right = A + ( A_limbs - 1 );
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cur_limb_left <= cur_limb_right;
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cur_limb_left++, cur_limb_right-- )
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{
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mbedtls_mpi_uint tmp;
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/* Note that if cur_limb_left == cur_limb_right,
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* this code effectively swaps the bytes only once. */
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tmp = mpi_bigendian_to_host( *cur_limb_left );
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*cur_limb_left = mpi_bigendian_to_host( *cur_limb_right );
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*cur_limb_right = tmp;
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}
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}
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/* Whether min <= A, in constant time.
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* A_limbs must be at least 1. */
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unsigned mbedtls_mpi_core_uint_le_mpi( mbedtls_mpi_uint min,
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const mbedtls_mpi_uint *A,
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size_t A_limbs )
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{
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/* min <= least significant limb? */
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unsigned min_le_lsl = 1 ^ mbedtls_ct_mpi_uint_lt( A[0], min );
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/* limbs other than the least significant one are all zero? */
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mbedtls_mpi_uint msll_mask = 0;
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for( size_t i = 1; i < A_limbs; i++ )
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msll_mask |= A[i];
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/* The most significant limbs of A are not all zero iff msll_mask != 0. */
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unsigned msll_nonzero = mbedtls_ct_mpi_uint_mask( msll_mask ) & 1;
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/* min <= A iff the lowest limb of A is >= min or the other limbs
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* are not all zero. */
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return( min_le_lsl | msll_nonzero );
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}
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void mbedtls_mpi_core_cond_assign( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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unsigned char assign )
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{
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if( X == A )
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return;
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mbedtls_ct_mpi_uint_cond_assign( limbs, X, A, assign );
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}
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void mbedtls_mpi_core_cond_swap( mbedtls_mpi_uint *X,
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mbedtls_mpi_uint *Y,
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size_t limbs,
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unsigned char swap )
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{
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if( X == Y )
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return;
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/* all-bits 1 if swap is 1, all-bits 0 if swap is 0 */
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mbedtls_mpi_uint limb_mask = mbedtls_ct_mpi_uint_mask( swap );
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for( size_t i = 0; i < limbs; i++ )
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{
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mbedtls_mpi_uint tmp = X[i];
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X[i] = ( X[i] & ~limb_mask ) | ( Y[i] & limb_mask );
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Y[i] = ( Y[i] & ~limb_mask ) | ( tmp & limb_mask );
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}
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}
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int mbedtls_mpi_core_read_le( mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length )
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{
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const size_t limbs = CHARS_TO_LIMBS( input_length );
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if( X_limbs < limbs )
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return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
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if( X != NULL )
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{
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memset( X, 0, X_limbs * ciL );
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for( size_t i = 0; i < input_length; i++ )
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{
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size_t offset = ( ( i % ciL ) << 3 );
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X[i / ciL] |= ( (mbedtls_mpi_uint) input[i] ) << offset;
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}
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}
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return( 0 );
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}
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int mbedtls_mpi_core_read_be( mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length )
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{
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const size_t limbs = CHARS_TO_LIMBS( input_length );
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if( X_limbs < limbs )
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return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
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/* If X_limbs is 0, input_length must also be 0 (from previous test).
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* Nothing to do. */
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if( X_limbs == 0 )
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return( 0 );
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memset( X, 0, X_limbs * ciL );
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/* memcpy() with (NULL, 0) is undefined behaviour */
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if( input_length != 0 )
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{
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size_t overhead = ( X_limbs * ciL ) - input_length;
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unsigned char *Xp = (unsigned char *) X;
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memcpy( Xp + overhead, input, input_length );
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}
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mbedtls_mpi_core_bigendian_to_host( X, X_limbs );
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return( 0 );
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}
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int mbedtls_mpi_core_write_le( const mbedtls_mpi_uint *A,
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size_t A_limbs,
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unsigned char *output,
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size_t output_length )
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{
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size_t stored_bytes = A_limbs * ciL;
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size_t bytes_to_copy;
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if( stored_bytes < output_length )
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{
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bytes_to_copy = stored_bytes;
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}
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else
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{
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bytes_to_copy = output_length;
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/* The output buffer is smaller than the allocated size of A.
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* However A may fit if its leading bytes are zero. */
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for( size_t i = bytes_to_copy; i < stored_bytes; i++ )
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{
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if( GET_BYTE( A, i ) != 0 )
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return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
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}
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}
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for( size_t i = 0; i < bytes_to_copy; i++ )
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output[i] = GET_BYTE( A, i );
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if( stored_bytes < output_length )
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{
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/* Write trailing 0 bytes */
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memset( output + stored_bytes, 0, output_length - stored_bytes );
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}
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return( 0 );
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}
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int mbedtls_mpi_core_write_be( const mbedtls_mpi_uint *X,
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size_t X_limbs,
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unsigned char *output,
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size_t output_length )
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{
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size_t stored_bytes;
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size_t bytes_to_copy;
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unsigned char *p;
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stored_bytes = X_limbs * ciL;
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if( stored_bytes < output_length )
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{
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/* There is enough space in the output buffer. Write initial
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* null bytes and record the position at which to start
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* writing the significant bytes. In this case, the execution
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* trace of this function does not depend on the value of the
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* number. */
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bytes_to_copy = stored_bytes;
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p = output + output_length - stored_bytes;
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memset( output, 0, output_length - stored_bytes );
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}
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else
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{
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/* The output buffer is smaller than the allocated size of X.
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* However X may fit if its leading bytes are zero. */
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bytes_to_copy = output_length;
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p = output;
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for( size_t i = bytes_to_copy; i < stored_bytes; i++ )
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{
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if( GET_BYTE( X, i ) != 0 )
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return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
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}
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}
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for( size_t i = 0; i < bytes_to_copy; i++ )
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p[bytes_to_copy - i - 1] = GET_BYTE( X, i );
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return( 0 );
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}
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void mbedtls_mpi_core_shift_r( mbedtls_mpi_uint *X, size_t limbs,
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size_t count )
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{
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size_t i, v0, v1;
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mbedtls_mpi_uint r0 = 0, r1;
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v0 = count / biL;
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v1 = count & (biL - 1);
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if( v0 > limbs || ( v0 == limbs && v1 > 0 ) )
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{
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memset( X, 0, limbs * ciL );
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return;
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}
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/*
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* shift by count / limb_size
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*/
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if( v0 > 0 )
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{
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for( i = 0; i < limbs - v0; i++ )
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X[i] = X[i + v0];
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for( ; i < limbs; i++ )
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X[i] = 0;
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}
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/*
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* shift by count % limb_size
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*/
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if( v1 > 0 )
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{
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for( i = limbs; i > 0; i-- )
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{
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r1 = X[i - 1] << (biL - v1);
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X[i - 1] >>= v1;
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X[i - 1] |= r0;
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r0 = r1;
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}
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}
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}
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mbedtls_mpi_uint mbedtls_mpi_core_add( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t limbs )
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{
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mbedtls_mpi_uint c = 0;
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for( size_t i = 0; i < limbs; i++ )
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{
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mbedtls_mpi_uint t = c + A[i];
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c = ( t < A[i] );
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t += B[i];
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c += ( t < B[i] );
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X[i] = t;
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}
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return( c );
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}
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mbedtls_mpi_uint mbedtls_mpi_core_add_if( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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unsigned cond )
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{
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mbedtls_mpi_uint c = 0;
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/* all-bits 0 if cond is 0, all-bits 1 if cond is non-0 */
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const mbedtls_mpi_uint mask = mbedtls_ct_mpi_uint_mask( cond );
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for( size_t i = 0; i < limbs; i++ )
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{
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mbedtls_mpi_uint add = mask & A[i];
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mbedtls_mpi_uint t = c + X[i];
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c = ( t < X[i] );
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t += add;
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c += ( t < add );
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X[i] = t;
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}
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return( c );
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}
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mbedtls_mpi_uint mbedtls_mpi_core_sub( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t limbs )
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{
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mbedtls_mpi_uint c = 0;
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for( size_t i = 0; i < limbs; i++ )
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{
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mbedtls_mpi_uint z = ( A[i] < c );
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mbedtls_mpi_uint t = A[i] - c;
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c = ( t < B[i] ) + z;
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X[i] = t - B[i];
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}
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return( c );
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}
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mbedtls_mpi_uint mbedtls_mpi_core_mla( mbedtls_mpi_uint *d, size_t d_len,
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const mbedtls_mpi_uint *s, size_t s_len,
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mbedtls_mpi_uint b )
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{
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mbedtls_mpi_uint c = 0; /* carry */
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/*
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* It is a documented precondition of this function that d_len >= s_len.
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* If that's not the case, we swap these round: this turns what would be
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* a buffer overflow into an incorrect result.
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*/
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if( d_len < s_len )
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s_len = d_len;
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size_t excess_len = d_len - s_len;
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size_t steps_x8 = s_len / 8;
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size_t steps_x1 = s_len & 7;
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while( steps_x8-- )
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{
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MULADDC_X8_INIT
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MULADDC_X8_CORE
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MULADDC_X8_STOP
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}
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while( steps_x1-- )
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{
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MULADDC_X1_INIT
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MULADDC_X1_CORE
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MULADDC_X1_STOP
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}
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while( excess_len-- )
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{
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*d += c;
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c = ( *d < c );
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d++;
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}
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return( c );
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}
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/*
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* Fast Montgomery initialization (thanks to Tom St Denis).
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_montmul_init( const mbedtls_mpi_uint *N )
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{
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mbedtls_mpi_uint x = N[0];
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x += ( ( N[0] + 2 ) & 4 ) << 1;
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for( unsigned int i = biL; i >= 8; i /= 2 )
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x *= ( 2 - ( N[0] * x ) );
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return( ~x + 1 );
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}
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void mbedtls_mpi_core_montmul( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t B_limbs,
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const mbedtls_mpi_uint *N,
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size_t AN_limbs,
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mbedtls_mpi_uint mm,
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mbedtls_mpi_uint *T )
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{
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memset( T, 0, ( 2 * AN_limbs + 1 ) * ciL );
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for( size_t i = 0; i < AN_limbs; i++ )
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{
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/* T = (T + u0*B + u1*N) / 2^biL */
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mbedtls_mpi_uint u0 = A[i];
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mbedtls_mpi_uint u1 = ( T[0] + u0 * B[0] ) * mm;
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(void) mbedtls_mpi_core_mla( T, AN_limbs + 2, B, B_limbs, u0 );
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(void) mbedtls_mpi_core_mla( T, AN_limbs + 2, N, AN_limbs, u1 );
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T++;
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}
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/*
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* The result we want is (T >= N) ? T - N : T.
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*
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* For better constant-time properties in this function, we always do the
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* subtraction, with the result in X.
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*
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* We also look to see if there was any carry in the final additions in the
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* loop above.
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*/
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mbedtls_mpi_uint carry = T[AN_limbs];
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mbedtls_mpi_uint borrow = mbedtls_mpi_core_sub( X, T, N, AN_limbs );
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/*
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* Using R as the Montgomery radix (auxiliary modulus) i.e. 2^(biL*AN_limbs):
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*
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* T can be in one of 3 ranges:
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*
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* 1) T < N : (carry, borrow) = (0, 1): we want T
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* 2) N <= T < R : (carry, borrow) = (0, 0): we want X
|
|
* 3) T >= R : (carry, borrow) = (1, 1): we want X
|
|
*
|
|
* and (carry, borrow) = (1, 0) can't happen.
|
|
*
|
|
* So the correct return value is already in X if (carry ^ borrow) = 0,
|
|
* but is in (the lower AN_limbs limbs of) T if (carry ^ borrow) = 1.
|
|
*/
|
|
mbedtls_ct_mpi_uint_cond_assign( AN_limbs, X, T, (unsigned char) ( carry ^ borrow ) );
|
|
}
|
|
|
|
int mbedtls_mpi_core_get_mont_r2_unsafe( mbedtls_mpi *X,
|
|
const mbedtls_mpi *N )
|
|
{
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 1 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, N->n * 2 * biL ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( X, X, N ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( X, N->n ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
MBEDTLS_STATIC_TESTABLE
|
|
void mbedtls_mpi_core_ct_uint_table_lookup( mbedtls_mpi_uint *dest,
|
|
const mbedtls_mpi_uint *table,
|
|
size_t limbs,
|
|
size_t count,
|
|
size_t index )
|
|
{
|
|
for( size_t i = 0; i < count; i++, table += limbs )
|
|
{
|
|
unsigned char assign = mbedtls_ct_size_bool_eq( i, index );
|
|
mbedtls_mpi_core_cond_assign( dest, table, limbs, assign );
|
|
}
|
|
}
|
|
|
|
/* Fill X with n_bytes random bytes.
|
|
* X must already have room for those bytes.
|
|
* The ordering of the bytes returned from the RNG is suitable for
|
|
* deterministic ECDSA (see RFC 6979 §3.3 and the specification of
|
|
* mbedtls_mpi_core_random()).
|
|
*/
|
|
int mbedtls_mpi_core_fill_random(
|
|
mbedtls_mpi_uint *X, size_t X_limbs,
|
|
size_t n_bytes,
|
|
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
|
{
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
const size_t limbs = CHARS_TO_LIMBS( n_bytes );
|
|
const size_t overhead = ( limbs * ciL ) - n_bytes;
|
|
|
|
if( X_limbs < limbs )
|
|
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
|
|
|
memset( X, 0, overhead );
|
|
memset( (unsigned char *) X + limbs * ciL, 0, ( X_limbs - limbs ) * ciL );
|
|
MBEDTLS_MPI_CHK( f_rng( p_rng, (unsigned char *) X + overhead, n_bytes ) );
|
|
mbedtls_mpi_core_bigendian_to_host( X, limbs );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
int mbedtls_mpi_core_random( mbedtls_mpi_uint *X,
|
|
mbedtls_mpi_uint min,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t limbs,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng )
|
|
{
|
|
unsigned ge_lower = 1, lt_upper = 0;
|
|
size_t n_bits = mbedtls_mpi_core_bitlen( N, limbs );
|
|
size_t n_bytes = ( n_bits + 7 ) / 8;
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
|
|
/*
|
|
* When min == 0, each try has at worst a probability 1/2 of failing
|
|
* (the msb has a probability 1/2 of being 0, and then the result will
|
|
* be < N), so after 30 tries failure probability is a most 2**(-30).
|
|
*
|
|
* When N is just below a power of 2, as is the case when generating
|
|
* a random scalar on most elliptic curves, 1 try is enough with
|
|
* overwhelming probability. When N is just above a power of 2,
|
|
* as when generating a random scalar on secp224k1, each try has
|
|
* a probability of failing that is almost 1/2.
|
|
*
|
|
* The probabilities are almost the same if min is nonzero but negligible
|
|
* compared to N. This is always the case when N is crypto-sized, but
|
|
* it's convenient to support small N for testing purposes. When N
|
|
* is small, use a higher repeat count, otherwise the probability of
|
|
* failure is macroscopic.
|
|
*/
|
|
int count = ( n_bytes > 4 ? 30 : 250 );
|
|
|
|
/*
|
|
* Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
|
|
* when f_rng is a suitably parametrized instance of HMAC_DRBG:
|
|
* - use the same byte ordering;
|
|
* - keep the leftmost n_bits bits of the generated octet string;
|
|
* - try until result is in the desired range.
|
|
* This also avoids any bias, which is especially important for ECDSA.
|
|
*/
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_core_fill_random( X, limbs,
|
|
n_bytes,
|
|
f_rng, p_rng ) );
|
|
mbedtls_mpi_core_shift_r( X, limbs, 8 * n_bytes - n_bits );
|
|
|
|
if( --count == 0 )
|
|
{
|
|
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
|
goto cleanup;
|
|
}
|
|
|
|
ge_lower = mbedtls_mpi_core_uint_le_mpi( min, X, limbs );
|
|
lt_upper = mbedtls_mpi_core_lt_ct( X, N, limbs );
|
|
}
|
|
while( ge_lower == 0 || lt_upper == 0 );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/* BEGIN MERGE SLOT 1 */
|
|
|
|
static size_t exp_mod_get_window_size( size_t Ebits )
|
|
{
|
|
size_t wsize = ( Ebits > 671 ) ? 6 : ( Ebits > 239 ) ? 5 :
|
|
( Ebits > 79 ) ? 4 : 1;
|
|
|
|
#if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
|
|
if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
|
|
wsize = MBEDTLS_MPI_WINDOW_SIZE;
|
|
#endif
|
|
|
|
return( wsize );
|
|
}
|
|
|
|
size_t mbedtls_mpi_core_exp_mod_working_limbs( size_t AN_limbs, size_t E_limbs )
|
|
{
|
|
const size_t wsize = exp_mod_get_window_size( E_limbs * biL );
|
|
const size_t welem = ( (size_t) 1 ) << wsize;
|
|
|
|
/* How big does each part of the working memory pool need to be? */
|
|
const size_t table_limbs = welem * AN_limbs;
|
|
const size_t select_limbs = AN_limbs;
|
|
const size_t temp_limbs = 2 * AN_limbs + 1;
|
|
|
|
return( table_limbs + select_limbs + temp_limbs );
|
|
}
|
|
|
|
static void exp_mod_precompute_window( const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
const mbedtls_mpi_uint *RR,
|
|
size_t welem,
|
|
mbedtls_mpi_uint *Wtable,
|
|
mbedtls_mpi_uint *temp )
|
|
{
|
|
/* W[0] = 1 (in Montgomery presentation) */
|
|
memset( Wtable, 0, AN_limbs * ciL );
|
|
Wtable[0] = 1;
|
|
mbedtls_mpi_core_montmul( Wtable, Wtable, RR, AN_limbs, N, AN_limbs, mm, temp );
|
|
|
|
/* W[1] = A (already in Montgomery presentation) */
|
|
mbedtls_mpi_uint *W1 = Wtable + AN_limbs;
|
|
memcpy( W1, A, AN_limbs * ciL );
|
|
|
|
/* W[i+1] = W[i] * W[1], i >= 2 */
|
|
mbedtls_mpi_uint *Wprev = W1;
|
|
for( size_t i = 2; i < welem; i++ )
|
|
{
|
|
mbedtls_mpi_uint *Wcur = Wprev + AN_limbs;
|
|
mbedtls_mpi_core_montmul( Wcur, Wprev, W1, AN_limbs, N, AN_limbs, mm, temp );
|
|
Wprev = Wcur;
|
|
}
|
|
}
|
|
|
|
/* Exponentiation: X := A^E mod N.
|
|
*
|
|
* A must already be in Montgomery form.
|
|
*
|
|
* As in other bignum functions, assume that AN_limbs and E_limbs are nonzero.
|
|
*
|
|
* RR must contain 2^{2*biL} mod N.
|
|
*
|
|
* The algorithm is a variant of Left-to-right k-ary exponentiation: HAC 14.82
|
|
* (The difference is that the body in our loop processes a single bit instead
|
|
* of a full window.)
|
|
*/
|
|
void mbedtls_mpi_core_exp_mod( mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
const mbedtls_mpi_uint *E,
|
|
size_t E_limbs,
|
|
const mbedtls_mpi_uint *RR,
|
|
mbedtls_mpi_uint *T )
|
|
{
|
|
const size_t wsize = exp_mod_get_window_size( E_limbs * biL );
|
|
const size_t welem = ( (size_t) 1 ) << wsize;
|
|
|
|
/* This is how we will use the temporary storage T, which must have space
|
|
* for table_limbs, select_limbs and (2 * AN_limbs + 1) for montmul. */
|
|
const size_t table_limbs = welem * AN_limbs;
|
|
const size_t select_limbs = AN_limbs;
|
|
|
|
/* Pointers to specific parts of the temporary working memory pool */
|
|
mbedtls_mpi_uint *const Wtable = T;
|
|
mbedtls_mpi_uint *const Wselect = Wtable + table_limbs;
|
|
mbedtls_mpi_uint *const temp = Wselect + select_limbs;
|
|
|
|
/*
|
|
* Window precomputation
|
|
*/
|
|
|
|
const mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init( N );
|
|
|
|
/* Set Wtable[i] = A^(2^i) (in Montgomery representation) */
|
|
exp_mod_precompute_window( A, N, AN_limbs,
|
|
mm, RR,
|
|
welem, Wtable, temp );
|
|
|
|
/*
|
|
* Fixed window exponentiation
|
|
*/
|
|
|
|
/* X = 1 (in Montgomery presentation) initially */
|
|
memcpy( X, Wtable, AN_limbs * ciL );
|
|
|
|
/* We'll process the bits of E from most significant
|
|
* (limb_index=E_limbs-1, E_bit_index=biL-1) to least significant
|
|
* (limb_index=0, E_bit_index=0). */
|
|
size_t E_limb_index = E_limbs;
|
|
size_t E_bit_index = 0;
|
|
/* At any given time, window contains window_bits bits from E.
|
|
* window_bits can go up to wsize. */
|
|
size_t window_bits = 0;
|
|
mbedtls_mpi_uint window = 0;
|
|
|
|
do
|
|
{
|
|
/* Square */
|
|
mbedtls_mpi_core_montmul( X, X, X, AN_limbs, N, AN_limbs, mm, temp );
|
|
|
|
/* Move to the next bit of the exponent */
|
|
if( E_bit_index == 0 )
|
|
{
|
|
--E_limb_index;
|
|
E_bit_index = biL - 1;
|
|
}
|
|
else
|
|
{
|
|
--E_bit_index;
|
|
}
|
|
/* Insert next exponent bit into window */
|
|
++window_bits;
|
|
window <<= 1;
|
|
window |= ( E[E_limb_index] >> E_bit_index ) & 1;
|
|
|
|
/* Clear window if it's full. Also clear the window at the end,
|
|
* when we've finished processing the exponent. */
|
|
if( window_bits == wsize ||
|
|
( E_bit_index == 0 && E_limb_index == 0 ) )
|
|
{
|
|
/* Select Wtable[window] without leaking window through
|
|
* memory access patterns. */
|
|
mbedtls_mpi_core_ct_uint_table_lookup( Wselect, Wtable,
|
|
AN_limbs, welem, window );
|
|
/* Multiply X by the selected element. */
|
|
mbedtls_mpi_core_montmul( X, X, Wselect, AN_limbs, N, AN_limbs, mm,
|
|
temp );
|
|
window = 0;
|
|
window_bits = 0;
|
|
}
|
|
}
|
|
while( ! ( E_bit_index == 0 && E_limb_index == 0 ) );
|
|
}
|
|
|
|
/* END MERGE SLOT 1 */
|
|
|
|
/* BEGIN MERGE SLOT 2 */
|
|
|
|
/* END MERGE SLOT 2 */
|
|
|
|
/* BEGIN MERGE SLOT 3 */
|
|
|
|
mbedtls_mpi_uint mbedtls_mpi_core_sub_int( mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
mbedtls_mpi_uint c, /* doubles as carry */
|
|
size_t limbs )
|
|
{
|
|
for( size_t i = 0; i < limbs; i++ )
|
|
{
|
|
mbedtls_mpi_uint s = A[i];
|
|
mbedtls_mpi_uint t = s - c;
|
|
c = ( t > s );
|
|
X[i] = t;
|
|
}
|
|
|
|
return( c );
|
|
}
|
|
|
|
mbedtls_mpi_uint mbedtls_mpi_core_check_zero_ct( const mbedtls_mpi_uint *A,
|
|
size_t limbs )
|
|
{
|
|
mbedtls_mpi_uint bits = 0;
|
|
|
|
for( size_t i = 0; i < limbs; i++ )
|
|
bits |= A[i];
|
|
|
|
return( bits );
|
|
}
|
|
|
|
void mbedtls_mpi_core_to_mont_rep( mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
const mbedtls_mpi_uint *rr,
|
|
mbedtls_mpi_uint *T )
|
|
{
|
|
mbedtls_mpi_core_montmul( X, A, rr, AN_limbs, N, AN_limbs, mm, T );
|
|
}
|
|
|
|
void mbedtls_mpi_core_from_mont_rep( mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
mbedtls_mpi_uint *T )
|
|
{
|
|
const mbedtls_mpi_uint Rinv = 1; /* 1/R in Mont. rep => 1 */
|
|
|
|
mbedtls_mpi_core_montmul( X, A, &Rinv, 1, N, AN_limbs, mm, T );
|
|
}
|
|
|
|
/* END MERGE SLOT 3 */
|
|
|
|
/* BEGIN MERGE SLOT 4 */
|
|
|
|
/* END MERGE SLOT 4 */
|
|
|
|
/* BEGIN MERGE SLOT 5 */
|
|
|
|
/* END MERGE SLOT 5 */
|
|
|
|
/* BEGIN MERGE SLOT 6 */
|
|
|
|
/* END MERGE SLOT 6 */
|
|
|
|
/* BEGIN MERGE SLOT 7 */
|
|
|
|
/* END MERGE SLOT 7 */
|
|
|
|
/* BEGIN MERGE SLOT 8 */
|
|
|
|
/* END MERGE SLOT 8 */
|
|
|
|
/* BEGIN MERGE SLOT 9 */
|
|
|
|
/* END MERGE SLOT 9 */
|
|
|
|
/* BEGIN MERGE SLOT 10 */
|
|
|
|
/* END MERGE SLOT 10 */
|
|
|
|
#endif /* MBEDTLS_BIGNUM_C */
|