445 lines
12 KiB
C
445 lines
12 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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#if defined(MBEDTLS_PLATFORM_C)
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#include "mbedtls/platform.h"
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#else
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#include <stdio.h>
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#include <stdlib.h>
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#define mbedtls_printf printf
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#define mbedtls_calloc calloc
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#define mbedtls_free free
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#endif
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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 defined(__BYTE_ORDER__)
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/* Nothing to do on bigendian systems. */
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#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
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return( a );
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#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
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#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
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/* For GCC and Clang, have builtins for byte swapping. */
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#if defined(__GNUC__) && defined(__GNUC_PREREQ)
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#if __GNUC_PREREQ(4,3)
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#define have_bswap
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#endif
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#endif
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#if defined(__clang__) && defined(__has_builtin)
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#if __has_builtin(__builtin_bswap32) && \
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__has_builtin(__builtin_bswap64)
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#define have_bswap
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#endif
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#endif
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#if defined(have_bswap)
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/* The compiler is hopefully able to statically evaluate this! */
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switch( sizeof(mbedtls_mpi_uint) )
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{
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case 4:
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return( __builtin_bswap32(a) );
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case 8:
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return( __builtin_bswap64(a) );
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}
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#endif
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#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
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#endif /* __BYTE_ORDER__ */
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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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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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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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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
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* 3) T >= R : (carry, borrow) = (1, 1): we want X
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*
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* and (carry, borrow) = (1, 0) can't happen.
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*
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* So the correct return value is already in X if (carry ^ borrow) = 0,
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* but is in (the lower AN_limbs limbs of) T if (carry ^ borrow) = 1.
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*/
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mbedtls_ct_mpi_uint_cond_assign( AN_limbs, X, T, (unsigned char) ( carry ^ borrow ) );
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}
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#endif /* MBEDTLS_BIGNUM_C */
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