1009 lines
41 KiB
C
Executable file
1009 lines
41 KiB
C
Executable file
/**
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* \file bignum.h
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*
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* \brief Multi-precision integer library
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*/
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/*
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* Copyright The Mbed TLS Contributors
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* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
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*
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* This file is provided under the Apache License 2.0, or the
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* GNU General Public License v2.0 or later.
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*
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* **********
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* Apache License 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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* **********
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*
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* **********
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* GNU General Public License v2.0 or later:
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* **********
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*/
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#ifndef MBEDTLS_BIGNUM_H
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#define MBEDTLS_BIGNUM_H
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#if !defined(MBEDTLS_CONFIG_FILE)
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#include "config.h"
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#else
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#include MBEDTLS_CONFIG_FILE
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#endif
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#include <stddef.h>
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#include <stdint.h>
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#if defined(MBEDTLS_FS_IO)
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#include <stdio.h>
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#endif
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#define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
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#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
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#define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
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#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
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#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
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#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
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#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
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#define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */
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#define MBEDTLS_MPI_CHK(f) \
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do \
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{ \
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if( ( ret = (f) ) != 0 ) \
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goto cleanup; \
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} while( 0 )
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/*
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* Maximum size MPIs are allowed to grow to in number of limbs.
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*/
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#define MBEDTLS_MPI_MAX_LIMBS 10000
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#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
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/*
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* Maximum window size used for modular exponentiation. Default: 6
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* Minimum value: 1. Maximum value: 6.
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*
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* Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
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* for the sliding window calculation. (So 64 by default)
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*
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* Reduction in size, reduces speed.
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*/
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#define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum window size used. */
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#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
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#if !defined(MBEDTLS_MPI_MAX_SIZE)
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/*
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* Maximum size of MPIs allowed in bits and bytes for user-MPIs.
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* ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
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*
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* Note: Calculations can temporarily result in larger MPIs. So the number
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* of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
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*/
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#define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
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#endif /* !MBEDTLS_MPI_MAX_SIZE */
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#define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
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/*
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* When reading from files with mbedtls_mpi_read_file() and writing to files with
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* mbedtls_mpi_write_file() the buffer should have space
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* for a (short) label, the MPI (in the provided radix), the newline
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* characters and the '\0'.
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*
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* By default we assume at least a 10 char label, a minimum radix of 10
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* (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
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* Autosized at compile time for at least a 10 char label, a minimum radix
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* of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
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*
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* This used to be statically sized to 1250 for a maximum of 4096 bit
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* numbers (1234 decimal chars).
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*
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* Calculate using the formula:
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* MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
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* LabelSize + 6
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*/
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#define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS )
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#define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332
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#define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
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/*
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* Define the base integer type, architecture-wise.
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*
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* 32 or 64-bit integer types can be forced regardless of the underlying
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* architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
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* respectively and undefining MBEDTLS_HAVE_ASM.
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*
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* Double-width integers (e.g. 128-bit in 64-bit architectures) can be
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* disabled by defining MBEDTLS_NO_UDBL_DIVISION.
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*/
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#if !defined(MBEDTLS_HAVE_INT32)
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#if defined(_MSC_VER) && defined(_M_AMD64)
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/* Always choose 64-bit when using MSC */
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#if !defined(MBEDTLS_HAVE_INT64)
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#define MBEDTLS_HAVE_INT64
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#endif /* !MBEDTLS_HAVE_INT64 */
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typedef int64_t mbedtls_mpi_sint;
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typedef uint64_t mbedtls_mpi_uint;
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#elif defined(__GNUC__) && ( \
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defined(__amd64__) || defined(__x86_64__) || \
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defined(__ppc64__) || defined(__powerpc64__) || \
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defined(__ia64__) || defined(__alpha__) || \
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( defined(__sparc__) && defined(__arch64__) ) || \
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defined(__s390x__) || defined(__mips64) )
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#if !defined(MBEDTLS_HAVE_INT64)
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#define MBEDTLS_HAVE_INT64
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#endif /* MBEDTLS_HAVE_INT64 */
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typedef int64_t mbedtls_mpi_sint;
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typedef uint64_t mbedtls_mpi_uint;
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#if !defined(MBEDTLS_NO_UDBL_DIVISION)
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/* mbedtls_t_udbl defined as 128-bit unsigned int */
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typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
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#define MBEDTLS_HAVE_UDBL
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#endif /* !MBEDTLS_NO_UDBL_DIVISION */
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#elif defined(__ARMCC_VERSION) && defined(__aarch64__)
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/*
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* __ARMCC_VERSION is defined for both armcc and armclang and
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* __aarch64__ is only defined by armclang when compiling 64-bit code
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*/
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#if !defined(MBEDTLS_HAVE_INT64)
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#define MBEDTLS_HAVE_INT64
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#endif /* !MBEDTLS_HAVE_INT64 */
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typedef int64_t mbedtls_mpi_sint;
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typedef uint64_t mbedtls_mpi_uint;
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#if !defined(MBEDTLS_NO_UDBL_DIVISION)
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/* mbedtls_t_udbl defined as 128-bit unsigned int */
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typedef __uint128_t mbedtls_t_udbl;
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#define MBEDTLS_HAVE_UDBL
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#endif /* !MBEDTLS_NO_UDBL_DIVISION */
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#elif defined(MBEDTLS_HAVE_INT64)
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/* Force 64-bit integers with unknown compiler */
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typedef int64_t mbedtls_mpi_sint;
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typedef uint64_t mbedtls_mpi_uint;
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#endif
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#endif /* !MBEDTLS_HAVE_INT32 */
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#if !defined(MBEDTLS_HAVE_INT64)
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/* Default to 32-bit compilation */
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#if !defined(MBEDTLS_HAVE_INT32)
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#define MBEDTLS_HAVE_INT32
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#endif /* !MBEDTLS_HAVE_INT32 */
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typedef int32_t mbedtls_mpi_sint;
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typedef uint32_t mbedtls_mpi_uint;
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#if !defined(MBEDTLS_NO_UDBL_DIVISION)
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typedef uint64_t mbedtls_t_udbl;
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#define MBEDTLS_HAVE_UDBL
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#endif /* !MBEDTLS_NO_UDBL_DIVISION */
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#endif /* !MBEDTLS_HAVE_INT64 */
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#ifdef __cplusplus
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extern "C" {
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#endif
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/**
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* \brief MPI structure
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*/
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typedef struct mbedtls_mpi
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{
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int s; /*!< Sign: -1 if the mpi is negative, 1 otherwise */
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size_t n; /*!< total # of limbs */
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mbedtls_mpi_uint *p; /*!< pointer to limbs */
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}
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mbedtls_mpi;
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/**
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* \brief Initialize an MPI context.
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*
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* This makes the MPI ready to be set or freed,
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* but does not define a value for the MPI.
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*
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* \param X The MPI context to initialize. This must not be \c NULL.
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*/
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void mbedtls_mpi_init( mbedtls_mpi *X );
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/**
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* \brief This function frees the components of an MPI context.
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*
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* \param X The MPI context to be cleared. This may be \c NULL,
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* in which case this function is a no-op. If it is
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* not \c NULL, it must point to an initialized MPI.
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*/
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void mbedtls_mpi_free( mbedtls_mpi *X );
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/**
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* \brief Enlarge an MPI to the specified number of limbs.
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*
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* \note This function does nothing if the MPI is
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* already large enough.
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*
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* \param X The MPI to grow. It must be initialized.
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* \param nblimbs The target number of limbs.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
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/**
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* \brief This function resizes an MPI downwards, keeping at least the
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* specified number of limbs.
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*
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* If \c X is smaller than \c nblimbs, it is resized up
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* instead.
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*
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* \param X The MPI to shrink. This must point to an initialized MPI.
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* \param nblimbs The minimum number of limbs to keep.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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* (this can only happen when resizing up).
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
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/**
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* \brief Make a copy of an MPI.
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*
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* \param X The destination MPI. This must point to an initialized MPI.
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* \param Y The source MPI. This must point to an initialized MPI.
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*
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* \note The limb-buffer in the destination MPI is enlarged
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* if necessary to hold the value in the source MPI.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
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/**
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* \brief Swap the contents of two MPIs.
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*
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* \param X The first MPI. It must be initialized.
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* \param Y The second MPI. It must be initialized.
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*/
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void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
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/**
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* \brief Perform a safe conditional copy of MPI which doesn't
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* reveal whether the condition was true or not.
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*
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* \param X The MPI to conditionally assign to. This must point
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* to an initialized MPI.
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* \param Y The MPI to be assigned from. This must point to an
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* initialized MPI.
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* \param assign The condition deciding whether to perform the
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* assignment or not. Possible values:
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* * \c 1: Perform the assignment `X = Y`.
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* * \c 0: Keep the original value of \p X.
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*
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* \note This function is equivalent to
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* `if( assign ) mbedtls_mpi_copy( X, Y );`
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* except that it avoids leaking any information about whether
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* the assignment was done or not (the above code may leak
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* information through branch prediction and/or memory access
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* patterns analysis).
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
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/**
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* \brief Perform a safe conditional swap which doesn't
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* reveal whether the condition was true or not.
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*
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* \param X The first MPI. This must be initialized.
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* \param Y The second MPI. This must be initialized.
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* \param assign The condition deciding whether to perform
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* the swap or not. Possible values:
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* * \c 1: Swap the values of \p X and \p Y.
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* * \c 0: Keep the original values of \p X and \p Y.
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*
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* \note This function is equivalent to
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* if( assign ) mbedtls_mpi_swap( X, Y );
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* except that it avoids leaking any information about whether
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* the assignment was done or not (the above code may leak
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* information through branch prediction and/or memory access
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* patterns analysis).
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*
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*/
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int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
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/**
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* \brief Store integer value in MPI.
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*
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* \param X The MPI to set. This must be initialized.
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* \param z The value to use.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
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/**
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* \brief Get a specific bit from an MPI.
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*
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* \param X The MPI to query. This must be initialized.
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* \param pos Zero-based index of the bit to query.
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*
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* \return \c 0 or \c 1 on success, depending on whether bit \c pos
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* of \c X is unset or set.
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* \return A negative error code on failure.
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*/
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int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
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/**
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* \brief Modify a specific bit in an MPI.
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*
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* \note This function will grow the target MPI if necessary to set a
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* bit to \c 1 in a not yet existing limb. It will not grow if
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* the bit should be set to \c 0.
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*
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* \param X The MPI to modify. This must be initialized.
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* \param pos Zero-based index of the bit to modify.
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* \param val The desired value of bit \c pos: \c 0 or \c 1.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
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* \return Another negative error code on other kinds of failure.
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*/
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int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
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/**
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* \brief Return the number of bits of value \c 0 before the
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* least significant bit of value \c 1.
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*
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* \note This is the same as the zero-based index of
|
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* the least significant bit of value \c 1.
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*
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* \param X The MPI to query.
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*
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* \return The number of bits of value \c 0 before the least significant
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* bit of value \c 1 in \p X.
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*/
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size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
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/**
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|
* \brief Return the number of bits up to and including the most
|
|
* significant bit of value \c 1.
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|
*
|
|
* * \note This is same as the one-based index of the most
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* significant bit of value \c 1.
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|
*
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|
* \param X The MPI to query. This must point to an initialized MPI.
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*
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* \return The number of bits up to and including the most
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* significant bit of value \c 1.
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*/
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|
size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
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|
|
/**
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|
* \brief Return the total size of an MPI value in bytes.
|
|
*
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|
* \param X The MPI to use. This must point to an initialized MPI.
|
|
*
|
|
* \note The value returned by this function may be less than
|
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* the number of bytes used to store \p X internally.
|
|
* This happens if and only if there are trailing bytes
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* of value zero.
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*
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* \return The least number of bytes capable of storing
|
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* the absolute value of \p X.
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*/
|
|
size_t mbedtls_mpi_size( const mbedtls_mpi *X );
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|
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/**
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|
* \brief Import an MPI from an ASCII string.
|
|
*
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* \param X The destination MPI. This must point to an initialized MPI.
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|
* \param radix The numeric base of the input string.
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|
* \param s Null-terminated string buffer.
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|
*
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* \return \c 0 if successful.
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* \return A negative error code on failure.
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|
*/
|
|
int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
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|
|
/**
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|
* \brief Export an MPI to an ASCII string.
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|
*
|
|
* \param X The source MPI. This must point to an initialized MPI.
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|
* \param radix The numeric base of the output string.
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|
* \param buf The buffer to write the string to. This must be writable
|
|
* buffer of length \p buflen Bytes.
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|
* \param buflen The available size in Bytes of \p buf.
|
|
* \param olen The address at which to store the length of the string
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|
* written, including the final \c NULL byte. This must
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* not be \c NULL.
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|
*
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|
* \note You can call this function with `buflen == 0` to obtain the
|
|
* minimum required buffer size in `*olen`.
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|
*
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|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
|
|
* is too small to hold the value of \p X in the desired base.
|
|
* In this case, `*olen` is nonetheless updated to contain the
|
|
* size of \p buf required for a successful call.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
|
|
char *buf, size_t buflen, size_t *olen );
|
|
|
|
#if defined(MBEDTLS_FS_IO)
|
|
/**
|
|
* \brief Read an MPI from a line in an opened file.
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param radix The numeric base of the string representation used
|
|
* in the source line.
|
|
* \param fin The input file handle to use. This must not be \c NULL.
|
|
*
|
|
* \note On success, this function advances the file stream
|
|
* to the end of the current line or to EOF.
|
|
*
|
|
* The function returns \c 0 on an empty line.
|
|
*
|
|
* Leading whitespaces are ignored, as is a
|
|
* '0x' prefix for radix \c 16.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
|
|
* is too small.
|
|
* \return Another negative error code on failure.
|
|
*/
|
|
int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
|
|
|
|
/**
|
|
* \brief Export an MPI into an opened file.
|
|
*
|
|
* \param p A string prefix to emit prior to the MPI data.
|
|
* For example, this might be a label, or "0x" when
|
|
* printing in base \c 16. This may be \c NULL if no prefix
|
|
* is needed.
|
|
* \param X The source MPI. This must point to an initialized MPI.
|
|
* \param radix The numeric base to be used in the emitted string.
|
|
* \param fout The output file handle. This may be \c NULL, in which case
|
|
* the output is written to \c stdout.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return A negative error code on failure.
|
|
*/
|
|
int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
|
|
int radix, FILE *fout );
|
|
#endif /* MBEDTLS_FS_IO */
|
|
|
|
/**
|
|
* \brief Import an MPI from unsigned big endian binary data.
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param buf The input buffer. This must be a readable buffer of length
|
|
* \p buflen Bytes.
|
|
* \param buflen The length of the input buffer \p p in Bytes.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
|
|
size_t buflen );
|
|
|
|
/**
|
|
* \brief Export an MPI into unsigned big endian binary data
|
|
* of fixed size.
|
|
*
|
|
* \param X The source MPI. This must point to an initialized MPI.
|
|
* \param buf The output buffer. This must be a writable buffer of length
|
|
* \p buflen Bytes.
|
|
* \param buflen The size of the output buffer \p buf in Bytes.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
|
|
* large enough to hold the value of \p X.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
|
|
size_t buflen );
|
|
|
|
/**
|
|
* \brief Perform a left-shift on an MPI: X <<= count
|
|
*
|
|
* \param X The MPI to shift. This must point to an initialized MPI.
|
|
* \param count The number of bits to shift by.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
|
|
|
|
/**
|
|
* \brief Perform a right-shift on an MPI: X >>= count
|
|
*
|
|
* \param X The MPI to shift. This must point to an initialized MPI.
|
|
* \param count The number of bits to shift by.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
|
|
|
|
/**
|
|
* \brief Compare the absolute values of two MPIs.
|
|
*
|
|
* \param X The left-hand MPI. This must point to an initialized MPI.
|
|
* \param Y The right-hand MPI. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 1 if `|X|` is greater than `|Y|`.
|
|
* \return \c -1 if `|X|` is lesser than `|Y|`.
|
|
* \return \c 0 if `|X|` is equal to `|Y|`.
|
|
*/
|
|
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
|
|
|
|
/**
|
|
* \brief Compare two MPIs.
|
|
*
|
|
* \param X The left-hand MPI. This must point to an initialized MPI.
|
|
* \param Y The right-hand MPI. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 1 if \p X is greater than \p Y.
|
|
* \return \c -1 if \p X is lesser than \p Y.
|
|
* \return \c 0 if \p X is equal to \p Y.
|
|
*/
|
|
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
|
|
|
|
/**
|
|
* \brief Check if an MPI is less than the other in constant time.
|
|
*
|
|
* \param X The left-hand MPI. This must point to an initialized MPI
|
|
* with the same allocated length as Y.
|
|
* \param Y The right-hand MPI. This must point to an initialized MPI
|
|
* with the same allocated length as X.
|
|
* \param ret The result of the comparison:
|
|
* \c 1 if \p X is less than \p Y.
|
|
* \c 0 if \p X is greater than or equal to \p Y.
|
|
*
|
|
* \return 0 on success.
|
|
* \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
|
|
* the two input MPIs is not the same.
|
|
*/
|
|
int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
|
|
unsigned *ret );
|
|
|
|
/**
|
|
* \brief Compare an MPI with an integer.
|
|
*
|
|
* \param X The left-hand MPI. This must point to an initialized MPI.
|
|
* \param z The integer value to compare \p X to.
|
|
*
|
|
* \return \c 1 if \p X is greater than \p z.
|
|
* \return \c -1 if \p X is lesser than \p z.
|
|
* \return \c 0 if \p X is equal to \p z.
|
|
*/
|
|
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
|
|
|
|
/**
|
|
* \brief Perform an unsigned addition of MPIs: X = |A| + |B|
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first summand. This must point to an initialized MPI.
|
|
* \param B The second summand. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The minuend. This must point to an initialized MPI.
|
|
* \param B The subtrahend. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*
|
|
*/
|
|
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a signed addition of MPIs: X = A + B
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first summand. This must point to an initialized MPI.
|
|
* \param B The second summand. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a signed subtraction of MPIs: X = A - B
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The minuend. This must point to an initialized MPI.
|
|
* \param B The subtrahend. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a signed addition of an MPI and an integer: X = A + b
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first summand. This must point to an initialized MPI.
|
|
* \param b The second summand.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Perform a signed subtraction of an MPI and an integer:
|
|
* X = A - b
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The minuend. This must point to an initialized MPI.
|
|
* \param b The subtrahend.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Perform a multiplication of two MPIs: X = A * B
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first factor. This must point to an initialized MPI.
|
|
* \param B The second factor. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*
|
|
*/
|
|
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a multiplication of an MPI with an unsigned integer:
|
|
* X = A * b
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first factor. This must point to an initialized MPI.
|
|
* \param b The second factor.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*
|
|
*/
|
|
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
mbedtls_mpi_uint b );
|
|
|
|
/**
|
|
* \brief Perform a division with remainder of two MPIs:
|
|
* A = Q * B + R
|
|
*
|
|
* \param Q The destination MPI for the quotient.
|
|
* This may be \c NULL if the value of the
|
|
* quotient is not needed.
|
|
* \param R The destination MPI for the remainder value.
|
|
* This may be \c NULL if the value of the
|
|
* remainder is not needed.
|
|
* \param A The dividend. This must point to an initialized MPi.
|
|
* \param B The divisor. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a division with remainder of an MPI by an integer:
|
|
* A = Q * b + R
|
|
*
|
|
* \param Q The destination MPI for the quotient.
|
|
* This may be \c NULL if the value of the
|
|
* quotient is not needed.
|
|
* \param R The destination MPI for the remainder value.
|
|
* This may be \c NULL if the value of the
|
|
* remainder is not needed.
|
|
* \param A The dividend. This must point to an initialized MPi.
|
|
* \param b The divisor.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
|
|
mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Perform a modular reduction. R = A mod B
|
|
*
|
|
* \param R The destination MPI for the residue value.
|
|
* This must point to an initialized MPI.
|
|
* \param A The MPI to compute the residue of.
|
|
* This must point to an initialized MPI.
|
|
* \param B The base of the modular reduction.
|
|
* This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
|
|
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*
|
|
*/
|
|
int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Perform a modular reduction with respect to an integer.
|
|
* r = A mod b
|
|
*
|
|
* \param r The address at which to store the residue.
|
|
* This must not be \c NULL.
|
|
* \param A The MPI to compute the residue of.
|
|
* This must point to an initialized MPi.
|
|
* \param b The integer base of the modular reduction.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
|
|
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
|
|
mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Perform a sliding-window exponentiation: X = A^E mod N
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The base of the exponentiation.
|
|
* This must point to an initialized MPI.
|
|
* \param E The exponent MPI. This must point to an initialized MPI.
|
|
* \param N The base for the modular reduction. This must point to an
|
|
* initialized MPI.
|
|
* \param _RR A helper MPI depending solely on \p N which can be used to
|
|
* speed-up multiple modular exponentiations for the same value
|
|
* of \p N. This may be \c NULL. If it is not \c NULL, it must
|
|
* point to an initialized MPI. If it hasn't been used after
|
|
* the call to mbedtls_mpi_init(), this function will compute
|
|
* the helper value and store it in \p _RR for reuse on
|
|
* subsequent calls to this function. Otherwise, the function
|
|
* will assume that \p _RR holds the helper value set by a
|
|
* previous call to mbedtls_mpi_exp_mod(), and reuse it.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
|
|
* even, or if \c E is negative.
|
|
* \return Another negative error code on different kinds of failures.
|
|
*
|
|
*/
|
|
int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *E, const mbedtls_mpi *N,
|
|
mbedtls_mpi *_RR );
|
|
|
|
/**
|
|
* \brief Fill an MPI with a number of random bytes.
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param size The number of random bytes to generate.
|
|
* \param f_rng The RNG function to use. This must not be \c NULL.
|
|
* \param p_rng The RNG parameter to be passed to \p f_rng. This may be
|
|
* \c NULL if \p f_rng doesn't need a context argument.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on failure.
|
|
*
|
|
* \note The bytes obtained from the RNG are interpreted
|
|
* as a big-endian representation of an MPI; this can
|
|
* be relevant in applications like deterministic ECDSA.
|
|
*/
|
|
int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Compute the greatest common divisor: G = gcd(A, B)
|
|
*
|
|
* \param G The destination MPI. This must point to an initialized MPI.
|
|
* \param A The first operand. This must point to an initialized MPI.
|
|
* \param B The second operand. This must point to an initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return Another negative error code on different kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
|
|
const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Compute the modular inverse: X = A^-1 mod N
|
|
*
|
|
* \param X The destination MPI. This must point to an initialized MPI.
|
|
* \param A The MPI to calculate the modular inverse of. This must point
|
|
* to an initialized MPI.
|
|
* \param N The base of the modular inversion. This must point to an
|
|
* initialized MPI.
|
|
*
|
|
* \return \c 0 if successful.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
|
|
* or equal to one.
|
|
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse
|
|
* with respect to \p N.
|
|
*/
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int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
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|
const mbedtls_mpi *N );
|
|
|
|
#if !defined(MBEDTLS_DEPRECATED_REMOVED)
|
|
#if defined(MBEDTLS_DEPRECATED_WARNING)
|
|
#define MBEDTLS_DEPRECATED __attribute__((deprecated))
|
|
#else
|
|
#define MBEDTLS_DEPRECATED
|
|
#endif
|
|
/**
|
|
* \brief Perform a Miller-Rabin primality test with error
|
|
* probability of 2<sup>-80</sup>.
|
|
*
|
|
* \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows
|
|
* specifying the number of Miller-Rabin rounds.
|
|
*
|
|
* \param X The MPI to check for primality.
|
|
* This must point to an initialized MPI.
|
|
* \param f_rng The RNG function to use. This must not be \c NULL.
|
|
* \param p_rng The RNG parameter to be passed to \p f_rng.
|
|
* This may be \c NULL if \p f_rng doesn't use a
|
|
* context parameter.
|
|
*
|
|
* \return \c 0 if successful, i.e. \p X is probably prime.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
#undef MBEDTLS_DEPRECATED
|
|
#endif /* !MBEDTLS_DEPRECATED_REMOVED */
|
|
|
|
/**
|
|
* \brief Miller-Rabin primality test.
|
|
*
|
|
* \warning If \p X is potentially generated by an adversary, for example
|
|
* when validating cryptographic parameters that you didn't
|
|
* generate yourself and that are supposed to be prime, then
|
|
* \p rounds should be at least the half of the security
|
|
* strength of the cryptographic algorithm. On the other hand,
|
|
* if \p X is chosen uniformly or non-adversially (as is the
|
|
* case when mbedtls_mpi_gen_prime calls this function), then
|
|
* \p rounds can be much lower.
|
|
*
|
|
* \param X The MPI to check for primality.
|
|
* This must point to an initialized MPI.
|
|
* \param rounds The number of bases to perform the Miller-Rabin primality
|
|
* test for. The probability of returning 0 on a composite is
|
|
* at most 2<sup>-2*\p rounds</sup>.
|
|
* \param f_rng The RNG function to use. This must not be \c NULL.
|
|
* \param p_rng The RNG parameter to be passed to \p f_rng.
|
|
* This may be \c NULL if \p f_rng doesn't use
|
|
* a context parameter.
|
|
*
|
|
* \return \c 0 if successful, i.e. \p X is probably prime.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
|
|
* \return Another negative error code on other kinds of failure.
|
|
*/
|
|
int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
/**
|
|
* \brief Flags for mbedtls_mpi_gen_prime()
|
|
*
|
|
* Each of these flags is a constraint on the result X returned by
|
|
* mbedtls_mpi_gen_prime().
|
|
*/
|
|
typedef enum {
|
|
MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
|
|
MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
|
|
} mbedtls_mpi_gen_prime_flag_t;
|
|
|
|
/**
|
|
* \brief Generate a prime number.
|
|
*
|
|
* \param X The destination MPI to store the generated prime in.
|
|
* This must point to an initialized MPi.
|
|
* \param nbits The required size of the destination MPI in bits.
|
|
* This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
|
|
* \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
|
|
* \param f_rng The RNG function to use. This must not be \c NULL.
|
|
* \param p_rng The RNG parameter to be passed to \p f_rng.
|
|
* This may be \c NULL if \p f_rng doesn't use
|
|
* a context parameter.
|
|
*
|
|
* \return \c 0 if successful, in which case \p X holds a
|
|
* probably prime number.
|
|
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
|
|
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
|
|
* \c 3 and #MBEDTLS_MPI_MAX_BITS.
|
|
*/
|
|
int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
#if defined(MBEDTLS_SELF_TEST)
|
|
|
|
/**
|
|
* \brief Checkup routine
|
|
*
|
|
* \return 0 if successful, or 1 if the test failed
|
|
*/
|
|
int mbedtls_mpi_self_test( int verbose );
|
|
|
|
#endif /* MBEDTLS_SELF_TEST */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif /* bignum.h */
|