a0b67c2f3e
When using a primality testing function the tolerable error rate depends on the scheme in question, the required security strength and wether it is used for key generation or parameter validation. To support all use cases we need more flexibility than what the old API provides.
821 lines
28 KiB
C
821 lines
28 KiB
C
/**
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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 (C) 2006-2015, ARM Limited, All Rights Reserved
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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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* This file is part of mbed TLS (https://tls.mbed.org)
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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) do { if( ( ret = f ) != 0 ) goto cleanup; } 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 windows 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; /*!< integer sign */
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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 one MPI (make internal references valid)
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* This just makes it 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 One MPI to initialize.
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*/
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void mbedtls_mpi_init( mbedtls_mpi *X );
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/**
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* \brief Unallocate one MPI
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*
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* \param X One MPI to unallocate.
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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 to the specified number of limbs
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*
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* This function does nothing if the MPI is already large enough.
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*
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* \param X MPI to grow
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* \param nblimbs The target number of limbs
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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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 Resize down, keeping at least the 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 MPI to shrink
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* \param nblimbs The minimum number of limbs to keep
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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* (this can only happen when resizing up).
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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 Copy the contents of Y into X
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*
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* \param X Destination MPI. It is enlarged if necessary.
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* \param Y Source MPI.
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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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 X and Y
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*
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* \param X First MPI value
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* \param Y Second MPI value
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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 Safe conditional assignement X = Y if assign is 1
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*
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* \param X MPI to conditionally assign to
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* \param Y Value to be assigned
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* \param assign 1: perform the assignment, 0: keep X's original value
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
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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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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 Safe conditional swap X <-> Y if swap is 1
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*
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* \param X First mbedtls_mpi value
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* \param Y Second mbedtls_mpi value
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* \param assign 1: perform the swap, 0: keep X and Y's original values
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
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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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int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
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/**
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* \brief Set value from integer
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*
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* \param X MPI to set
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* \param z Value to use
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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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 X
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*
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* \param X MPI to use
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* \param pos Zero-based index of the bit in X
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*
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* \return Either a 0 or a 1
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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 Set a bit of X to a specific value of 0 or 1
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*
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* \note Will grow X if necessary to set a bit to 1 in a not yet
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* existing limb. Will not grow if bit should be set to 0
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*
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* \param X MPI to use
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* \param pos Zero-based index of the bit in X
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* \param val The value to set the bit to (0 or 1)
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
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* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
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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 zero-bits before the least significant
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* '1' bit
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*
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* Note: Thus also the zero-based index of the least significant '1' bit
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*
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* \param X MPI to use
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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
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* significant '1' bit'
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*
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* Note: Thus also the one-based index of the most significant '1' bit
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*
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* \param X MPI to use
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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 in bytes
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*
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* \param X MPI to use
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*/
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size_t mbedtls_mpi_size( const mbedtls_mpi *X );
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/**
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* \brief Import from an ASCII string
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*
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* \param X Destination MPI
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* \param radix Input numeric base
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* \param s Null-terminated string buffer
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*
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* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
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*/
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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 into an ASCII string
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*
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* \param X Source MPI
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* \param radix Output numeric base
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* \param buf Buffer to write the string to
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* \param buflen Length of buf
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* \param olen Length of the string written, including final NUL byte
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*
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* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
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* *olen is always updated to reflect the amount
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* of data that has (or would have) been written.
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*
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* \note Call this function with buflen = 0 to obtain the
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* minimum required buffer size in *olen.
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*/
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int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
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char *buf, size_t buflen, size_t *olen );
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#if defined(MBEDTLS_FS_IO)
|
|
/**
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|
* \brief Read MPI from a line in an opened file
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*
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|
* \param X Destination MPI
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* \param radix Input numeric base
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* \param fin Input file handle
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*
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* \return 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
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* the file read buffer is too small or a
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* MBEDTLS_ERR_MPI_XXX error code
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*
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|
* \note On success, this function advances the file stream
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* to the end of the current line or to EOF.
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*
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|
* The function returns 0 on an empty line.
|
|
*
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* Leading whitespaces are ignored, as is a
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* '0x' prefix for radix 16.
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*
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*/
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int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
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|
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/**
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|
* \brief Write X into an opened file, or stdout if fout is NULL
|
|
*
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|
* \param p Prefix, can be NULL
|
|
* \param X Source MPI
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* \param radix Output numeric base
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* \param fout Output file handle (can be NULL)
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|
*
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* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
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*
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* \note Set fout == NULL to print X on the console.
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*/
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int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
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|
#endif /* MBEDTLS_FS_IO */
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|
|
/**
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|
* \brief Import X from unsigned binary data, big endian
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|
*
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|
* \param X Destination MPI
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|
* \param buf Input buffer
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|
* \param buflen Input buffer size
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|
*
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|
* \return 0 if successful,
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|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
|
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|
|
/**
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|
* \brief Export X into unsigned binary data, big endian.
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|
* Always fills the whole buffer, which will start with zeros
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|
* if the number is smaller.
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|
*
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|
* \param X Source MPI
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* \param buf Output buffer
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|
* \param buflen Output buffer size
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*
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* \return 0 if successful,
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* MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
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*/
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|
int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
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|
|
|
/**
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|
* \brief Left-shift: X <<= count
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|
*
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|
* \param X MPI to shift
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|
* \param count Amount to shift
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|
*
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|
* \return 0 if successful,
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
|
|
int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
|
|
|
|
/**
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|
* \brief Right-shift: X >>= count
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|
*
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|
* \param X MPI to shift
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|
* \param count Amount to shift
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*
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|
* \return 0 if successful,
|
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* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
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|
*/
|
|
int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
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|
|
/**
|
|
* \brief Compare unsigned values
|
|
*
|
|
* \param X Left-hand MPI
|
|
* \param Y Right-hand MPI
|
|
*
|
|
* \return 1 if |X| is greater than |Y|,
|
|
* -1 if |X| is lesser than |Y| or
|
|
* 0 if |X| is equal to |Y|
|
|
*/
|
|
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
|
|
|
|
/**
|
|
* \brief Compare signed values
|
|
*
|
|
* \param X Left-hand MPI
|
|
* \param Y Right-hand MPI
|
|
*
|
|
* \return 1 if X is greater than Y,
|
|
* -1 if X is lesser than Y or
|
|
* 0 if X is equal to Y
|
|
*/
|
|
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
|
|
|
|
/**
|
|
* \brief Compare signed values
|
|
*
|
|
* \param X Left-hand MPI
|
|
* \param z The integer value to compare to
|
|
*
|
|
* \return 1 if X is greater than z,
|
|
* -1 if X is lesser than z or
|
|
* 0 if X is equal to z
|
|
*/
|
|
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
|
|
|
|
/**
|
|
* \brief Unsigned addition: X = |A| + |B|
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Unsigned subtraction: X = |A| - |B|
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
|
|
*/
|
|
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Signed addition: X = A + B
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Signed subtraction: X = A - B
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Signed addition: X = A + b
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param b The integer value to add
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Signed subtraction: X = A - b
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param b The integer value to subtract
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Baseline multiplication: X = A * B
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Baseline multiplication: X = A * b
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param b The unsigned integer value to multiply with
|
|
*
|
|
* \note b is unsigned
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
|
|
|
|
/**
|
|
* \brief Division by mbedtls_mpi: A = Q * B + R
|
|
*
|
|
* \param Q Destination MPI for the quotient
|
|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
|
|
*
|
|
* \note Either Q or R can be NULL.
|
|
*/
|
|
int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Division by int: A = Q * b + R
|
|
*
|
|
* \param Q Destination MPI for the quotient
|
|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
|
|
* \param b Integer to divide by
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
|
|
*
|
|
* \note Either Q or R can be NULL.
|
|
*/
|
|
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Modulo: R = A mod B
|
|
*
|
|
* \param R Destination MPI for the rest value
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
|
|
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
|
|
*/
|
|
int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Modulo: r = A mod b
|
|
*
|
|
* \param r Destination mbedtls_mpi_uint
|
|
* \param A Left-hand MPI
|
|
* \param b Integer to divide by
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
|
|
* MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
|
|
*/
|
|
int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
|
|
|
|
/**
|
|
* \brief Sliding-window exponentiation: X = A^E mod N
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param E Exponent MPI
|
|
* \param N Modular MPI
|
|
* \param _RR Speed-up MPI used for recalculations
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
|
|
* if E is negative
|
|
*
|
|
* \note _RR is used to avoid re-computing R*R mod N across
|
|
* multiple calls, which speeds up things a bit. It can
|
|
* be set to NULL if the extra performance is unneeded.
|
|
*/
|
|
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 X with size bytes of random
|
|
*
|
|
* \param X Destination MPI
|
|
* \param size Size in bytes
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*
|
|
* \note The bytes obtained from the PRNG 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 Greatest common divisor: G = gcd(A, B)
|
|
*
|
|
* \param G Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param B Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
|
|
|
|
/**
|
|
* \brief Modular inverse: X = A^-1 mod N
|
|
*
|
|
* \param X Destination MPI
|
|
* \param A Left-hand MPI
|
|
* \param N Right-hand MPI
|
|
*
|
|
* \return 0 if successful,
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
|
|
MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
|
|
*/
|
|
int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 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 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 MPI to check
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
|
|
*/
|
|
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 MPI to check
|
|
* \param rounds Number of bases to perform 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 RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
|
|
*/
|
|
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 Prime number generation
|
|
*
|
|
* \param X Destination MPI
|
|
* \param nbits Required size of X in bits
|
|
* ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
|
|
* \param flags Mask of flags of type #mbedtls_mpi_gen_prime_flag_t
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
|
|
*/
|
|
int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Checkup routine
|
|
*
|
|
* \return 0 if successful, or 1 if the test failed
|
|
*/
|
|
int mbedtls_mpi_self_test( int verbose );
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif /* bignum.h */
|