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708 lines
22 KiB
C
708 lines
22 KiB
C
/**
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* \file bignum_alt.h
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*
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* \brief Multi-precision integer library
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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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*/
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#ifndef BIGNUM_ALT_H
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#define BIGNUM_ALT_H
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#include "c_types.h"
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#include "rom/ets_sys.h"
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#include "rom/bigint.h"
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#define ESP_BIGNUM_ALT
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#define MPI_DEBUG_ALT
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#if defined(ESP_BIGNUM_ALT)
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#define ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */
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#define ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */
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#define ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */
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#define ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */
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#define ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */
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#define ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */
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#define ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */
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#define ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */
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#define MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
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#if defined(MPI_DEBUG_ALT)
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#define mpi_printf ets_printf
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#else
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#define mpi_printf
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#endif
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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 MPI_MAX_LIMBS 10000
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#if !defined(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 << 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 MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */
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#endif /* !MPI_WINDOW_SIZE */
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#if !defined(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 results temporarily in larger MPIs. So the number
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* of limbs required (MPI_MAX_LIMBS) is higher.
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*/
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#define MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */
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#endif /* !MPI_MAX_SIZE */
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#define MPI_MAX_BITS ( 8 * MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */
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/*
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* When reading from files with mpi_read_file() and writing to files with
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* 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 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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* MPI_RW_BUFFER_SIZE = ceil(MPI_MAX_BITS / ln(10) * ln(2)) +
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* LabelSize + 6
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*/
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#define MPI_MAX_BITS_SCALE100 ( 100 * MPI_MAX_BITS )
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#define LN_2_DIV_LN_10_SCALE100 332
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#define MPI_RW_BUFFER_SIZE ( ((MPI_MAX_BITS_SCALE100 + LN_2_DIV_LN_10_SCALE100 - 1) / 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-bit integers can be forced on 64-bit arches (eg. for testing purposes)
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* by defining HAVE_INT32 and undefining HAVE_ASM
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*/
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#if ( ! defined(HAVE_INT32) && \
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defined(_MSC_VER) && defined(_M_AMD64) )
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#define HAVE_INT64
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typedef int64_t mpi_sint;
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typedef uint64_t mpi_uint;
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#else
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#if ( ! defined(HAVE_INT32) && \
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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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#define HAVE_INT64
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typedef int64_t mpi_sint;
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typedef uint64_t mpi_uint;
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/* t_udbl defined as 128-bit unsigned int */
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typedef unsigned int t_udbl __attribute__((mode(TI)));
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#define HAVE_UDBL
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#else
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#define HAVE_INT32
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typedef int32_t mpi_sint;
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typedef uint32_t mpi_uint;
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typedef uint64_t t_udbl;
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#define HAVE_UDBL
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#endif /* !HAVE_INT32 && __GNUC__ && 64-bit platform */
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#endif /* !HAVE_INT32 && _MSC_VER && _M_AMD64 */
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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
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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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mpi_uint *p; /*!< pointer to limbs */
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}
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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 mpi_init( 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 mpi_free( 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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* \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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_grow( 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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* \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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_shrink( 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
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* \param Y Source MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_copy( mpi *X, const 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 mpi_swap( mpi *X, 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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* 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 ) 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 mpi_safe_cond_assign( mpi *X, const 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 mpi value
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* \param Y Second 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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* 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 ) 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 mpi_safe_cond_swap( mpi *X, 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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_lset( mpi *X, 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 mpi_get_bit( const 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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* ERR_MPI_ALLOC_FAILED if memory allocation failed,
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* ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
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*/
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int mpi_set_bit( 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 mpi_lsb( const 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 mpi_bitlen( const 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 mpi_size( const 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 ERR_MPI_XXX error code
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*/
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int mpi_read_string( 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 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 mpi_write_string( const mpi *X, int radix,
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char *buf, size_t buflen, size_t *olen );
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#if defined(FS_IO)
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/**
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* \brief Read X from 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, ERR_MPI_BUFFER_TOO_SMALL if
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* the file read buffer is too small or a
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* ERR_MPI_XXX error code
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*/
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int mpi_read_file( mpi *X, int radix, FILE *fin );
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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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*
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* \param p Prefix, can be NULL
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* \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 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 mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout );
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#endif /* 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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_read_binary( 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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* ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
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*/
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int mpi_write_binary( const 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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_shift_l( mpi *X, size_t count );
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/**
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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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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_shift_r( mpi *X, size_t count );
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/**
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* \brief Compare unsigned values
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*
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* \param X Left-hand MPI
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* \param Y Right-hand MPI
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*
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* \return 1 if |X| is greater than |Y|,
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* -1 if |X| is lesser than |Y| or
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* 0 if |X| is equal to |Y|
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*/
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int mpi_cmp_abs( const mpi *X, const mpi *Y );
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/**
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* \brief Compare signed values
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*
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* \param X Left-hand MPI
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* \param Y Right-hand MPI
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*
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* \return 1 if X is greater than Y,
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* -1 if X is lesser than Y or
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* 0 if X is equal to Y
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*/
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int mpi_cmp_mpi( const mpi *X, const mpi *Y );
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/**
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* \brief Compare signed values
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*
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* \param X Left-hand MPI
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* \param z The integer value to compare to
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*
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* \return 1 if X is greater than z,
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* -1 if X is lesser than z or
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* 0 if X is equal to z
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*/
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int mpi_cmp_int( const mpi *X, mpi_sint z );
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/**
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* \brief Unsigned addition: X = |A| + |B|
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_add_abs( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Unsigned subtraction: X = |A| - |B|
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_NEGATIVE_VALUE if B is greater than A
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*/
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int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed addition: X = A + B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed subtraction: X = A - B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Signed addition: X = A + b
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param b The integer value to add
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_add_int( mpi *X, const mpi *A, mpi_sint b );
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/**
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* \brief Signed subtraction: X = A - b
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param b The integer value to subtract
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_sub_int( mpi *X, const mpi *A, mpi_sint b );
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/**
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* \brief Baseline multiplication: X = A * B
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B );
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/**
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* \brief Baseline multiplication: X = A * b
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*
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* \param X Destination MPI
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* \param A Left-hand MPI
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* \param b The unsigned integer value to multiply with
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*
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* \note b is unsigned
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed
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*/
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int mpi_mul_int( mpi *X, const mpi *A, mpi_uint b );
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/**
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* \brief Division by mpi: A = Q * B + R
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*
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* \param Q Destination MPI for the quotient
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* \param R Destination MPI for the rest value
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* \param A Left-hand MPI
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* \param B Right-hand MPI
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed,
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* ERR_MPI_DIVISION_BY_ZERO if B == 0
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*
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* \note Either Q or R can be NULL.
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*/
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int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B );
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/**
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* \brief Division by int: A = Q * b + R
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*
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* \param Q Destination MPI for the quotient
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* \param R Destination MPI for the rest value
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|
* \param A Left-hand MPI
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* \param b Integer to divide by
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*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed,
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* ERR_MPI_DIVISION_BY_ZERO if b == 0
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*
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* \note Either Q or R can be NULL.
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*/
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int mpi_div_int( mpi *Q, mpi *R, const mpi *A, mpi_sint b );
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/**
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* \brief Modulo: R = A mod B
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*
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* \param R Destination MPI for the rest value
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* \param A Left-hand MPI
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|
* \param B Right-hand MPI
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|
*
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* \return 0 if successful,
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* ERR_MPI_ALLOC_FAILED if memory allocation failed,
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* ERR_MPI_DIVISION_BY_ZERO if B == 0,
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* ERR_MPI_NEGATIVE_VALUE if B < 0
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*/
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int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B );
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|
/**
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|
* \brief Modulo: r = A mod b
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|
*
|
|
* \param r Destination mpi_uint
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|
* \param A Left-hand MPI
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|
* \param b Integer to divide by
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|
*
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|
* \return 0 if successful,
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed,
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|
* ERR_MPI_DIVISION_BY_ZERO if b == 0,
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|
* ERR_MPI_NEGATIVE_VALUE if b < 0
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|
*/
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|
int mpi_mod_int( mpi_uint *r, const mpi *A, mpi_sint b );
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|
|
|
/**
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|
* \brief Sliding-window exponentiation: X = A^E mod N
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|
*
|
|
* \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,
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* 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 mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, 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,
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mpi_fill_random( 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,
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed
|
|
*/
|
|
int mpi_gcd( mpi *G, const mpi *A, const 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,
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* ERR_MPI_BAD_INPUT_DATA if N is negative or nil
|
|
ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
|
|
*/
|
|
int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N );
|
|
|
|
/**
|
|
* \brief Miller-Rabin primality test
|
|
*
|
|
* \param X MPI to check
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* ERR_MPI_NOT_ACCEPTABLE if X is not prime
|
|
*/
|
|
int mpi_is_prime( const mpi *X,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
|
|
/**
|
|
* \brief Prime number generation
|
|
*
|
|
* \param X Destination MPI
|
|
* \param nbits Required size of X in bits
|
|
* ( 3 <= nbits <= MPI_MAX_BITS )
|
|
* \param dh_flag If 1, then (X-1)/2 will be prime too
|
|
* \param f_rng RNG function
|
|
* \param p_rng RNG parameter
|
|
*
|
|
* \return 0 if successful (probably prime),
|
|
* ERR_MPI_ALLOC_FAILED if memory allocation failed,
|
|
* ERR_MPI_BAD_INPUT_DATA if nbits is < 3
|
|
*/
|
|
int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng );
|
|
#endif
|
|
|
|
#endif
|
|
|