698 lines
21 KiB
C++
698 lines
21 KiB
C++
/*
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* Copyright (c) 2012-2020 MIRACL UK Ltd.
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*
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* This file is part of MIRACL Core
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* (see https://github.com/miracl/core).
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may 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,
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* WITHOUT 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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* @file big.h
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* @author Mike Scott
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* @date 23rd February 2016
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* @brief Big number Header File
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*
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*
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*/
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#ifndef BIG_B448_60_H
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#define BIG_B448_60_H
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#include <stdio.h>
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#include <stdlib.h>
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#include <inttypes.h>
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#include "arch.h"
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#include "core.h"
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#include "config_big_B448_60.h"
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using namespace core;
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/* could comment this out if code size is a major issue */
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#define UNWOUND
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/* Normally recommended, but may not be optimal for some architectures, for example 32-bit ARM M4 */
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#define USE_KARATSUBA
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#define BIGBITS_B448_60 (8*MODBYTES_B448_60)
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#define NLEN_B448_60 (1+((8*MODBYTES_B448_60-1)/BASEBITS_B448_60))
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#define DNLEN_B448_60 2*NLEN_B448_60
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#define BMASK_B448_60 (((chunk)1<<BASEBITS_B448_60)-1) /**< Mask = 2^BASEBITS-1 */
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#define NEXCESS_B448_60 (1<<(CHUNK-BASEBITS_B448_60-1)) /**< 2^(CHUNK-BASEBITS-1) - digit cannot be multiplied by more than this before normalisation */
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#define HBITS_B448_60 (BASEBITS_B448_60/2) /**< Number of bits in number base divided by 2 */
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#define HMASK_B448_60 (((chunk)1<<HBITS_B448_60)-1) /**< Mask = 2^HBITS-1 */
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//#define DEBUG_NORM
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#ifdef DEBUG_NORM /* Add an extra location to track chunk extension */
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#define MPV_B448_60 NLEN_B448_60
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#define MNV_B448_60 (NLEN_B448_60+1)
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#define DMPV_B448_60 DNLEN_B448_60
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#define DMNV_B448_60 (DNLEN_B448_60+1)
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#endif
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namespace B448_60 {
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//extern int BIGMULS;
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//extern int BIGSQRS;
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#ifdef DEBUG_NORM
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typedef chunk BIG[NLEN_B448_60 + 2]; /**< Define type BIG as array of chunks */
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typedef chunk DBIG[DNLEN_B448_60 + 2]; /**< Define type DBIG as array of chunks */
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#else
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typedef chunk BIG[NLEN_B448_60]; /**< Define type BIG as array of chunks */
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typedef chunk DBIG[DNLEN_B448_60]; /**< Define type DBIG as array of chunks */
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#endif
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/* BIG number prototypes */
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/** @brief Tests for BIG equal to zero (Constant Time)
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*
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@param x a BIG number
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@return 1 if zero, else returns 0
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*/
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extern int BIG_iszilch(BIG x);
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/** @brief Tests for BIG equal to one (Constant Time)
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*
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@param x a BIG number
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@return 1 if one, else returns 0
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*/
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extern int BIG_isunity(BIG x);
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/** @brief Tests for DBIG equal to zero (Constant Time)
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*
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@param x a DBIG number
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@return 1 if zero, else returns 0
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*/
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extern int BIG_diszilch(DBIG x);
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/** @brief Outputs a BIG number to the console (Variable Time)
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*
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@param x a BIG number
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*/
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extern void BIG_output(BIG x);
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/** @brief Outputs a BIG number to the console in raw form (Variable Time for debugging)
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*
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@param x a BIG number
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*/
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extern void BIG_rawoutput(BIG x);
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/** @brief Conditional constant time swap of two BIG numbers
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*
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Conditionally swaps parameters in constant time (Constant Time without branching)
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@param x a BIG number
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@param y another BIG number
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@param s swap takes place if not equal to 0
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@return ignore
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*/
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extern chunk BIG_cswap(BIG x, BIG y, int s);
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/** @brief Conditional copy of BIG number
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*
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Conditionally copies second parameter to the first (Constant Time without branching)
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@param x a BIG number
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@param y another BIG number
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@param s copy takes place if not equal to 0
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@return ignore
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*/
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extern chunk BIG_cmove(BIG x, BIG y, int s);
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/** @brief Conditional copy of DBIG number
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*
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Conditionally copies second parameter to the first (Constant Time without branching)
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@param x a DBIG number
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@param y another DBIG number
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@param s copy takes place if not equal to 0
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@return ignore
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*/
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extern chunk BIG_dcmove(BIG x, BIG y, int s);
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/** @brief Convert from BIG number to byte array (Constant Time)
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*
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@param a byte array
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@param x BIG number
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*/
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extern void BIG_toBytes(char *a, BIG x);
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/** @brief Convert to BIG number from byte array (Constant Time)
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*
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@param x BIG number
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@param a byte array
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*/
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extern void BIG_fromBytes(BIG x, char *a);
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/** @brief Convert to BIG number from byte array of given length (Variable Time)
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*
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@param x BIG number
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@param a byte array
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@param s byte array length
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*/
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extern void BIG_fromBytesLen(BIG x, char *a, int s);
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/**@brief Convert to DBIG number from byte array of given length (Variable Time)
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*
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@param x DBIG number
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@param a byte array
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@param s byte array length
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*/
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extern void BIG_dfromBytesLen(DBIG x, char *a, int s);
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/** @brief Outputs a DBIG number to the console (Variable Time)
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*
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@param x a DBIG number
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*/
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extern void BIG_doutput(DBIG x);
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/** @brief Outputs a DBIG number to the console (Variable Time)
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*
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@param x a DBIG number
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*/
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extern void BIG_drawoutput(DBIG x);
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/** @brief Copy BIG from Read-Only Memory to a BIG (Constant Time)
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*
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@param x BIG number
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@param y BIG number in ROM
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*/
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extern void BIG_rcopy(BIG x, const BIG y);
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/** @brief Copy BIG to another BIG (Constant Time)
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*
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@param x BIG number
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@param y BIG number to be copied
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*/
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extern void BIG_copy(BIG x, BIG y);
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/** @brief Copy DBIG to another DBIG (Constant Time)
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*
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@param x DBIG number
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@param y DBIG number to be copied
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*/
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extern void BIG_dcopy(DBIG x, DBIG y);
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/** @brief Copy BIG to upper half of DBIG (Constant Time)
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*
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@param x DBIG number
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@param y BIG number to be copied
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*/
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extern void BIG_dsucopy(DBIG x, BIG y);
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/** @brief Copy BIG to lower half of DBIG (Constant Time)
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*
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@param x DBIG number
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@param y BIG number to be copied
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*/
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extern void BIG_dscopy(DBIG x, BIG y);
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/** @brief Copy lower half of DBIG to a BIG (Constant Time)
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*
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@param x BIG number
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@param y DBIG number to be copied
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*/
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extern void BIG_sdcopy(BIG x, DBIG y);
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/** @brief Copy upper half of DBIG to a BIG (Constant Time)
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*
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@param x BIG number
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@param y DBIG number to be copied
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*/
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extern void BIG_sducopy(BIG x, DBIG y);
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/** @brief Set BIG to zero (Constant Time)
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*
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@param x BIG number to be set to zero
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*/
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extern void BIG_zero(BIG x);
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/** @brief Set DBIG to zero (Constant Time)
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*
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@param x DBIG number to be set to zero
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*/
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extern void BIG_dzero(DBIG x);
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/** @brief Set BIG to one (unity) (Constant Time)
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*
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@param x BIG number to be set to one.
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*/
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extern void BIG_one(BIG x);
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/** @brief Set BIG to inverse mod 2^256 (Constant Time)
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*
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@param x BIG number to be inverted
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*/
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extern void BIG_invmod2m(BIG x);
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/** @brief Set BIG to sum of two BIGs - output not normalised (Constant Time)
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*
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@param x BIG number, sum of other two
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@param y BIG number
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@param z BIG number
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*/
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extern void BIG_add(BIG x, BIG y, BIG z);
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/** @brief Set BIG to logical or of two BIGs - output not normalised (Constant Time)
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*
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@param x BIG number, or of other two
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@param y BIG number
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@param z BIG number
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*/
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extern void BIG_or(BIG x, BIG y, BIG z);
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/** @brief Increment BIG by a small integer - output not normalised (Constant Time)
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*
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@param x BIG number to be incremented
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@param i integer
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*/
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extern void BIG_inc(BIG x, int i);
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/** @brief Set BIG to difference of two BIGs (Constant Time)
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*
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@param x BIG number, difference of other two - output not normalised
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@param y BIG number
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@param z BIG number
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*/
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extern void BIG_sub(BIG x, BIG y, BIG z);
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/** @brief Decrement BIG by a small integer - output not normalised (Constant Time)
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*
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@param x BIG number to be decremented
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@param i integer
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*/
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extern void BIG_dec(BIG x, int i);
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/** @brief Set DBIG to sum of two DBIGs (Constant Time)
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*
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@param x DBIG number, sum of other two - output not normalised
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@param y DBIG number
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@param z DBIG number
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*/
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extern void BIG_dadd(DBIG x, DBIG y, DBIG z);
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/** @brief Set DBIG to difference of two DBIGs (Constant Time)
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*
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@param x DBIG number, difference of other two - output not normalised
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@param y DBIG number
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@param z DBIG number
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*/
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extern void BIG_dsub(DBIG x, DBIG y, DBIG z);
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/** @brief Multiply BIG by a small integer - output not normalised (Constant Time)
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*
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@param x BIG number, product of other two
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@param y BIG number
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@param i small integer
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*/
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extern void BIG_imul(BIG x, BIG y, int i);
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/** @brief Multiply BIG by not-so-small small integer - output normalised (Constant Time)
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*
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@param x BIG number, product of other two
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@param y BIG number
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@param i small integer
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@return Overflowing bits
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*/
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extern chunk BIG_pmul(BIG x, BIG y, int i);
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/** @brief Divide BIG by 3 - output normalised (Constant Time)
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*
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@param x BIG number
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@return Remainder
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*/
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extern int BIG_div3(BIG x);
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/** @brief Multiply BIG by even bigger small integer resulting in a DBIG - output normalised (Constant Time)
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*
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@param x DBIG number, product of other two
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@param y BIG number
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@param i small integer
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*/
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extern void BIG_pxmul(DBIG x, BIG y, int i);
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/** @brief Multiply BIG by another BIG resulting in DBIG - inputs normalised and output normalised (Constant Time)
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*
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@param x DBIG number, product of other two
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@param y BIG number
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@param z BIG number
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*/
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extern void BIG_mul(DBIG x, BIG y, BIG z);
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/** @brief Multiply BIG by another BIG resulting in another BIG - inputs normalised and output normalised (Constant Time)
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*
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Note that the product must fit into a BIG, and x must be distinct from y and z
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@param x BIG number, product of other two
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@param y BIG number
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@param z BIG number
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*/
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extern void BIG_smul(BIG x, BIG y, BIG z);
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/** @brief Square BIG resulting in a DBIG - input normalised and output normalised (Constant Time)
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*
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@param x DBIG number, square of a BIG
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@param y BIG number to be squared
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*/
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extern void BIG_sqr(DBIG x, BIG y);
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/** @brief Montgomery reduction of a DBIG to a BIG - input normalised and output normalised (Constant Time)
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*
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@param a BIG number, reduction of a BIG
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@param md BIG number, the modulus
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@param MC the Montgomery Constant
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@param d DBIG number to be reduced
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*/
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extern void BIG_monty(BIG a, BIG md, chunk MC, DBIG d);
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/** @brief Shifts a BIG left by any number of bits - input must be normalised, output normalised (Constant Time)
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*
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@param x BIG number to be shifted
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@param s Number of bits to shift
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*/
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extern void BIG_shl(BIG x, int s);
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/** @brief Fast shifts a BIG left by a small number of bits - input must be normalised, output will be normalised (Constant Time)
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*
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The number of bits to be shifted must be less than BASEBITS
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@param x BIG number to be shifted
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@param s Number of bits to shift
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@return Overflow bits
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*/
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extern int BIG_fshl(BIG x, int s);
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/** @brief Shifts a DBIG left by any number of bits - input must be normalised, output normalised (Constant Time)
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*
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@param x DBIG number to be shifted
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@param s Number of bits to shift
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*/
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extern void BIG_dshl(DBIG x, int s);
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/** @brief Shifts a BIG right by any number of bits - input must be normalised, output normalised (Constant Time)
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*
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@param x BIG number to be shifted
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@param s Number of bits to shift
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*/
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extern void BIG_shr(BIG x, int s);
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/** @brief Fast time-critical combined shift by 1 bit, subtract and normalise (Constant Time)
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*
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@param r BIG number normalised output
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@param a BIG number to be subtracted from
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@param m BIG number to be shifted and subtracted
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@return sign of r
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*/
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extern int BIG_ssn(BIG r, BIG a, BIG m);
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/** @brief Fast shifts a BIG right by a small number of bits - input must be normalised, output will be normalised (Constant Time)
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*
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The number of bits to be shifted must be less than BASEBITS
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@param x BIG number to be shifted
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@param s Number of bits to shift
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@return Shifted out bits
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*/
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extern int BIG_fshr(BIG x, int s);
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/** @brief Shifts a DBIG right by any number of bits - input must be normalised, output normalised (Constant Time)
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*
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@param x DBIG number to be shifted
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@param s Number of bits to shift
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*/
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extern void BIG_dshr(DBIG x, int s);
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/** @brief Splits a DBIG into two BIGs - input must be normalised, outputs normalised (Constant Time as used)
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*
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Internal function. The value of s must be approximately in the middle of the DBIG.
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Typically used to extract z mod 2^MODBITS and z/2^MODBITS
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@param x BIG number, top half of z
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@param y BIG number, bottom half of z
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@param z DBIG number to be split in two.
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@param s Bit position at which to split
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@return carry-out from top half
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*/
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extern chunk BIG_split(BIG x, BIG y, DBIG z, int s);
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/** @brief Normalizes a BIG number - output normalised (Constant Time)
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*
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All digits of the input BIG are reduced mod 2^BASEBITS
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@param x BIG number to be normalised
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*/
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extern chunk BIG_norm(BIG x);
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/** @brief Normalizes a DBIG number - output normalised (Constant Time)
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*
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All digits of the input DBIG are reduced mod 2^BASEBITS
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@param x DBIG number to be normalised
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*/
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extern void BIG_dnorm(DBIG x);
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/** @brief Compares two BIG numbers. Inputs must be normalised externally (Constant Time)
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*
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@param x first BIG number to be compared
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@param y second BIG number to be compared
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@return -1 is x<y, 0 if x=y, 1 if x>y
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*/
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extern int BIG_comp(BIG x, BIG y);
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/** @brief Compares two DBIG numbers. Inputs must be normalised externally (Constant Time)
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*
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@param x first DBIG number to be compared
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@param y second DBIG number to be compared
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@return -1 is x<y, 0 if x=y, 1 if x>y
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*/
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extern int BIG_dcomp(DBIG x, DBIG y);
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/** @brief Calculate number of bits in a BIG - output normalised (Variable Time)
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*
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@param x BIG number
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@return Number of bits in x
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*/
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extern int BIG_nbits(BIG x);
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/** @brief Calculate number of bits in a DBIG - output normalised (Variable Time)
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*
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@param x DBIG number
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@return Number of bits in x
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*/
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extern int BIG_dnbits(DBIG x);
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/** @brief Reduce x mod n - constant time for fixed bd
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*
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Slow but rarely used
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@param x BIG number to be reduced mod n
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@param n The modulus
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@param bd non-negative bit difference between maximum x and n
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*/
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extern void BIG_ctmod(BIG x, BIG n, int bd);
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/** @brief x=y mod n - constant time for fixed bd
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*
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Slow but rarely used. y is destroyed.
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@param x BIG number, on exit = y mod n
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@param y DBIG number
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@param n Modulus
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@param bd non-negative bit difference between maximum y and n
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*/
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extern void BIG_ctdmod(BIG x, DBIG y, BIG n, int bd);
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/** @brief Divide x by n - constant time for fixed bd
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*
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Slow but rarely used
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@param x BIG number to be divided by n
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@param n The Divisor
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@param bd non-negative bit difference between maximum x and n
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*/
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extern void BIG_ctsdiv(BIG x,BIG n,int bd);
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/** @brief x=y/n - constant time for fixed bd
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*
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Slow but rarely used. y is destroyed.
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@param x BIG number, on exit = y/n
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@param y DBIG number
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@param n Modulus
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@param bd non-negative bit difference between maximum y and n
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*/
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extern void BIG_ctddiv(BIG x, DBIG y, BIG n,int bd);
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/** @brief Reduce x mod n - input and output normalised (Variable Time)
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*
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Slow but rarely used
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@param x BIG number to be reduced mod n
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@param n The modulus
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*/
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extern void BIG_mod(BIG x, BIG n);
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/** @brief Divide x by n - output normalised (Variable Time)
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*
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Slow but rarely used
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@param x BIG number to be divided by n
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@param n The Divisor
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*/
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extern void BIG_sdiv(BIG x, BIG n);
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/** @brief x=y mod n - output normalised (Variable Time)
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*
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Slow but rarely used. y is destroyed.
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@param x BIG number, on exit = y mod n
|
|
@param y DBIG number
|
|
@param n Modulus
|
|
*/
|
|
extern void BIG_dmod(BIG x, DBIG y, BIG n);
|
|
/** @brief x=y/n - output normalised (Variable Time)
|
|
*
|
|
Slow but rarely used. y is destroyed.
|
|
@param x BIG number, on exit = y/n
|
|
@param y DBIG number
|
|
@param n Modulus
|
|
*/
|
|
extern void BIG_ddiv(BIG x, DBIG y, BIG n);
|
|
/** @brief return parity of BIG, that is the least significant bit (Constant Time)
|
|
*
|
|
@param x BIG number
|
|
@return 0 or 1
|
|
*/
|
|
extern int BIG_parity(BIG x);
|
|
/** @brief return i-th of BIG (Constant Time)
|
|
*
|
|
@param x BIG number
|
|
@param i the bit of x to be returned
|
|
@return 0 or 1
|
|
*/
|
|
extern int BIG_bit(BIG x, int i);
|
|
/** @brief return least significant bits of a BIG (Constant Time)
|
|
*
|
|
@param x BIG number
|
|
@param n number of bits to return. Assumed to be less than BASEBITS.
|
|
@return least significant n bits as an integer
|
|
*/
|
|
extern int BIG_lastbits(BIG x, int n);
|
|
/** @brief Create a random BIG from a random number generator (Constant Time)
|
|
*
|
|
Assumes that the random number generator has been suitably initialised
|
|
@param x BIG number, on exit a random number
|
|
@param r A pointer to a Cryptographically Secure Random Number Generator
|
|
*/
|
|
extern void BIG_random(BIG x, csprng *r);
|
|
/** @brief Create an unbiased random BIG from a random number generator, reduced with respect to a modulus (Constant Time as used)
|
|
*
|
|
Assumes that the random number generator has been suitably initialised
|
|
@param x BIG number, on exit a random number
|
|
@param n The modulus
|
|
@param r A pointer to a Cryptographically Secure Random Number Generator
|
|
*/
|
|
extern void BIG_randomnum(BIG x, BIG n, csprng *r);
|
|
|
|
/** @brief Create an unbiased random BIG from a random number generator, reduced with respect to a modulus and truncated to max bit length (Constant Time as used)
|
|
*
|
|
Assumes that the random number generator has been suitably initialised
|
|
@param x BIG number, on exit a random number
|
|
@param n The modulus
|
|
@param t Maximum bit length
|
|
@param r A pointer to a Cryptographically Secure Random Number Generator
|
|
*/
|
|
extern void BIG_randtrunc(BIG x, BIG n, int t, csprng *r);
|
|
|
|
/** brief return NAF (Non-Adjacent-Form) value as +/- 1, 3 or 5, inputs must be normalised
|
|
*
|
|
Given x and 3*x extracts NAF value from given bit position, and returns number of bits processed, and number of trailing zeros detected if any
|
|
param x BIG number
|
|
param x3 BIG number, three times x
|
|
param i bit position
|
|
param nbs pointer to integer returning number of bits processed
|
|
param nzs pointer to integer returning number of trailing 0s
|
|
return + or - 1, 3 or 5
|
|
*/
|
|
|
|
/** @brief Calculate x=y*z mod n (Variable Time)
|
|
*
|
|
Slow method for modular multiplication
|
|
@param x BIG number, on exit = y*z mod n
|
|
@param y BIG number
|
|
@param z BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_modmul(BIG x, BIG y, BIG z, BIG n);
|
|
/** @brief Calculate x=y/z mod n (Variable Time)
|
|
*
|
|
Slow method for modular division
|
|
@param x BIG number, on exit = y/z mod n
|
|
@param y BIG number
|
|
@param z BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_moddiv(BIG x, BIG y, BIG z, BIG n);
|
|
/** @brief Calculate x=y^2 mod n (Variable Time)
|
|
*
|
|
Slow method for modular squaring
|
|
@param x BIG number, on exit = y^2 mod n
|
|
@param y BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_modsqr(BIG x, BIG y, BIG n);
|
|
/** @brief Calculate x=-y mod n (Variable Time)
|
|
*
|
|
Modular negation
|
|
@param x BIG number, on exit = -y mod n
|
|
@param y BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_modneg(BIG x, BIG y, BIG n);
|
|
|
|
/** @brief Calculate x=y+z mod n (Variable Time)
|
|
*
|
|
Slow method for modular addition
|
|
@param x BIG number, on exit = y+z mod n
|
|
@param y BIG number
|
|
@param z BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_modadd(BIG x, BIG y, BIG z, BIG n);
|
|
|
|
/** @brief Calculate jacobi Symbol (x/y) (Variable Time)
|
|
*
|
|
@param x BIG number
|
|
@param y BIG number
|
|
@return Jacobi symbol, -1,0 or 1
|
|
*/
|
|
extern int BIG_jacobi(BIG x, BIG y);
|
|
/** @brief Calculate x=1/y mod n (Variable Time)
|
|
*
|
|
Modular Inversion - This is slow. Uses binary method.
|
|
@param x BIG number, on exit = 1/y mod n
|
|
@param y BIG number
|
|
@param n The BIG Modulus
|
|
*/
|
|
extern void BIG_invmodp(BIG x, BIG y, BIG n);
|
|
/** @brief Calculate x=x mod 2^m (Variable Time)
|
|
*
|
|
Truncation
|
|
@param x BIG number, on reduced mod 2^m
|
|
@param m new truncated size
|
|
*/
|
|
extern void BIG_mod2m(BIG x, int m);
|
|
|
|
/** @brief Calculates a*b+c+*d
|
|
*
|
|
Calculate partial product of a.b, add in carry c, and add total to d (Constant Time)
|
|
@param a multiplier
|
|
@param b multiplicand
|
|
@param c carry
|
|
@param d pointer to accumulated bottom half of result
|
|
@return top half of result
|
|
*/
|
|
|
|
|
|
extern int step1(BIG,BIG,BIG);
|
|
extern void step2(BIG,BIG,BIG);
|
|
|
|
#ifdef dchunk
|
|
|
|
/* Method required to calculate x*y+c+r, bottom half in r, top half returned */
|
|
inline chunk muladd(chunk x, chunk y, chunk c, chunk *r)
|
|
{
|
|
dchunk prod = (dchunk)x * y + c + *r;
|
|
*r = (chunk)prod & BMASK_B448_60;
|
|
return (chunk)(prod >> BASEBITS_B448_60);
|
|
}
|
|
|
|
#else
|
|
|
|
/* No integer type available that can store double the wordlength */
|
|
/* accumulate partial products */
|
|
|
|
inline chunk muladd(chunk x, chunk y, chunk c, chunk *r)
|
|
{
|
|
chunk x0, x1, y0, y1;
|
|
chunk bot, top, mid, carry;
|
|
x0 = x & HMASK_B448_60;
|
|
x1 = (x >> HBITS_B448_60);
|
|
y0 = y & HMASK_B448_60;
|
|
y1 = (y >> HBITS_B448_60);
|
|
bot = x0 * y0;
|
|
top = x1 * y1;
|
|
mid = x0 * y1 + x1 * y0;
|
|
x0 = mid & HMASK_B448_60;
|
|
x1 = (mid >> HBITS_B448_60);
|
|
bot += x0 << HBITS_B448_60;
|
|
bot += *r;
|
|
bot += c;
|
|
|
|
top += x1;
|
|
carry = bot >> BASEBITS_B448_60;
|
|
bot &= BMASK_B448_60;
|
|
top += carry;
|
|
|
|
*r = bot;
|
|
return top;
|
|
}
|
|
|
|
#endif
|
|
|
|
}
|
|
|
|
#endif
|