MPI (Multiple Precision Integer Arithmetic) More...

#include <stdio.h>
#include "core/crypto.h"

Data Structures
struct	Mpi
	Arbitrary precision integer. More...

Macros
#define	MPI_MAX_BIT_SIZE 4096

#define	MPI_INT_SIZE sizeof(uint_t)

#define	MPI_MAX_INT_SIZE ((MPI_MAX_BIT_SIZE + (MPI_INT_SIZE * 8) - 1) / (MPI_INT_SIZE * 8))

#define	MPI_CHECK(f) if((error = f) != NO_ERROR) goto end

#define	mpiIsEven(a) !mpiGetBitValue(a, 0)

#define	mpiIsOdd(a) mpiGetBitValue(a, 0)

Enumerations
enum	MpiFormat { MPI_FORMAT_LITTLE_ENDIAN = 0, MPI_FORMAT_BIG_ENDIAN = 1 }
	MPI import/export format. More...

Functions
void	mpiInit (Mpi *r)
	Initialize a multiple precision integer. More...

void	mpiFree (Mpi *r)
	Release a multiple precision integer. More...

error_t	mpiGrow (Mpi *r, uint_t size)
	Adjust the size of multiple precision integer. More...

uint_t	mpiGetLength (const Mpi *a)
	Get the actual length in words. More...

uint_t	mpiGetByteLength (const Mpi *a)
	Get the actual length in bytes. More...

uint_t	mpiGetBitLength (const Mpi *a)
	Get the actual length in bits. More...

error_t	mpiSetBitValue (Mpi *r, uint_t index, uint_t value)
	Set the bit value at the specified index. More...

uint_t	mpiGetBitValue (const Mpi *a, uint_t index)
	Get the bit value at the specified index. More...

int_t	mpiComp (const Mpi a, const Mpi b)
	Compare two multiple precision integers. More...

int_t	mpiCompInt (const Mpi *a, int_t b)
	Compare a multiple precision integer with an integer. More...

int_t	mpiCompAbs (const Mpi a, const Mpi b)
	Compare the absolute value of two multiple precision integers. More...

error_t	mpiCopy (Mpi r, const Mpi a)
	Copy a multiple precision integer. More...

error_t	mpiSetValue (Mpi *a, int_t b)
	Set the value of a multiple precision integer. More...

error_t	mpiRand (Mpi r, uint_t length, const PrngAlgo prngAlgo, void *prngContext)
	Generate a random value. More...

error_t	mpiRandRange (Mpi r, const Mpi p, const PrngAlgo prngAlgo, void prngContext)
	Generate a random value in the range 1 to p-1. More...

error_t	mpiCheckProbablePrime (const Mpi *a)
	Test whether a number is probable prime. More...

error_t	mpiImport (Mpi r, const uint8_t data, uint_t length, MpiFormat format)
	Octet string to integer conversion. More...

error_t	mpiExport (const Mpi a, uint8_t data, uint_t length, MpiFormat format)
	Integer to octet string conversion. More...

error_t	mpiAdd (Mpi r, const Mpi a, const Mpi *b)
	Multiple precision addition. More...

error_t	mpiAddInt (Mpi r, const Mpi a, int_t b)
	Add an integer to a multiple precision integer. More...

error_t	mpiSub (Mpi r, const Mpi a, const Mpi *b)
	Multiple precision subtraction. More...

error_t	mpiSubInt (Mpi r, const Mpi a, int_t b)
	Subtract an integer from a multiple precision integer. More...

error_t	mpiAddAbs (Mpi r, const Mpi a, const Mpi *b)
	Helper routine for multiple precision addition. More...

error_t	mpiSubAbs (Mpi r, const Mpi a, const Mpi *b)
	Helper routine for multiple precision subtraction. More...

error_t	mpiShiftLeft (Mpi *r, uint_t n)
	Left shift operation. More...

error_t	mpiShiftRight (Mpi *r, uint_t n)
	Right shift operation. More...

error_t	mpiMul (Mpi r, const Mpi a, const Mpi *b)
	Multiple precision multiplication. More...

error_t	mpiMulInt (Mpi r, const Mpi a, int_t b)
	Multiply a multiple precision integer by an integer. More...

error_t	mpiDiv (Mpi q, Mpi r, const Mpi a, const Mpi b)
	Multiple precision division. More...

error_t	mpiDivInt (Mpi q, Mpi r, const Mpi *a, int_t b)
	Divide a multiple precision integer by an integer. More...

error_t	mpiMod (Mpi r, const Mpi a, const Mpi *p)
	Modulo operation. More...

error_t	mpiAddMod (Mpi r, const Mpi a, const Mpi b, const Mpi p)
	Modular addition. More...

error_t	mpiSubMod (Mpi r, const Mpi a, const Mpi b, const Mpi p)
	Modular subtraction. More...

error_t	mpiMulMod (Mpi r, const Mpi a, const Mpi b, const Mpi p)
	Modular multiplication. More...

error_t	mpiInvMod (Mpi r, const Mpi a, const Mpi *p)
	Modular inverse. More...

error_t	mpiExpMod (Mpi r, const Mpi a, const Mpi e, const Mpi p)
	Modular exponentiation. More...

error_t	mpiExpModFast (Mpi r, const Mpi a, const Mpi e, const Mpi p)
	Modular exponentiation (fast calculation) More...

error_t	mpiExpModRegular (Mpi r, const Mpi a, const Mpi e, const Mpi p)
	Modular exponentiation (regular calculation) More...

error_t	mpiMontgomeryMul (Mpi r, const Mpi a, const Mpi b, uint_t k, const Mpi p, Mpi *t)
	Montgomery multiplication. More...

error_t	mpiMontgomeryRed (Mpi r, const Mpi a, uint_t k, const Mpi p, Mpi t)
	Montgomery reduction. More...

void	mpiMulAccCore (uint_t r, const uint_t a, int_t m, const uint_t b)
	Multiply-accumulate operation. More...

void	mpiDump (FILE stream, const char_t prepend, const Mpi *a)
	Display the contents of a multiple precision integer. More...

Detailed Description

MPI (Multiple Precision Integer Arithmetic)

License

SPDX-License-Identifier: GPL-2.0-or-later

This file is part of CycloneCRYPTO Open.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

Author: Oryx Embedded SARL (www.oryx-embedded.com)

Version: 2.4.4

Definition in file mpi.h.

Macro Definition Documentation

◆ MPI_CHECK

#define MPI_CHECK ( f ) if((error = f) != NO_ERROR) goto end

Definition at line 52 of file mpi.h.

◆ MPI_INT_SIZE

#define MPI_INT_SIZE sizeof(uint_t)

Definition at line 46 of file mpi.h.

◆ MPI_MAX_BIT_SIZE

#define MPI_MAX_BIT_SIZE 4096

Definition at line 40 of file mpi.h.

◆ MPI_MAX_INT_SIZE

#define MPI_MAX_INT_SIZE ((MPI_MAX_BIT_SIZE + (MPI_INT_SIZE * 8) - 1) / (MPI_INT_SIZE * 8))

Definition at line 49 of file mpi.h.

◆ mpiIsEven

#define mpiIsEven ( a ) !mpiGetBitValue(a, 0)

Definition at line 55 of file mpi.h.

◆ mpiIsOdd

#define mpiIsOdd ( a ) mpiGetBitValue(a, 0)

Definition at line 56 of file mpi.h.

Enumeration Type Documentation

◆ MpiFormat

enum MpiFormat

MPI import/export format.

Enumerator
MPI_FORMAT_LITTLE_ENDIAN
MPI_FORMAT_BIG_ENDIAN

Definition at line 68 of file mpi.h.

Function Documentation

◆ mpiAdd()

error_t mpiAdd	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Multiple precision addition.

Parameters

[out]	r	Resulting integer R = A + B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 787 of file mpi.c.

◆ mpiAddAbs()

error_t mpiAddAbs	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Helper routine for multiple precision addition.

Parameters

[out]	r	Resulting integer R = \|A + B\|
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 941 of file mpi.c.

◆ mpiAddInt()

error_t mpiAddInt	(	Mpi *	r,
		const Mpi *	a,
		int_t	b
	)

Add an integer to a multiple precision integer.

Parameters

[out]	r	Resulting integer R = A + B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 836 of file mpi.c.

◆ mpiAddMod()

error_t mpiAddMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b,
		const Mpi *	p
	)

Modular addition.

Parameters

[out]	r	Resulting integer R = A + B mod P
[in]	a	The first operand A
[in]	b	The second operand B
[in]	p	The modulus P

Returns: Error code

Definition at line 1509 of file mpi.c.

◆ mpiCheckProbablePrime()

error_t mpiCheckProbablePrime ( const Mpi * a )

Test whether a number is probable prime.

Parameters

[in] a Pointer to a multiple precision integer

Returns: Error code

Definition at line 581 of file pic32cx_bz_crypto_pkc.c.

◆ mpiComp()

int_t mpiComp	(	const Mpi *	a,
		const Mpi *	b
	)

Compare two multiple precision integers.

Parameters

[in]	a	The first multiple precision integer to be compared
[in]	b	The second multiple precision integer to be compared

Returns: Comparison result

Definition at line 338 of file mpi.c.

◆ mpiCompAbs()

int_t mpiCompAbs	(	const Mpi *	a,
		const Mpi *	b
	)

Compare the absolute value of two multiple precision integers.

Parameters

[in]	a	The first multiple precision integer to be compared
[in]	b	The second multiple precision integer to be compared

Returns: Comparison result

Definition at line 409 of file mpi.c.

◆ mpiCompInt()

int_t mpiCompInt	(	const Mpi *	a,
		int_t	b
	)

Compare a multiple precision integer with an integer.

Parameters

[in]	a	Multiple precision integer to be compared
[in]	b	Integer to be compared

Returns: Comparison result

Definition at line 382 of file mpi.c.

◆ mpiCopy()

error_t mpiCopy	(	Mpi *	r,
		const Mpi *	a
	)

Copy a multiple precision integer.

Parameters

[out]	r	Pointer to a multiple precision integer (destination)
[in]	a	Pointer to a multiple precision integer (source)

Returns: Error code

Definition at line 447 of file mpi.c.

◆ mpiDiv()

error_t mpiDiv	(	Mpi *	q,
		Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Multiple precision division.

Parameters

[out]	q	The quotient Q = A / B
[out]	r	The remainder R = A mod B
[in]	a	The dividend A
[in]	b	The divisor B

Returns: Error code

Definition at line 1343 of file mpi.c.

◆ mpiDivInt()

error_t mpiDivInt	(	Mpi *	q,
		Mpi *	r,
		const Mpi *	a,
		int_t	b
	)

Divide a multiple precision integer by an integer.

Parameters

[out]	q	The quotient Q = A / B
[out]	r	The remainder R = A mod B
[in]	a	The dividend A
[in]	b	The divisor B

Returns: Error code

Definition at line 1416 of file mpi.c.

◆ mpiDump()

void mpiDump	(	FILE *	stream,
		const char_t *	prepend,
		const Mpi *	a
	)

Display the contents of a multiple precision integer.

Parameters

[in]	stream	Pointer to a FILE object that identifies an output stream
[in]	prepend	String to prepend to the left of each line
[in]	a	Pointer to a multiple precision integer

Definition at line 2028 of file mpi.c.

◆ mpiExpMod()

error_t mpiExpMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	e,
		const Mpi *	p
	)

Modular exponentiation.

Parameters

[out]	r	Resulting integer R = A ^ E mod P
[in]	a	Pointer to a multiple precision integer
[in]	e	Exponent
[in]	p	Modulus

Returns: Error code

Definition at line 202 of file esp32_crypto_pkc.c.

◆ mpiExpModFast()

error_t mpiExpModFast	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	e,
		const Mpi *	p
	)

Modular exponentiation (fast calculation)

Parameters

[out]	r	Resulting integer R = A ^ E mod P
[in]	a	Pointer to a multiple precision integer
[in]	e	Exponent
[in]	p	Modulus

Returns: Error code

Definition at line 143 of file m460_crypto_pkc.c.

◆ mpiExpModRegular()

error_t mpiExpModRegular	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	e,
		const Mpi *	p
	)

Modular exponentiation (regular calculation)

Parameters

[out]	r	Resulting integer R = A ^ E mod P
[in]	a	Pointer to a multiple precision integer
[in]	e	Exponent
[in]	p	Modulus

Returns: Error code

Definition at line 225 of file m460_crypto_pkc.c.

◆ mpiExport()

error_t mpiExport	(	const Mpi *	a,
		uint8_t *	data,
		uint_t	length,
		MpiFormat	format
	)

Integer to octet string conversion.

Converts an integer to an octet string of a specified length

Parameters

[in]	a	Non-negative integer to be converted
[out]	data	Octet string resulting from the conversion
[in]	length	Intended length of the resulting octet string
[in]	format	Output format

Returns: Error code

Definition at line 709 of file mpi.c.

◆ mpiFree()

void mpiFree ( Mpi * r )

Release a multiple precision integer.

Parameters

[in,out] r Pointer to the multiple precision integer to be freed

Definition at line 64 of file mpi.c.

◆ mpiGetBitLength()

uint_t mpiGetBitLength ( const Mpi * a )

Get the actual length in bits.

Parameters

[in] a Pointer to a multiple precision integer

Returns: The actual bit count

Definition at line 234 of file mpi.c.

◆ mpiGetBitValue()

uint_t mpiGetBitValue	(	const Mpi *	a,
		uint_t	index
	)

Get the bit value at the specified index.

Parameters

[in]	a	Pointer to a multiple precision integer
[in]	index	Position where to read the bit

Returns: The actual bit value

Definition at line 313 of file mpi.c.

◆ mpiGetByteLength()

uint_t mpiGetByteLength ( const Mpi * a )

Get the actual length in bytes.

Parameters

[in] a Pointer to a multiple precision integer

Returns: The actual byte count

Definition at line 195 of file mpi.c.

◆ mpiGetLength()

uint_t mpiGetLength ( const Mpi * a )

Get the actual length in words.

Parameters

[in] a Pointer to a multiple precision integer

Returns: The actual length in words

Definition at line 168 of file mpi.c.

◆ mpiGrow()

error_t mpiGrow	(	Mpi *	r,
		uint_t	size
	)

Adjust the size of multiple precision integer.

Parameters

[in,out]	r	A multiple precision integer whose size is to be increased
[in]	size	Desired size in words

Returns: Error code

Definition at line 94 of file mpi.c.

◆ mpiImport()

error_t mpiImport	(	Mpi *	r,
		const uint8_t *	data,
		uint_t	length,
		MpiFormat	format
	)

Octet string to integer conversion.

Converts an octet string to a non-negative integer

Parameters

[out]	r	Non-negative integer resulting from the conversion
[in]	data	Octet string to be converted
[in]	length	Length of the octet string
[in]	format	Input format

Returns: Error code

Definition at line 624 of file mpi.c.

◆ mpiInit()

void mpiInit ( Mpi * r )

Initialize a multiple precision integer.

Parameters

[in,out] r Pointer to the multiple precision integer to be initialized

Definition at line 48 of file mpi.c.

◆ mpiInvMod()

error_t mpiInvMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	p
	)

Modular inverse.

Parameters

[out]	r	Resulting integer R = A^-1 mod P
[in]	a	The multiple precision integer A
[in]	p	The modulus P

Returns: Error code

Definition at line 356 of file pic32cx_bz_crypto_pkc.c.

◆ mpiMod()

error_t mpiMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	p
	)

Modulo operation.

Parameters

[out]	r	Resulting integer R = A mod P
[in]	a	The multiple precision integer to be reduced
[in]	p	The modulus P

Returns: Error code

Definition at line 1444 of file mpi.c.

◆ mpiMontgomeryMul()

error_t mpiMontgomeryMul	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b,
		uint_t	k,
		const Mpi *	p,
		Mpi *	t
	)

Montgomery multiplication.

Parameters

[out]	r	Resulting integer R = A * B / 2^k mod P
[in]	a	An integer A such as 0 <= A < 2^k
[in]	b	An integer B such as 0 <= B < 2^k
[in]	k	An integer k such as P < 2^k
[in]	p	Modulus P
[in]	t	An preallocated integer T (for internal operation)

Returns: Error code

Definition at line 1877 of file mpi.c.

◆ mpiMontgomeryRed()

error_t mpiMontgomeryRed	(	Mpi *	r,
		const Mpi *	a,
		uint_t	k,
		const Mpi *	p,
		Mpi *	t
	)

Montgomery reduction.

Parameters

[out]	r	Resulting integer R = A / 2^k mod P
[in]	a	An integer A such as 0 <= A < 2^k
[in]	k	An integer k such as P < 2^k
[in]	p	Modulus P
[in]	t	An preallocated integer T (for internal operation)

Returns: Error code

Definition at line 1950 of file mpi.c.

◆ mpiMul()

error_t mpiMul	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Multiple precision multiplication.

Parameters

[out]	r	Resulting integer R = A * B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 75 of file esp32_crypto_pkc.c.

◆ mpiMulAccCore()

void mpiMulAccCore	(	uint_t *	r,
		const uint_t *	a,
		int_t	m,
		const uint_t	b
	)

Multiply-accumulate operation.

Parameters

[out]	r	Resulting integer
[in]	a	First operand A
[in]	m	Size of A in words
[in]	b	Second operand B

Definition at line 1980 of file mpi.c.

◆ mpiMulInt()

error_t mpiMulInt	(	Mpi *	r,
		const Mpi *	a,
		int_t	b
	)

Multiply a multiple precision integer by an integer.

Parameters

[out]	r	Resulting integer R = A * B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 1314 of file mpi.c.

◆ mpiMulMod()

error_t mpiMulMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b,
		const Mpi *	p
	)

Modular multiplication.

Parameters

[out]	r	Resulting integer R = A * B mod P
[in]	a	The first operand A
[in]	b	The second operand B
[in]	p	The modulus P

Returns: Error code

Definition at line 60 of file mimxrt1160_crypto_pkc.c.

◆ mpiRand()

error_t mpiRand	(	Mpi *	r,
		uint_t	length,
		const PrngAlgo *	prngAlgo,
		void *	prngContext
	)

Generate a random value.

Parameters

[out]	r	Pointer to a multiple precision integer
[in]	length	Desired length in bits
[in]	prngAlgo	PRNG algorithm
[in]	prngContext	Pointer to the PRNG context

Returns: Error code

Definition at line 515 of file mpi.c.

◆ mpiRandRange()

error_t mpiRandRange	(	Mpi *	r,
		const Mpi *	p,
		const PrngAlgo *	prngAlgo,
		void *	prngContext
	)

Generate a random value in the range 1 to p-1.

Parameters

[out]	r	Pointer to a multiple precision integer
[in]	p	The upper bound of the range
[in]	prngAlgo	PRNG algorithm
[in]	prngContext	Pointer to the PRNG context

Returns: Error code

Definition at line 564 of file mpi.c.

◆ mpiSetBitValue()

error_t mpiSetBitValue	(	Mpi *	r,
		uint_t	index,
		uint_t	value
	)

Set the bit value at the specified index.

Parameters

[in]	r	Pointer to a multiple precision integer
[in]	index	Position of the bit to be written
[in]	value	Bit value

Returns: Error code

Definition at line 275 of file mpi.c.

◆ mpiSetValue()

error_t mpiSetValue	(	Mpi *	r,
		int_t	a
	)

Set the value of a multiple precision integer.

Parameters

[out]	r	Pointer to a multiple precision integer
[in]	a	Value to be assigned to the multiple precision integer

Returns: Error code

Definition at line 484 of file mpi.c.

◆ mpiShiftLeft()

error_t mpiShiftLeft	(	Mpi *	r,
		uint_t	n
	)

Left shift operation.

Parameters

[in,out]	r	The multiple precision integer to be shifted to the left
[in]	n	The number of bits to shift

Returns: Error code

Definition at line 1111 of file mpi.c.

◆ mpiShiftRight()

error_t mpiShiftRight	(	Mpi *	r,
		uint_t	n
	)

Right shift operation.

Parameters

[in,out]	r	The multiple precision integer to be shifted to the right
[in]	n	The number of bits to shift

Returns: Error code

Definition at line 1178 of file mpi.c.

◆ mpiSub()

error_t mpiSub	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Multiple precision subtraction.

Parameters

[out]	r	Resulting integer R = A - B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 864 of file mpi.c.

◆ mpiSubAbs()

error_t mpiSubAbs	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b
	)

Helper routine for multiple precision subtraction.

Parameters

[out]	r	Resulting integer R = \|A - B\|
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 1021 of file mpi.c.

◆ mpiSubInt()

error_t mpiSubInt	(	Mpi *	r,
		const Mpi *	a,
		int_t	b
	)

Subtract an integer from a multiple precision integer.

Parameters

[out]	r	Resulting integer R = A - B
[in]	a	First operand A
[in]	b	Second operand B

Returns: Error code

Definition at line 913 of file mpi.c.

◆ mpiSubMod()

error_t mpiSubMod	(	Mpi *	r,
		const Mpi *	a,
		const Mpi *	b,
		const Mpi *	p
	)

Modular subtraction.

Parameters

[out]	r	Resulting integer R = A - B mod P
[in]	a	The first operand A
[in]	b	The second operand B
[in]	p	The modulus P

Returns: Error code

Definition at line 1532 of file mpi.c.

Data Structures

Macros

Enumerations

Functions

Detailed Description

License

Macro Definition Documentation

◆ MPI_CHECK

◆ MPI_INT_SIZE

◆ MPI_MAX_BIT_SIZE

◆ MPI_MAX_INT_SIZE

◆ mpiIsEven

◆ mpiIsOdd

Enumeration Type Documentation

◆ MpiFormat

Function Documentation

◆ mpiAdd()

◆ mpiAddAbs()

◆ mpiAddInt()

◆ mpiAddMod()

◆ mpiCheckProbablePrime()

◆ mpiComp()

◆ mpiCompAbs()

◆ mpiCompInt()

◆ mpiCopy()

◆ mpiDiv()

◆ mpiDivInt()

◆ mpiDump()

◆ mpiExpMod()

◆ mpiExpModFast()

◆ mpiExpModRegular()

◆ mpiExport()

◆ mpiFree()

◆ mpiGetBitLength()

◆ mpiGetBitValue()

◆ mpiGetByteLength()

◆ mpiGetLength()

◆ mpiGrow()

◆ mpiImport()

◆ mpiInit()

◆ mpiInvMod()

◆ mpiMod()

◆ mpiMontgomeryMul()

◆ mpiMontgomeryRed()

◆ mpiMul()

◆ mpiMulAccCore()

◆ mpiMulInt()

◆ mpiMulMod()

◆ mpiRand()

◆ mpiRandRange()

◆ mpiSetBitValue()

◆ mpiSetValue()

◆ mpiShiftLeft()

◆ mpiShiftRight()

◆ mpiSub()

◆ mpiSubAbs()

◆ mpiSubInt()

◆ mpiSubMod()