Documentation

MontgomeryMult extends Montgomery

in package

• PHP

PHP Montgomery Modular Exponentiation Engine with interleaved multiplication

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author

Jim Wigginton terrafrost@php.net

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public

Table of Contents

Constants

DATA  = 1

$cache[self::DATA] contains the cached data.

ENGINE_DIR  = 'PHP'

Engine Directory

FAST_BITWISE  = true

Can Bitwise operations be done fast?

KARATSUBA_CUTOFF  = 25

Karatsuba Cutoff

SIGN  = 1

$result[self::SIGN] contains the sign.

VALUE  = 0

$result[self::VALUE] contains the value.

VARIABLE  = 0

Cache constants

Properties

$bitmask  : mixed

Precision Bitmask

$is_negative  : bool

Holds the BigInteger's sign

$precision  : mixed

Precision

$reduce  : callable

Recurring Modulo Function

$value  : mixed

Holds the BigInteger's value

Methods

__construct()  : PHP

Default constructor

__debugInfo()  : mixed

__debugInfo() magic method

__toString()  : string

Converts a BigInteger to a base-10 number.

abs()  : PHP

Absolute value.

bitwise_leftRotate()  : Engine

Logical Left Rotate

bitwise_leftShift()  : PHP

Logical Left Shift

bitwise_not()  : Engine|string

Logical Not

bitwise_rightRotate()  : Engine

Logical Right Rotate

bitwise_rightShift()  : PHP

Logical Right Shift

bitwise_split()  : array<string|int, PHP>

Bitwise Split

createRecurringModuloFunction()  : callable

Create Recurring Modulo Function

getLength()  : int

Return the size of a BigInteger in bits

getLengthInBytes()  : int

Return the size of a BigInteger in bytes

getPrecision()  : int

Get Precision

isNegative()  : bool

Is Negative?

isOdd()  : bool

Is Odd?

isPrime()  : bool

Checks a numer to see if it's prime

isValidEngine()  : bool

Test for engine validity

minMaxBits()  : array<string|int, Engine>

Returns the smallest and largest n-bit number

multiplyReduce()  : array<string|int, mixed>

Montgomery Multiply

negate()  : BigInteger

Negate

random()  : Engine

Generates a random number of a certain size

randomPrime()  : Engine

Generates a random prime number of a certain size

root()  : Engine

Calculates the nth root of a biginteger.

scan1divide()  : int

Scan for 1 and right shift by that amount

serialize()  : string

Serialize

setModExpEngine()  : mixed

Sets engine type.

setPrecision()  : mixed

Set Precision

subtractHelper()  : array<string|int, mixed>

Performs subtraction.

testBit()  : bool

Tests if a bit is set

toBits()  : string

Converts a BigInteger to a bit string (eg. base-2).

toBytes()  : string

Converts a BigInteger to a byte string (eg. base-256).

toHex()  : string

Converts a BigInteger to a hex string (eg. base-16).

toString()  : string

Converts a BigInteger to a base-10 number.

unserialize()  : mixed

Serialize

addHelper()  : array<string|int, mixed>

Performs addition.

array_repeat()  : array<string|int, mixed>

Array Repeat

base256_lshift()  : string

Logical Left Shift

baseSquare()  : array<string|int, mixed>

Performs traditional squaring on two BigIntegers

bitwiseAndHelper()  : Engine

Logical And

bitwiseOrHelper()  : Engine

Logical Or

bitwiseXorHelper()  : Engine

Logical Exclusive Or

compareHelper()  : mixed

convertToObj()  : mixed

extendedGCDHelper()  : Engine

Calculates the greatest common divisor and Bezout's identity.

initialize()  : mixed

Initialize a PHP BigInteger Engine instance

karatsubaSquare()  : array<string|int, mixed>

Performs Karatsuba "squaring" on two BigIntegers

lshift()  : mixed

Logical Left Shift

make_odd()  : mixed

Make the current number odd

maxHelper()  : Engine

Return the minimum BigInteger between an arbitrary number of BigIntegers.

minHelper()  : Engine

Return the minimum BigInteger between an arbitrary number of BigIntegers.

modInverse67108864()  : int

Modular Inverse of a number mod 2**26 (eg. 67108864)

modInverseHelper()  : Engine|false

Calculates modular inverses.

multiplyHelper()  : array<string|int, mixed>

Performs multiplication.

normalize()  : PHP

Normalize

pad()  : string

Pads strings so that unpack may be used on them

powHelper()  : PHP

Performs exponentiation.

powModHelper()  : PHP

Performs modular exponentiation.

powModInner()  : PHP

Performs modular exponentiation.

powModOuter()  : bool|Engine

Performs some pre-processing for powMod

prepareReduce()  : array<string|int, mixed>

Prepare a number for use in Montgomery Modular Reductions

randomRangeHelper()  : Engine

Generate a random number between a range

randomRangePrimeInner()  : bool|Engine

Performs some post-processing for randomRangePrime

randomRangePrimeOuter()  : bool|Engine

Performs some pre-processing for randomRangePrime

reduce()  : array<string|int, mixed>

Montgomery Multiply

regularMultiply()  : array<string|int, mixed>

Performs long multiplication on two BigIntegers

rootHelper()  : Engine

Performs a few preliminary checks on root

rootInner()  : Engine

Calculates the nth root of a biginteger.

rshift()  : mixed

Logical Right Shift

setBitmask()  : Engine

Set Bitmask

setupIsPrime()  : int

Sets the $t parameter for primality testing

slidingWindow()  : Engine

Performs modular exponentiation.

square()  : array<string|int, mixed>

Performs squaring

squareReduce()  : array<string|int, mixed>

Modular square

testPrimality()  : bool

Tests Primality

testSmallPrimes()  : mixed

Test the number against small primes.

toBytesHelper()  : string

Converts a BigInteger to a byte string (eg. base-256).

trim()  : PHP

Trim

bitwise_small_split()  : array<string|int, PHP>

Bitwise Split where $split < static::BASE

divide_digit()  : array<string|int, mixed>

Divides a BigInteger by a regular integer

int2bytes()  : string

Converts 32-bit integers to bytes.

karatsuba()  : array<string|int, mixed>

Performs Karatsuba multiplication on two BigIntegers

safe_divide()  : int

Single digit division