BigInteger

Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256 numbers.

• Full name: \phpseclib\Math\BigInteger

Constants

Constant	Visibility	Type	Value
MONTGOMERY	public		0
BARRETT	public		1
POWEROF2	public		2
CLASSIC	public		3
NONE	public		4
VALUE	public		0
SIGN	public		1
VARIABLE	public		0
DATA	public		1
MODE_INTERNAL	public		1
MODE_BCMATH	public		2
MODE_GMP	public		3
KARATSUBA_CUTOFF	public		25

Properties

base

public static $base

• This property is static.

---

baseFull

public static $baseFull

• This property is static.

---

maxDigit

public static $maxDigit

• This property is static.

---

msb

public static $msb

• This property is static.

---

max10

$max10 in greatest $max10Len satisfying $max10 = 10$max10Len <= 2$base.

public static $max10

• This property is static.

---

max10Len

$max10Len in greatest $max10Len satisfying $max10 = 10$max10Len <= 2$base.

public static $max10Len

• This property is static.

---

maxDigit2

public static $maxDigit2

• This property is static.

---

value

Holds the BigInteger's value.

public array $value

---

is_negative

Holds the BigInteger's magnitude.

public bool $is_negative

---

precision

Precision

public $precision

See Also:

• \phpseclib\Math\self::setPrecision() -

---

bitmask

Precision Bitmask

public $bitmask

See Also:

• \phpseclib\Math\self::setPrecision() -

---

hex

Mode independent value used for serialization.

public string $hex

If the bcmath or gmp extensions are installed $this->value will be a non-serializable resource, hence the need for a variable that'll be serializable regardless of whether or not extensions are being used. Unlike $this->value, however, $this->hex is only calculated when $this->__sleep() is called.

See Also:

• \phpseclib\Math\self::__sleep() - * \phpseclib\Math\self::__wakeup() -

---

Methods

__construct

Converts base-2, base-10, base-16, and binary strings (base-256) to BigIntegers.

public __construct(int|string|resource $x, int $base = 10): \phpseclib\Math\BigInteger

If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using two's compliment. The sole exception to this is -10, which is treated the same as 10 is.

Here's an example:

toString(); // outputs 50 ?>

Parameters:

Parameter	Type	Description
$x	int|string|resource	base-10 number or base-$base number if $base set.
$base	int

---

getLength

Return the size of a BigInteger in bits

public getLength(): int

---

getLengthInBytes

Return the size of a BigInteger in bytes

public getLengthInBytes(): int

---

copy

Copy an object

public copy(): \phpseclib\Math\BigInteger

PHP5 passes objects by reference while PHP4 passes by value. As such, we need a function to guarantee that all objects are passed by value, when appropriate. More information can be found here:

{@link http://php.net/language.oop5.basic#51624}

See Also:

• \phpseclib\Math\self::__clone() -

---

__clone

__clone() magic method

public __clone(): \phpseclib\Math\BigInteger

Although you can call BigInteger::__toString() directly in PHP5, you cannot call BigInteger::__clone() directly in PHP5. You can in PHP4 since it's not a magic method, but in PHP5, you have to call it by using the PHP5 only syntax of $y = clone $x. As such, if you're trying to write an application that works on both PHP4 and PHP5, call BigInteger::copy(), instead.

See Also:

• \phpseclib\Math\self::copy() -

---

__sleep

__sleep() magic method

public __sleep(): mixed

Will be called, automatically, when serialize() is called on a BigInteger object.

See Also:

• \phpseclib\Math\self::__wakeup() -

---

__wakeup

__wakeup() magic method

public __wakeup(): mixed

Will be called, automatically, when unserialize() is called on a BigInteger object.

See Also:

• \phpseclib\Math\self::__sleep() -

---

__debugInfo

__debugInfo() magic method

public __debugInfo(): mixed

Will be called, automatically, when print_r() or var_dump() are called

---

_add

Performs addition.

public _add(array $x_value, bool $x_negative, array $y_value, bool $y_negative): array

Parameters:

Parameter	Type	Description
$x_value	array
$x_negative	bool
$y_value	array
$y_negative	bool

---

_subtract

Performs subtraction.

public _subtract(array $x_value, bool $x_negative, array $y_value, bool $y_negative): array

Parameters:

Parameter	Type	Description
$x_value	array
$x_negative	bool
$y_value	array
$y_negative	bool

---

multiply

Multiplies two BigIntegers

public multiply(\phpseclib\Math\BigInteger $x): \phpseclib\Math\BigInteger

Here's an example:

multiply($b); echo $c->toString(); // outputs 200 ?>

Parameters:

Parameter	Type	Description
$x	\phpseclib\Math\BigInteger

---

_multiply

Performs multiplication.

public _multiply(array $x_value, bool $x_negative, array $y_value, bool $y_negative): array

Parameters:

Parameter	Type	Description
$x_value	array
$x_negative	bool
$y_value	array
$y_negative	bool

---

_regularMultiply

Performs long multiplication on two BigIntegers

public _regularMultiply(array $x_value, array $y_value): array

Modeled after 'multiply' in MutableBigInteger.java.

Parameters:

Parameter	Type	Description
$x_value	array
$y_value	array

---

_karatsuba

Performs Karatsuba multiplication on two BigIntegers

public _karatsuba(array $x_value, array $y_value): array

See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm} and {@link http://math.libtomcrypt.com/files/tommath.pdf#page=120}.

Parameters:

Parameter	Type	Description
$x_value	array
$y_value	array

---

_square

Performs squaring

public _square(array $x = false): array

Parameters:

Parameter	Type	Description
$x	array

---

_baseSquare

Performs traditional squaring on two BigIntegers

public _baseSquare(array $value): array

Squaring can be done faster than multiplying a number by itself can be. See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=7} / {@link http://math.libtomcrypt.com/files/tommath.pdf#page=141} for more information.

Parameters:

Parameter	Type	Description
$value	array

---

_karatsubaSquare

Performs Karatsuba "squaring" on two BigIntegers

public _karatsubaSquare(array $value): array

See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm} and {@link http://math.libtomcrypt.com/files/tommath.pdf#page=151}.

Parameters:

Parameter	Type	Description
$value	array

---

_divide_digit

Divides a BigInteger by a regular integer

public _divide_digit(array $dividend, array $divisor): array

abc / x = a00 / x + b0 / x + c / x

Parameters:

Parameter	Type	Description
$dividend	array
$divisor	array

---

powMod

Performs modular exponentiation.

public powMod(\phpseclib\Math\BigInteger $e, \phpseclib\Math\BigInteger $n): \phpseclib\Math\BigInteger

Alias for modPow().

Parameters:

Parameter	Type	Description
$e	\phpseclib\Math\BigInteger
$n	\phpseclib\Math\BigInteger

---

_slidingWindow

Sliding Window k-ary Modular Exponentiation

public _slidingWindow(\phpseclib\Math\BigInteger $e, \phpseclib\Math\BigInteger $n, int $mode): \phpseclib\Math\BigInteger

Based on {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=27} / {@link http://math.libtomcrypt.com/files/tommath.pdf#page=210}. In a departure from those algorithims, however, this function performs a modular reduction after every multiplication and squaring operation. As such, this function has the same preconditions that the reductions being used do.

Parameters:

Parameter	Type	Description
$e	\phpseclib\Math\BigInteger
$n	\phpseclib\Math\BigInteger
$mode	int

---

_reduce

Modular reduction

public _reduce(array $x, array $n, int $mode): array

For most $modes this will return the remainder.

Parameters:

Parameter	Type	Description
$x	array
$n	array
$mode	int

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_prepareReduce

Modular reduction preperation

public _prepareReduce(array $x, array $n, int $mode): array

Parameters:

Parameter	Type	Description
$x	array
$n	array
$mode	int

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_multiplyReduce

Modular multiply

public _multiplyReduce(array $x, array $y, array $n, int $mode): array

Parameters:

Parameter	Type	Description
$x	array
$y	array
$n	array
$mode	int

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_squareReduce

Modular square

public _squareReduce(array $x, array $n, int $mode): array

Parameters:

Parameter	Type	Description
$x	array
$n	array
$mode	int

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_mod2

Modulos for Powers of Two

public _mod2(\phpseclib\Math\BigInteger $n): \phpseclib\Math\BigInteger

Calculates $x%$n, where $n = 2**$e, for some $e. Since this is basically the same as doing $x & ($n-1), we'll just use this function as a wrapper for doing that.

Parameters:

Parameter	Type	Description
$n	\phpseclib\Math\BigInteger

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_barrett

Barrett Modular Reduction

public _barrett(array $n, array $m): array

See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=14} / {@link http://math.libtomcrypt.com/files/tommath.pdf#page=165} for more information. Modified slightly, so as not to require negative numbers (initially, this script didn't support negative numbers).

Employs "folding", as described at {@link http://www.cosic.esat.kuleuven.be/publications/thesis-149.pdf#page=66}. To quote from it, "the idea [behind folding] is to find a value x' such that x (mod m) = x' (mod m), with x' being smaller than x."

Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that usable on account of (1) its not using reasonable radix points as discussed in {@link http://math.libtomcrypt.com/files/tommath.pdf#page=162} and (2) the fact that, even with reasonable radix points, it only works when there are an even number of digits in the denominator. The reason for (2) is that (x >> 1) + (x >> 1) != x / 2 + x / 2. If x is even, they're the same, but if x is odd, they're not. See the in-line comments for details.

Parameters:

Parameter	Type	Description
$n	array
$m	array

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_regularBarrett

(Regular) Barrett Modular Reduction

public _regularBarrett(array $x, array $n): array

For numbers with more than four digits BigInteger::_barrett() is faster. The difference between that and this is that this function does not fold the denominator into a smaller form.

Parameters:

Parameter	Type	Description
$x	array
$n	array

See Also:

• \phpseclib\Math\self::_slidingWindow() -

---

_multiplyLower

Performs long multiplication up to $stop digits

public _multiplyLower(array $x_value, bool $x_negative, array $y_value, bool $y_negative, int $stop): array

If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved.

Parameters:

Parameter	Type	Description
$x_value	array
$x_negative	bool
$y_value	array
$y_negative	bool
$stop	int

See Also:

• \phpseclib\Math\self::_regularBarrett() -

---

_montgomery

Montgomery Modular Reduction

public _montgomery(array $x, array $n): array

($x->_prepMontgomery($n))->_montgomery($n) yields $x % $n. {@link http://math.libtomcrypt.com/files/tommath.pdf#page=170} provides insights on how this can be improved upon (basically, by using the comba method). gcd($n, 2) must be equal to one for this function to work correctly.

Parameters:

Parameter	Type	Description
$x	array
$n	array

See Also:

• \phpseclib\Math\self::_prepMontgomery() - * \phpseclib\Math\self::_slidingWindow() -

---

_montgomeryMultiply

Montgomery Multiply

public _montgomeryMultiply(array $x, array $y, array $m): array

Interleaves the montgomery reduction and long multiplication algorithms together as described in {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13}

Parameters:

Parameter	Type	Description
$x	array
$y	array
$m	array

See Also:

• \phpseclib\Math\self::_prepMontgomery() - * \phpseclib\Math\self::_montgomery() -

---

_prepMontgomery

Prepare a number for use in Montgomery Modular Reductions

public _prepMontgomery(array $x, array $n): array

Parameters:

Parameter	Type	Description
$x	array
$n	array

See Also:

• \phpseclib\Math\self::_montgomery() - * \phpseclib\Math\self::_slidingWindow() -

---

_modInverse67108864

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

public _modInverse67108864(array $x): int

Based off of the bnpInvDigit function implemented and justified in the following URL:

{@link http://www-cs-students.stanford.edu/~tjw/jsbn/jsbn.js}

The following URL provides more info:

{@link http://groups.google.com/group/sci.crypt/msg/7a137205c1be7d85}

As for why we do all the bitmasking... strange things can happen when converting from floats to ints. For instance, on some computers, var_dump((int) -4294967297) yields int(-1) and on others, it yields int(-2147483648). To avoid problems stemming from this, we use bitmasks to guarantee that ints aren't auto-converted to floats. The outermost bitmask is present because without it, there's no guarantee that the "residue" returned would be the so-called "common residue". We use fmod, in the last step, because the maximum possible $x is 26 bits and the maximum $result is 16 bits. Thus, we have to be able to handle up to 40 bits, which only 64-bit floating points will support.

Thanks to Pedro Gimeno Fortea for input!

Parameters:

Parameter	Type	Description
$x	array

See Also:

• \phpseclib\Math\self::_montgomery() -

---

gcd

Calculates the greatest common divisor

public gcd(\phpseclib\Math\BigInteger $n): \phpseclib\Math\BigInteger

Say you have 693 and 609. The GCD is 21.

Here's an example:

extendedGCD($b); echo $gcd->toString() . "\r\n"; // outputs 21 ?>

Parameters:

Parameter	Type	Description
$n	\phpseclib\Math\BigInteger

---

abs

Absolute value.

public abs(): \phpseclib\Math\BigInteger

---

_compare

Compares two numbers.

public _compare(array $x_value, bool $x_negative, array $y_value, bool $y_negative): int

Parameters:

Parameter	Type	Description
$x_value	array
$x_negative	bool
$y_value	array
$y_negative	bool

See Also:

• \phpseclib\Math\self::compare() -

---

equals

Tests the equality of two numbers.

public equals(\phpseclib\Math\BigInteger $x): bool

If you need to see if one number is greater than or less than another number, use BigInteger::compare()

Parameters:

Parameter	Type	Description
$x	\phpseclib\Math\BigInteger

See Also:

• \phpseclib\Math\self::compare() -

---

setPrecision

Set Precision

public setPrecision(int $bits): mixed

Some bitwise operations give different results depending on the precision being used. Examples include left shift, not, and rotates.

Parameters:

Parameter	Type	Description
$bits	int

---

bitwise_leftRotate

Logical Left Rotate

public bitwise_leftRotate(int $shift): \phpseclib\Math\BigInteger

Instead of the top x bits being dropped they're appended to the shifted bit string.

Parameters:

Parameter	Type	Description
$shift	int

---

bitwise_rightRotate

Logical Right Rotate

public bitwise_rightRotate(int $shift): \phpseclib\Math\BigInteger

Instead of the bottom x bits being dropped they're prepended to the shifted bit string.

Parameters:

Parameter	Type	Description
$shift	int

---

_random_number_helper

Generates a random BigInteger

public _random_number_helper(int $size): \phpseclib\Math\BigInteger

Byte length is equal to $length. Uses \phpseclib\Crypt\Random if it's loaded and mt_rand if it's not.

Parameters:

Parameter	Type	Description
$size	int

---

_make_odd

Make the current number odd

public _make_odd(): mixed

If the current number is odd it'll be unchanged. If it's even, one will be added to it.

See Also:

• \phpseclib\Math\self::randomPrime() -

---

_lshift

Logical Left Shift

public _lshift(int $shift): mixed

Shifts BigInteger's by $shift bits.

Parameters:

Parameter	Type	Description
$shift	int

---

_rshift

Logical Right Shift

public _rshift(int $shift): mixed

Shifts BigInteger's by $shift bits.

Parameters:

Parameter	Type	Description
$shift	int

---

_normalize

Normalize

public _normalize(\phpseclib\Math\BigInteger $result): \phpseclib\Math\BigInteger

Removes leading zeros and truncates (if necessary) to maintain the appropriate precision

Parameters:

Parameter	Type	Description
$result	\phpseclib\Math\BigInteger

See Also:

• \phpseclib\Math\self::_trim() -

---

_trim

Trim

public _trim(array $value): \phpseclib\Math\BigInteger

Removes leading zeros

Parameters:

Parameter	Type	Description
$value	array

---

_array_repeat

Array Repeat

public _array_repeat(array $input, mixed $multiplier): array

Parameters:

Parameter	Type	Description
$input	array
$multiplier	mixed

---

_base256_lshift

Logical Left Shift

public _base256_lshift(string& $x, int $shift): string

Shifts binary strings $shift bits, essentially multiplying by 2**$shift.

Parameters:

Parameter	Type	Description
$x	string	(by reference)
$shift	int

---

_base256_rshift

Logical Right Shift

public _base256_rshift(string& $x, int $shift): string

Shifts binary strings $shift bits, essentially dividing by 2**$shift and returning the remainder.

Parameters:

Parameter	Type	Description
$x	string	(by referenc)
$shift	int

---

_int2bytes

Converts 32-bit integers to bytes.

public _int2bytes(int $x): string

Parameters:

Parameter	Type	Description
$x	int

---

_bytes2int

Converts bytes to 32-bit integers

public _bytes2int(string $x): int

Parameters:

Parameter	Type	Description
$x	string

---

_encodeASN1Length

DER-encode an integer

public _encodeASN1Length(int $length): string

The ability to DER-encode integers is needed to create RSA public keys for use with OpenSSL

Parameters:

Parameter	Type	Description
$length	int

See Also:

• \phpseclib\Math\self::modPow() -

---

_safe_divide

Single digit division

public _safe_divide(int $x, int $y): int

Even if int64 is being used the division operator will return a float64 value if the dividend is not evenly divisible by the divisor. Since a float64 doesn't have the precision of int64 this is a problem so, when int64 is being used, we'll guarantee that the dividend is divisible by first subtracting the remainder.

Parameters:

Parameter	Type	Description
$x	int
$y	int

---

---

Automatically generated on 2025-03-18