GMP Modular Exponentiation Engine
author | Jim Wigginton terrafrost@php.net |
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package | Default |
__construct(integer|\phpseclib3\Math\BigInteger\Engines\numeric-string $x,integer $base = 10)
integer|\phpseclib3\Math\BigInteger\Engines\numeric-string
integer Base-10 number or base-$base number if $base set.
integer
__debugInfo(): array
Will be called, automatically, when print_r() or var_dump() are called
array
__sleep(): array
Will be called, automatically, when serialize() is called on a BigInteger object.
array
__toString(): string
string
__wakeup(): void
Will be called, automatically, when unserialize() is called on a BigInteger object.
abs(): \phpseclib3\Math\BigInteger\Engines\GMP
add(\phpseclib3\Math\BigInteger\Engines\GMP $y): \phpseclib3\Math\BigInteger\Engines\GMP
base256_lshift(string &$x,integer $shift): void
Shifts binary strings $shift bits, essentially multiplying by 2**$shift.
string
integer
between(\phpseclib3\Math\BigInteger\Engines\GMP $min,\phpseclib3\Math\BigInteger\Engines\GMP $max): boolean
boolean
bitwise_and(\phpseclib3\Math\BigInteger\Engines\GMP $x): \phpseclib3\Math\BigInteger\Engines\GMP
bitwise_leftRotate(integer $shift): \phpseclib3\Math\BigInteger\Engines\Engine
Instead of the top x bits being dropped they're appended to the shifted bit string.
integer
\phpseclib3\Math\BigInteger\Engines\Engine
bitwise_leftShift(integer $shift): \phpseclib3\Math\BigInteger\Engines\GMP
Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.
integer
\phpseclib3\Math\BigInteger\Engines\GMP
bitwise_not(): \phpseclib3\Math\BigInteger\Engines\Engine|string
bitwise_or(\phpseclib3\Math\BigInteger\Engines\GMP $x): \phpseclib3\Math\BigInteger\Engines\GMP
bitwise_rightRotate(integer $shift): \phpseclib3\Math\BigInteger\Engines\Engine
Instead of the bottom x bits being dropped they're prepended to the shifted bit string.
integer
\phpseclib3\Math\BigInteger\Engines\Engine
bitwise_rightShift(integer $shift): \phpseclib3\Math\BigInteger\Engines\GMP
Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.
integer
\phpseclib3\Math\BigInteger\Engines\GMP
bitwise_split(integer $split): array<mixed,\phpseclib3\Math\BigInteger\Engines\Engine>
Splits BigInteger's into chunks of $split bits
integer
array<mixed,\phpseclib3\Math\BigInteger\Engines\Engine>
bitwise_xor(\phpseclib3\Math\BigInteger\Engines\GMP $x): \phpseclib3\Math\BigInteger\Engines\GMP
bitwiseAndHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
bitwiseOrHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
bitwiseXorHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
compare(\phpseclib3\Math\BigInteger\Engines\GMP $y): integer
Although one might think !$x->compare($y) means $x != $y, it, in fact, means the opposite. The reason for this is demonstrated thusly:
$x > $y: $x->compare($y) > 0 $x < $y: $x->compare($y) < 0 $x == $y: $x->compare($y) == 0
Note how the same comparison operator is used. If you want to test for equality, use $x->equals($y).
{@internal Could return $this->subtract($x), but that's not as fast as what we do do.}
see | \phpseclib3\Math\BigInteger\Engines\GMP::equals() |
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integer
in case < 0 if $this is less than $y; > 0 if $this is greater than $y, and 0 if they are equal.
createRecurringModuloFunction(): callable
Sometimes it may be desirable to do repeated modulos with the same number outside of modular exponentiation
callable
divide(\phpseclib3\Math\BigInteger\Engines\GMP $y): \phpseclib3\Math\BigInteger\Engines\array{GMP,
Returns an array whose first element contains the quotient and whose second element contains the "common residue". If the remainder would be positive, the "common residue" and the remainder are the same. If the remainder would be negative, the "common residue" is equal to the sum of the remainder and the divisor (basically, the "common residue" is the first positive modulo).
\phpseclib3\Math\BigInteger\Engines\array{GMP,
GMP}
equals(\phpseclib3\Math\BigInteger\Engines\GMP $x): boolean
If you need to see if one number is greater than or less than another number, use BigInteger::compare()
boolean
extendedGCD(\phpseclib3\Math\BigInteger\Engines\GMP $n): array<mixed,\phpseclib3\Math\BigInteger\Engines\GMP>
Say you have 693 and 609. The GCD is 21. Bezout's identity states that there exist integers x and y such that 693x + 609y == 21. In point of fact, there are actually an infinite number of x and y combinations and which combination is returned is dependent upon which mode is in use. See Bezout's identity - Wikipedia for more information.
array<mixed,\phpseclib3\Math\BigInteger\Engines\GMP>
extendedGCDHelper(\phpseclib3\Math\BigInteger\Engines\Engine $n): \phpseclib3\Math\BigInteger\Engines\array{gcd:
\phpseclib3\Math\BigInteger\Engines\array{gcd:
Engine, x: Engine, y: Engine}
gcd(\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
getLength(): integer
integer
getLengthInBytes(): integer
integer
getPrecision(): integer
Returns the precision if it exists, -1 if it doesn't
integer
initialize(integer $base)
see | \phpseclib3\Math\BigInteger\Engines\parent::__construct() |
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integer
isNegative(): boolean
boolean
isOdd(): boolean
boolean
isPrime(integer|boolean $t = false): boolean
Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the $t parameter is distributability. BigInteger::randomPrime() can be distributed across multiple pageloads on a website instead of just one.
integer|boolean
boolean
isValidEngine(): boolean
see | \phpseclib3\Math\BigInteger\Engines\parent::__construct() |
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boolean
jsonSerialize()
make_odd()
If the current number is odd it'll be unchanged. If it's even, one will be added to it.
see | self::randomPrime() |
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max(\phpseclib3\Math\BigInteger\Engines\GMP $nums): \phpseclib3\Math\BigInteger\Engines\GMP
maxHelper(array $nums): \phpseclib3\Math\BigInteger\Engines\Engine
min(\phpseclib3\Math\BigInteger\Engines\GMP $nums): \phpseclib3\Math\BigInteger\Engines\GMP
minHelper(array $nums): \phpseclib3\Math\BigInteger\Engines\Engine
minMaxBits(integer $bits): \phpseclib3\Math\BigInteger\Engines\array{min:
integer
\phpseclib3\Math\BigInteger\Engines\array{min:
static, max: static}
modInverse(\phpseclib3\Math\BigInteger\Engines\GMP $n): false|\phpseclib3\Math\BigInteger\Engines\GMP
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
false|\phpseclib3\Math\BigInteger\Engines\GMP
modInverseHelper(\phpseclib3\Math\BigInteger\Engines\Engine $n): static|false
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
{@internal See HAC 14.64 for more information.}
static|false
modPow(\phpseclib3\Math\BigInteger\Engines\GMP $e,\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
multiply(\phpseclib3\Math\BigInteger\Engines\GMP $x): \phpseclib3\Math\BigInteger\Engines\GMP
negate(): \phpseclib3\Math\BigInteger\Engines\GMP
normalize(\phpseclib3\Math\BigInteger\Engines\GMP $result): \phpseclib3\Math\BigInteger\Engines\GMP
Removes leading zeros and truncates (if necessary) to maintain the appropriate precision
\phpseclib3\Math\BigInteger\Engines\GMP
pow(\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
powMod(\phpseclib3\Math\BigInteger\Engines\GMP $e,\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
powModHelper(\phpseclib3\Math\BigInteger\Engines\GMP $x,\phpseclib3\Math\BigInteger\Engines\GMP $e,\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
powModInner(\phpseclib3\Math\BigInteger\Engines\GMP $e,\phpseclib3\Math\BigInteger\Engines\GMP $n): \phpseclib3\Math\BigInteger\Engines\GMP
powModOuter(\phpseclib3\Math\BigInteger\Engines\Engine $e,\phpseclib3\Math\BigInteger\Engines\Engine $n): static|false
static|false
random(integer $size): \phpseclib3\Math\BigInteger\Engines\Engine
Bit length is equal to $size
integer
\phpseclib3\Math\BigInteger\Engines\Engine
randomPrime(integer $size): \phpseclib3\Math\BigInteger\Engines\Engine
Bit length is equal to $size
integer
\phpseclib3\Math\BigInteger\Engines\Engine
randomRange(\phpseclib3\Math\BigInteger\Engines\GMP $min,\phpseclib3\Math\BigInteger\Engines\GMP $max): \phpseclib3\Math\BigInteger\Engines\GMP
Returns a random number between $min and $max where $min and $max can be defined using one of the two methods:
BigInteger::randomRange($min, $max) BigInteger::randomRange($max, $min)
\phpseclib3\Math\BigInteger\Engines\GMP
randomRangeHelper(\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): \phpseclib3\Math\BigInteger\Engines\Engine
Returns a random number between $min and $max where $min and $max can be defined using one of the two methods:
BigInteger::randomRange($min, $max) BigInteger::randomRange($max, $min)
\phpseclib3\Math\BigInteger\Engines\Engine
randomRangePrime(\phpseclib3\Math\BigInteger\Engines\GMP $min,\phpseclib3\Math\BigInteger\Engines\GMP $max): false|\phpseclib3\Math\BigInteger\Engines\GMP
If there's not a prime within the given range, false will be returned.
false|\phpseclib3\Math\BigInteger\Engines\GMP
randomRangePrimeInner(\phpseclib3\Math\BigInteger\Engines\Engine $x,\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): static|false
static|false
randomRangePrimeOuter(\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): static|false
static|false
root(integer $n = 2): \phpseclib3\Math\BigInteger\Engines\Engine
rootHelper(integer $n): \phpseclib3\Math\BigInteger\Engines\Engine
rootInner(integer $n): \phpseclib3\Math\BigInteger\Engines\Engine
Returns the nth root of a positive biginteger, where n defaults to 2
{@internal This function is based off of this page and this stackoverflow question.}
integer
\phpseclib3\Math\BigInteger\Engines\Engine
scan1divide(\phpseclib3\Math\BigInteger\Engines\GMP $r): integer
ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
integer
setBitmask(integer $bits): static
see | \phpseclib3\Math\BigInteger\Engines\Engine::setPrecision() |
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integer
static
setModExpEngine(\phpseclib3\Math\BigInteger\Engines\class-string<Engine> $engine)
Throws an exception if the type is invalid
\phpseclib3\Math\BigInteger\Engines\class-string
setPrecision(integer $bits)
Some bitwise operations give different results depending on the precision being used. Examples include left shift, not, and rotates.
integer
setupIsPrime(): integer
integer
slidingWindow(\phpseclib3\Math\BigInteger\Engines\Engine $x,\phpseclib3\Math\BigInteger\Engines\Engine $e,\phpseclib3\Math\BigInteger\Engines\Engine $n,\phpseclib3\Math\BigInteger\Engines\class-string<T> $class): \phpseclib3\Math\BigInteger\Engines\T
Based on HAC 14.85 / MPM 7.7. 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.
template | T of Engine |
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\phpseclib3\Math\BigInteger\Engines\class-string
\phpseclib3\Math\BigInteger\Engines\T
subtract(\phpseclib3\Math\BigInteger\Engines\GMP $y): \phpseclib3\Math\BigInteger\Engines\GMP
testBit( $x): boolean
boolean
testPrimality(integer $t): boolean
Uses the Miller-Rabin primality test. See HAC 4.24 for more info.
integer
boolean
toBits(boolean $twos_compliment = false): string
Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment.
boolean
string
toBytes(boolean $twos_compliment = false): string
boolean
string
toBytesHelper(): string
Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment.
string
toHex(boolean $twos_compliment = false): string
boolean
string
toString(): string
string
FAST_BITWISE
see | |
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ENGINE_DIR
see | |
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PRIMES
zero :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | static> |
---|
\phpseclib3\Math\BigInteger\Engines\array,
one :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | static> |
---|
\phpseclib3\Math\BigInteger\Engines\array,
two :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | static> |
---|
\phpseclib3\Math\BigInteger\Engines\array,
modexpEngine :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | class-string |
---|
\phpseclib3\Math\BigInteger\Engines\array,
isValidEngine :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | bool> |
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\phpseclib3\Math\BigInteger\Engines\array,
value :\GMP|string|array|integer
var |
---|
\GMP|string|array|integer
is_negative :boolean
var |
---|
boolean
precision :integer
see | |
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var |
integer
bitmask :static|false
see | |
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var |
static|false
reduce :callable
var |
---|
callable
hex :string
see | |
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var |
string