PHP Manual: Raise an arbitrary precision number to another, reduced by a specified modulus

string bcpowmod(
    string $num,
    string $exponent,
    string $modulus,
    intnull $scale = null
)

Use the fast-exponentiation method to raise num to the power exponent with respect to the modulus modulus.

num: The base, as an integral string (i.e. the scale has to be zero).
exponent: The exponent, as an non-negative, integral string (i.e. the scale has to be zero).
modulus: The modulus, as an integral string (i.e. the scale has to be zero).
scale: This parameter is used to set the number of digits after the decimal place in the result. If null, it will default to the default scale set with bcscale, or fallback to the value of the bcmath.scale INI directive.

Returns the result as a string.

This function throws a ValueError in the following cases:

This function throws a DivisionByZeroError exception if modulus is 0.

Version	Description
8.0.0	`scale` is now nullable.
8.0.0	Now throws a ValueError instead of returning `false` if `exponent` is a negative value.
8.0.0	Dividing by `0` now throws a DivisionByZeroError exception instead of returning `false`.

The following two statements are functionally identical. The bcpowmod version however, executes in less time and can accept larger parameters.

<?php
$a = bcpowmod($x, $y, $mod);

$b = bcmod(bcpow($x, $y), $mod);

// $a and $b are equal to each other.

?>

Note:
Because this method uses the modulus operation, numbers which are not positive integers may give unexpected results.

bcpowmod