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 optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale function, or fallback to 0 if this has not been set.

Returns the result as a string, or false if modulus is 0 or exponent is negative.

Version	Description
8.0.0	`scale` is now nullable.

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