In Programming Languages
Because modular exponentiation is an important operation in computer science, and there are efficient algorithms (see above) that are much faster than simply exponentiating and then taking the remainder, many programming languages and arbitrary-precision integer libraries have a dedicated function to perform modular exponentiation:
- Python's built-in pow (exponentiation) function takes an optional third argument which is the number to modulo by
- Java's java.math.BigInteger class has a
modPowmethod to perform modular exponentiation - Perl's Math::BigInt module has a bmodpow method to perform modular exponentiation
- Go's big.Int type contains an Exp (exponentiation) method whose third parameter, if non-nil, is the number to modulo by
- PHP's BC Math library has a bcpowmod function to perform modular exponentiation
- The GNU Multiple Precision Arithmetic Library (GMP) library contains a mpz_powm function to perform modular exponentiation
- Custom Function @PowerMod for FileMaker Pro (with 1024-bit RSA encryption example)
Read more about this topic: Modular Exponentiation
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