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Modular Exponentiation

Tool to compute modular exponentiation. Modular Exponentiation (or power modulo) is the result of the calculus a^b mod n. It is often used in informatics and cryptography.

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Modular Exponentiation -

Tag(s) : Mathematics,Arithmetics

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# Modular Exponentiation

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## Modular Exponentiation Calculus a^b mod n

Tool to compute modular exponentiation. Modular Exponentiation (or power modulo) is the result of the calculus a^b mod n. It is often used in informatics and cryptography.

### How to calculate a raised to power b modulo n?

It consists in an exponentiation followed by a modulus, but optimized with big numbers to return a fast result without having to actually perform the calculation (thanks to mathematical simplifications).

$$12^{34} \equiv 16 \mod 56$$

One talks about power to indicate the name of the operation, and exponent to indicate the operand.

### Why modular exponentiation is limited to integers?

Calculus uses exponent and modulos that are generally defined over the natural number domain set N. It is possible to use rational numbers but it is not handled here.