Math

Modular Exponentiation Calculator

Compute base^exponent mod modulus with BigInt square-and-multiply. Useful for understanding RSA-style operations (educational).

Runs entirely in your browser; input is not sent to our servers.

Messages, keys, passwords, plaintext, ciphertext, and files are never stored in localStorage, history, or analytics payloads.

Educational

Base (a)

Integer base; up to 256 digits.

Exponent (e)

Non-negative integer exponent; up to 256 digits.

Modulus (m)

Non-zero modulus; up to 256 digits.

a^e mod m

How it works

Modular exponentiation evaluates large powers without building the full integer, using repeated squaring modulo m. Runs in your browser with BigInt; operands are limited to 256 decimal digits each.

Enter base a, exponent e, and modulus m (non-zero). Related tools: Extended GCD / Modular Inverse and Toy RSA Demonstrator.

\[ a^{e} \bmod m \]
Square-and-multiply scans the bits of the exponent: it repeatedly squares the running base modulo m and multiplies into the result when a bit is set. That keeps the work proportional to the bit length of e instead of building the full integer a^e.

Reference →

Sources

https://en.wikipedia.org/wiki/Modular_exponentiation

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Modular Exponentiation Calculator

Sources

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