Modular Arithmetic & Modulo Inverse Calculator

Calculate modular arithmetic, modular exponentiation (a^b mod m), and Extended Euclidean modular multiplicative inverse.

Modular Arithmetic & Modulo Inverse Calculator

Calculate modular arithmetic, modular exponentiation (a^b mod m), and Extended Euclidean modular multiplicative inverse.

Integer a:

Modulus m:

Computed Result:

About This Tool

The Modular Arithmetic & Modulo Inverse Calculator performs modular congruence operations, modular exponentiation (b^e mod m) using fast binary squaring, and computes the Extended Euclidean modular multiplicative inverse.

Key Features

Calculates Modular Multiplicative Inverse (a⁻¹ mod m)

Computes Fast Modular Exponentiation (b^e mod m) for cryptography

Performs Basic Modulo Arithmetic (Addition, Subtraction, Multiplication mod m)

Arbitrary precision BigInt calculation support

How to Use This Tool

Enter Base Integer (a).
Enter Modulus (m).
Select operation (Modular Inverse, Modular Exponentiation, Modulo).
View the computed integer result.

Why Use This Tool

Compute RSA cryptographic private keys and Diffie-Hellman shared secrets.
Solve competitive programming number theory and congruence equations.

Pro Tips

A modular inverse a⁻¹ mod m exists if and only if a and m are coprime (gcd(a, m) = 1).

Frequently Asked Questions

What is a modular multiplicative inverse?

The modular inverse of an integer 'a' modulo 'm' is an integer 'x' such that (a × x) ≡ 1 (mod m). It is the modular equivalent of division.

When does a modular inverse exist?

A modular inverse exists if and only if 'a' and 'm' are coprime (their Greatest Common Divisor gcd(a, m) equals 1).

Modular Arithmetic & Modulo Inverse Calculator