Modular Multiplication Calculator

Understanding Modular Multiplication

Modular multiplication is a type of multiplication performed under modular arithmetic. The result is always reduced to fit within a specific range determined by the modulus m.

When we calculate (a × b) mod m, we find the remainder when the product of a and b is divided by m. This congruence is represented as:

(a * b) ≡ r (mod m)

Here, r is the remainder, satisfying 0 ≤ r < m.

Key Applications & Properties

Cryptography: Essential for algorithms like RSA, Diffie-Hellman, and Elliptic Curve Cryptography.
Number Theory: Used in finding modular inverses and solving systems of congruences.
Associative & Commutative: Like standard multiplication, modular multiplication is associative and commutative.
Distributive: Multiplication is distributive over addition under modulo operations.