Multiplicative Inverse Modulo Calculator
This calculator finds the modular multiplicative inverse of a number with respect to a given modulus. It’s a key tool in number theory and cryptography, used in algorithms like RSA, modular equations, and solving congruences.
Find Modular Multiplicative Inverse of a Number
Modular Inverse Formula
$$\text{Find } x \text{ such that } a \cdot x \equiv 1 \pmod{m}$$
Modular Inverse – Calculation Example
Find the modular inverse of 3 modulo 11
- Solve 3 × x ≡ 1 (mod 11)
- Try x = 4 → 3 × 4 = 12 ≡ 1 mod 11 ✅
Result: Modular inverse of 3 mod 11 is 4
The modular multiplicative inverse is essential in solving modular equations and cryptographic protocols like RSA key generation and decryption. This calculator uses the Extended Euclidean Algorithm to efficiently compute the inverse when it exists.