Affine Cipher

Encrypt and decrypt text using the Affine cipher — a substitution cipher using modular arithmetic with keys a and b.

What Does This Tool Do?

The Affine cipher encrypts each letter using E(x) = (ax + b) mod 26, where a must be coprime with 26. It is a generalisation of the Caesar cipher (a=1) and Atbash cipher (a=25, b=25).

Key Features

🔢
Two Keys
Keys a (multiplicative) and b (shift).
📐
Modular Arithmetic
E(x) = (ax+b) mod 26 formula shown.
🔄
Both Directions
Encrypt and decrypt.
✅
Valid Key Check
Warns if a is not coprime with 26.

How to Use

  1. Enter your message.
  2. Select key a (must be coprime with 26) and enter key b (0–25).
  3. Click Encrypt or Decrypt.

Frequently Asked Questions

Why must key a be coprime with 26?▾
For decryption to work, the modular inverse of a must exist. A modular inverse of a mod 26 exists only when gcd(a, 26) = 1 — i.e. a is coprime with 26.
What is the formula?▾
Encryption: E(x) = (a×x + b) mod 26. Decryption: D(y) = a⁻¹×(y − b) mod 26, where a⁻¹ is the modular inverse of a.
What are the special cases?▾
a=1 gives a Caesar cipher (shift by b). a=25, b=25 gives an Atbash cipher. a=1, b=0 gives no encryption at all.