Affine Cipher — Encrypt, Decrypt & Brute Force

The affine cipher maps each letter to a number (A = 0 … Z = 25), multiplies it by a, adds b and takes the remainder after dividing by 26. Caesar (a = 1) and Atbash (a = b = 25) are special cases. This tool encrypts and decrypts with any valid key, shows the modular inverse used for decryption and the full substitution table, and can break a message by trying all 312 keys.

How to use this tool

1. Choose encrypt, decrypt or the brute-force mode.
2. Paste the text; case, spaces and punctuation are kept.
3. Enter a (coprime with 26) and b (0–25), unless you are brute-forcing.
4. Copy the result, or pick the readable line from the ranked table.

Formula

E(x) = (a·x + b) mod 26 D(y) = a⁻¹·(y − b) mod 26

a⁻¹ is the number that gives a·a⁻¹ ≡ 1 (mod 26); it exists only when a and 26 share no factor, which leaves 12 values of a and 12 × 26 = 312 keys. Brute force decrypts with every key and ranks the results by χ² against English letter frequencies.

Example

With a = 5, b = 8, A (0) → 8 = I, F (5) → 33 mod 26 = 7 = H, so AFFINE CIPHER becomes IHHWVC SWFRCP. The inverse of 5 is 21 (5 × 21 = 105 = 4 × 26 + 1), so decryption is D(y) = 21(y − 8) mod 26.