How does the Affine cipher work?

Each letter is converted to a number 0-25, then encrypted with E(x) = (ax + b) mod 26. Decryption applies x = a^-1 (y - b) mod 26, where a^-1 is the modular inverse of a.

Why must key a be coprime with 26?

If a shares a factor with 26 it has no modular inverse, so different letters can map to the same ciphertext and decryption becomes impossible. Valid values are 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25.

What happens to spaces and punctuation?

Only letters A-Z are transformed. Spaces, digits and punctuation pass through unchanged, and letter case is preserved.

Is the Affine cipher secure?

No. With only 312 possible key combinations and vulnerability to frequency analysis, it offers no real security. Treat it as a learning exercise or puzzle, not encryption.

Is the Caesar cipher a special case of the Affine cipher?

Yes. Setting a = 1 reduces E(x) = (x + b) mod 26 to a plain Caesar shift, so the Affine cipher is a strict generalisation of it.

Affine Cipher Encrypt & Decrypt

The Affine cipher is a monoalphabetic substitution cipher in which each letter is mapped to a number, transformed by a simple linear function, and mapped back to a letter. It combines a multiplicative key and an additive key, making it more flexible than a plain Caesar shift while remaining easy to understand. This tool encrypts and decrypts text instantly in your browser with no upload.

How it works

Convert each letter to a number with A=0 through Z=25. Encryption applies the function E(x) = (a·x + b) mod 26, where a is the multiplicative key and b is the additive key. The result is mapped back to a letter.

Decryption reverses this with D(y) = a⁻¹·(y − b) mod 26, where a⁻¹ is the modular multiplicative inverse of a modulo 26. For the inverse to exist, a must be coprime with 26, so the tool only offers the valid values 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25.

Example

With a = 5 and b = 8, encrypt the letter A (x = 0): (5·0 + 8) mod 26 = 8, which is the letter I. Encrypting the phrase AFFINE CIPHER produces IHHWVC SWFRCP. Decrypting uses a⁻¹ = 21 (since 5·21 = 105 ≡ 1 mod 26) to recover the original text.

Notes

There are 12 valid choices for a and 26 for b, giving 312 possible keys — small enough to break by brute force. Because letter frequencies are preserved, the Affine cipher is also vulnerable to frequency analysis on longer messages.