What is the Hill cipher?

The Hill cipher is a classical polygraphic substitution cipher that uses linear algebra. Plaintext is grouped into vectors and multiplied by a key matrix modulo 26.

Why must the key matrix be invertible mod 26?

Without an inverse matrix modulo 26, you could encrypt but not decrypt. Our tool checks the determinant and computes the modular inverse for you.

Which alphabet does this tool use?

A=0, B=1, ..., Z=25. Non letters are stripped. Text is uppercased. If length is odd for a 2×2 cipher, we pad with X.

Hill Cipher Encoder/Decoder

Enter a 2×2 key matrix (mod 26), check invertibility, then encrypt or decrypt text. We strip non-letters and pad with X if needed.

1. Key matrix (2×2)

Values are integers mod 26 (0–25). A common demo key is [[3, 3], [2, 5]].

2. Text

Input text (we keep letters A–Z, uppercase, pad with X)

For decryption, paste ciphertext here and click “Decrypt”.

3. Actions

4. Output

Result

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Numeric vector (A=0 … Z=25)

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How the Hill cipher works (2×2)

1. Choose a 2×2 key matrix K with entries mod 26.

2. Convert text to numbers using A=0, B=1, …, Z=25, and group into 2-element column vectors.

3. For each vector P, compute C = K · P mod 26. Convert back to letters.


                K = [a b; c d], det(K) = ad − bc. 

                K is invertible mod 26 if gcd(det(K), 26) = 1.

To decrypt, we need the inverse matrix K⁻¹ mod 26 so that P = K⁻¹ · C mod 26. This page computes that for you.