Vigenère Cipher

Cryptography · Axiom Academy

The polyalphabetic cipher that resisted cryptanalysis for centuries The key innovation was using a keyword instead of a single shift value. Each letter of the keyword determines a different Caesar cipher shift, creating a polyalphabetic substitution. The animation shows how a keyword creates multiple different encryption layers, making each occurrence of the same letter potentially encrypt to different ciphertext letters. The Vigenère table (or tabula recta) is a 26×26 grid where each row represents a Caesar cipher shifted by the row's letter position. To encrypt, find the plaintext letter column and the key letter row, and their intersection gives the ciphertext. While the table is useful for manual encryption, we can also express this mathematically for computational purposes. We can represent the Vigenère cipher mathematically using modular arithmetic, where letters are mapped to numbers (A=0, B=1, ..., Z=25). C i = ciphertext letter at position i P i = plaintext letter at position i K i mod m = key letter (keyword repeats every m letters) mod 26 = wrap around the alphabet Let's encrypt the message "ATTACK" using the keyword "KEY" . 5. Defeating Frequency Analysis In simple substitution ciphers, each letter always maps to the same ciphertext letter, making frequency analysis effective. The Vigenère cipher breaks this pattern.

This is the written version of the interactive lesson above. See the full Cryptography course.