Kasiski examination

How it works

In a Vigenère ciphertext, a word that appears twice in the plaintext is enciphered the same way whenever the two copies sit at the same position of the key, that is, when their distance is a multiple of the key length $L$. So repeated sequences of three or more letters in the ciphertext tend to lie a multiple of $L$ apart.

The examination lists every repeat, measures the distances between the copies and factors them. The true key length divides most of the distances. Some repeats happen by chance and add noise, and small numbers such as 2 and 3 divide many distances anyway, so the tool looks for the largest length that divides nearly as many distances as the best one.

Friedrich Kasiski published the method in 1863 (Charles Babbage had found it earlier but never published), and it ended the reputation of the Vigenère cipher as “le chiffre indéchiffrable”. Cross-check it with the index of coincidence of the columns.