Kasiski Test for Vigenère

Vigenère held out for three centuries for a simple reason: with the key changing the alphabet on every letter, frequency analysis finds nothing. Friedrich Kasiski published in 1863 the observation that brought it down. If a stretch of plaintext repeats and lands aligned with the same part of the key, it produces the same ciphertext stretch — and the distance between the two occurrences is a multiple of the key length.

Paste the ciphertext and the page looks for repeated trigrams, lists the distances between their occurrences and computes the greatest common divisor. That divisor is the best estimate of the key length. With the length in hand the cipher falls apart: separating the letters into positions spaced by that length, each group was enciphered with a single alphabet, and each group yields to ordinary frequency analysis.

The method needs text to work — a few hundred characters at least, because trigram repetitions are rare in little material. It also produces false positives: trigrams repeating by chance, with no key alignment, contaminate the divisor. So it pays to look at the distances one by one rather than accepting the divisor blindly, discarding the ones that stand out.