Kasiski

Kasiski examination, also called the Kasiski method, is a classical cryptanalytic technique used to break polyalphabetic ciphers, particularly the Vigenère cipher. It is named after Friedrich Kasiski, a Prussian linguist who described the method in 1863. The core idea is that repeated sequences of letters in the ciphertext tend to reveal the length of the key: when the same plaintext segment is encrypted with the same key letters, the resulting ciphertext sequence reappears at a later position, producing repeated sequences. The distances between the starts of these repeats are measured. The factors of these distances (especially common divisors) are taken as candidates for the key length. The most frequent factor that recurs across many repeats is often the actual key length.

In practice one scans the ciphertext for repeated sequences of length three or more, records the distances between their occurrences, and looks for common factors among those distances. Once a likely key length L is obtained, the ciphertext can be divided into L groups, each containing characters encrypted with a single alphabet, effectively turning the problem into multiple monoalphabetic frequency analyses.

Limitations include insufficient text length, homophonic or irregular ciphers, or repeated patterns that yield misleading factors. Nevertheless, the Kasiski examination was a foundational step in classical cryptanalysis and helped motivate later statistical tools such as the index of coincidence and improved methods for breaking polyalphabetic ciphers.