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If multiple keys are used, the effective key length is the least common multiple of the lengths of the individual keys. For example, using the two keys GO and CAT, whose lengths are 2 and 3, one obtains an effective key length of 6 (the least common multiple of 2 and 3). This can be understood as the point where both keys line up.
Kasiski actually used "superimposition" to solve the Vigenère cipher. He started by finding the key length, as above. Then he took multiple copies of the message and laid them one-above-another, each one shifted left by the length of the key. Kasiski then observed that each column was made up of letters encrypted with a single alphabet. His ...
In 1863, Kasiski published a 95-page book on cryptography, Die Geheimschriften und die Dechiffrir-Kunst (German, "Secret writing and the Art of Deciphering"). This was the first published account of a procedure for attacking polyalphabetic substitution ciphers, especially the Vigenère cipher (although it is possible Charles Babbage was already aware of a similar method but had not published it).
In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key , there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key ...
This technique is used to cryptanalyze the Vigenère cipher, for example. For a repeating-key polyalphabetic cipher arranged into a matrix, the coincidence rate within each column will usually be highest when the width of the matrix is a multiple of the key length, and this fact can be used to determine the key length, which is the first step ...
In 1929, Lester S. Hill developed the Hill cipher, which uses matrix algebra to encrypt blocks of any desired length. However, encryption is very difficult to perform by hand for any sufficiently large block size, although it has been implemented by machine or computer. This is therefore on the frontier between classical and modern cryptography.
A polyalphabetic cipher is a substitution, using multiple substitution alphabets. The Vigenère cipher is probably the best-known example of a polyalphabetic cipher, though it is a simplified special case. The Enigma machine is more complex but is still fundamentally a polyalphabetic substitution cipher.
An autokey cipher (also known as the autoclave cipher) is a cipher that incorporates the message (the plaintext) into the key. The key is generated from the message in some automated fashion, sometimes by selecting certain letters from the text or, more commonly, by adding a short primer key to the front of the message.