Polyalphabetic cipher
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.
History
The work of
The Alberti cipher by Leon Battista Alberti around 1467 was an early polyalphabetic cipher. Alberti used a mixed alphabet to encrypt a message, but whenever he wanted to, he would switch to a different alphabet, indicating that he had done so by including an uppercase letter or a number in the cryptogram. For this encipherment Alberti used a decoder device, his cipher disk, which implemented a polyalphabetic substitution with mixed alphabets.
Trithemius's idea was to encipher the first letter of the message using the first shifted alphabet, so A became B, B became C, etc. The second letter of the message was enciphered using the second shifted alphabet, etc. Alberti's cipher disk implemented the same scheme. It had two alphabets, one on a fixed outer ring, and the other on the rotating disk. A letter is enciphered by looking for that letter on the outer ring, and encoding it as the letter underneath it on the disk. The disk started with A underneath B, and the user rotated the disk by one letter after encrypting each letter.
The cipher was trivial to break, and Alberti's machine implementation not much more difficult. Key progression in both cases was poorly concealed from attackers. Even Alberti's implementation of his polyalphabetic cipher was rather easy to break (the capitalized letter is a major clue to the cryptanalyst). For most of the next several hundred years, the significance of using multiple substitution alphabets was missed by almost everyone. Polyalphabetic substitution cipher designers seem to have concentrated on obscuring the choice of a few such alphabets (repeating as needed), not on the increased security possible by using many and never repeating any.
The principle (particularly Alberti's unlimited additional substitution alphabets) was a major advance—the most significant in the several hundred years since frequency analysis had been developed. A reasonable implementation would have been (and, when finally achieved, was) vastly harder to break. It was not until the mid-19th century (in Babbage's secret work during the Crimean War and Friedrich Kasiski's generally equivalent public disclosure some years later), that cryptanalysis of well-implemented polyalphabetic ciphers got anywhere at all. See Kasiski examination.
Notes
- ISBN 9780674985377.
- ^ Maclean, Donald (20 February 2012), Al-Kindi, retrieved 13 April 2012
- ^ Johann Tritheim, Polygraphiae libri sex … (Basel, Switzerland: Michael Furter and Adam Petri, 1518), Liber quintus (fifth book), pages 461-462; the Recta transpositionis tabula (square table of transpositions, or "Vigenère table") appears on page 463.
References
- Alberti, Leon Battista (1997), A Treatise on Ciphers, trans. A. Zaccagnini. Foreword by David Kahn, Torino: Galimberti
- Churchhouse, Robert (2002), Codes and Ciphers: Julius Caesar, the Enigma and the Internet, Cambridge: Cambridge University Press, ISBN 978-0-521-00890-7
- ISBN 0-486-20097-3
See also
- Vigenère cipher
- Topics in cryptography