rrences of certain ciphertext symbols and associations. The frequency properties of the English language were described in Chapter 9. We have seen that the two most likely letter associations are TH and HE, making THE the most likely three- letter word in English. Thus, any frequent two-symbol or three-symbol occurrence in a ciphertext is likely to correspond to these plaintext letter associations. In cryptography jargon, the word fragments, identified are called cribs. Based on a few cribs, the rest of the guess can progress very fast, should the context of the message (most likely words, e.g., in wartime) also be known to the code breaker. Frequency analysis and identification of cribs are basically the spirit of cryptanalysis as far as ancient (alphabetic-substitution) cryptosystems are concerned. Cryptography is over 2000 years old. The ingenuity and skills that were deployed through the ages to conceive and then break ever-complex ciphers are both phenom- enal and mind boggling. It is beyond the scope of this chapter to make even a brief survey of cipher development. I shall just mention here the intriguing Enigma machine, which was used by the German army during World War II.4 It represented a major turn in the history of cryptography, not solely because it was the first "cryptographic computer," but because of its highly sophisticated encryption and decryption algorithm. Probably one had never believed SO much in cryptosystem invulnerability! The Enigma cipher used only 26 typewriter characters with a three-rotor system, yielding as many as 58691676442400 or 10 million billion (or 10 peta) polyalphabetic substitution 3 For a detailed and illustrated review of historical alphabetic-substitution algorithms, see, for instance, my previous work: E. Desurvire, Wiley Survival Guide in Global Telecommunications, Broadband Access, Optical Components and Networks, and Cryptography (New York: J. Wiley & Sons, 2004), Ch. 3, pp. 345-477. There exist many excellent websites dedicated to the Enigma machine, see for inst