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  Since World War II, one of the most important military uses of mathematics and computers is in the field of cryptography (Greek, ‘writing down the hidden’, or ‘hidden writing’). Until this century, the codes used in warfare were usually simple substitution codes, where the same letter in the cipher always stands for the same letter in the original. From the advent of radio, which meant that the signal sent out could be intercepted by anyone with a receiver set to the same wavelength without even the knowledge of the sender, codes became far more important, and led to an immense increase in the complexity of the codes used. For example, the letter in the cipher which stood for a particular letter in the original could depend on many other things than which letter it represented—the date and time, the position in the message, the length of the message, the identity of the sender and receiver and so on. This presented a great challenge to code-breakers, and increasingly sophisticated statistical methods began to be used to solve the new codes. Code-breaking was the first major application for digital computers, with the Enigma code being cracked in the 1940s by a team including Alan Turing (1912 - 1954).

Cryptography does not only have military uses. It is also important in today\'s world of digital communication. The major needs are for methods to encode information as sequences of 0s and 1s which are as short as possible and secure from corruption if mistakes are made in transmission, and, in some cases, secure from interpretation by competing firms. SMcL

See also coding theory.



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