The Oxford English Dictionary gives the following definition of cryptography.

‘A secret manner of writing, either by arbitrary characters, by using letters or characters in other than their ordinary sense, or by other methods intelligible only to those possessing the key; also anything written in this way. Generally, the art of writing or solving ciphers.’

Cryptography is an ancient art, and until relatively recently the above definition would have been quite adequate. However, in the last thirty years it has expanded to encompass much more than secret messages or ciphers.

For example cryptographic protocols for securely proving your identity online (perhaps to your bank's website) or signing binding digital contracts are now at least as important as ciphers.

As the scope of cryptography has broadened in recent years attempts have been made to lay more rigorous mathematical foundations for the subject. While cryptography has historically been seen as an art rather than a science this has always really depended on which side of the ‘cryptographic fence’ you belong. We distinguish between cryptographers, whose job it is to design cryptographic systems, and cryptanalysts, whose job it is to try to break them. Cryptanalysts have been using mathematics to break ciphers for more than a thousand years. Indeed Mary Queen of Scots fell victim to a mathematical cryptanalyst using statistical frequency analysis in 1586!

The development of computers from Babbage's early designs for his ‘Difference Engines’ to Turing's involvement in breaking the Enigma code owes much to cryptanalysts desire to automate their mathematically based methods for breaking ciphers.