A Tour of Public Key Cryptography (and of Number Theory)

Like other branches of mathematics, number theory has seen many surprising developments in recent years. One of the most surprising is the fact that number theory, long considered the most "useless" of any field of mathematics, has become vital to the development of modern codes and ciphers. We will take a tour of some of these ciphers, focusing on the "public key" ciphers --- ciphers which answer the question "Can two persons who have never had a secret in common, by a public discussion agree upon a common secret?" (Beutelspacher) For perhaps the first time in history, the answer is yes in practical terms. The ideas are very easy to understand, and yet underlie large portions of both modern number theory and modern cryptography.

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