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.