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. As an example, the RSA cryptosystem, developed in
the 1970's by Rivest, Shamir, and Adleman, uses some ideas that are
very easy to understand. Yet, these ideas underlie large portions of
both modern number theory and modern cryptography. We will explore
these ideas, and show how they make RSA the first practical "trap
door" cipher. This means that anyone can encode a message but only the
recipient can decode it!