# A Tour of Public Key Cryptography

# (and of Number Theory)

## Joshua Holden

## Rose-Hulman Institute of Technology

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.

Go to talk