Undergraduate Mathematical Sciences Seminar
Wednesday, 15 November 2006, 12:30--1:50pm
Cryptography: Helping Number Theorists Bring Home the Bacon Since 1977
Dan Shumow
Gauss once said that "Mathematics is the queen of sciences, and number-theory the queen of mathematics;" because he saw number-theory as the most pure form of mathematics with no real world applications. However, with the rise of the internet at the end of the 20th century number-theory found a very relevant application: cryptography, the science of communicating secretly. Until the rise of the internet, cryptography was mainly of interest for espionage and military purposes. However, with ecommerce and online privacy the technology has become exceedingly useful for the general population. Accordingly academic, commercial, and military research and development in this field has rapidly grown in the last 30 years. Modern cryptosystems are based on number-theory, abstract algebra, and computational complexity theory. While using number-theory in such a practical manner is probably making Gauss spin in his grave, it is gainfully employing number theorists the whole world over.
This talk will give a basic introduction to modern cryptography and will not assume any prior knowledge of abstract algebra, number theory, or computational complexity.