Undergraduate Mathematical Sciences Seminar
Thursday, February 19, 2009, 12:30 -- 1:50pm
Random Number Generation in Cryptography: The Paradox of Trying to be Consistently Inconsistent
Dan Shumow, UW Department of Mathematics
Abstract: 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 e-commerce 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 crypto systems are based on number-theory, abstract algebra, and computational complexity theory. One of the basic elements of cryptography is securely generating random numbers to be used as secret data. This talk will cover the basic definitions and axioms of what it means to "securely" generate random numbers. I will provide an algorithm that appears to be secure, but ultimately has a serious flaw