Encryption is essential to the security of transactions and communications, but the algorithms on which they rely might not be as secure as we all assume. In this paper, we investigate the randomness of the discrete exponentiation function used frequently in encryption. We show how we used exponential generating functions to gain theoretical data for mapping statistics in ternary functional graphs. Then, we compare mapping statistics of discrete exponentiation functional graphs, for a range of primes, with mapping statistics of the respective ternary functional graphs.

Author Bio

Christina Frederick attends the University of Maryland, College Park where she plans to earn a B.S. in mathematics in May 2008. Currently, Christina is an undergraduate TA for Calculus 1 at the University of Maryland and is conducting research with the Norbert Weiner Center for Harmonic Analysis and finishing up research from the Rose-Hulman REU. She enjoys traveling, spending time with friends, and jogging.

Max Brugger attends Oregon State University. He plans to earn a B.S. in mathematics in May 2008. Currently, Max is a part of the Honors Activity and Advisory Committee and is finishing up research from the REU at Rose Hulman. Max enjoys reading, creative writing, theater, and math.