Structure and Randomness of the Discrete Lambert Map

Authors

JingJing Chen, Pomona CollegeFollow
Mark Lotts, Randolph-Macon CollegeFollow

Abstract

We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM), the mapping x --> xgx mod p, for p a prime and some fixed g \in (Z/pZ)* The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS.

Author Bio

JingJing Chen is a current senior at Pomona College majoring in math. She is interested in algebra and number theory and plans to pursue graduate studies in related areas. Outside of math, she spends her time studying studio arts, computer science, and yoga.

Mark Lotts is a recent graduate of Randolph-Macon College with a BS in mathematics and computer science. Mark is interested in cryptography, number theory, and geometric topology, and will pursue a PhD in mathematics at the University of Tennessee. In his spare time, he enjoys music, movies, sports, and photography.

Faculty Sponsor

Joshua Holden

Recommended Citation

Chen, JingJing and Lotts, Mark (2012) "Structure and Randomness of the Discrete Lambert Map," Rose-Hulman Undergraduate Mathematics Journal: Vol. 13: Iss. 1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol13/iss1/5