Discrete Mathematics and Combinatorics Commons^™

Mapping The Discrete Logarithm, Daniel R. Cloutier

Mathematical Sciences Technical Reports (MSTR)

The discrete logarithm is a problem that surfaces frequently in the field of cryptog- raphy as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph is largely dependent on an interaction between g and p-1. In fact, there are precisely as many different functional graph structures as there are divisors of p-1. This paper extracts two of these structures, permutations and binary functional graphs. Estimates exist for the shape of a random permutation, but …