  The increased use of cryptography to protect our personal information makes
us want to understand the security of cryptosystems. The security of many
cryptosystems relies on solving the discrete logarithm, which is thought to be
relatively difficult. Therefore, we focus on the statistical analysis of
certain properties of the graph of the discrete logarithm. We discovered the
expected value and variance of a certain property of the graph and compared the
expected value to experimental data. Our finding did not coincide with our
intuition of the data following a Gaussian distribution given a large sample
size. Thus, we found the theoretical asymptotic distributions of certain
properties of the graph.
