Spectra of Des S-Boxes

摘要

We typically do not associate the field of graph theory with the field of cryptography. In graph theory, the aim is to model relationships with a graph and examine properties of that graph. The goal of cryptography is to design a communication system over a nonsecure channel. One connection between the two fields can be found with Cayley graphs and Boolean functions (BF). Accordingly, we can represent a cryptographic Boolean function with a Cayley graph and examine its properties. In this thesis, we convert the substitution boxes within the Data Encryption Standard (DES) to Boolean functions and represent them with Cayley graphs. From the Cayley graph, we analyze the graph spectra and attempt to determine a relationship with the cryptographic properties of the corresponding Boolean functions. With the spectra, we also make some inferences about the structure of the Cayley graph.