Hoffman, Frederick

In this thesis two different types of computer algorithms, Deterministic and Monte Carlo, are illustrated. Implementations of the Berlekamp-Massey algorithm and the Parallelized Pollard Rho Search are described here. The questions of what these two algorithms provide to the field of cryptography and why they have proven themselves important to cryptography are briefly discussed. It is also shown that with a little extra knowledge, the Parallelized Pollard Rho Search may be easily modified to improve its performance.

Today new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK cryptosystem. averages several uncoupled logistic maps. Averaging the maps increases the dimension of such a system, thus providing greater security. This thesis will explore the strengths and weaknesses of the HK cryptosystem and will end by introducing a modified version, called the HK8 cryptosystem that does not have the apparent weakness of the HK system.

This report details an approach to solving the Traveling Salesman Problem (TSP) using learning automata and a unique geometric approach. Two-dimensional Euclidean TSPs are considered and the type of learning automata used are commonly called neural networks. A standard neural net algorithm called back propagation proved to be fairly good at learning the sample figures, but a newer substitute for back propagation, called counter propagation, performed extremely well. An important goal of this research was to derive increased theoretical understanding of the TSP. This goal has been satisfied, especially with regard to instabilities in path length and the order of points traversed along the minimal path route. In addition, some applications to larger point problems are considered, and it is shown that configurations with isolated clusters of relatively closely spaced points relative to the convex hull apexes and the fixed points map quite well into the geometric figures presented here.