Search for Optimal Five-Neighbor FPGA-Based Cellular Automata Random Number Generators

Abstract

Cellular automata are recognized as efficient solutions for high-rate random number generators. However, for good randomness, the CA rule and the number of neighbor cells must be chosen with care. If a cell has N neighbors, 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> rules are possible, and finding the optimal rule is a time-consuming task. To reduce its complexity, the search procedure is usually done using a genetic algorithm, which is not guaranteed to find the best rule. In this paper, an exhaustive search is used to find the optimal rule for a CA based on a neighborhood of 5. The search is performed based on statistical tests and entropy measures implemented on an FPGA. The use of an FPGA boost the speed of the search by an order of magnitude. Implementation results of the four statistical tests are given in terms of area and maximum clock frequency, and exhibit a significant improvement over previous works. This study shows that an increase in the number of neighbors in a CA enhances the entropy in the context of high-rate pseudo-random number generators. Moreover, searching the optimal rule for a given seed will improve randomness.