Maximal length cellular automata in GF(q) and pseudo-random number generation

Abstract

This work explores the randomness quality of maximal length cellular automata (CAs) in GF([Formula: see text]), where [Formula: see text]. A greedy strategy is chosen to select the candidate CAs which satisfy unpredictability criterion essential for a good pseudo-random number generator (PRNG). Then, performance of these CAs as PRNGs is empirically analyzed by using Diehard battery of tests. It is observed that, up to GF(11), increase in [Formula: see text] improves randomness quality of the CAs, but after that, it saturates. Finally, we propose an implementable design of a good PRNG based on a 13-cell maximal length cellular automaton over GF(11) which can compete with the existing well-known PRNGs.