Analysis of Elementary Cellular Automata Chaotic Rules Behavior

We present detailed and in depth analysis of Elementary Cellular Automata (ECA) with periodic cylindrical configuration. The focus is to determine whether Cellular Automata (CA) is suitable for the generation of pseudo random number sequences (PRNs) of cryptographic strength. Additionally, we identify the rules that are most suitable for such applications. It is found that only two sub-clusters of the chaotic rule space are actually capable of producing viable PRNs. Furthermore, these two sub-clusters consist of two majorly non-linear rules. Each sub-cluster of rules is derived from a cluster leader rule by reflection or negation or the combined two transformations. It is shown that the members of each subcluster share the same dynamical behavior. Results of testing the ECA running under these rules for comprehensively large number of lattice lengths using the Diehard Test suite have shown that apart from some anomaly, the whole output sequence can be potentially utilized for cryptographic strength pseudo random sequence generation with sufficiently large number of p-values pass rates.