Simple method of selecting totalistic rules for pseudorandom number generator based on nonuniform cellular automaton

Abstract

This paper is devoted to selecting rules for one-dimensional (1D) totalistic cellular automaton (TCA). These rules are used for the generation of pseudorandom sequences, which could be useful in cryptography. The power of pseudorandom number generator (PRNG) based on nonuniform TCA can be improved using not only one rule but a large set of rules. For this purpose, each subset of rules should be analyzed with its assignation to cellular automaton (CA) cells should be analyzed. We examine each of the subsets of totalistic rules, consisting of rules with neighborhood radius equal to 1 and 2. The entropy of bitstreams generated by the nonuniform TCA points out the best set of rules appropriate for the TCA-based generator. The paper also presents the method of simple selection of CA rules based on a cryptographic criterion known as a balance. The proposed method selects a maximal size of the set of available CA rules for a given neighborhood radius and suitable for PRNG. The method guarantees to avoid conflicting assignments of rules resulting in the creation of unwanted stable bit sequences, and provides high-quality pseudorandom sequences. This technique is used to verify the subsets of rules selected experimentally. Verified rules are proposed for 1D TCA-based PRNG as a new subset of best nonuniform TCA rules. New picked, examined, and verified subset of rules could be used in TCA-based PRNG and provide cryptographically strong bit sequences and huge keyspace.