On the Exploration of the Natural Sequence of Primes With Cellular Automata Targeting Enhanced Data Security and Privacy

Abstract

Enhanced data security and privacy are one of the major concerns in today’s digital society. The role of Primes towards the enhancements of data security and privacy is undeniable. Though several prime generations were presented, yet a cost effective and an easy to implement generation of Prime sequence should always have an advantage targeting real life applications. Hence, prime sequence generation using Cellular Automata (CA) is presented in this article as CA based modelling are easy to implement at the cost of flip-flops. The main contribution of this research is to explore the natural sequence of primes (i.e., primes A000040) with a special class of group CA, at fixed boundary environment; which may potentially be used as a Prime source towards the enhancements of data security and privacy. Experimental results confirm that the first 50 members of A000040 series may be explored at automata size 8 only. Detailed investigations towards the CA configuration and its dynamics in view of the generation of prime A000040 sequence, are also presented in this article.