Investigating four neighbourhood cellular automata as better cryptographic primitives

Abstract

Three-neighbourhood Cellular Automata (CA) are widely studied and accepted as suitable cryptographic primitive. Rule 30, a 3-neighbourhood nonlinear CA rule, was proposed as an ideal candidate for cryptographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack [11]. The cryptographic properties like diffusion and randomness increase with increase in neighbourhood radius and thus opens the avenue of exploring the cryptographic properties of 4-neighbourhood CA. This work explores whether 4-neighbourhood CA can be a better cryptographic primitive. We construct a class of cryptographically suitable 4-neighbourhood nonlinear CA rules that resembles rule 30 and study its cryptographic properties. Four-neighbourhood nonlinear CA are shown to be resistant against Meier-Staffelbach attack on rule 30, justifying the applicability of 4-neighbourhood CA as better cryptographic primitives.