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 CA rule, was proposed as an ideal candidate for cryp-tographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack [7]. 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 four-neighbourhood CA can be a better cryptographic primitive. We construct a class of crypto-graphically suitable 4-neighbourhood nonlinear CA rules that resembles rule 30. One 4-neighbourhood nonlinear CA from this selected class is shown to be resistant against Meier-Staffelbach attack on rule 30, jus-tifying the applicability of 4-neighbourhood CA as better cryptographic primitives. Key words: Cellular Automata, nonlinearity, CA rule 30