A 2-Dimensional Cellular Automata Pseudorandom Number Generator with Non-linear Neighborhood Relationship

Abstract

Until recently, two-dimensional (2-D) cellular automata (CA) pseudorandom number generator (PRNG) research areas have been done based on von Neumann with linear neighborhood relationship. Although the linear neighborhood relationship has an excellent random quality, its cycle length is less than the linear neighborhood relationship. The cycle length is an important w.r.t. cryptographically secure PRNG because of the property of non-prediction for next sequence. This paper proposes 2-D CA PRNG based on von Neumann method with non-linear neighborhood relationship. In the proposed scheme, five elements (i.e. self, top, bottom, left and right) and two control elements (i.e. c 1 and c 2) with the combination of Boolean operator AND, XOR, or OR are used. The evolution function chooses one combination of XOR & AND and XOR & OR by two control elements. The number of rules in the proposed scheme is higher than previous schemes. To evaluate between the proposed scheme and previous schemes, the ENT and DIEHARD test suites are used in the experiments. In the experimental result, the randomness quality of the proposed PRNG was slightly less than or much the same previous schemes. However, the proposed scheme can generate various CA rule patterns and the number of rules is higher than previous schemes. The correlation coefficient between global state G (t) and G (t + 1) of the proposed scheme is reduced because of using the non-linear neighborhood relationship. © Springer-Verlag Berlin Heidelberg 2012.