Optimization of 2-d lattice cellular automata for pseudorandom number generation

Abstract

This paper proposes a generalized approach to 2-d CA PRNGs – the 2-d lattice CA PRNG – by introducing vertical connections to arrays of 1-d CA. The structure of a 2-d lattice CA PRNG lies in between that of 1-d CA and 2-d CA grid PRNGs. With the generalized approach, 2-d lattice CA PRNG offers more 2-d CA PRNG variations. It is found that they can do better than the conventional 2-d CA grid PRNGs. In this paper, the structure and properties of 2-d lattice CA are explored by varying the number and location of vertical connections, and by searching for different 2-d array settings that can give good randomness based on Diehard test. To get the most out of 2-d lattice CA PRNGs, genetic algorithm is employed in searching for good neighborhood characteristics. By adopting an evolutionary approach, the randomness quality of 2-d lattice CA PRNGs is optimized. In this paper, a new metric, #rn is introduced as a way of finding a 2-d lattice CA PRNG with the least number of cells required to pass Diehard test. Following the introduction of the new metric #rn, a cropping technique is presented to further boost the CA PRNG performance. The cost and efficiency of 2-d lattice CA PRNG is compared with past works on CA PRNGs.