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

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

A transformation sequencing approach to pseudorandom number generation

This paper presents a new approach to designing pseudorandom number generators based on cellular automata. Current cellular automata designs either focus on i) ensuring desirable sequence properties such as maximum length period, balanced distribution of bits and uniform distribution of n-bit tuples etc. or ii) ensuring the generated sequences pass stringent randomness tests. In this work, important design patterns are first identified from the latter approach and then incorporated into cellular automata such that the desirable sequence properties are preserved like in the former approach. Preliminary experiment results show that the new cellular automata designed have potential in passing all DIEHARD tests

Permutation and sampling with maximum length CA for pseudorandom number generation

In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested - Weighted Permutation Vector Sampling with Controlled Multiplexing, Weighted Permutation Vector Sampling with Irregular Decimation and Permutation Programmed CA Sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA

Layered cellular automata for pseudorandom number generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

2-D CA Variation With Asymmetric Neighborship for Pseudorandom Number Generation

10.1109/TCAD.2004.823344IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems233378-388ITCS