Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators

TL;DR

This paper introduces new cellular automata-based pseudo-random number generators that are resource-efficient, achieve maximal equidistribution, and perform comparably to Mersenne Twister in empirical tests.

Contribution

The paper proposes a novel class of lightweight, combined CA-based PRNGs with maximal period and equidistribution, improving upon existing CA-based generators.

Findings

Achieve maximal period and equidistribution

Pass most empirical randomness tests

Comparable speed to Mersenne Twister

Abstract

An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number generators (PRNGs) are weak in the equidistribution characteristic. Then we propose a list of light-weight combined CA-based PRNGs with time spacing ($2 \leq s \leq 10$) using linear maximal length cellular automata of degree $31 \leq k \leq 128$ (close to computer word size). We show that these PRNGs achieve maximal period as well as satisfy the maximal equidistribution property. Finally, we show that these combined maximal length CA-based PRNGs pass almost all the empirical testbeds, with speed and performance comparable to the Mersenne Twister.