Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators
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 () using linear maximal length cellular automata of degree (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.
Cite
@article{arxiv.2603.19656,
title = {Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators},
author = {Bhuvaneswari A and Kamalika Bhattacharjee},
journal= {arXiv preprint arXiv:2603.19656},
year = {2026}
}