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

Computer Science > Cryptography and Security [Submitted on 20 Mar 2026] Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators Bhuvaneswari A, Kamalika Bhattacharjee 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. Subjects: Cryptography and Security (cs.CR); Formal Languages and Automata Theory (cs.FL); Mathematical Software (cs.MS) Cite as: arXiv:2603.19656 [cs.CR]   (or arXiv:2603.19656v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2603.19656 Focus to learn more Submission history From: Kamalika Bhattacharjee [view email] [v1] Fri, 20 Mar 2026 05:45:11 UTC (2,969 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.FL cs.MS References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)