Maximal length cellular automata in GF(q) and pseudo-random number generation

Sumit Adak, Kamalika Bhattacharjee () and Sukanta Das ()
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Sumit Adak: Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
Kamalika Bhattacharjee: Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
Sukanta Das: Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 03, 1-21

Abstract: This work explores the randomness quality of maximal length cellular automata (CAs) in GF(q), where q≥2. A greedy strategy is chosen to select the candidate CAs which satisfy unpredictability criterion essential for a good pseudo-random number generator (PRNG). Then, performance of these CAs as PRNGs is empirically analyzed by using Diehard battery of tests. It is observed that, up to GF(11), increase in q improves randomness quality of the CAs, but after that, it saturates. Finally, we propose an implementable design of a good PRNG based on a 13-cell maximal length cellular automaton over GF(11) which can compete with the existing well-known PRNGs.

Keywords: Pseudo-random number generator (PRNG); cellular automata (CAs); maximal length CA; primitive polynomial; linear rule; Diehard (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500370

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