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Maximal length cellular automata in GF(q) and pseudo-random number generation
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DOI：10.1142/S0129183120500370.png)
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Abstract
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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
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