A walsh exploration of elementary CA rules

Bruno Martin 1
1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : In this paper, we explore the 256 elementary cellular automata rules by a Walsh transform in order to find correlation-immune rules for generating good pseudo-random sequences. We prove that, except the 8 linear rules, there is no correlation-immune rule among the 256 rules. Thus, elementary cellular automata cannot be used as a cryptographic pseudo-random generator since the generated pseudo-random sequences are susceptible of correlation attacks. We conclude with some remarks on cryptography with cellular automata.
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Journal articles
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Contributor : Bruno Martin <>
Submitted on : Thursday, July 17, 2008 - 4:58:59 PM
Last modification on : Monday, November 5, 2018 - 3:48:02 PM


  • HAL Id : hal-00300231, version 1



Bruno Martin. A walsh exploration of elementary CA rules. Journal of Cellular Automata, Old City Publishing, 2008, 3 (2), pp.145-156. 〈hal-00300231〉



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