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A Walsh Exploration of Elementary CA Rules
Bruno Martin

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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