A Walsh exploration of elementary CA rules

Bruno Martin (1)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3

In this paper, we explore the 256 elementary cellular automata rules by a Walsh transform in order to find out 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, Wolfram 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.

Mots clés: cellular automata; pseudo-random functions; Walsh transform

Domaines: Autre [cs.OH]

Bruno Martin. A Walsh exploration of elementary CA rules. International Workshop on Cellular Automata, Sep 2006, Hiroshima, Japan. pp.25-30. ⟨hal-00305489⟩