# Enumerating Orthogonal Latin Squares Generated by Bipermutive Cellular Automata

2 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : We consider the problem of enumerating pairs of bipermutive cellular automata (CA) which generate orthogonal Latin squares. Since the problem has already been settled for bipermutive CA with linear local rules, we address the general case of nonlinear rules, which could be interesting for cryptographic applications such as the design of cheater-immune secret sharing schemes. We first prove that two bipermutive CA generating orthogonal Latin squares must have pairwise balanced local rules. Then, we count the number of pairwise balanced bipermutive Boolean functions and enumerate those which generate orthogonal Latin squares up to $n=6$ variables, classifying them with respect to their nonlinearity values.
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Submitted on : Tuesday, December 5, 2017 - 3:42:09 PM
Last modification on : Tuesday, December 7, 2021 - 4:10:11 PM

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### Citation

Luca Mariot, Enrico Formenti, Alberto Leporati. Enumerating Orthogonal Latin Squares Generated by Bipermutive Cellular Automata. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.151-164, ⟨10.1007/978-3-319-58631-1_12⟩. ⟨hal-01656352⟩

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