Enumerating Orthogonal Latin Squares Generated by Bipermutive Cellular Automata

  • Luca MariotEmail author
  • Enrico Formenti
  • Alberto Leporati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)


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.


Cellular automata Latin squares Bipermutivity Pairwise balancedness 


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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Luca Mariot
    • 1
    • 2
    Email author
  • Enrico Formenti
    • 2
  • Alberto Leporati
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanItaly
  2. 2.Université Côte d’Azur, CNRS, I3SSophia AntipolisFrance

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