%0 Conference Proceedings
%T Enumerating Orthogonal Latin Squares Generated by Bipermutive Cellular Automata
%+ Università degli Studi di Milano-Bicocca = University of Milano-Bicocca (UNIMIB)
%+ Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
%A Mariot, Luca
%A Formenti, Enrico
%A Leporati, Alberto
%Z Part 2: Regular Papers
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA)
%C Milan, Italy
%Y Alberto Dennunzio
%Y Enrico Formenti
%Y Luca Manzoni
%Y Antonio E. Porreca
%I Springer International Publishing
%3 Cellular Automata and Discrete Complex Systems
%V LNCS-10248
%P 151-164
%8 2017-06-07
%D 2017
%R 10.1007/978-3-319-58631-1_12
%K Pairwise balancedness
%K Bipermutivity
%K Latin squares
%K Cellular automata
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%Z TC 1
%Z WG 1.5
%2 https://inria.hal.science/hal-01656352/document
%2 https://inria.hal.science/hal-01656352/file/447449_1_En_12_Chapter.pdf
%L hal-01656352
%U https://inria.hal.science/hal-01656352
%~ UNICE
%~ CNRS
%~ I3S
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-WG1-5
%~ IFIP-AUTOMATA
%~ IFIP-LNCS-10248
%~ UNIV-COTEDAZUR