Connections between Latin Squares, Cellular Automata and Coprime Polynomials


Cellular Automata (CA) provide a very simple model of parallel computation, with applications in diverse domains. Starting from a cryptographic scenario (secret sharing), we show how to use CA for the generation of orthogonal Latin squares, a type of combinatorial designs that are equivalent toi threshold secret sharing schemes where only two players are required to reconstruct a secret. More indetail, we illustrate an interesting algebraic characterization of these objects in terms of coprime polynomials, and present a new construction of bent functions leveraging CA-based MOLS.

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