Combinatorial Designs and Cellular Automata: A Survey

• URL: http://arxiv.org/abs/2503.10320v1
• Date: Thu, 13 Mar 2025 12:54:49 GMT
• Title: Combinatorial Designs and Cellular Automata: A Survey
• Authors: Luca Manzoni, Luca Mariot, Giuliamaria Menara,
• Abstract summary: We consider Cellular Automata (CA) as a type of algebraic systems, focusing on the designs induced by their short-term behavior.<n>We review the main results published in the literature concerning the construction of mutually Latin squares via bipermutive CA, considering both the linear and nonlinear cases.<n>We then survey some significant applications of these results to cryptography, and conclude with a discussion of open problems to be addressed in future research on CA-based designs.
• Score: 1.474723404975345
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by their short-term behavior. Specifically, we review the main results published in the literature concerning the construction of mutually orthogonal Latin squares via bipermutive CA, considering both the linear and nonlinear cases. We then survey some significant applications of these results to cryptography, and conclude with a discussion of open problems to be addressed in future research on CA-based combinatorial designs.

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