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We investigate S-boxes defined by pairs of Orthogonal Cellular Automata (OCA), motivated by the fact that such CA always define bijective vectorial Boolean functions, and could thus be interesting for the design of block ciphers. In…

Cryptography and Security · Computer Science 2022-05-17 Luca Mariot , Luca Manzoni

It is known that no-boundary Cellular Automata (CA) defined by bipermutive local rules give rise to Latin squares. In this paper, we study under which conditions the Latin square generated by a bipermutive CA is self-orthogonal, i.e.…

Discrete Mathematics · Computer Science 2025-04-15 Luca Mariot , Federico Mazzone

Orthogonal Cellular Automata (OCA) have been recently investigated in the literature as a new approach to construct orthogonal Latin squares for cryptographic applications such as secret sharing schemes. In this paper, we consider OCA for a…

Cryptography and Security · Computer Science 2021-06-16 Luca Mariot

We undertake an investigation of combinatorial designs engendered by cellular automata (CA), focusing in particular on orthogonal Latin squares and orthogonal arrays. The motivation is of cryptographic nature. Indeed, we consider the…

Discrete Mathematics · Computer Science 2016-10-04 Luca Mariot , Enrico Formenti , Alberto Leporati

We investigate sets of Mutually Orthogonal Latin Squares (MOLS) generated by Cellular Automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter $d$ over an alphabet of $q$ elements…

Discrete Mathematics · Computer Science 2019-11-01 Luca Mariot , Maximilien Gadouleau , Enrico Formenti , Alberto Leporati

Cellular Automata (CA) are an interesting computational model for designing Pseudorandom Number Generators (PRNG), due to the complex dynamical behavior they can exhibit depending on the underlying local rule. Most of the CA-based PRNGs…

Cryptography and Security · Computer Science 2022-03-08 Luca Mariot

In this short paper, we begin to investigate the conditions under which a generic Bipermutive Cellular Automaton (BCA) with no-boundary conditions of diameter $d$ generates a Latin square of order $N=2^{d-1}$ admitting an orthogonal mate,…

Formal Languages and Automata Theory · Computer Science 2026-05-20 Alberto Dennunzio , Maximilien Gadouleau , Luca Mariot

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…

Combinatorics · Mathematics 2025-03-14 Luca Manzoni , Luca Mariot , Giuliamaria Menara

We consider the problem of exhaustively visiting all pairs of linear cellular automata which give rise to orthogonal Latin squares, i.e., linear Orthogonal Cellular Automata (OCA). The problem is equivalent to enumerating all pairs of…

Discrete Mathematics · Computer Science 2023-07-17 Enrico Formenti , Luca Mariot

Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having a low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we…

Cellular Automata and Lattice Gases · Physics 2020-05-19 Luca Mariot , Martina Saletta , Alberto Leporati , Luca Manzoni

In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…

Cellular Automata and Lattice Gases · Physics 2012-09-04 Birendra Kumar Nayak , Sudhakar Sahoo , Sagarika Biswal

Latin squares and hypercubes are combinatorial designs with several applications in statistics, cryptography and coding theory. In this paper, we generalize a construction of Latin squares based on bipermutive cellular automata (CA) to the…

Discrete Mathematics · Computer Science 2020-04-16 Maximilien Gadouleau , Luca Mariot

We propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a 5-cell cellular automaton based on a unique well-chosen rule and bijective affine transformations. In particular, the cellular…

Cryptography and Security · Computer Science 2025-07-04 Thomas Prévost , Bruno Martin

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

Cellular Automata and Lattice Gases · Physics 2025-05-30 Rolf Hoffmann , Mariusz Białecki

Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…

Formal Languages and Automata Theory · Computer Science 2013-11-28 Sukanta Das , Biplab K Sikdar

Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing), and in which the global…

Formal Languages and Automata Theory · Computer Science 2019-02-25 Alberto Dennunzio , Enrico Formenti , Luca Manzoni , Luciano Margara , Antonio E. Porreca

Cellular Automata (CA) have been extensively used to implement symmetric cryptographic primitives, such as pseudorandom number generators and S-boxes. However, most of the research in this field, except the very early works, seems to be…

Cryptography and Security · Computer Science 2024-05-07 Luca Mariot

An "odd-rule" cellular automaton (CA) is defined by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF.…

Combinatorics · Mathematics 2015-03-24 Shalosh B. Ekhad , N. J. A. Sloane , Doron Zeilberger

Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…

Cellular Automata and Lattice Gases · Physics 2026-04-02 Manuel Pita

We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log^2 t) using gates with binary inputs, or O(log t)…

patt-sol · Physics 2009-10-30 Cristopher Moore
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