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Inversion of Mutually Orthogonal Cellular Automata

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Cellular Automata (ACRI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11115))

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Abstract

Mutually Orthogonal Cellular Automata (MOCA) are sets of bipermutive CA which can be used to construct pairwise orthogonal Latin squares. In this work, we consider the inversion problem of pairs of configurations in MOCA. In particular, we design an algorithm based on coupled de Bruijn graphs which solves this problem for generic MOCA, without assuming any linearity on the underlying bipermutive rules. Next, we analyze the computational complexity of this algorithm, remarking that it runs in exponential time with respect to the diameter of the CA rule, but that it can be straightforwardly parallelized to yield a linear time complexity. As a cryptographic application of this algorithm, we finally show how to design a (2, n) threshold Secret Sharing Scheme (SSS) based on MOCA where any combination of two players can reconstruct the secret by applying our inversion algorithm.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi Milano-Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Luca Mariot & Alberto Leporati

Authors
  1. Luca Mariot
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  2. Alberto Leporati
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Corresponding author

Correspondence to Luca Mariot .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Giancarlo Mauri

  2. University of Perpignan, Perpignan, France

    Samira El Yacoubi

  3. University of Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  4. University of Tokyo, Tokyo, Japan

    Katsuhiro Nishinari

  5. University of Milano-Bicocca, Milan, Italy

    Luca Manzoni

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Mariot, L., Leporati, A. (2018). Inversion of Mutually Orthogonal Cellular Automata. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds) Cellular Automata. ACRI 2018. Lecture Notes in Computer Science(), vol 11115. Springer, Cham. https://doi.org/10.1007/978-3-319-99813-8_33

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  • DOI: https://doi.org/10.1007/978-3-319-99813-8_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99812-1

  • Online ISBN: 978-3-319-99813-8

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