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Cellular Automata Pseudo-Random Number Generators and Their Resistance to Asynchrony

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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

Cellular Automata (CA) have a long history being employed as pseudo-random number generators (PRNG), especially for cryptographic applications such as keystream generation in stream ciphers. Initially starting from the study of rule 30 of elementary CA, multiple rules where the objects of investigation and were shown to be able to pass most of the rigorous statistical tests used to assess the quality of PRNG. In all cases, the CA employed where of the classical, synchronous kind. This assumes a global clock regulating all CA updates which can be a weakness if an attacker is able to tamper it. Here we study how much asynchrony is necessary to make a CA-based PRNG ineffective. We have found that elementary CA are subdivided into three class: (1) there is a “state transition” where, after a certain level of asynchrony, the CA loses the ability to generate strong random sequences, (2) the randomness of the sequences increases with a limited level of asynchrony, or (3) CA normally unable to be used as PRNG exhibit a much stronger ability to generate random sequences when asynchrony is introduced.

Luca Manzoni was partially supported by “Premio giovani talenti 2017” of Università degli Studi di Milano-Bicocca and Accademia dei Lincei.

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Authors and Affiliations

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

    Luca Manzoni & Luca Mariot

Authors
  1. Luca Manzoni
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  2. Luca Mariot
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Correspondence to Luca Manzoni .

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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Manzoni, L., Mariot, L. (2018). Cellular Automata Pseudo-Random Number Generators and Their Resistance to Asynchrony. 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_39

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  • DOI: https://doi.org/10.1007/978-3-319-99813-8_39

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