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A New Angle: On Evolving Rotation Symmetric Boolean Functions

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Applications of Evolutionary Computation (EvoApplications 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14634))

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Abstract

Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent cryptographic properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.

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Notes

  1. 1.

    Some works also combine theory and search techniques, e.g., [12, 25].

  2. 2.

    One could still assume the hybrid mode where one 1) considers the equivalences that preserve the parameters of interest, 2) classify the functions under these equivalences, and 3) study each representative.

  3. 3.

    Note that the sum is calculated in \({\mathbb Z}\).

  4. 4.

    The algebraic degree \(deg_f\) of a Boolean function f is defined as the number of variables in the largest product term of the function’s algebraic normal form having a non-zero coefficient, see, e.g., [16]. The algebraic normal form is a unique representation where an n variable Boolean function can be considered to be a multivariate polynomial over \(\mathbb {F}_{2}\).

  5. 5.

    Evolutionary Computation Framework, http://solve.fer.hr/ECF/.

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Authors and Affiliations

  1. Department of Mathematics, Université Paris 8, 2 Rue de la Liberté, 93526, Saint-DenisCedex, France

    Claude Carlet

  2. University of Bergen, Bergen, Norway

    Claude Carlet

  3. University of Zagreb Faculty of Electrical Engineering and Computing, Zagreb, Croatia

    Marko Durasevic, Bruno Gasperov & Domagoj Jakobovic

  4. Semantics, Cybersecurity & Services Group, University of Twente Drienerlolaan 5, 7522 NB, Enschede, The Netherlands

    Luca Mariot

  5. Digital Security Group, Radboud University, PO Box 9010, Nijmegen, The Netherlands

    Stjepan Picek

Authors
  1. Claude Carlet
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  2. Marko Durasevic
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  3. Bruno Gasperov
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  4. Domagoj Jakobovic
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  5. Luca Mariot
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  6. Stjepan Picek
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Corresponding author

Correspondence to Domagoj Jakobovic .

Editor information

Editors and Affiliations

  1. University of York, York, UK

    Stephen Smith

  2. University of Coimbra, Coimbra, Portugal

    João Correia

  3. University of Málaga, Málaga, Spain

    Christian Cintrano

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Carlet, C., Durasevic, M., Gasperov, B., Jakobovic, D., Mariot, L., Picek, S. (2024). A New Angle: On Evolving Rotation Symmetric Boolean Functions. In: Smith, S., Correia, J., Cintrano, C. (eds) Applications of Evolutionary Computation. EvoApplications 2024. Lecture Notes in Computer Science, vol 14634. Springer, Cham. https://doi.org/10.1007/978-3-031-56852-7_19

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  • DOI: https://doi.org/10.1007/978-3-031-56852-7_19

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  • Online ISBN: 978-3-031-56852-7

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