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Look into the Mirror: Evolving Self-dual Bent Boolean Functions

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Genetic Programming (EuroGP 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14631))

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Abstract

Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions, even when the size of the Boolean function is large (e.g., more than 20 inputs). While bent Boolean functions represent only a small part of all Boolean functions, there are several subclasses of bent functions providing specific properties and challenges. One of the more interesting subclasses comprises (anti-)self-dual bent Boolean functions.

This paper provides a detailed experimentation with evolutionary algorithms with the goal of evolving (anti-)self-dual bent Boolean functions. We experiment with two encodings and two fitness functions to evolve self-dual bent Boolean functions. Our experiments consider Boolean functions with sizes of up to 16 inputs, and we successfully construct self-dual bent functions for each dimension. Moreover, we notice that the difficulty of evolving self-dual bent functions is similar to evolving bent Boolean functions, despite self-dual bent functions being much rarer.

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Notes

  1. 1.

    The function AND2 behaves the same as the function AND but with the second input inverted.

  2. 2.

    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-Denis Cedex, France

    Claude Carlet & Stjepan Picek

  2. University of Bergen, Bergen, Norway

    Claude Carlet

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

    Marko Durasevic & Domagoj Jakobovic

  4. Semantics, Cybersecurity & Services Group, University of Twente, Drienerlolaan 5, 7522, Enschede, NB, 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. Domagoj Jakobovic
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  4. Luca Mariot
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  5. Stjepan Picek
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Correspondence to Domagoj Jakobovic .

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Editors and Affiliations

  1. University of Torino, Grugliasco, Italy

    Mario Giacobini

  2. Victoria University of Wellington, Wellington, New Zealand

    Bing Xue

  3. University of Trieste, Trieste, Italy

    Luca Manzoni

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Carlet, C., Durasevic, M., Jakobovic, D., Mariot, L., Picek, S. (2024). Look into the Mirror: Evolving Self-dual Bent Boolean Functions. In: Giacobini, M., Xue, B., Manzoni, L. (eds) Genetic Programming. EuroGP 2024. Lecture Notes in Computer Science, vol 14631. Springer, Cham. https://doi.org/10.1007/978-3-031-56957-9_10

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  • DOI: https://doi.org/10.1007/978-3-031-56957-9_10

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  • Online ISBN: 978-3-031-56957-9

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