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European Conference on Genetic Programming

EuroGP 2019: Genetic Programming pp 262–277Cite as

Hyper-bent Boolean Functions and Evolutionary Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11451))

Abstract

Bent Boolean functions play an important role in the design of secure symmetric ciphers, since they achieve the maximum distance from affine functions allowed by Parseval’s relation. Hyper-bent functions, in turn, are those bent functions which additionally reach maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being characterized by a stricter definition, hyper-bent functions are rarer than bent functions, and much more difficult to construct. In this paper, we employ several evolutionary algorithms in order to evolve hyper-bent Boolean functions of various sizes. Our results show that hyper-bent functions are extremely difficult to evolve, since we manage to find such functions only for the smallest investigated size. Interestingly, we are able to identify this difficulty as not lying in the evolution of hyper-bent functions itself, but rather in evolving some of their components, i.e. bent functions. Finally, we present an additional parameter to evaluate the performance of evolutionary algorithms when evolving Boolean functions: the diversity of the obtained solutions.

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Acknowledgments

The authors wish to thank the anonymous referees for their useful comments on improving the presentation quality of the paper. This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-4882. In addition, this work was supported in part by the Research Council KU Leuven (C16/15/058) and IOF project EDA-DSE (HB/13/020).

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Authors and Affiliations

  1. DISCo, Università degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy

    Luca Mariot & Alberto Leporati

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

    Domagoj Jakobovic

  3. Cyber Security Research Group, Delft University of Technology, Mekelweg 2, Delft, The Netherlands

    Stjepan Picek

Authors
  1. Luca Mariot
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  2. Domagoj Jakobovic
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  3. Alberto Leporati
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  4. Stjepan Picek
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Corresponding author

Correspondence to Luca Mariot .

Editor information

Editors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Lukas Sekanina

  2. Memorial University, St. John's, NL, Canada

    Ting Hu

  3. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  4. HTWK Leipzig University of Applied Sciences, Leipzig, Germany

    Hendrik Richter

  5. University of Granada, Granada, Spain

    Pablo García-Sánchez

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Mariot, L., Jakobovic, D., Leporati, A., Picek, S. (2019). Hyper-bent Boolean Functions and Evolutionary Algorithms. In: Sekanina, L., Hu, T., Lourenço, N., Richter, H., García-Sánchez, P. (eds) Genetic Programming. EuroGP 2019. Lecture Notes in Computer Science(), vol 11451. Springer, Cham. https://doi.org/10.1007/978-3-030-16670-0_17

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  • DOI: https://doi.org/10.1007/978-3-030-16670-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16669-4

  • Online ISBN: 978-3-030-16670-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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