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Distribution of the autocorrelation of random Boolean functions

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Abstract

The nonlinearity of Boolean functions is well known and the behaviour of the nonlinearity of random Boolean functions has been studied, showing that they concentrate around one point. We show that it is the same for the autocorrelation of Boolean function. As an application, we show that the autocorrelation can distinguish a non random binary sequence from a random one.

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Acknowledgements

We want to thank the reviewers for the comments and suggestions which greatly improved the text.

Funding

This work was partially done while Florian Caullery was funded by the Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ - Brazil and the foundation of Coordenaçao de Aperfeiçoamento de Pessoal de Nivel Superior (Capes) of the Brazilian ministry of education.

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Author notes

  1. Florian Caullery and Eric Férard contributed equally to this work.

Authors and Affiliations

  1. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    François Rodier

  2. Qualcomm France S.A.R.L., 1240 Route des Dolines, Valbonne Sophia-Antipolis, France

    Florian Caullery

  3. GAATI team, University of French Polynesia, Tahiti, French Polynesia

    Eric Férard

Authors
  1. François Rodier
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  2. Florian Caullery
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  3. Eric Férard
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Contributions

François Rodier and Florian Caullery wrote the main manuscript and Eric Férard worked on section 3. All authors reviewed the manuscript.

Corresponding author

Correspondence to François Rodier.

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The authors have no competing interests as defined by Springer, or other interests that might be perceived to influence the results and/or discussion reported in this paper.

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Rodier, F., Caullery, F. & Férard, E. Distribution of the autocorrelation of random Boolean functions. Cryptogr. Commun. 15, 995–1009 (2023). https://doi.org/10.1007/s12095-023-00653-3

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