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On the Non-linearity of Power Functions

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Abstract

We study the Boolean functions arising from power functions by means of Stickelberger’s congruences on Gauss sum. We obtain a new criterion for high non-linearity of such boolean functions in terms of permutation polynomials. Finally, a new characteristic property of Gold exponents is given.

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Authors and Affiliations

  1. GRIM, Université de Toulon, France

    Philippe Langevin & Pascal Véron

Authors
  1. Philippe Langevin
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  2. Pascal Véron
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Correspondence to Philippe Langevin.

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Communicated by: A. Pott

AMS Classification: 06E30

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Langevin, P., Véron, P. On the Non-linearity of Power Functions. Des Codes Crypt 37, 31–43 (2005). https://doi.org/10.1007/s10623-004-3803-9

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  • DOI: https://doi.org/10.1007/s10623-004-3803-9

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