On the Non-linearity of Power Functions

Abstract : We study the Boolean functions arising from power functions by means of Stickelberger's con- gruences 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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Philippe Langevin, Pascal Véron. On the Non-linearity of Power Functions. Designs, Codes and Cryptography, Springer Verlag, 2005, 37, pp.31-43. ⟨10.1007/s10623-004-3803-9⟩. ⟨hal-00674664⟩

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