On the nonlinearity of Boolean functions with restricted input

Abstract

Very recently, Carlet, Méaux and Rotella have studied the main cryptographic features of Boolean functions when, for a given number n of variables, the input to these functions is restricted to some subset E of \(\mathbb {F}_{2}^{n}\). Their study includes the particular case when E equals the set of vectors of fixed Hamming weight, which is important in the robustness of the Boolean function involved in the FLIP stream cipher. In this paper we focus on the nonlinearity of Boolean functions with restricted input and present new results related to the analysis of this nonlinearity improving the upper bound given by Carlet et al.

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Correspondence to Sihem Mesnager.

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This article is part of the Topical Collection on Special Issue on Boolean Functions and Their Applications

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Mesnager, S., Zhou, Z. & Ding, C. On the nonlinearity of Boolean functions with restricted input. Cryptogr. Commun. 11, 63–76 (2019). https://doi.org/10.1007/s12095-018-0293-6

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Keywords

  • Boolean functions
  • Nonlinearity
  • Walsh Hadamard transform
  • FLIP cipher

Mathematics Subject Classification (2010)

  • 11T71
  • 11T06