Cryptography and Communications

, Volume 11, Issue 1, pp 63–76 | Cite as

On the nonlinearity of Boolean functions with restricted input

  • Sihem MesnagerEmail author
  • Zhengchun Zhou
  • Cunsheng Ding
Part of the following topical collections:
  1. Special Issue on Boolean Functions and Their Applications


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.


Boolean functions Nonlinearity Walsh Hadamard transform FLIP cipher 

Mathematics Subject Classification (2010)

11T71 11T06 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Paris VIIISaint-DenisFrance
  2. 2.LAGA, UMR 7539, CNRSUniversity of Paris XIIIVilletaneuseFrance
  3. 3.Telecom ParisTechParisFrance
  4. 4.Department of MathematicsSothwest Jiaotong UniversityChengduChina
  5. 5.Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyHong KongChina

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