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A large family of Boolean functions

Volume 172 / 2016

Huaning Liu, Min Zhang Acta Arithmetica 172 (2016), 251-262 MSC: Primary 94C10; Secondary 94A60, 11T71, 11T24. DOI: 10.4064/aa8107-1-2016 Published online: 20 January 2016

Abstract

In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.

Authors

  • Huaning LiuSchool of Mathematics
    Northwest University
    Xi’an 710127, Shaanxi, P.R. China
    e-mail
  • Min ZhangSchool of Mathematics
    Northwest University
    Xi’an 710127, Shaanxi, P.R. China
    e-mail

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