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The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. By investigating the lower bound of the nonlinearity of the derivative of the function f, this paper tightens the lower bound of the second-order nonlinearity of a class of Boolean functions over \({F_{2^n}}\) with high nonlinearity in the form f(x) = tr(λ x d), where \({\lambda\in F_{2^r}^*, d=2^{2r}+2^{r}+1}\) and n = 4r.

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Authors and Affiliations

  1. College of Sciences, Hohai University, 210098, Nanjing, China

    Guanghong Sun

  2. The State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, 100190, Beijing, China

    Guanghong Sun & Chuankun Wu

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  1. Guanghong Sun
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  2. Chuankun Wu
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Correspondence to Guanghong Sun.

Additional information

This work was supported by the Natural Science Foundation of China under Grant No.60673068, the Fundamental Research Funds for the Central Universities No. 2009B27414, and the Natural Science Foundation of Hohai University under Grant No. 2084/409270.

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Sun, G., Wu, C. The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity. AAECC 22, 37–45 (2011). https://doi.org/10.1007/s00200-010-0136-y

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  • DOI: https://doi.org/10.1007/s00200-010-0136-y

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