Balanced Odd-Variable RSBFs with Optimum AI, High Nonlinearity and Good Behavior against FAAs

Yindong CHEN; Fei GUO; Hongyan XIANG; Weihong CAI; Xianmang HE

doi:10.1587/transfun.E102.A.818

Regular Section

Balanced Odd-Variable RSBFs with Optimum AI, High Nonlinearity and Good Behavior against FAAs

Yindong CHEN, Fei GUO, Hongyan XIANG, Weihong CAI, Xianmang HE

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Keywords: rotation symmetric Boolean function, algebraic immunity, nonlinearity, algebraic degree, fast algebraic immunity

JOURNAL RESTRICTED ACCESS

2019 Volume E102.A Issue 6 Pages 818-824

DOI https://doi.org/10.1587/transfun.E102.A.818

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Abstract

Rotation symmetric Boolean functions which are invariant under the action of cyclic group have been used in many different cryptosystems. This paper presents a new construction of balanced odd-variable rotation symmetric Boolean functions with optimum algebraic immunity. It is checked that, at least for some small variables, such functions have very good behavior against fast algebraic attacks. Compared with some known rotation symmetric Boolean functions with optimum algebraic immunity, the new construction has really better nonlinearity. Further, the algebraic degree of the constructed functions is also high enough.

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