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

Yindong CHEN
Hongyan XIANG
Weihong CAI
Xianmang HE

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A    No.6    pp.818-824
Publication Date: 2019/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.818
Type of Manuscript: PAPER
Category: Cryptography and Information Security
rotation symmetric Boolean function,  algebraic immunity,  nonlinearity,  algebraic degree,  fast algebraic immunity,  

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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.