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Constructions of even-variable RSBFs with optimal algebraic immunity and high nonlinearity

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Abstract

Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, two classes of rotation symmetric Boolean functions having optimal algebraic immunity on even number of variables are presented. We give a lower bound of the algebraic degree of the functions in the first class, and derive the algebraic degree of the second class of functions. Moreover, the algebraic degree of the second class of functions is high enough. It is shown that both classes of functions have much better nonlinearity than all the previously obtained rotation symmetric Boolean functions with optimal algebraic immunity, and have good behavior against fast algebraic attacks at least for small numbers of input variables.

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Acknowledgements

This research was supported by the National Key Basic Research Program of China under Grant No. 2013CB834204, and the National Natural Science Foundation of China under Grant Nos. 61571243 and 61171082.

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Authors and Affiliations

  1. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China

    Lei Sun & Fang-Wei Fu

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  1. Lei Sun
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  2. Fang-Wei Fu
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Correspondence to Lei Sun.

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Sun, L., Fu, FW. Constructions of even-variable RSBFs with optimal algebraic immunity and high nonlinearity. J. Appl. Math. Comput. 56, 593–610 (2018). https://doi.org/10.1007/s12190-017-1088-1

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  • DOI: https://doi.org/10.1007/s12190-017-1088-1

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