Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity

Authors:
Shaojing Fu;Chao Li;Kanta Matsuura;Longjiang Qu
Affiliations:
Department of Mathematics and System Science, National University of Defence Technology, Changsha, China and Institute of Industrial Science, University of Tokyo, Tokyo, Japan 153-8505;Department of Mathematics and System Science, National University of Defence Technology, Changsha, China and State Key Laboratory of Information Security, Beijing, China;Institute of Industrial Science, University of Tokyo, Tokyo, Japan 153-8505;Department of Mathematics and System Science, National University of Defence Technology, Changsha, China
Venue:
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Year:
2009

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Abstract

Rotation symmetric Boolean functions (RSBFs) which are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, we study the construction of RSBFs with maximum algebraic immunity. First, a new construction of RSBFs on odd number of variables with maximum possible Algebraic Immunity is given. Then by using the relationship between some flats and support of a n -variables Boolean function f , we prove that a construction of RSBFs on even number of variables has maximum possible Algebraic Immunity. Furthermore, we study the nonlinearity of functions by our construction.