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Title:
Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
Authors: Senshan Pan, Xiaotong Fu, Weiguo Zhang
Abstract:This paper presents a construction for a class of 1-resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying the generating matrix. For n is small (e.g. n=6), a part of these functions achieve almost optimal nonlinearity. Apart from their good nonlinearity, the functions reach Siegenthaler’s \cite{Siegenthaler} upper bound of algebraic degree. Furthermore, a class of 1-resilient functions on any number n>2 of variables with at least sub-optimal algebraic immunity is provided.
ePrint: https://eprint.iacr.org/2010/243
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