Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity

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.