Construction of Rotation Symmetric Boolean Functions with optimal Algebraic Immunity⋆ Construcción de Funciones Booleanas de Rotación Simétrica con Inmunidad Algebraica ´Optima

In this paper, we present theoretical constructions of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with the maximum possible algebraic immunity. To get high nonlinearity, we generalize our construction to a search technique in the RSBF class. We present RSBFs with the maximum algebraic immunity and high nonlinearity for odd number of variables. We also study the RSBFs on even number of variables for max-imum algebraic immunity