Balanced [formula omitted]-variable rotation symmetric Boolean functions with maximum algebraic immunity

Abstract

In this paper, we study the construction of Rotation Symmetric Boolean Functions (RSBFs) which achieve a maximum algebraic immunity (AI). For the first time, a construction of balanced 2 p -variable ( p is an odd prime) RSBFs with maximum AI was provided, and the nonlinearity of the constructed RSBFs is not less than 2 2 p − 1 − ( 2 p − 1 p ) + ( p − 2 ) ( p − 3 ) + 2 ; this nonlinearity result is significantly higher than the previously best known nonlinearity of RSBFs with maximum AI.