Balanced 2p2p-variable rotation symmetric Boolean functions with maximum algebraic immunity

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 2p2p-variable (pp is an odd prime) RSBFs with maximum AI was provided, and the nonlinearity of the constructed RSBFs is not less than 22p−1−(2p−1p)+(p−2)(p−3)+2; this nonlinearity result is significantly higher than the previously best known nonlinearity of RSBFs with maximum AI.