Balanced odd-variable rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity

Abstract

By modifying the support of the majority function, we propose a construction of balanced odd-variable rotation symmetric Boolean functions with optimal algebraic immunity. For n ≥ 17 , the nonlinearity of these constructed functions is the highest among all known rotation symmetric Boolean functions with optimal algebraic immunity. The algebraic degree can reach the maximum for some special numbers of variables. Moreover, simulations show that such functions have good fast algebraic immunity for some small numbers of variables.