A new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity

Abstract Rotation symmetric Boolean functions are potentially rich in functions of cryptographic significance. In this paper, a new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity is presented. By a direct calculation, the nonlinearity of the newly constructed functions is higher than the nonlinearities of all the known odd-variable rotation symmetric Boolean functions with optimal algebraic immunity. The algebraic degree and the fast algebraic immunity of our functions are also considered.