A construction of highly nonlinear Boolean functions with optimal algebraic immunity and low hardware implementation cost

Abstract

In this paper we put forward a method to construct balanced Boolean functions by modifying the Tang–Carlet–Tang functions with the help of functions in Generalized Maiorana–McFarland class. Essential cryptographic properties, for instance, nonlinearity, algebraic immunity and immunity to fast algebraic attacks are considered. A new lower bound on the nonlinearity of the functions that are contained in our construction is obtained. It is slightly better than the known result. Owing to a combinatorial fact, it can be demonstrated that the proposed functions have optimal algebraic immunity. Meanwhile, they also possess high nonlinearity and a moderate behavior against fast algebraic attacks. Apart from theoretical contributions, hardware implementation efficiency on the proposed functions is also analyzed. Since the participation of GMM class component, experimental results imply that functions constructed in this paper have a small implementation size and employ fewer logic gates compared with the construction containing an iterative structure.