Construction of Resilient and Nonlinear Boolean Functions with Almost Perfect Immunity to Algebraic and Fast Algebraic Attacks

摘要

In this paper, we study a class of Boolean functions with good cryptographic properties. We show that the functions of this class are 1-resilient and have optimal algebraic degree and good nonlinearity. Further, we prove that the functions of this class have at least sub-maximum algebraic immunity. We also check that, at least for small values of the number of variables, the functions of this class have very good nonlinearity, maximum algebraic immunity and almost perfect immunity to fast algebraic attacks.