Improved lower bound for algebraic immunity of a subclass of MM bent Boolean functions

Abstract

It is known that algebraic immunity of an n-variable Boolean function is upper bounded by []. In literature, it was shown algebraic immunity of a subclass of Maiorana-McFarland (MM) bent Boolean functions is lower bounded by 2 and upper bounded by . In this paper, this lower bound is further improved. Given a Boolean function of -variables with algebraic immunity k ≥ 4, the improved lower bound helps a cryptographer to find a MM bent function of this class whose algebraic immunity is at least k − 2.