On upper bounds on algebraic immunity of some PSap and Niho bent functions

In this paper we obtain nontrivial upper bounds on algebraic immunity of Boolean bent functions belonging to a subclass of PS_ap and another of Niho bent functions. Some recent results indicate the existence of bent functions in PS_ap having maximum algebraic immunity. On contrary, we identify a class of bent functions in PS_ap, having monomial trace representation, which cannot have maximum algebraic immunity when the number of input variables n ≥ 16. We also consider a class of Niho bent functions having two terms in their trace representation and obtain an upper bound on their algebraic immunity which is again not optimal.