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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 PSap and another of Niho bent functions. Some recent results indicate the existence of bent functions in PSap having maximum algebraic immunity. On contrary, we identify a class of bent functions in PSap, 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.