Monomial bent functions and Stickelberger's theorem

In this paper we use certain results on the divisibility of Gauss sums, mainly Stickelberger's theorem, to study monomial bent functions. This approach turns out to be especially nice in the Kasami, Gold and Dillon case. As one of our main results we give an alternative proof of bentness in the case of the Kasami exponent. Using the techniques developed here, this proof turns out to be very short and generalizes the previous results by Dillon and Dobbertin to the case where n is divisible by 3. Furthermore, our approach can also be used to deduce properties of the dual function. More precisely, we show that the dual of the Kasami function is not a monomial Boolean function.