Construction of bent functions via Niho power functions

A Boolean function with an even number n=2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. Boolean functions of the form f(x)=tr(α1xd1+α2xd2), α1,α2,x∈F2n, are considered, where the exponents di (i=1,2) are of Niho type, i.e. the restriction of xdi on F2k is linear. We prove for several pairs of (d1,d2) that f is a bent function, when α1 and α2 fulfill certain conditions. To derive these results we develop a new method to prove that certain rational mappings on F2n are bijective.