Construction of bent functions via Niho power functions

Hans Dobbertin, Gregor Leander, Anne Canteaut, Claude Carlet, Patrick Felke, Philippe Gaborit
2006 Journal of combinatorial theory. Series A  
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( 1 x d 1 + 2 x d 2 ), 1 , 2 , x ∈ F 2 n , are considered, where the exponents d i (i = 1, 2) are of Niho type, i.e. the restriction of x d i on F 2 k is linear. We prove for several pairs of (d 1 , d 2 ) that f is a bent function, when 1 and 2 fulfill certain conditions. To derive these results we
more » ... velop a new method to prove that certain rational mappings on F 2 n are bijective.
doi:10.1016/j.jcta.2005.07.009 fatcat:nvur3trxizgfxc6mxi4miohvjy