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( 1xd1 + 2xd2 ), 1, 2, 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 1 and 2 fulfill certain conditions. To derive these results we develop a new method to prove that certain rational mappings on F2n are bijective.

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Hans Dobbertin, Gregor Leander, Anne Canteaut, Claude Carlet, Patrick Felke, Philippe Gaborit
• Keywords: Bent Function, Boolean Functions, JCT 2006, Niho Type