Finding nonnormal bent functions |
| |
Authors: | Anne Canteaut Hans Dobbertin |
| |
Institution: | a INRIA-Projet CODES, BP 105, 78153 Le Chesnay Cedex, France b Ruhr-University Bochum, Postfach 102148, 44780 Bochum, Germany |
| |
Abstract: | The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions. |
| |
Keywords: | Algorithm Boolean function Bent function Normal function |
本文献已被 ScienceDirect 等数据库收录! |
|