A new characterization of almost bent functions


A. Canteaut
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Anne.Canteaut@inria.fr

Pascale Charpin
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Pascale.Charpin@inria.fr

Hans Dobbertin
German Information Security Agency
P.O.Box 20 03 63
D-53133 Bonn, Germany
dobbertin@skom.rhein.de

In Fast Software Encryption 99, LNCS 1636 , pages 186-200.
Springer-Verlag, 1999.

Abstract

We study the functions from GF(2^m) into GF(2^m) for odd m which oppose an optimal resistance to linear cryptanalysis. These functions are called almost bent. It is known that almost bent functions are also almost perfect nonlinear, i.e. they also ensure an optimal resistance to differential cryptanalysis but the converse is not true. We here give a necessary and sufficient condition for an almost perfect nonlinear function to be almost bent. This notably enables us to exhibit some infinite families of power functions which are not almost bent.