Cyclic codes and permutations suitable for DES-like cryptosystems


Claude Carlet
GREYC, Université de Caen
14032 Caen Cdex, Farnce
and
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Claude.Carlet@inria.fr

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

Victor Zinoviev
Institute for Problems of Information Transmission
Bol'shoi Karetnyi 19
GSP-4 Moscow 101447, Russia

Designs, Codes and Cryptography, 15, pages 125-156, 1998.

Abstract

Almost bent functions oppose an optimum resistance to linear and differential cryptanalysis. We present basic properties of almost bent functions; particularly we give an upper bound on the degree. We develop the "coding theory" point of view for studying the existence of almost bent functions, showing explicitly the links with cyclic codes. We also give new characterizations of almost bent functions by means of associated Boolean functions.

Keywords

almost perfect nonlinear, almost bent, bent, Boolean functions, sequence, linear code, cyclic code.