On Cryptographic Properties of the Cosets of R(1,m)


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

Claude Carlet
GREYC, Université de Caen
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

Caroline Fontaine
LIFL
Université des Sciences et Technologies de Lille
59655 Villeneuve d'Ascq Cedex, France
Caroline.Fontaine@lifl.fr

IEEE Transactions on Information Theory, 47(4):1494--1513, May 2001.

Abstract

We introduce a new approach for the study of weight distributions of cosets of the Reed-Muller code of order 1. Our approach is based on the method introduced by Kasami, using Pless identities. By interpreting some equations, we obtain a necessary condition for a coset to have a ``high'' minimum weight. We next examine the impact of our results when some cryptographic criteria of Boolean functions are considered.

Keywords

Reed-Muller codes, Boolean function, nonlinearity, derivation, propagation criterion.