On cryptographic properties of the cosets of R(1, m)

Author

Canteaut, Anne ; Carlet, Claude ; Charpin, Pascale ; Fontaine, Caroline

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France

Volume

47

Issue

4

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

1494

Lastpage

1513

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 (1968), using Pless (1963) identities. By interpreting some equations, we obtain a necessary condition for a coset to have a “high” minimum weight. Most notably, we are able to distinguish such cosets which have three weights only. We then apply our results to the problem of the nonlinearity of Boolean functions. We particularly study the links between this criterion and the propagation characteristics of a function

Keywords

Boolean functions; Reed-Muller codes; binary codes; cryptography; nonlinear functions; Pless identities; Reed-Muller code; binary codes; cosets; cryptographic properties; high minimum weight; necessary condition; nonlinear Boolean functions; propagation characteristics; weight distributions; Algebra; Boolean functions; Codes; Cryptography; Galois fields; Hamming distance; Helium; Kernel; Nonlinear equations; Vectors;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.923730

Filename

923730