Linear codes in generalized construction of resilient functions with very high nonlinearity

Author

Pasalic, Enes ; Maitra, Subhamoy

Author_Institution

Dept. of Inf. Technol., Lund Univ., Sweden

Volume

48

Issue

8

fYear

2002

fDate

8/1/2002 12:00:00 AM

Firstpage

2182

Lastpage

2191

Abstract

We provide a new generalized construction method for highly nonlinear t-resilient functions, F:F₂ⁿ→ F₂^m. The construction is based on the use of linear error-correcting codes together with highly nonlinear multiple output functions. Given a linear [u, m, t+1] code we show that it is possible to construct n-variable, m-output, t-resilient functions with very high nonlinearity for n>u. The method provides the currently best known nonlinearity results for most of the cases.

Keywords

Boolean functions; binary codes; error correction codes; linear codes; nonlinear functions; binary linear code; generalized construction method; linear codes; linear error-correcting codes; linear feedback shift registers; multiple-output Boolean functions; nonlinear multiple output functions; nonlinear resilient functions; stream cipher systems; Boolean functions; Clocks; Cryptography; Distributed computing; Error correction codes; Fault tolerant systems; Linear code; Linear feedback shift registers; Quantum computing; Random sequences;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIR.2002.800492

Filename

1019831