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Cryptography and Communications

, Volume 4, Issue 1, pp 65–77 | Cite as

A new construction of highly nonlinear S-boxes

  • Peter Beelen
  • Gregor Leander
Article

Abstract

In this paper we give a new construction of highly nonlinear vectorial Boolean functions. This construction is based on coding theory, more precisely we use concatenation to construct Boolean functions from codes over \(\mathbb{F}_q\) containing a first-order generalized Reed–Muller code. As it turns out this construction has a very compact description in terms of Boolean functions, which is of independent interest. The construction allows one to design functions with better nonlinearities than known before.

Keywords

Boolean functions Linear codes Nonlinearity Reed–Muller codes Concatenation 

Mathematics Subject Classifications (2010)

06E30 94A60 14G50 65T50 

Notes

Acknowledgements

We would like to thank Anne Canteaut and Claude Carlet for suggesting to investigate more explicitly the functions obtained by using concatenation of codes.

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Copyright information

© Springer Science + Business Media, LLC 2011

Authors and Affiliations

  1. 1.DTU MathematicsTechnical University DenmarkLyngbyDenmark

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