Cryptography and Communications

, Volume 4, Issue 1, pp 65–77

A new construction of highly nonlinear S-boxes


DOI: 10.1007/s12095-011-0052-4

Cite this article as:
Beelen, P. & Leander, G. Cryptogr. Commun. (2012) 4: 65. doi:10.1007/s12095-011-0052-4


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.


Boolean functionsLinear codesNonlinearityReed–Muller codesConcatenation

Mathematics Subject Classifications (2010)


Copyright information

© Springer Science + Business Media, LLC 2011

Authors and Affiliations

  1. 1.DTU MathematicsTechnical University DenmarkLyngbyDenmark