Designs, Codes and Cryptography

, Volume 59, Issue 1–3, pp 69–87 | Cite as

CCZ-equivalence of bent vectorial functions and related constructions

Open Access
Article

Abstract

We observe that the CCZ-equivalence of bent vectorial functions over \({{\bf F}_2^n}\) (n even) reduces to their EA-equivalence. Then we show that in spite of this fact, CCZ-equivalence can be used for constructing bent functions which are new up to EA-equivalence and therefore to CCZ-equivalence: applying CCZ-equivalence to a non-bent vectorial function F which has some bent components, we get a function F′ which also has some bent components and whose bent components are CCZ-inequivalent to the components of the original function F. Using this approach we construct classes of nonquadratic bent Boolean and bent vectorial functions.

Keywords

Affine equivalence Almost perfect nonlinear Bent function Boolean function CCZ-equivalence Nonlinearity 

Mathematics Subject Classification (2000)

06E30 11T71 

Notes

Acknowledgment

We would like to thank Gregor Leander for useful discussions.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LAGA, UMR 7539, CNRS, Universities of Paris 8 and Paris 13, Department of MathematicsUniversity of Paris 8Saint-Denis cedex 02France

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