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Results on Constructions of Rotation Symmetric Bent and Semi-bent Functions

  • Claude Carlet
  • Guangpu GaoEmail author
  • Wenfen Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8865)

Abstract

In this paper, we introduce a class of cubic rotation symmetric (RotS) functions and prove that it can yield bent and semi-bent functions. To the best of our knowledge, this is the second primary construction of an infinite class of nonquadratic RotS bent functions which could be found and the first class of nonquadratic RotS semi-bent functions. We also study a class of idempotents (giving RotS functions through the choice of a normal basis of \(GF(2^n)\) over \(GF(2)\)). We derive a characterization of the bent functions among these idempotents and we relate their precise determination to a problem studied in the framework of APN functions. Incidentally, the proofs of bentness given here are useful for a paper studying a construction of idempotents from RotS functions, entitled “A secondary construction and a transformation on rotation symmetric functions, and their action on bent and semi-bent functions” by the same authors, to appear in the journal JCT series A.

Keywords

Rotation symmetric Boolean function Bent Semi-bent Maiorana-McFarland class Idempotent Permutation 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.LAGA (UMR 7539)University of Paris 8 and University of Paris 13, CNRSSaint-Denis, CedexFrance
  2. 2.State Key Laboratory of Mathematical Engineering and Advanced ComputingZhengzhouChina
  3. 3.State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina

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