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

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Sequences and Their Applications - SETA 2014 (SETA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8865))

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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.

The work of G. Gao, and W. Liu is supported in part by 973 Program under Grant No. 2012CB315905 and Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications)(SKLNST-2013-1-06).

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Authors and Affiliations

  1. LAGA (UMR 7539), University of Paris 8 and University of Paris 13, CNRS, 2 Rue de la Liberté, 93526, Saint-Denis, Cedex, France

    Claude Carlet

  2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, China

    Guangpu Gao & Wenfen Liu

  3. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China

    Guangpu Gao & Wenfen Liu

Authors
  1. Claude Carlet
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  2. Guangpu Gao
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  3. Wenfen Liu
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Corresponding author

Correspondence to Guangpu Gao .

Editor information

Editors and Affiliations

  1. Otto-von-Guericke University, Magdeburg, Germany

    Kai-Uwe Schmidt

  2. Austrian Academy of Sciences, Linz, Austria

    Arne Winterhof

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Carlet, C., Gao, G., Liu, W. (2014). Results on Constructions of Rotation Symmetric Bent and Semi-bent Functions. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-12325-7_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12324-0

  • Online ISBN: 978-3-319-12325-7

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