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On Plateaued Functions, Linear Structures and Permutation Polynomials

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Codes, Cryptology and Information Security (C2SI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11445))

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Abstract

We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some applications of our new notion of linear translator to the construction of permutation polynomials. Furthermore, we give explicit classes of permutation polynomials over \(\mathbb {F}_{q^n}\) using some properties of \(\mathbb {F}_q\) and some conditions of 2011, Akbary, Ghioca and Wang.

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Acknowledgments

We thank the reviewers for their insightful and fruitful remarks which greatly improved the presentation of the paper.

The research of the second and third authors has been funded by METU Coordinatorship of Scientific Research Projects via grant for projects GAP-101-2018-2782.

Author information

Authors and Affiliations

  1. LAGA, UMR 7539, CNRS, University Paris XIII - Sorbonne Paris Cité, University Paris VIII (Department of Mathematics) and Telecom ParisTech, Paris, France

    Sihem Mesnager

  2. Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Kübra Kaytancı

  3. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Ferruh Özbudak

Authors
  1. Sihem Mesnager
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  2. Kübra Kaytancı
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  3. Ferruh Özbudak
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Corresponding author

Correspondence to Ferruh Özbudak .

Editor information

Editors and Affiliations

  1. Université Paris 8, Saint-Denis, France

    Claude Carlet

  2. Institut MINES-TELECOM, Paris, France

    Sylvain Guilley

  3. Université de Caen, Caen, France

    Abderrahmane Nitaj

  4. Mohammed V University, Rabat, Morocco

    El Mamoun Souidi

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Mesnager, S., Kaytancı, K., Özbudak, F. (2019). On Plateaued Functions, Linear Structures and Permutation Polynomials. In: Carlet, C., Guilley, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2019. Lecture Notes in Computer Science(), vol 11445. Springer, Cham. https://doi.org/10.1007/978-3-030-16458-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-16458-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16457-7

  • Online ISBN: 978-3-030-16458-4

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