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More constructions of semi-bent and plateaued functions in polynomial forms

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Abstract

Plateaued functions and their subclass semi-bent functions have useful applications in cryptography and communications. In this paper we give new constructions of quadratic semi-bent functions in polynomial forms on the finite field \(\mathbb {F}_{2^n}\) for both odd and even n. We also present some characterizations of e-plateaued functions with few trace terms when n is even.

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Acknowledgements

We are grateful to the anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper.

Funding

This work was supported by Youth Research Project of educational department of Hubei province of China (B2017149) and Doctoral Program of Hubei Normal University (R201707).

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Authors and Affiliations

  1. College of Mathematic and Statistic, Hubei Normal University, Huangshi, 435002, China

    Tao Xie

  2. School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Gaojun Luo

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  1. Tao Xie
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  2. Gaojun Luo
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Correspondence to Tao Xie.

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Xie, T., Luo, G. More constructions of semi-bent and plateaued functions in polynomial forms. Cluster Comput 22 (Suppl 4), 9281–9291 (2019). https://doi.org/10.1007/s10586-018-2126-y

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  • DOI: https://doi.org/10.1007/s10586-018-2126-y

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