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New results on permutation polynomials of the form (x p m − x + δ)s + xp m + x over 𝔽 p 2m

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Abstract

Permutation polynomials over finite fields have significant applications in coding theory, cryptography, combinatorial designs and many other areas of mathematics and engineering. In this paper, we study the permutation behavior of polynomials with the form \((x^{p^{m}}-x+\delta )^{s}+x^{p^{m}}+x\) over the finite field \(\mathbb {F}_{p^{2m}}\). By using the Akbary-Ghioca-Wang (AGW) criterion, we present several new classes of permutations over \(\mathbb {F}_{p^{2m}}\) based on some bijections over the set \(\{t\in \mathbb {F}_{p^{2m}}|t^{p^{m}}+t=0\}\) or the subfield \(\mathbb {F}_{p^{m}}\).

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and helpful suggestions which improved both the quality and presentation of this paper. The work of this paper was supported by the National Natural Science Foundation of China (Grants 11571005, 61472417 and 11371184), and the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant 16HASTIT039.

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Authors and Affiliations

  1. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471934, China

    Zhengbang Zha & Zhizheng Zhang

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Lei Hu

  3. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, China

    Zhengbang Zha

  4. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, China

    Lei Hu

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  1. Zhengbang Zha
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  2. Lei Hu
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  3. Zhizheng Zhang
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Correspondence to Zhengbang Zha.

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Zha, Z., Hu, L. & Zhang, Z. New results on permutation polynomials of the form (x p m − x + δ)s + xp m + x over 𝔽 p 2m . Cryptogr. Commun. 10, 567–578 (2018). https://doi.org/10.1007/s12095-017-0234-9

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  • DOI: https://doi.org/10.1007/s12095-017-0234-9

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