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More classes of permutation trinomials with Niho exponents

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Abstract

This paper presents two classes of permutation trinomials with the form \(x^{s(2^{m}-1)+ 1}+x^{t(2^{m}-1)+ 1}+x\) over the finite field \( \mathbb {F}_{2^{2m}}\) as a supplement of the recent works of Li and Helleseth, and a class of permutation trinomials like this form over \( \mathbb {F}_{3^{2m}}\). Moreover, we give a method to construct permutation polynomials from known ones.

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Acknowledgements

The authors wish to thank the anonymous referees for their helpful comments. The work was partially supported by National Natural Science Foundation of China (NSFC) under Grant 11101131.

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  1. Hubei Province Key Laboratory of Applied Mathematics, Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, China

    Huali Deng & Dabin Zheng

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  1. Huali Deng
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  2. Dabin Zheng
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Correspondence to Dabin Zheng.

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Deng, H., Zheng, D. More classes of permutation trinomials with Niho exponents. Cryptogr. Commun. 11, 227–236 (2019). https://doi.org/10.1007/s12095-018-0284-7

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  • DOI: https://doi.org/10.1007/s12095-018-0284-7

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