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Further results on permutation trinomials with Niho exponents

  • Libo WangEmail author
  • Baofeng Wu
  • Xiaoqiang Yue
  • Yanbin Zheng
Article
  • 39 Downloads

Abstract

In this paper, we prove a conjecture proposed by Deng and Zheng about a class of permutation trinomials over finite fields \({\mathbb {F}}_{2^{2m}}\). In addition, we also construct four classes of permutation trinomials with Niho exponents over \({\mathbb {F}}_{3^{2m}}\).

Keywords

Permutation polynomials Niho exponents Algebraic curves 

Mathematics Subject Classification (2010)

05A05 11T06 11T55 

Notes

Acknowledgments

We would like to thank the editor and anonymous reviewers for their detailed and insightful comments, which have highly improved this paper. This work is partially supported by the Fundamental Research Funds for the Central Universities under Grant No. 21618331, the National Natural Science Foundation of China under Grant Nos. 61502482, 11871248, 11601462 and 61602125, the Natural Science Foundation of Guangxi under Grant No. 2016GXNSFBA380153, and the China Postdoctoral Science Foundation under Grant No. 2018M633041.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyJinan UniversityGuangzhouChina
  2. 2.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  3. 3.School of Mathematics and Computational ScienceXiangtan UniversityHunanChina
  4. 4.Guangxi Key Laboratory of Cryptography and Information SecurityGuilin University of Electronic TechnologyGuilinChina

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