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On inverses of some permutation polynomials over finite fields of characteristic three
Affiliation:1. School of Mathematical Sciences, Qufu Normal University, Qufu, China;2. School of Computer Science and Technology, Dongguan University of Technology, Dongguan, China;3. Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China;4. College of Information Science and Technology, Jinan University, Guangzhou, China;1. College of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;2. College of Information Science and Technology, Jinan University, Guangzhou 510632, China;3. National Center for Applied Mathematics in Hunan, Xiangtan University, Xiangtan 411105, China;1. School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, China;2. Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science,Fudan University, Shanghai, 200433, China;3. Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Shanghai Engineering Research Center of Blockchain Shanghai, 200433, China;4. Mathematics and Science College of Shanghai Normal University, Guilin Road #100, Shanghai, 200234, China;5. College of Computer Science and Communication Engineering, Guangxi University of Science and Technology, Liuzhou, 545006, China;1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China;2. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;3. Department of Informatics, University of Bergen, Bergen N-5020, Norway;4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;5. Department of Electrical Engineering and Computer Science, University of Stavanger, 4036, Stavanger, Norway
Abstract:By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping permutation polynomials over finite fields of characteristic three.
Keywords:Permutation polynomials  Inverses  Reversed Dickson polynomials
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