A new class of generalized almost perfect nonlinear power function |
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| Institution: | 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 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. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;2. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;1. College of Information Science and Technology, Jinan University, Guangzhou 510632, China;2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;1. Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China;2. Department of Informatics, University of Bergen, N-5020 Bergen, Norway;1. School of Mathematical Sciences, Henan Key Laboratory of Big Data Processing and Analysis, Luoyang Normal University, Luoyang 471934, China;2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;3. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, China;4. School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | As a generalization of almost perfect nonlinear functions, generalized almost perfect nonlinear (GAPN) functions defined over finite fields of odd characteristic have also important applications in cryptography and finite geometry. In this paper, we mainly focus on GAPN power functions, and a new class of such function (up to EA equivalence) is obtained. Furthermore, using our method, almost all the known GAPN power functions can be confirmed in a simple way. |
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| Keywords: | Generalized almost perfect nonlinear function Newton's formula Algebraic degree |
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