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研究生：	陳彥儒 Chen, Yen-Ju
論文名稱：	對於已知排列多項式的推廣 Generalizations of Known Permutation Polynomials
指導教授：	夏良忠 Hsia, Liang-Chung
口試委員：	夏良忠 Hsia, Liang-Chung 李華介 Li, Hua-Chieh 王姿月 Wang, Tzu-Yueh
口試日期：	2025/01/21
學位類別：	碩士 Master
系所名稱：	數學系 Department of Mathematics
論文出版年：	2025
畢業學年度：	113
語文別：	英文
論文頁數：	49
英文關鍵詞：	Permutation polynomials, Finite field, AGW criterion
DOI URL：	http://doi.org/10.6345/NTNU202500217
論文種類：	學術論文
相關次數：	點閱：7 下載：0
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Permutation polynomials and their compositional inverses have wide applications in cryptography and coding theory. In this thesis, we present generalizations of two distinct known types of permutation polynomials and their compositional inverses, base on the AGW criterion.

Introduction 1
1 Known permutation polynomials and generalizations 1
2 AGW criterion 3
Permutation polynomial arising from characters 7
1 General properties of fr,m(x) 7
2 Prime number case 9
3 Prime power case 15
4 Product of two distinct primes case 19
5 Compositional inverse of f1,1(x) 22
6 Unsolved problems 32
Permutation polynomial arising from q-polynomial 35
1 Origin of Ai(x) and Ei(x) 35
2 Properties of Ei(x) 38
3 Construct permutation polynomial from Ei(x) 42
References 49
                                

[1] Lidl, R., Niederreiter, H. (1997). Finite Fields, Encyclopedia Math. Appl., Cambridge University Press.
[2] Akbary, A., Ghioca D., & Wang Q. (2001). On constructing permutations of finite fields, Finite Fields and Their Applications, 17, 51-67.
[3] Yuan, P. (2024). Local Method for Compositional Inverses of Permutation Polynomials, Communications in Algebra, 52, 3070-3080.

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