Two classes of permutation trinomials with Niho exponents over finite fields with even characteristic

被引：12
作者：
Zheng, Lijing [1 ,5 ]
Kan, Haibin [2 ,3 ]
Peng, Jie [4 ]
机构：
[1] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China
[2] Fudan Univ, Sch Comp Sci, Shanghai Key Lab Intelligent Inform Proc, Shanghai 200433, Peoples R China
[3] Shanghai Engn Res Ctr Blockchain Shanghai, Fudan Zhongan Joint Lab Blockchain & Inform Secur, Shanghai 200433, Peoples R China
[4] Shanghai Normal Univ, Math & Sci Coll, Guilin Rd 100, Shanghai 200234, Peoples R China
[5] Guangxi Univ Sci & Technol, Coll Comp Sci & Commun Engn, Liuzhou 545006, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2020年 / 68卷
基金：
中国国家自然科学基金; 国家重点研发计划;
关键词：
Finite field; Niho exponent; Permutation trinomial; POLYNOMIALS; CONSTRUCTIONS;
D O I：
10.1016/j.ffa.2020.101754
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider two classes of permutation trinomials with Niho-type exponents over the finite field F-22m. Some sufficient conditions are obtained to characterize the coefficients of the permutation trinomials. Our numerical result suggests that those sufficient conditions for one class are also necessary. (C) 2020 Published by Elsevier Inc.
引用
收藏
页数：14
相关论文
共 34 条
[1]  
Akbary A., 2007, Int. J. Math. Math. Sci.
[2]   On constructing permutations of finite fields [J].
Akbary, Amir ;
Ghioca, Dragos ;
Wang, Qiang .
FINITE FIELDS AND THEIR APPLICATIONS, 2011, 17 (01) :51-67
[3]   On a conjecture about a class of permutation trinomials [J].
Bartoli, Daniele .
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 52 :30-50
[4]  
Bartoli D, 2018, DESIGN CODE CRYPTOGR, V86, P1589, DOI 10.1007/s10623-017-0415-8
[5]   PERMUTATION TRINOMIALS OVER FINITE FIELDS WITH EVEN CHARACTERISTIC [J].
Ding, Cunsheng ;
Qu, Longjiang ;
Wang, Qiang ;
Yuan, Jin ;
Yuan, Pingzhi .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2015, 29 (01) :79-92
[6]   Further results on permutation polynomials of the form (xpm - x plus δ)s + x over Fp2m [J].
Gupta, Rohit ;
Sharma, R. K. .
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 50 :196-208
[7]   Some new classes of permutation trinomials over finite fields with even characteristic [J].
Gupta, Rohit ;
Sharma, R. K. .
FINITE FIELDS AND THEIR APPLICATIONS, 2016, 41 :89-96
[8]  
Hou X., 2019, ARXIV190607240V1
[9]   On a class of permutation trinomials in characteristic 2 [J].
Hou, Xiang-dong .
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2019, 11 (06) :1199-1210
[10]   Determination of a type of permutation trinomials over finite fields, II [J].
Hou, Xiang-dong .
FINITE FIELDS AND THEIR APPLICATIONS, 2015, 35 :16-35
1234