Three classes of permutation quadrinomials in odd characteristic

被引：2

作者：

Chen, Changhui ^{[1
]}

Kan, Haibin ^{[2
,3
]}

Peng, Jie ^{[1
]}

Zheng, Lijing ^{[4
]}

Li, Yanjun ^{[5
]}

机构：

[1] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China

[2] Fudan Univ, Sch Comp Sci, Shanghai Key Lab Intelligent Informat Proc, Shanghai, Peoples R China

[3] Shanghai Inst Adv Commun & Data Sci, Shanghai Engn Res Ctr Blockchain, Shanghai 200433, Peoples R China

[4] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China

[5] Anhui Univ Finance & Econ, Inst Stat & Appl Math, Bengbu 233030, Anhui, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2024年 / 16卷 / 02期

关键词：

Finite field; Niho exponent; Permutation polynomial; Quadrinomial; FINITE-FIELDS; POLYNOMIALS; TRINOMIALS; BINOMIALS;

D O I：

10.1007/s12095-023-00672-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we construct three classes of permutation quadrinomials with Niho exponents of the form f (x) = alpha(0)x(r) + alpha(1)x(s1(pm-1)+r) + alpha(2)x(s2(pm-1)+r) + alpha(3)x(s3(pm-1)+r) is an element of F-pn [x], where p is an odd prime, n = 2m is a positive even integer, and (r, s(1), s(2), s(3)) = (1, -1/p(k)-2, 1, p(k)-1/p(k)-2), (1, p(k)+1/p(k)+2, 1, 1/p(k)+2) and (3, 1, 2, 3), respectively. The exponents of the first two classes are considered for the first time, and the third class covers all the permutation polynomials proposed by Gupta (Designs Codes and Cryptography 88, 1-17, 2020).

引用

页码：351 / 365

页数：15

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