A class of permutation trinomials over finite fields of odd characteristic

被引：18

作者：

Tu, Ziran ^{[1
]}

Zeng, Xiangyong ^{[2
]}

机构：

[1] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471003, Peoples R China

[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2019年 / 11卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Finite field; Permutation trinomial; Trace function; POLYNOMIALS; BINOMIALS;

D O I：

10.1007/s12095-018-0307-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper studies the permutation behavior of the polynomial f(x)=x+a1xq(q-1)+1+a2x2(q-1)+1 in Fq2[x] for odd q, and finds a set of the coefficient pairs (a1,a2) that leads f(x) to be a permutation of Fq2. We transform the problem of proving that f is a permutation into determining the number of solutions to some low-degree equations in the unit circle of F(q)2.

引用

页码：563 / 583

页数：21

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