Research Progress on Permutation Polynomials in Finite Fields

doi:10.19678/j.issn.1000-3428.0050912

Computer Engineering ›› 2019, Vol. 45 ›› Issue (9): 124-127. doi: 10.19678/j.issn.1000-3428.0050912

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Research Progress on Permutation Polynomials in Finite Fields

ZHENG Yanbin¹, YI Zongxiang^2,3

1. Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China;
2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
3. Department of Public Foundation, Guangdong University of Science and Technology, Dongguan, Guangdong 523083, China

Received:2018-03-23 Revised:2018-04-27 Online:2019-09-15 Published:2019-09-03
Supported by:
This work is supported by the Science and Technology Program of SGCC(No.5217L017000N).

有限域上置换多项式的研究进展

郑彦斌¹, 易宗向^2,3

1. 桂林电子科技大学广西密码学与信息安全重点实验室, 广西桂林 541004;
2. 广州大学数学与信息科学学院, 广州 510006;
3. 广东科技学院公共基础部, 广东东莞 523083

作者简介:郑彦斌(1983-),男,讲师、博士,主研方向为密码学、有限域;易宗向,博士。
基金资助:
国家自然科学基金（61602125，61502113）；广西自然科学基金（2016GXNSFBA380153，2017GXNSFAA198192）；广西密码学与信息安全重点实验室项目（GCIS201625）。

Abstract

Abstract: The Akbary-Ghioca-Wang(AGW) criterion and piecewise method are two main methods for constructing permutation polynomials of finite fields.This paper introduces the application of permutation polynomials in cryptography and coding theory,reviews the research progress of the permutation polynomials and their inverses constructed by AGW criterion and piecewise method,describes the problem of permutation polynomials,and finally the next step is to look into the research work.

Key words: cryptography, finite fields, inverses of permutation, polynomials, Akbary-Ghioca-Wang(AGW) criterion, piecewise method

摘要： AGW准则和分段方法是构造有限域上置换多项式的两种主要方法。介绍有限域上置换多项式在密码学和编码理论中的应用，总结利用AGW准则和分段方法构造有限域上置换多项式和逆置换的研究进展，阐述置换多项式存在的问题，并对下一步研究工作进行展望。

关键词: 密码学, 有限域, 逆置换, 多项式, AGW准则, 分段方法

CLC Number:

TP309

ZHENG Yanbin, YI Zongxiang. Research Progress on Permutation Polynomials in Finite Fields[J]. Computer Engineering, 2019, 45(9): 124-127.

郑彦斌, 易宗向. 有限域上置换多项式的研究进展[J]. 计算机工程, 2019, 45(9): 124-127.

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