计算机工程 ›› 2019, Vol. 45 ›› Issue (9): 124-127.doi: 10.19678/j.issn.1000-3428.0050912

• 安全技术 • 上一篇    下一篇

有限域上置换多项式的研究进展

郑彦斌1, 易宗向2,3   

  1. 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
  • 收稿日期:2018-03-23 修回日期:2018-04-27 出版日期:2019-09-15 发布日期:2019-09-03
  • 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。
  • 基金项目:
    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)。

Research Progress on Permutation Polynomials in Finite Fields

ZHENG Yanbin1, YI Zongxiang2,3   

  1. 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).

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

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

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