计算机科学 ›› 2017, Vol. 44 ›› Issue (5): 170-171, 177.doi: 10.11896/j.issn.1002-137X.2017.05.030

• 信息安全 • 上一篇    下一篇

一类有限域上的置换多项式

魏晴,孙光洪   

  1. 河海大学理学院 南京211100,河海大学理学院 南京211100
  • 出版日期:2018-11-13 发布日期:2018-11-13
  • 基金资助:
    本文受国家自然科学基金(61103184,4,61272542)资助

Class of Permutation Polynomials over Finite Fields

WEI Qing and SUN Guang-hong   

  • Online:2018-11-13 Published:2018-11-13

摘要: 有限域上的置换多项式在科学工程中的多个领域有着广泛的应用,尤其应用于现代通讯、密码学等领域中。基于Zha等人在文献[23]中提出,当t为偶数时,有限域Fpn上形如(xpk-x+δ)t+γx+βTr(x)的多项式是置换的,通过进一步研究,运用证明置换多项式的一般方法,将其改进为无论t为奇数或偶数,(xpk+1-xp+δ)t+γx+βTr(x)形式的多项式在Fpn上均是置换的。

关键词: 有限域,置换多项式,迹函数

Abstract: Permutation polynomials over finite fields have been applied in wild areas of science and engineering,especially in the modern communication technology,cryptography and so on.Based on paper [23],it has been proved that when t is any even integer,the form (xpk-x+δ)t+γx+βTr(x) is a class of permutation polynomials over Fpn.Our work proved that whenever t is any even or odd integer,the form (xpk+1-xp+δ)t+γx+βTr(x)is permutation polynomials over Fpn.

Key words: Finite fields,Permutation polynomials,Trace function

[1] COHEN S D.Permutation group theory and permutation polynomials [M]∥Algebra and Combinatorics.Hong Kong,Sprin-ger,Singapore,1999:133-146
[2] LAIGLE-CHAPUY Y.Permutation polynomials and applica-tions to coding theory [J].Finite Fields Appl.,2007:13(1):58-70.
[3] LIDL R,NIEDERREITER H.Introduction to finite fields and their applications[M].Cambridge University Press,1986.
[4] MULLEN G L.Permutation polynomials over finite fields[C]∥Proc.Conf.Finite Fields and Their Applications in Lect.Notes Pure Appl.Math.,Marcel Dekker,New York,1993:131-151.
[5] LIDL R,MULLEN G L.When does a polynomial over a finite field permute the elements of the field [J].American Math Monthly,1988,95(3):243-246.
[6] LIDL R,MULLEN G L.When does a polynomial over a finite field permute the elements of the field? II [J].Amer Math Monthly,1993,100:71-74.
[7] COULTER R,HENDERSON M,MATTHEWS R.A note onconstructing permutation polynomials [J].Finite Fields Appl,2009,15:553-557.
[8] MARCOS J E.Specific permutation polynomials over finite fi-elds [J].Finite Fields and Their Applications 2008,7(2):105-112.
[9] ZIEVE M E.Classes of permutation polynomials based on cyclotomy and an additive analogue[M]∥Additive Number Theo-ry.Springer-Verlag,2010:366-361.
[10] HELLESETH T,ZINOVIEV V.New Klooserman sums identities over F2m for all m [J].Finite Fields Their Applications,2003,9(2):187-193.
[11] YUAN J,DING C,WANG H,et al.Permutation polynomials of the form (xp-x+δ)s+L(x) [J].Finite Fields Appl,2008,14:482-493.
[12] ZHENG X,ZHU X,HU L.Two new permutation polynomials with the form (x2k+x+δ)s+x over F2n [J].Applicable Algebra in Engineering,Communication and Computing,2010,21(2):145-150.
[13] CAO X,HU L,ZHA Z.Constructing permutation polynomials from piecewise permutations[J].Finite Fields & Their Appllications,2014,26(3):162-174.
[14] ZHENG Y,YU Y,ZHANG Y,et al.Peicewise constructions if inverses of cyclotomic mapping permutation polynomials [J].Finite Fields & Their Appllications,2016,40(c):1-9.
[15] HOU X.Permutation polynomials over finite fields—A survey of recent advances [J].Finite Fields & Their Appllications,2015,32:82-119.
[16] ZHENG Y,YUAN P,PEI D.Peicewise constructions of inverses of some permutation polynomials [J].Finite Fields & Their Appllications,2015,36:151-169.
[17] YUAN P,DING C.Further results on permutation polynomials over finite fields [J].Finite Fields & Their Appllications,2014,27:88-103.
[18] YUAN P,ZHENG Y.Permutation polynomials from piecewise functions [J].Finite Fields & Their Appllications,2015,35(c):215-230.
[19] ZHENG Y,YUAN P,PEI D.Large classes of permutation polynomials over Fq2[M].Springer Science+ Business Media New York,2016.
[20] TU Z,ZENG X,LI C,et al.Permutation polynomials of theform (xpm-x+δ)s+L(x) over the finite field Fp2mof odd characteristic [J].Finite Fields Appl,2015,34(c):20-35.
[21] TU Z,ZENG X,JIANG Y.Two classes of permutation polynomials having the form (x2m+x+δ)s+x[J].Finite Fields Appl,2015,31:12-24.
[22] ZENG X,TIAN S,TU Z.Permutation polynomials from trace functions over finite fields [J].Finite Fields Appl,2015,35:36-51.
[23] ZHA Z,HU L.Two classes of permutation polynomials over finite fields [J].Finite Fields Appl,2012,18(4):781-790.

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 雷丽晖,王静. 可能性测度下的LTL模型检测并行化研究[J]. 计算机科学, 2018, 45(4): 71 -75, 88 .
[2] 夏庆勋,庄毅. 一种基于局部性原理的远程验证机制[J]. 计算机科学, 2018, 45(4): 148 -151, 162 .
[3] 厉柏伸,李领治,孙涌,朱艳琴. 基于伪梯度提升决策树的内网防御算法[J]. 计算机科学, 2018, 45(4): 157 -162 .
[4] 王欢,张云峰,张艳. 一种基于CFDs规则的修复序列快速判定方法[J]. 计算机科学, 2018, 45(3): 311 -316 .
[5] 孙启,金燕,何琨,徐凌轩. 用于求解混合车辆路径问题的混合进化算法[J]. 计算机科学, 2018, 45(4): 76 -82 .
[6] 张佳男,肖鸣宇. 带权混合支配问题的近似算法研究[J]. 计算机科学, 2018, 45(4): 83 -88 .
[7] 伍建辉,黄中祥,李武,吴健辉,彭鑫,张生. 城市道路建设时序决策的鲁棒优化[J]. 计算机科学, 2018, 45(4): 89 -93 .
[8] 刘琴. 计算机取证过程中基于约束的数据质量问题研究[J]. 计算机科学, 2018, 45(4): 169 -172 .
[9] 钟菲,杨斌. 基于主成分分析网络的车牌检测方法[J]. 计算机科学, 2018, 45(3): 268 -273 .
[10] 史雯隽,武继刚,罗裕春. 针对移动云计算任务迁移的快速高效调度算法[J]. 计算机科学, 2018, 45(4): 94 -99, 116 .