由APN幂函数构造<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML">  <msub>  <mi>F</mi>  <mrow>   <msup>    <mn>2</mn>    <mrow>     <mn>2</mn><mi>n</mi></mrow>   </msup>   </mrow> </msub> </math></inline-formula>上的置换

田诗竹

doi:10.11959/j.issn.2096-109x.2017.00203

您当前的位置：

首页 >

文章列表页 >

由APN幂函数构造

F_{2^{2 n}}

上的置换

学术论文 | 更新时间：2024-06-03

- 由APN幂函数构造 $F_{2^{2 n}}$ 上的置换
- Permutations from APN power functions over $F_{2^{2 n}}$
- 网络与信息安全学报 2017年3卷第10期页码：72-76
- 作者机构：
  
  1. 中国科学院信息工程研究所信息安全国家重点实验室，北京100093
  2. 中国科学院大学，北京 100049
- 作者简介：
  
  [ "田诗竹（1991-），女，湖北黄冈人，中国科学院信息工程研究所博士生，主要研究方向为信息安全、密码学。" ]
- 基金信息：
  
  国家自然科学基金资助项目;The National Natural Science Foundation of China(61379142)
- DOI：10.11959/j.issn.2096-109x.2017.00203
  中图分类号： TP393
- 网络首发：2017-10，
  
  纸质出版：2017-10-15
- 稿件说明：
移动端阅览
田诗竹. 由APN幂函数构造 $F_{2^{2 n}}$ 上的置换[J]. 网络与信息安全学报, 2017,3(10):72-76.

Shi-zhu TIAN. Permutations from APN power functions over $F_{2^{2 n}}$ [J]. Chinese Journal of Network and Information Security, 2017, 3(10): 72-76.
田诗竹. 由APN幂函数构造 $F_{2^{2 n}}$ 上的置换[J]. 网络与信息安全学报, 2017,3(10):72-76. DOI： 10.11959/j.issn.2096-109x.2017.00203.

Shi-zhu TIAN. Permutations from APN power functions over $F_{2^{2 n}}$ [J]. Chinese Journal of Network and Information Security, 2017, 3(10): 72-76. DOI： 10.11959/j.issn.2096-109x.2017.00203.

由APN幂函数构造

F_{2^{2 n}}

上的置换

PDF下载

摘要

APN 函数是特征为 2 的有限域上达到最低差分均匀度的函数，其中最经典的是 APN 幂函数。在

上的APN幂函数都是3-1函数。推广了前人在奇特征有限域上由2-1函数构造置换的思想，得到偶特征域上由3-1函数构造置换的方法，并由

上的APN幂函数构造置换。根据这种构造，研究了此类置换的差分性质。

Abstract

APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over

.By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics

methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over

were constructed.According to the construction

the differential properties of permutations obtained by this method were discussed.

关键词

Keywords

references

LIDL R , NIEDERREITER H . Finite fields [M ] . Massachusetts : Addison-Wesley Publishing CompanyPress , 1983 .

HOU X D . Determination of a type of permutation trinomials over finite fields [J ] . Finite Fields and Their Applications , 2015 ( 35 ): 16 - 35 .

NYBERG K , . Differentially uniform mappings for cryptography [C ] // The Workshop on the Theory and Application of of Cryptographic Techniques . 1993 : 55 - 64 .

CARLET C . Vectorial boolean functions for cryptography [M ] . Cambridge : Cambridge University PressPress , 2010 .

GOLD R . Maximal recursive sequences with 3-value recursive crosscorrelation functions [J ] . IEEE Trans Inform Theory , 1968 ( 14 ): 154 - 156 .

KASAMI T . The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes [J ] . Information and Control , 1971 ( 18 ): 369 - 394 .

DOBBERTIN H . Almost perfect nonlinear power functions on GF(2 n ):a new case for n divisible by 5 [J ] . Proceedings of Finite Fields and Applications Fq5 , 2000 : 113 - 121 .

BROWNING K , DILLON J , MCQUISTAN M , et al . An APN permutation in dimension six [J ] . Contemporary Mathematics , 2010 ( 58 ):: 33 - 42 .

QU L J , TAN Y , TAN C , et al . Constructing differentially 4-uniform permutations over <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math> via theswitching method [J ] . IEEE Trans Inf Theory , 2013 , 59 ( 7 ): 4675 - 4686 .

LI Y Q , WANG M S . Constructing differentially 4-uniform permutations over GF(2 n ) from quadraticAPN permutations over GF(2 2 n+1 ) [J ] . Designs Codes ＆ Cryptography , 2014 , 61 ( 6 ): 249 - 264 .

TANG D , CARLET C , TANG X H . Differentially 4-uniform bijections by permuting the inverse function [J ] . Designs Codes ＆ Cryptography , 2015 , 77 ( 1 ): 117 - 141 .

PERRIN L , UDOVENKO A , BIRYUKOV A . Cryptanalysis of a theorem:Decomposing the only known solution to the big APN problem [C ] // The 36th Annual International Cryptology Conference . 2016 : 93 - 122 .

CANTEAUT A , DUVAL S , PERRIN L . A generalisation of Dillon’s APN permutation with the best known differential and nonlinear propertiesfor all fields of size 24k+2 [J ] . IEEE Transactions on Information Theory , 2016 ,( 99 ): 1 - 1 .

FU S H , FENG X T . Further results of the cryptographic properties onthe butterfly structure [J ] . Computer Science—Information Theory , 2016 ,( 7 ):

JIA W J , ZENG X Y , LI C L , et al . Permutation polynomials with low differential uniformity over finite fields of odd charateristic [J ] . Science China Mathematics , 2013 ( 56 ): 1429 - 1440 .

BLUHER A B . On x q+1 +ax+b [J ] . Finite Fields and their Applications , 2004 ( 10 ): 285 - 305 .

浏览量

2300

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

暂无数据

由APN幂函数构造 F 2 2n 上的置换

Permutations from APN power functions over F 2 2n

DOI：10.11959/j.issn.2096-109x.2017.00203

摘要

Abstract

关键词

Keywords

references

由APN幂函数构造 $F_{2^{2 n}}$ 上的置换

Permutations from APN power functions over $F_{2^{2 n}}$