Research on affine equivalence enumeration of the three families vectorial function

Feng YUAN; Ji-jun JIANG; Yang YANG; Sheng-wei XU

doi:10.11959/j.issn.1000-436x.2017206

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Research on affine equivalence enumeration of the three families vectorial function

Papers | 更新时间：2024-06-05

- Research on affine equivalence enumeration of the three families vectorial function
- Journal on Communications Vol. 38, Issue 11, Pages: 84-92(2017)
- 作者机构：
  
  1. 北京电子科技学院信息安全研究所，北京 100070
  2. 福州大学数学与计算机科学学院，福建福州 350108
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61402112);The Fundamental Research Funds for the Central Universities(2014XSYJ09);The Fundamental Research Funds for the Central Universities(328201509);The Fund of Beijing Electronic Science and Technology Institute(2014TD2-OHW)
- DOI：10.11959/j.issn.1000-436x.2017206
  CLC： TP309.7
- Online First：2017-11，
  
  Published：25 November 2017
- 稿件说明：
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Feng YUAN, Ji-jun JIANG, Yang YANG, et al. Research on affine equivalence enumeration of the three families vectorial function[J]. Journal on Communications, 2017, 38(11): 84-92.
DOI：

Feng YUAN, Ji-jun JIANG, Yang YANG, et al. Research on affine equivalence enumeration of the three families vectorial function[J]. Journal on Communications, 2017, 38(11): 84-92. DOI： 10.11959/j.issn.1000-436x.2017206.

摘要

Qu-Tan-Tan-Li函数、Zha-Hu-Sun函数和Tang-Carlet-Tang函数是近些年提出的差分均匀度为4、各项安全性指标均优良的向量值密码函数。研究与这3种密码函数仿射等价函数的计数问题。利用有限域的一些性质，分别计算出与Zha-Hu-Sun函数仿射等价函数数量的上下界，与Qu-Tan-Tan-Li函数和Tang-Carlet-Tang函数仿射等价函数数量的上界。此外，对于Zha-Hu-Sun函数仿射等价函数数量的精确值提出了猜测。研究结果表明，有限域GF(2

)上至少有5

个与Zha-Hu-Sun函数仿射等价的密码函数可直接用于分组密码的S盒。

Abstract

In recent years

Qu-Tan-Tan-Li function

Zha-Hu-Sun function and Tang-Carlet-Tang function have been proposed with differential uniformity 4 and many good cryptographic properties.the counting problem of affine equivalent to the three families cryptographic functions was investigated.By using some properties of finite fields

the upper and lower bound of the number of affine equivalent to the Zha-Hu-Sun function

and the upper bound of the number of affine equivalent to the Qu-Tan-Tan-Li function and Tang-Carlet-Tang function were computed

respectively.Moreover

a conjecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function.Results show that there are at least

cryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF(2

)

which can be chosen as S-boxes of block ciphers.

关键词

Keywords

references

DAEMEN J , RIJMEN V . The design of rijndael:AES-the advanced encryption standard [M ] . Springer-Verlag , 2002 .

ZHA Z B , HU L , SUN S . Constructing new differentially 4-uniform permutations from the Inverse function [J ] . Finite Fields and Their Applications , 2014 , 25 : 64 - 78 .

BERGER T P , CANTEAUT A , CHARPIN P , et al . On almost perfect nonlinear functions over GF(2 n ) [J ] . IEEE Transactions on Information Theory , 2006 , 52 ( 9 ): 4160 - 4170 .

CARLET C , GONG G , TAN Y . Quadratic zero-difference balanced functions,APN functions and strongly regular graphs [J ] . Designs,Codes and Crytography , 2016 , 78 ( 3 ): 629 - 654 .

BROWNING K A , DILLCN J F , MCQUISTAN M T , et al . An APN permutation in dimension six [C ] // The 9th Interactional Conference on Finite Fields and Their Applications (FQ9) . 2010 : 33 - 42 .

CARLET C , . On known and new differentially uniform functions [C ] // The 16th Australasian Conference on Information Security and Privacy (ACISP 2011) . 2011 : 1 - 15 .

QU L , TAN Y , TAN C H , et al . Constructing differentially 4-uniform permutations over GF(22 k ) via the switching method [J ] . IEEE Transactions on Information Theory , 2013 , 59 ( 7 ): 4675 - 4686 .

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

CARLET C , CHARPIN P , ZINOVIEV V . Codes,bent functions and permutations suitable for DES-like cryptosystems [J ] . Designs,Codes and Cryptography , 1998 , 15 ( 2 ): 125 - 156 .

LIDL R , NIEDERREITER H . Finite fields [M ] . Second edition,Cambridge,U . K. : Cambridge University PressPress , 1983 .

WAN Z . Geometry of classical groups over finite fields [M ] . Second edition,Bejing : Science PressPress , 2006 .

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