与3类向量值密码函数仿射等价的函数数量研究  

Research on affine equivalence enumeration of the three families vectorial function

作　　者：袁峰 江继军 杨旸[2] 许盛伟 

机构地区：[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

出　　处：《通信学报》2017年第11期84-92,共9页Journal on Communications

基　　金：国家自然科学基金资助项目(No.61402112);中央高校基本科研业务费专项基金资助项目(No.2014XSYJ09;No.328201509);北京电子科技学院科研团队基金资助项目(No.2014 TD2-OHW)~~

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(2~8)上至少有2^(53)[8∏i-1(2i-1)]~2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。In recent years, Qu-Tan-Tan-Li function, Zha-Hu-Sun function and Tang-Carlet-Tang function have been pro-posed 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 con-jecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function. Results show that there are at [i=1∏^8（2^i-1）]^2least 2^53 ryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF（2^8）,which can be chosen as S-boxes of block ciphers.

关 键 词：密码学 密码函数 S盒 仿射等价 计数 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]