通信学报2017，Vol.38Issue(11)：84-92,9.DOI:10.11959/j.issn.1000-436x.2017206
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
摘要
Abstract
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 conjecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function. Results show that there are at least 253[8Πi=1(2i-1]2cryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF(28), 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Key words
cryptography/cryptographic functions/S-box/affine equivalence/enumeration分类
信息技术与安全科学引用本文复制引用
袁峰,江继军,杨旸,许盛伟..与3类向量值密码函数仿射等价的函数数量研究[J].通信学报,2017,38(11):84-92,9.基金项目
国家自然科学基金资助项目(No.61402112) （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) （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) The National Natural Science Foundation of China (No.61402112),The Fundamental Research Funds for the Central Universities (No.2014XSYJ09,No.328201509),The Fund of Beijing Electronic Science and Technology Institute (No.2014 TD2-OHW) （No.2014 TD2-OHW）
