与3类向量值密码函数仿射等价的函数数量研究

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

Journal on Communications ›› 2017, Vol. 38 ›› Issue (11): 84-92.doi: 10.11959/j.issn.1000-436x.2017206

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Research on affine equivalence enumeration of the three families vectorial function

Feng YUAN¹(),Ji-jun JIANG¹,Yang YANG²,Sheng-wei XU¹

¹ Information Security Institute,Beijing Electronic Science and Technology Institute,Beijing 100070,China
² College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China

Revised:2017-07-05 Online:2017-11-01 Published:2017-12-13
Supported by:
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)

Abstract

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 $2^{53} {[\prod_{i = 1}^{8} (2^{i} - 1)]}^{2}$ cryptographic 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.

Key words: cryptography, cryptographic functions, S-box, affine equivalence, enumeration

CLC Number:

TP309.7

Feng YUAN,Ji-jun JIANG,Yang YANG,Sheng-wei XU. Research on affine equivalence enumeration of the three families vectorial function[J]. Journal on Communications, 2017, 38(11): 84-92.

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Research on affine equivalence enumeration of the three families vectorial function

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