关杰,
黄俊君^,
战略支援部队信息工程大学 郑州 450001
基金项目:国家自然科学基金(61572516, 61272041, 61272488)

详细信息

作者简介:关杰：女，1974年生，教授、博士生导师，主要研究方向为密码理论和密码算法分析
黄俊君：男，1995年生，硕士生，主要研究方向为对称密码设计与分析

通讯作者:黄俊君　hjj7752@outlook.com

中图分类号:TN918.1

计量

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被引次数:0

出版历程

收稿日期:2019-07-29
修回日期:2020-04-19
网络出版日期:2020-04-29
刊出日期:2020-07-23

Research on Linear Properties of Keccak-like S-box

Jie GUAN,
Junjun HUANG^,
PLA SSF Information Engineering University, Zhengzhou 450001, China
Funds:The National Natural Science Foundation of China (61572516, 61272041, 61272488)


摘要
摘要:该文将Keccak的S盒一般化为n元Keccak类S盒，研究了Keccak类S盒的线性性质。证明了这类S盒的相关优势的取值都为0或
\begin{document}${2^{ - k}}$\end{document}，其中
且
，并且对于此范围内的任意k，都存在输入输出掩码使得相关优势取到
；证明了当输出掩码确定时，其非平凡相关优势都相等；给出了非平凡相关优势为最大值
时的充要条件与计数，解决了这类S盒的Walsh谱分布规律问题。
关键词:哈希函数/
Keccak/
S盒/
线性性质
Abstract:In this paper, the S-box of Keccak is generalized into n-variable Keccak-like S-box, and the linear properties of n-variable Keccak-like S-box is studied. It is proved that all the values of correlation advantages of this kind of S-box are 0 or
\begin{document}${2^{ - k}}$\end{document}, where
and
, and for any k in this range, there is an input mask and an output mask that make the correlation advantage be
. Furthermore, it is proved that when the output mask is fixed, the values of the nontrivial correlation advantages of the S-box are determined. Then, the necessary and sufficient condition are given when the count for the nontrivial correlation advantage is the maximum value
. Finally, the value distribution of the Walsh spectrum of Keccak-like S-box is presented.
Key words:Hash function/
Keccak/
S-box/
Linear properties



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