Research on Linear Properties of Keccak-like S-box
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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。
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.
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Key words:
- Hash function /
- Keccak /
- S-box /
- Linear properties
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