Keccak类S盒的线性性质研究

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。

Research on Linear Properties of Keccak-like S-box

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}, whereand, 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.