Keccak類S盒的線性性質(zhì)研究
doi: 10.11999/JEIT190570 cstr: 32379.14.JEIT190570
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戰(zhàn)略支援部隊(duì)信息工程大學(xué) 鄭州 450001
Research on Linear Properties of Keccak-like S-box
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PLA SSF Information Engineering University, Zhengzhou 450001, China
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摘要:
該文將Keccak的S盒一般化為n元Keccak類S盒，研究了Keccak類S盒的線性性質(zhì)。證明了這類S盒的相關(guān)優(yōu)勢的取值都為0或
\begin{document}${2^{ - k}}$\end{document} ，其中
且
，并且對于此范圍內(nèi)的任意k，都存在輸入輸出掩碼使得相關(guān)優(yōu)勢取到
；證明了當(dāng)輸出掩碼確定時(shí)，其非平凡相關(guān)優(yōu)勢都相等；給出了非平凡相關(guān)優(yōu)勢為最大值
時(shí)的充要條件與計(jì)數(shù)，解決了這類S盒的Walsh譜分布規(guī)律問題。
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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