n 比特置换的差分分支数上界

我们利用编码理论方法, 对F2n上的非线性置换(S盒)的差分分支数进行了分析并给出了差分分支数上界的一般性公式. 我们根据编码理论中关于给定码长和最小距离的最大二元码码字的个数, 估计出长度为2n、码字个数大于2n的二元码的最小距离, 然后将编码理论中二元码和S盒对应起来, 获得n比特S盒的差分分支数上界的估计. 接着将我们的上界与Griesmer界、Sarkar界进行了比较, 结果表明, 我们得到的渐进界更加紧致. 同时, 我们对n=8的情况进行了讨论, 首次得到了8比特S盒的差分分支数的上确界并给出了具体的构造....

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Published inJournal of Cryptologic Research Vol. 7; no. 6; p. 789
Main Authors Qi-Di, YOU, ZHOU, Xuan, LI, Shun, ZHANG, Ying-Jie, 尤启迪, 周旋, 李顺, 张英杰
Format Journal Article
LanguageChinese
Published Beijing Chinese Association for Cryptologic Research, Journal of Cryptologic Research 01.01.2020
Subjects
Binary codes
Boxes
Permutations
Upper bounds
Online AccessGet full text
ISSN2097-4116
DOI10.13868/j.cnki.jcr.000406

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Abstract 我们利用编码理论方法, 对F2n上的非线性置换(S盒)的差分分支数进行了分析并给出了差分分支数上界的一般性公式. 我们根据编码理论中关于给定码长和最小距离的最大二元码码字的个数, 估计出长度为2n、码字个数大于2n的二元码的最小距离, 然后将编码理论中二元码和S盒对应起来, 获得n比特S盒的差分分支数上界的估计. 接着将我们的上界与Griesmer界、Sarkar界进行了比较, 结果表明, 我们得到的渐进界更加紧致. 同时, 我们对n=8的情况进行了讨论, 首次得到了8比特S盒的差分分支数的上确界并给出了具体的构造.
AbstractList 我们利用编码理论方法, 对F2n上的非线性置换(S盒)的差分分支数进行了分析并给出了差分分支数上界的一般性公式. 我们根据编码理论中关于给定码长和最小距离的最大二元码码字的个数, 估计出长度为2n、码字个数大于2n的二元码的最小距离, 然后将编码理论中二元码和S盒对应起来, 获得n比特S盒的差分分支数上界的估计. 接着将我们的上界与Griesmer界、Sarkar界进行了比较, 结果表明, 我们得到的渐进界更加紧致. 同时, 我们对n=8的情况进行了讨论, 首次得到了8比特S盒的差分分支数的上确界并给出了具体的构造.
Author LI, Shun
李顺
Qi-Di, YOU
ZHOU, Xuan
ZHANG, Ying-Jie
周旋
张英杰
尤启迪
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Snippet 我们利用编码理论方法, 对F2n上的非线性置换(S盒)的差分分支数进行了分析并给出了差分分支数上界的一般性公式. 我们根据编码理论中关于给定码长和最小距离的最大二元码码字的个数, 估计出长度为2n、码字个数大于2n的二元码的最小距离, 然后将编码理论中二元码和S盒对应起来, 获得n比特S盒的差分分支数上界的估计....
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Boxes
Permutations
Upper bounds
Title n 比特置换的差分分支数上界
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