一类非平衡Feistel网络的线性偏差分析

Linear Deviation Analysis of the Unbalanced Feistel Networks

M.M atsui 1993年就指出线性密码分析是分组密码设计最重要的安全性能指标之一,所以有必要估计分组密码抵抗线性密码分析的能力.M.Kanda等人1999年讨论了传统Feistel密码的线性偏差,K.Nyberg和张如文等人对一类特殊的非平衡Feistel网络的线性偏差进行了研究.本文对一类m分组非平衡Feistel网络的线性偏差关系进行了深入的研究和分析,给出了任意轮线性偏差与轮函数F的线性偏差的数学关系,对其线性偏差的上界进行了讨论,并证明了有关线性偏差关于密钥的平方均值的两个特性.本文的研究推广了K.Nyberg和张如文等人的结论.

In 1993, Matsui put forward that linear cryptanalysis is one of the most important security indeies for designing block ciphers, So it is necessary to estimate the resisting linear cryptanalysis ability of block ciphers, M, Kanda discussed the linear deviation of traditional Feistel ciphers in 1999. Nyberg and Zhang Lu-wen investigated the linear deviation of a kind of special unbalanced Feistel networks, In this paper,we investigated and analyzed the linear deviation of a kind of m-group unbalanced Feistel networks. The mathematical relation between linear deviations of unbalanced Feistel networks and round function F is given. The upperbounds of linear deviation is discussed. Two properties about the average for the square of linear deviation is also proved. Our researches extend the results of K. Nyberg and Zhang Lu-wen.