非平衡Feistel网络的线性可证明安全性的进一步分析

Furthermore Analyses of Linear Provable Security for a Class of Unbalanced Feistel Networks

线性密码分析已成为分组密码最主要的密码分析方法之一.基于此,本文深入研究了一类非平衡Feis-tel网络的线性可证明安全性.设LP为该非平衡Feistel网络的轮函数F的线性偏差的最大值,本文从非平衡Feistel网络的线性偏差的结构形式入手,在轮子密钥是相互独立且均匀分布的假设下,证明了当轮数不少于m轮时,该非平衡Feistel网络的线性偏差关于密钥的平方均值的上界为LP的平方;当轮数不少于2m轮时,证明了该非平衡Feistel网络的线性偏差关于密钥的平方均值的上界为LP四次方的2倍.

Linear Cryptanalysis is one of the most important attacks on block ciphers.In this paper,the linear provable security for a class of unbalanced Feistel networks is investigated deeply. Using the structure of linear deviation, we prove that the upper bound of r-round（ r ≥ m） linear hull probabilities are bounded by LP x LP and r-round（ r ≥ 2m） linear hull probabilities are bounded by 2（LP× LP× LP×LP） when the maximal linear hull probabilities of round function is LP and rounds keys are independent and uniformly random.