非线性不变性及相关矩阵方法在密码分析中的应用  

The application of nonlinear invariants and correlation matrix in cryptanalysis

作　　者：张文英[1] 孙晓萌 雷虹[2] ZHANG Wenying;SUN Xiaomeng;LEI Hong(School of Information Science and Engineering,Shandong Normal University,250014,Jinan;Dongying Vocational College,257091,Dongying,Shandong,PRC)

机构地区：[1]山东师范大学信息科学与工程学院,济南市250014 [2]东营职业学院,山东省东营市257091

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期51-57,共7页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(61672330);山东省自然科学基金(ZR2020KF011).

摘　　要：对称密码体制中的许多映射是布尔映射.该文在向量布尔映射和实向量空间的特殊线性映射之间建立联系,将函数的一些密码性质用相关矩阵来刻画.相关矩阵中的元素定义为输入的线性组合与输出线性组合的相关系数.相关矩阵不仅直接刻画向量布尔函数输出线性组合与输入线性组合的符合率,是线性密码分析的有力工具,还能够为弱密钥攻击提供理论支持.In many symmetrical encryptions,the cryptographic functions are boolean functions.In this paper,a bridge between the vectorial boolean functions and their correlation matrices is build.Some cryptographic characters can be described by their correlation matrices.The entries in correlation matrices are the correlation coefficients of the input bits and the output bits.The correlation matrices can not only describes the match rate between the inputs and the outputs of the encryption function.Hence it is the tool for linear cryptanalysis.It is also a useful tool for finding weak keys.

关 键 词：分组密码 相关矩阵 线性密码分析 弱密钥 非线性不变性 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]