分组密码Cauchy型MDS扩散结构的几点注记  

Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher

作　　者：崔霆[1] 金晨辉[1] 

机构地区：[1]信息工程大学电子技术学院,河南郑州450004

出　　处：《电子学报》2011年第7期1603-1607,共5页Acta Electronica Sinica

基　　金：河南省杰出青年科学基金(No.0312001800)

摘　　要：MDS矩阵是设计分组密码扩散结构的一种重要手段,由有序数组生成的Cauchy矩阵是一类基本的MDS矩阵.本文给出了两个有序数组生成的Cauchy矩阵相同的充要条件,证明了有限域上Cauchy矩阵的个数,证明了Cauchy矩阵一定不是循环移位矩阵;给出了Cauchy矩阵的不同元素个数达到最小值的充要条件,给出了使不同元素个数达到最少,同时1的个数达到最多的Cauchy矩阵的构造方法.此外,本文还提出了对合Cauchy矩阵的一种构造方法.Designing MDS matrices is one of the most important methods to construct diffusion layer for block ciphers,and Cauchy matrices generated by ordered-array is a basic kind of MDS matrices.This paper provides the necessary and sufficient condition of two distinct ordered-arrays generating one same Cauchy matrix.We show the count value of Cauchy matrices over finite field,and predicate that a Cauchy matrix could never be a cyclic-shift matrix.Further,this paper provides the necessary and sufficient condition of Cauchy matrices with minimum number of entries,and supplies the construct method of Cauchy matrix with minimum number of entries and maximum number of occurrences of 1.Additionally,this paper provides a construction for involution Cauchy matrices.

关 键 词：分组密码 扩散结构 MDS(Maximum Distance Separable)矩阵 CAUCHY矩阵 对合矩阵 

分 类 号：TN918.1[电子电信—通信与信息系统]