摘要
循环矩阵根据矩阵的第一行元素生成,每一行元素都是对第一行元素进行移位得到,所以循环矩阵不仅可以实现硬件电路利用最大化,还能够节省存储空间,具有较高的运算效率。构造符合保密通信系统要求的可逆循环矩阵是一个值得研究的问题。文章纠正部分文献中对可逆矩阵在保密通信中的错误应用,给出正确的应用范例与标准。首先,通过对范德蒙行列式与循环矩阵之间的联系进行研究,获得构造可逆循环矩阵的一个充要条件;然后,根据G(2~8)域的运算特性,将实数域上构造可逆循环矩阵的充要条件推广至有限域上,并提出一种可逆循环矩阵的快速生成算法;最后,对分支数与扩散性进行深入研究,提出一种构造具有最优扩散性能循环矩阵的充分条件。
The cyclic matrix is generated by its fi rst row of elements,and then each row is shiftedby the first row.Therefore,the cyclic matrix can not only maximize the utilization of the hardwarecircuit,but also save the storage space and have high computational efficiency.Constructing areversible cyclic matrix conforming to the requirements of secure communication systems is a problemworthy of study.This paper corrects the erroneous application of the reversible matrix in securecommunication in some documents,and gives the correct application examples and standards.Firstly,anecessary and suffi cient condition for constructing the reversible cyclic matrix is obtained by studyingthe relation between the van Vandermonde Matrix and the cyclic matrix.Secondly,according to thefi nite fi eld G(28)characteristics,the necessary and suffi cient conditions for constructing the reversiblecyclic matrix on the real fi eld are extended to the fi nite fi eld,and a fast generation algorithm of thereversible cyclic matrix is proposed.Finally,a suffi cient condition for constructing the cyclic matrixwith optimal diffusion performance is proposed.
作者
陈小明
游伟青
李文喜
蒋浩
CHEN Xiaoming;YOU Weiqing;LI Wenxi;JIANG Hao(Beijing Electronic Science & Technology Institute, Beijing 100070, China;School of Mathematics & Physics,Anhui University of Technology, Maanshan Anhui 243032, China)
出处
《信息网络安全》
CSCD
2017年第5期7-13,共7页
Netinfo Security
基金
国家重点研发计划[2016YFB0800304]
安徽工业大学大学生创新训练项目(省级)[201510360298]
关键词
保密通信
最优扩散矩阵
可逆矩阵
加密
循环矩阵
secure communication
the optimal diffusion matrix
reversible matrix
encryption
cyclic matrix
