信息网络安全

信息网络安全 ›› 2017, Vol. 17 ›› Issue (5): 7-7.doi: 10.3969/j.issn.1671-1122.2017.05.002

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一类可逆矩阵在保密通信中的应用

陈小明1, 游伟青1(), 李文喜2, 蒋浩2   

  1. 1. 北京电子科技学院,北京 100070
    2. 安徽工业大学数理科学与工程学院,安徽马鞍山 243032
  • 收稿日期:2017-03-25 出版日期:2017-05-20 发布日期:2020-05-12
  • 作者简介:

    作者简介： 陈小明（1964—）,男,湖南,教授,博士,主要研究方向为密码学与信息安全、理论计算机科学;游伟青（1994—）,男,安徽,硕士研究生,主要研究方向为密码算法设计与分析、代数学;李文喜（1979—）,男,安徽,副教授,博士,主要研究方向为代数学、密码与信息安全;蒋浩（1994—）,男,安徽,本科,主要研究方向为代数学。

  • 基金资助:
    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]

The Application of a Kind of Reversible Matrix in Secure Communication

Xiaoming CHEN1, Weiqing YOU1(), Wenxi LI2, Hao JIANG2   

  1. 1. Beijing Electronic Science & Technology Institute, Beijing 100070, China;
    2. School of Mathematics & Physics, Anhui University of Technology, Maanshan Anhui 243032, China;
  • Received:2017-03-25 Online:2017-05-20 Published:2020-05-12

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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(28)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。

关键词: 保密通信, 最优扩散矩阵, 可逆矩阵, 加密, 循环矩阵

Abstract:

The cyclic matrix is generated by its first row of elements, and then each row is shifted by the first row. Therefore, the cyclic matrix can not only maximize the utilization of the hardware circuit, but also save the storage space and have high computational efficiency. Constructing a reversible cyclic matrix conforming to the requirements of secure communication systems is a problem worthy of study. This paper corrects the erroneous application of the reversible matrix in secure communication in some documents, and gives the correct application examples and standards. Firstly, a necessary and sufficient condition for constructing the reversible cyclic matrix is obtained by studying the relation between the van Vandermonde Matrix and the cyclic matrix. Secondly, according to the finite field G(28) characteristics, the necessary and sufficient conditions for constructing the reversible cyclic matrix on the real field are extended to the finite field, and a fast generation algorithm of the reversible cyclic matrix is proposed. Finally, a sufficient condition for constructing the cyclic matrix with optimal diffusion performance is proposed.

Key words: secure communication, the optimal diffusion matrix, reversible matrix, encryption, cyclic matrix

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