The cryptologic characteristics of circulant matrices

被引：0

作者：

Han H. ^{[1
,2
]}

Zhu S. ^{[3
]}

Li Q. ^{[4
]}

He Y. ^{[2
]}

Wang X. ^{[2
]}

Wang Y. ^{[2
]}

机构：

[1] School of Computer, Wuhan University, Hubei, Wuhan

[2] School of Mathematics and Physics, Hubei Polytechnic University, Hubei, Huangshi

[3] Air Force Early Warning Academy of PLA, Hubei Province, Wuhan City

[4] Normal Department, Hubei Polytechnic University, Hubei Province, Huangshi

来源：

Li, Qin (qinliip@163.com) | 1600年 / Inderscience Publishers卷 / 12期

关键词：

Branch number; Circulant matrix; Cryptologic characteristic; Orthormorphic matrix; Symmetrical permutation;

D O I：

10.1504/IJICA.2021.119302

中图分类号：

学科分类号：

摘要：

A 4 × 4 invertible circulant matrix on GF(28) can represent the Mixcolumn operation of AES, which plays an important role as a confusion operation. Starting from the analysis of the Mixcolumns operation of AES, we have mainly research the properties of circulant matrix over finite field, and present a novel algorithm that generates the 4 × 4 circulant inverse matrices and the 4 × 4 circulant matrices with the maximal branch number in this paper. At last, some characteristics of the orthormorphic or symmetrical circulant matrices to arrive at the maximal branch number have been discussed in this paper. An algorithm for generating the 4 × 4 orthormorphic circulant matrix with the maximal branch number is also obtained on the finite field. Furthermore, the conclusion is gained that the symmetrical matrix with maximal branch number does not exist. Copyright © 2021 Inderscience Enterprises Ltd.

引用

页码：248 / 254

页数：6

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