Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher

CUI Ting; JIN Chen-hui

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Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher

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- Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher
- Acta Electronica Sinica Vol. 39, Issue 7, Pages: 1603-1607(2011)
- 作者机构：
  
  信息工程大学电子技术学院,河南,郑州,450004
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2011
- 稿件说明：
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CUI Ting, JIN Chen-hui. Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher[J]. Acta Electronica Sinica, 2011, 39(7): 1603-1607.
DOI：

CUI Ting, JIN Chen-hui. Several Remarks of Cauchy Type MDS Diffusion Layer for Block Cipher[J]. Acta Electronica Sinica, 2011, 39(7): 1603-1607. DOI：

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.

Abstract

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.

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Related Institution

Strategic Support Force Information Engineering University

State Key Laboratory of Information Security， Institute of Information Engineering， Chinese Academy of Sciences

College of Information and Communication， National University of Defense Technology

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