一类ARIA型扩散结构分支数的研究  

Research on the Branch Number of ARIA-Type Diffusion Structures

作　　者：马宿东 金晨辉 关杰[1] MA Su-dong;JIN Chen-hui;GUAN Jie(Strategic Support Force Information Engineering University,Zhengzhou,Henan 450001,China)

机构地区：[1]战略支援部队信息工程大学,河南郑州450001

出　　处：《电子学报》2020年第3期449-455,共7页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61572516,No.61272041,No.61272488)。

摘　　要：分支数达到最大的二元矩阵被广泛应用到分组密码扩散层的设计中.本文针对ARIA算法的扩散层,首先给出了ARIA型扩散结构的定义,给出了16阶ARIA型扩散结构的分支数情况,进一步给出了分支数为8的16阶ARIA型扩散结构的充要条件,从而构造了一大批可供选择的分支数为8的16阶二元矩阵.其次,解决了16阶ARIA型扩散结构分支数为8的计数问题,最后,给出了分支数为8的16阶对合ARIA型扩散结构的构造方法.本文的研究成果为构造分支数达到最大的16阶对合二元方阵提供了一种新方法.The binary matrix with the largest branch number is widely used in the design of diffusion layers in block cipher.In this paper,for the diffusion layer of ARIA algorithm,the definition of ARIA diffusion structure is given firstly,and the branch number of 16-order ARIA diffusion structure is given.The necessary and sufficient conditions for the 16-order ARIA-type diffusion structures with the branch number 8 are further given,and a large number of 16-order ARIA-type diffusion structures with the branch number 8 are constructed.Secondly,the counting problem of 16-order ARIA-type diffusion structures with the branch number 8 is solved.Finally,the construction methods of the 16-order involution ARIA-type diffusion structure are given.The research results of this paper provide a method for constructing 16-order involution binary matrix with the largest branch number.

关 键 词：分组密码 ARIA算法 扩散结构 二元矩阵 分支数 ARIA型扩散结构 对合矩阵 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]