一类ARIA型扩散结构分支数的研究

doi:10.3969/j.issn.0372-2112.2020.03.005

电子学报 ›› 2020, Vol. 48 ›› Issue (3): 449-455.DOI: 10.3969/j.issn.0372-2112.2020.03.005

一类ARIA型扩散结构分支数的研究

马宿东, 金晨辉, 关杰

战略支援部队信息工程大学, 河南郑州 450001

收稿日期:2019-02-21 修回日期:2019-06-08 出版日期:2020-03-25
- 作者简介:
- 马宿东 男,1995年8月出生于安徽宿州.现为信息工程大学硕士研究生.从事对称密码相关研究.E-mail:1668945764@qq.com;金晨辉 男,信息工程大学教授、博士生导师.1965年3月出生于河南扶沟.研究方向为密码学与信息安全.E-mail:jinchenhui@126.com;关杰女,信息工程大学教授、博士生导师.1974年9月生于河南郑州.研究方向为对称密码的设计与分析.E-mail:guanjie007@163.com
- 基金资助:
- 国家自然科学基金 (No.61572516，No.61272041，No.61272488）

Research on the Branch Number of ARIA-Type Diffusion Structures

MA Su-dong, JIN Chen-hui, GUAN Jie

Strategic Support Force Information Engineering University, Zhengzhou, Henan 450001, China

Received:2019-02-21 Revised:2019-06-08 Online:2020-03-25 Published:2020-03-25
- Supported by:
- National Natural Science Foundation of China (No.61572516, No.61272041, No.61272488)

摘要/Abstract

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.

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

Abstract: 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.

Key words: block cipher, ARIA algorithm, diffusion layer, binary matrix, branch number, ARIA-type diffusion structures, involution matrix

中图分类号:

TP309

马宿东, 金晨辉, 关杰. 一类ARIA型扩散结构分支数的研究[J]. 电子学报, 2020, 48(3): 449-455.

MA Su-dong, JIN Chen-hui, GUAN Jie . Research on the Branch Number of ARIA-Type Diffusion Structures[J]. Acta Electronica Sinica, 2020, 48(3): 449-455.

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一类ARIA型扩散结构分支数的研究

Research on the Branch Number of ARIA-Type Diffusion Structures

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