Research on the Branch Number of ARIA-Type Diffusion Structures

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

doi:10.3969/j.issn.0372-2112.2020.03.005

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Research on the Branch Number of ARIA-Type Diffusion Structures

更新时间：2025-07-16

- Research on the Branch Number of ARIA-Type Diffusion Structures
- Acta Electronica Sinica Vol. 48, Issue 3, Pages: 449-455(2020)
- 作者机构：
  
  战略支援部队信息工程大学,河南,郑州,450001
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61572516, No.61272041, No.61272488)
- DOI：10.3969/j.issn.0372-2112.2020.03.005
  CLC： TP309
- Published Online：25 March 2020，
  
  Published：2020
- 稿件说明：
移动端阅览
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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2020.03.005.

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.

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.

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