Cryptanalysis of a key exchange protocol based on a modified tropical structure

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-08-03 DOI:10.1007/s10623-024-01469-9

Huawei Huang, Changgen Peng, Lunzhi Deng

引用次数: 0

Abstract

This article analyzes a key exchange protocol based on a modified tropical structure proposed by Ahmed et al. in 2023. It is shown that the modified tropical semiring is isomorphic to the \(2\times 2\) tropical circular matrix semiring. Therefore, matrices in this modified tropical semiring can be represented as tropical matrices, and the key exchange protocol is actually based on the tropical matrix semiring. Tropical irreducible matrices exhibit almost linear periodic property. Efficient algorithms for calculating the linear period and defect of irreducible matrices are designed. Based on the public information of the protocol, the equivalent private key can be computed and then the shared key is easily obtained. The analysis shows that the key exchange protocol based on this modified tropical structure is not secure.

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基于改进热带结构的密钥交换协议的密码分析

本文分析了 Ahmed 等人在 2023 年提出的基于修正热带结构的密钥交换协议。结果表明，修正的热带结构与热带圆矩阵结构同构。因此，该修正热带配系中的矩阵可以表示为热带矩阵，而密钥交换协议实际上是基于热带矩阵配系的。热带不可还原矩阵表现出几乎线性的周期特性。本文设计了计算不可还原矩阵线性周期和缺陷的高效算法。根据协议的公开信息，可以计算出等价私钥，然后很容易得到共享密钥。分析表明，基于这种改进的热带结构的密钥交换协议并不安全。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.