On the security of the STR key exchange protocol

In this paper, we consider the security of the Sakalauskas-Tvarijonas-Raulynaitis (STR) key exchange protocol. We perform an analysis by exploring various cases of the canonical form of the publicly known matrix using elements of linear algebra and number theory. Additionally, we consider the multip...

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Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 2; pp. 1967 - 1980
Main Author Mihalkovich, Aleksejus
Format Journal Article
LanguageEnglish
Published AIMS Press 01.02.2025
Subjects
canonical forms
key exchange protocol
linear algebra
noncommutative cryptography
security analysis
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Summary:In this paper, we consider the security of the Sakalauskas-Tvarijonas-Raulynaitis (STR) key exchange protocol. We perform an analysis by exploring various cases of the canonical form of the publicly known matrix using elements of linear algebra and number theory. Additionally, we consider the multiplicative order of matrices and show how these two factors affect the security of the considered protocol. We show that regardless of the choice of publicly known matrix, the considered protocol is secure under the discrete logarithm assumption. In other words, if at least one of the secret exponents is found, then the STR protocol can be broken in polynomial time.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025092