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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| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025092 |
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| author | Aleksejus Mihalkovich |
| author_facet | Aleksejus Mihalkovich |
| author_sort | Aleksejus Mihalkovich |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2ec011e2161d4a068f7d54096944d4ba |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2ec011e2161d4a068f7d54096944d4ba2025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011021967198010.3934/math.2025092On the security of the STR key exchange protocolAleksejus Mihalkovich0Department of Applied Mathematics, Kaunas University of Technology, Studentu Str. 50, Kaunas, LT-51368, LithuaniaIn 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.https://www.aimspress.com/article/doi/10.3934/math.2025092security analysisnoncommutative cryptographykey exchange protocollinear algebracanonical forms |
| spellingShingle | Aleksejus Mihalkovich On the security of the STR key exchange protocol AIMS Mathematics security analysis noncommutative cryptography key exchange protocol linear algebra canonical forms |
| title | On the security of the STR key exchange protocol |
| title_full | On the security of the STR key exchange protocol |
| title_fullStr | On the security of the STR key exchange protocol |
| title_full_unstemmed | On the security of the STR key exchange protocol |
| title_short | On the security of the STR key exchange protocol |
| title_sort | on the security of the str key exchange protocol |
| topic | security analysis noncommutative cryptography key exchange protocol linear algebra canonical forms |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025092 |
| work_keys_str_mv | AT aleksejusmihalkovich onthesecurityofthestrkeyexchangeprotocol |