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Title: Modifying the tropical version of Stickel's key exchange protocol (English)
Author: Muanalifah, Any
Author: Sergeev, Sergei
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 65
Issue: 6
Year: 2020
Pages: 727-753
Summary lang: English
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Category: math
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Summary: A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application of that generalized attack to all our new protocols. (English)
Keyword: Stickel's protocol
Keyword: tropical algebra
Keyword: cryptography
Keyword: commuting matrices
MSC: 15A80
MSC: 94A60
idZBL: Zbl 07285954
idMR: MR4191366
DOI: 10.21136/AM.2020.0325-19
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Date available: 2020-11-18T09:37:25Z
Last updated: 2021-04-08
Stable URL: http://hdl.handle.net/10338.dmlcz/148394
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Reference: [1] Butkovič, P.: Max-Linear Systems: Theory and Algorithms.Springer Monographs in Mathematics. Springer, London (2010). Zbl 1202.15032, MR 2681232, 10.1007/978-1-84996-299-5
Reference: [2] Grigoriev, D., Shpilrain, V.: Tropical cryptography.Commun. Algebra 42 (2014), 2624-2632. Zbl 1301.94114, MR 3169729, 10.1080/00927872.2013.766827
Reference: [3] Grigoriev, D., Shpilrain, V.: Tropical cryptography II. Extensions by homomorphisms.Commun. Algebra 47 (2019), 4224-4229. Zbl 07089368, MR 3976001, 10.1080/00927872.2019.1581213
Reference: [4] Jones, D.: Special and Structured Matrices in Max-Plus Algebra: PhD Thesis.University of Birmingham, Birmingham (2018).
Reference: [5] Kotov, M., Ushakov, A.: Analysis of a key exchange protocol based on tropical matrix algebra.J. Math. Cryptol. 12 (2018), 137-141. Zbl 1397.94082, MR 3849682, 10.1515/jmc-2016-0064
Reference: [6] Linde, J., Puente, M. J. de la: Matrices commuting with a given normal tropical matrix.Linear Algebra Appl. 482 (2015), 101-121. Zbl 1321.15046, MR 3365268, 10.1016/j.laa.2015.04.032
Reference: [7] Shpilrain, V.: Cryptanalysis of Stickel's key exchange scheme.Computer Science - Theory and Applications Lecture Notes in Computer Science 5010. Springer, Berlin (2008), 283-288. Zbl 1142.94360, MR 2475176, 10.1007/978-3-540-79709-8_29
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