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Keywords:
Stickel's protocol; tropical algebra; cryptography; commuting matrices
Stickel's protocol; tropical algebra; cryptography; commuting matrices
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.
References:
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[2] Grigoriev, D., Shpilrain, V.: Tropical cryptography. Commun. Algebra 42 (2014), 2624-2632. DOI 10.1080/00927872.2013.766827 | MR 3169729 | Zbl 1301.94114
[3] Grigoriev, D., Shpilrain, V.: Tropical cryptography II. Extensions by homomorphisms. Commun. Algebra 47 (2019), 4224-4229. DOI 10.1080/00927872.2019.1581213 | MR 3976001 | Zbl 07089368
[4] Jones, D.: Special and Structured Matrices in Max-Plus Algebra: PhD Thesis. University of Birmingham, Birmingham (2018).
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