Applications of Mathematics, Vol. 65, No. 6, pp. 727-753, 2020


Modifying the tropical version of Stickel's key exchange protocol

Any Muanalifah, Sergeĭ Sergeev

Received November 29, 2019.   Published online October 27, 2020.

Abstract:  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.
Keywords:  Stickel's protocol; tropical algebra; cryptography; commuting matrices
Classification MSC:  15A80, 94A60
DOI:  10.21136/AM.2020.0325-19


References:
[1] P. Butkovič: Max-Linear Systems: Theory and Algorithms. Springer Monographs in Mathematics. Springer, London (2010). DOI 10.1007/978-1-84996-299-5 | MR 2681232 | Zbl 1202.15032
[2] D. Grigoriev, V. Shpilrain: Tropical cryptography. Commun. Algebra 42 (2014), 2624-2632. DOI 10.1080/00927872.2013.766827 | MR 3169729 | Zbl 1301.94114
[3] D. Grigoriev, V. Shpilrain: Tropical cryptography II. Extensions by homomorphisms. Commun. Algebra 47 (2019), 4224-4229. DOI 10.1080/00927872.2019.1581213 | MR 3976001 | Zbl 07089368
[4] D. Jones: Special and Structured Matrices in Max-Plus Algebra: PhD Thesis. University of Birmingham, Birmingham (2018).
[5] M. Kotov, A. Ushakov: Analysis of a key exchange protocol based on tropical matrix algebra. J. Math. Cryptol. 12 (2018), 137-141. DOI 10.1515/jmc-2016-0064 | MR 3849682 | Zbl 1397.94082
[6] J. Linde, M. J. de la Puente: Matrices commuting with a given normal tropical matrix. Linear Algebra Appl. 482 (2015), 101-121. DOI 10.1016/j.laa.2015.04.032 | MR 3365268 | Zbl 1321.15046
[7] V. Shpilrain: Cryptanalysis of Stickel's key exchange scheme. Computer Science - Theory and Applications. Lecture Notes in Computer Science 5010. Springer, Berlin, 2008, 283-288. DOI 10.1007/978-3-540-79709-8_29 | MR 2475176 | Zbl 1142.94360

Affiliations:   Any Muanalifah, Sergeĭ Sergeev (corresponding author), University of Birmingham, School of Mathematics, Birmingham, Edgbaston B15 2TT, United Kingdom, e-mail: any.math13@gmail.com, s.sergeev@bham.ac.uk


 
PDF available at: