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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti


CiteScore 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

Online
ISSN
1862-2984
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Volume 12, Issue 3

Issues

Analysis of a key exchange protocol based on tropical matrix algebra

Matvei Kotov / Alexander Ushakov
Published Online: 2018-07-07 | DOI: https://doi.org/10.1515/jmc-2016-0064

Abstract

In this paper, we consider a two party key-exchange protocol proposed in [D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 43 (2014), 2624–2632, Section 2], which uses tropical matrix algebra as the platform. Our analysis shows that the scheme is not secure.

Keywords: Tropical algebra; cryptography; key-exchange; min-plus systems

MSC 2010: 94A60; 68W30

References

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    P. Butkovič, Max-linear Systems: Theory and Algorithms, Springer Monogr. Math., Springer, London, 2010. Google Scholar

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    T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, 3rd ed., MIT Press, Cambridge, MA, 2009. Google Scholar

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    D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 42 (2014), no. 6, 2624–2632. CrossrefGoogle Scholar

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    M. Kotov and A. Ushakov, Implementation of FBA, available at https://github.com/mkotov/polycyclic.

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    C. Mullan, Cryptanalysing variants of Stickel’s key agreement scheme, J. Math. Cryptol. 4 (2011), no. 4, 365–373. Google Scholar

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    A. Myasnikov, V. Shpilrain And A. Ushakov, Non-Commutative Cryptography and Complexity of Group-Theoretic Problems, Math. Surveys Monogr. 177, American Mathematical Society, Providence, 2011, Google Scholar

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    V. Shpilrain, Cryptanalysis of Stickel’s key exchange scheme, Computer Science in Russia – CSR 2008, Lecture Notes in Comput. Sci. 5010, Springer, Berlin (2008), 283–288. Google Scholar

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    The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.7.7, 2015, http://www.gap-system.org.

About the article


Received: 2016-11-14

Revised: 2018-05-16

Accepted: 2018-06-26

Published Online: 2018-07-07

Published in Print: 2018-09-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 14-01-00068

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1318716

The first author has been partially supported by RFBR, project No. 14-01-00068. The second author has been partially supported by NSF grant DMS-1318716.


Citation Information: Journal of Mathematical Cryptology, Volume 12, Issue 3, Pages 137–141, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2016-0064.

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