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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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CiteScore 2016: 0.35

SCImago Journal Rank (SJR) 2015: 1.208
Source Normalized Impact per Paper (SNIP) 2015: 2.294

Mathematical Citation Quotient (MCQ) 2015: 0.48

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Key agreement under tropical parallels

Jean-Marie Chauvet
  • Corresponding author
  • MassiveRand, 62, ave. Pierre Grenier, 92100 Boulogne-Billancourt, France
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/ Eric Mahé
  • MassiveRand, 62, ave. Pierre Grenier, 92100 Boulogne-Billancourt, France
  • Email:
Published Online: 2015-09-16 | DOI: https://doi.org/10.1515/gcc-2015-0013


A semiring is an algebraic structure satisfying the usual axioms for a not necessarily commutative ring, but without the requirement that addition be invertible. Aside from rings, well-studied instances in cryptographic applications include the Boolean semiring and the tropical semiring. The latter, in particular, behaves to a large extent like a field and exhibits interesting properties in the cryptographic context. This short note explores a GPU-based highly parallel implementation of a protocol recently proposed by Grigoriev and Shpilrain [Comm. Algebra 42 (2014), 2624–2632], in the context of Diffie–Hellman key agreements.

Keywords: Cryptography; Diffie–Hellman; key exchange; tropical algebra; GPU; parallel programming

MSC: 11T71

About the article

Received: 2015-06-04

Published Online: 2015-09-16

Published in Print: 2015-11-01

Citation Information: Groups Complexity Cryptology, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2015-0013. Export Citation

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