Key agreement under tropical parallels

Jean-Marie Chauvet 1  and Eric Mahé 2
  • 1 MassiveRand, 62, ave. Pierre Grenier, 92100 Boulogne-Billancourt, France
  • 2 MassiveRand, 62, ave. Pierre Grenier, 92100 Boulogne-Billancourt, France

Abstract

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.

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Groups – Complexity – Cryptology is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, computer algebra, complexity theory, and cryptology. GCC primarily publishes research papers, but comprehensive and timely survey articles on a topic inside the scope of the journal are also welcome.

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