Cryptoanalysis of a tropical triad matrix semiring key exchange protocol
Alvaro Otero Sanchez
TL;DR
The paper investigates a key exchange protocol based on the triad tropical semiring and establishes an isomorphism to circulant matrices over the tropical semiring, enabling the protocol to be analyzed within tropical matrix algebra. By reducing the problem to tropical two-sided discrete logarithms over $\mathbb{M}_{3n}(\mathbb{T})$ and applying an efficient CSR-based attack, the authors demonstrate that the protocol is insecure, with the attack achieving near-complete success. The work formalizes the isomorphisms $\mathbb{M}_n(\overline{\mathbb{T}}) \cong \mathbb{M}_n(Circ\mathbb{M}_3(\mathbb{T}))$ and embeds the triad semiring into tropical matrix algebra, thereby translating the public-key exchange into a well-studied cryptanalytic setting. This has practical impact by showing that tropical-semirings-based key exchanges of this form do not provide secure post-quantum resistance under the analyzed framework.
Abstract
This article analyzes a key exchange protocol based on the triad tropical semiring, recently proposed by Jackson, J. and Perumal, R. We demonstrate that the triad tropical semiring is isomorphic to a circulant matrix over tropical numbers. Consequently, matrices in this semiring can be represented as tropical matrices. As a result, we conduct a cryptanalysis of the key exchange protocol using an algorithm introduced by Sulaiman Alhussaini, Craig Collett, and Sergei Sergeev to solve the double discrete logarithm problem over tropical matrices