Cryptology ePrint Archive: Report 2021/040
On the tropical discrete logarithm problem and security of a protocol based on tropical semidirect product
Any Muanalifah and Serge˘ı Sergeev
Abstract: Tropical linear algebra has been recently put forward by Grigoriev and Shpilrain
~\cite{grigoriev2014tropical,grigoriev2018tropical} as a promising platform for the implementation of protocols of Diffie-Hellman and Stickel type. Based on the CSR expansion of tropical matrix powers, we suggest a simple algorithm for the following tropical discrete logarithm problem: ``Given that $A=V\otimes F^{\otimes t}$ for a unique $t$ and matrices $A$, $V$, $F$ of appropriate dimensions, find this $t$.'' We then use this algorithm to suggest a simple attack on a protocol based on the tropical semidirect product. The algorithm and the attack are guaranteed to work in some important special cases and are shown to be efficient in our numerical experiments.
Category / Keywords: public-key cryptography / Tropical algebra, semidirect product, matrix powers, cryptanalysis
Date: received 11 Jan 2021
Contact author: any math13 at gmail com,s sergeev@bham ac uk
Available format(s): PDF | BibTeX Citation
Version: 20210112:131217 (All versions of this report)
Short URL: ia.cr/2021/040
[ Cryptology ePrint archive ]