Cryptanalysis of a 2-party key establishment based on a semigroup action problem

An Advances in Mathematics of Communications article from 2007 proposes an informal 2-party key establishment along the lines of the classic Diffie-Hellman construction, but using a two-sided matrix semiring action. The article contains no formal security analysis, but a specific parameter choice has been considered. We describe a heuristic attack technique against the suggested instance, which for the published "challenge value" results in a complete session key recovery with only a minor computational effort.