  Tropical linear algebra has been recently put forward by Grigoriev and
Shpilrain as a promising platform for 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.
