A Closer Look at the Tropical Cryptography

We examine two recently proposed public key exchange protocols that are based upon tropical matrix algebras. We observe the first protocol to exhibit a pattern. We introduce a fast attack on the first protocol that exploits this pattern to extract a private parameter of the protocol, and consequently the shared key, in seconds. We go on to show that the second protocol cannot be implemented as it is described in the proposal. The protocol is reliant on an operation being associative. We prove by counterexample that this operation is not associative.