On the security of the STR key exchange protocol

In this paper, we consider the security of the Sakalauskas-Tvarijonas-Raulynaitis (STR) key exchange protocol. We perform an analysis by exploring various cases of the canonical form of the publicly known matrix using elements of linear algebra and number theory. Additionally, we consider the multiplicative order of matrices and show how these two factors affect the security of the considered protocol. We show that regardless of the choice of publicly known matrix, the considered protocol is secure under the discrete logarithm assumption. In other words, if at least one of the secret exponents is found, then the STR protocol can be broken in polynomial time.