Cryptanalysis of a key exchange scheme based on block matrices

In this paper we describe a cryptanalysis of a key exchange scheme recently proposed by Álvarez, Tortosa, Vicent and Zamora. The scheme is based on exponentiation of block matrices over a finite field of prime order, and its security is claimed to rely in the hardness of a discrete logarithm problem in a subgroup of GLn(p). However, the proposal's design allows for a clean attack strategy which exploits the fact that exponents are at some point added instead of multiplied as in a standard Diffie-Hellman construction. This strategy is moreover successful for a much more general choice of parameters than that put forward by Álvarez et al.