Cryptanalysis of Álvarez et al. key exchange scheme

Álvarez et al., Information Sciences 179 (12) (2009) proposed a new key exchange scheme where the secret key is obtained by multiplying powers of block upper triangular matrices whose elements are defined over ZpZp. In this note, we show that breaking this system with security parameters (r,s,p)(r,s,p) is equivalent to solving a set of 3(r+s)23(r+s)2 linear equations with 2(r+s)22(r+s)2 unknowns in ZpZp, which renders this system insecure for all the suggested practical choices of the security parameters.