  The paper analyzes a new public key cryptosystem whose security is based on a
matrix version of the discrete logarithm problem over an elliptic curve. It is
shown that the complexity of solving the underlying problem for the proposed
system is dominated by the complexity of solving a fixed number of discrete
logarithm problems in the group of an elliptic curve. Using an adapted Pollard
rho algorithm it is shown that this problem is essentially as hard as solving
one discrete logarithm problem in the group of an elliptic curve.
