Elliptic curve cryptosystems are nowadays widely used in the design of many security devices. Nevertheless, since not every elliptic curve is useful for cryptographic purposes, mechanisms for providing good curves are highly needed. The generation of the volcano graph of elliptic curves can help to provide such good curves. However, this procedure turns out to be very expensive when performed sequentially. Hence, a parallel application for the calculation of such volcano graphs is proposed in this paper. In order to obtain high efficiency, a theoretical analysis is provided for obtaining an accurate granularity and for giving the appropriate number of tasks to be created. Experimental results show the benefits obtained in the speedup when executing the application in a cluster of workstations with message-passing for the generation of different volcano graphs. By the use of simulation, we study the scalability of the implementation and show that a speedup of more than 80 can be achieved in some cases.