OpenSSL represents the open source tool-kit of SSL and TLS protocols. This tool-kit includes the elliptic curve cryptography (ECC) among other things. The ECC part of OpenSSL provides curves of many standards and also curves of many sizes. The ECC is a current issue of information and communication technologies and it is implemented in many communication devices. We tested the elliptic curve cryptography on an embedded device MSP430, which is may be used i.e. in smart grid network with limited resources for securing communication. This article shows the results of these tests, it shows the efficiency of these curves and also discovers general problems and general questions of ECC. All the obtained results including practical outputs are concluded at the end of our paper.