It is well known that the network protocols frequently used in Internet and Local Area Networks do not ensure the security level required for current distributed applications. This is even more crucial for the Grid environment. Therefore asymmetric cryptography algorithms have been applied in order to secure information transmitted over the network. The security level enforced by means of the algorithms is found sufficient, however it introduces additional transmission overhead. In this paper we describe experiments performed in order to evaluate transmission efficiency depending on the security level applied.