The invention concerns the security of the data connections of a telephone user. The basic idea of the invention is to forward the authentication of a telephone system to the leg between two private data networks connected via an arbitrating network. When establishing the connection, the private network connected to the telephone system forwards the authenticated subscriber identity to the other private network. To provide the identity forwarded with authenticity, the message containing the identity is signed. To provide encryption of the subscriber identity, the message is encrypted using a public key method. In response the second private network generates a session key to be used in the connection. This key is signed and encrypted using a public key method and sent to the first private network. During the connection, a symmetrical encryption method with the session key is used.