A method operates an arrangement having a substation and a terminal device connected to the substation. The terminal device is equipped with a terminal device certificate and a private key. The certificate enables a signed data transmission, indicates the substation as the certificate issuer, has a signature of the substation and contains a reference to a public key of the terminal device. Following a connection of a control station to the substation, the control station recertifies the public key of the substation by creating a signed certificate for the substation containing the public key of the substation, for the authentication of data which are or are intended to be transmitted from the terminal device to another terminal device. The terminal device certificate indicating the substation as the certificate issuer is transferred to the other terminal device and the certificate verification is carried out based on recertified public key.