Abstract: In a data communication system a plurality of users are equipped with respective devices for computation and authentication of message authenticators. Each device stores a common cryptographic function; a common secret key and a respective non-secret offset for the key. They are programmed to perform the functions of: (i) computing and outputting an authenticator for an entered message using the cryptographic function and key combined with the respective offset; and (ii) computing an authenticator for an entered message using the cryptographic function and key combined with any entered offset, comparing that authenticator with one received with the message and displaying a "pass" or "fail" decision. The devices are incapable of displaying or otherwise outputting any authenticator computed using any offset other than its respective stored offset, however. In this way it can be ensured that a transmitted authenticator can act as a verifiable "signature" to a message uniquely identifying the sender.