Abstract: In order to improve the security of message transmission from a terminal apparatus in an electronic banking or other data communications system a check-sum or MAC is computed from the data within the message in dependence upon a cryptographic key. This MAC is issued as a "challenge" to the user who is also equipped with a separate portable token for computing a "response" in dependence upon a second cryptographic key which is unique to his token. This "response" is then entered into the terminal and appended to the message as its authentication code before transmission. A recipient of the message and authentication code equipped with the same cryptographic keys can therefore check both the contents of the message and the correct identity of the sender by computing an expected authentication code from the received message and comparing it with the code received.