Authentication codes: An area where coding and cryptology meet

Among many applications of cryptography, the use of authentication schemes is of great practical importance. The purpose of authentication schemes [3], [10] is to add proof to a message that the message is authentic, i.e. it was not sent by an imposter and it has not been altered on its way to the receiver. The imposter may replace an authenticated message by another message (substitution) or may just try to send his own message (impersonation). The aspect of secrecy could also be introduced here, but in many cases the receiver just wants to be sure that the message is genuine. Think for instance of offices that are communicating with each other. An important distinction to be made is that between authentication schemes that are unconditionally secure and schemes that are based on certain complexity theoretic assumptions. It is the first category that will be the main topic of this paper. A common technique here is to append to a message a (relatively short) tail that depends in an essential way on every bit in the message and also on a key that is shared with the legitimate receiver. Some well-known bounds on the probability of successful substitution and impersonation will be given. Further, a direct connection with the existence of error-correcting codes will be given. (This relation is not a direct one-to-one correspondence!) Interesting results have already been obtained in this way, but there is ample room for improvement. It is the purpose of this paper to make the reader acquainted with this area of research.