The author of this paper uses a model of authentication theory developed by G. J. Simmons [1,2,3]. Three participants in a communications transaction are identified. These are a transmitter, a receiver, and an opponent. The first two of these play the obvious roles. The opponent can either impersonate the transmitter, making the receiver accept a fraudulent message as authentic, or modify a message that has been sent by the transmitter.

A mathematical basis is expounded for the impersonation game and the substitution game. A value is defined for each of these games, representing the possibility that the opponent can deceive the legitimate game participants. The balance of the paper is devoted to computing upper and lower bounds for such values according to the encoding rules being utilized. Some guidelines are then developed for the construction of authentication systems that can be regarded as optimal.

It is unfortunate that the author has not extended the paper to include some details of practical implementations. Overall, the level of presentation is such as to require some advanced knowledge of mathematics on the part of the reader. However, it is probable that the paper will interest those working in academic and research environments.