Some remarks on authentication systems

Brickell, Simmons and others have discussed doubly perfect authentication systems in which an opponent's chance of deceiving the receiver is a minimum for a given number of encoding rules. Brickell has shown that in some instances to achieve this minimum the system needs to have splitting. Such a system uses a larger message space. Motivated by Brickell's ideas we consider authentication systems with splitting and the problems of reducing the message space.