Abstract: We at Caiss, the Center for Algorithms and Interactive Scientific Software, have created a game called Expacon which makes use of simple descriptions of groups called presentations. In this talk I will demonstrate the game as a way of introducing presentations and move on from there to showing how some of these ideas can be used in a cryptographic protocol, due also to Ben Fine, which involves the identification of zeros of polynomial equations with recursive functions. The talk will be geared to a fairly general audience.