A Novel Statistical Model of Users’ Behavior in Key Distribution Schemes

Access control for group communication must ensure that the legitimate users are able to access the authorized data streams, while preventing the non-legitimate users from gleaning any unauthorized data stream. This could be done by distributing an encrypting key to each member of the group to be secured. To achieve a high level of security, the group key should be changed every time a user joins or leaves the group, so that a former group member has no access to current communications and a new member has no access to previous communications. Since group memberships could be very dynamic, the group key should be changed frequently. So far, different schemes for efficient key distribution have been proposed to limit the key-distribution overhead. In previous works, the performance comparison among these different schemes have been based on simulative experiments, where a set of users join and leave a secure group according to a basic statistical representation of users’ behavior. In this paper we propose a new statistical model to represent users’ behavior and compare it to the modelling approach so far adopted in the literature. Our new model is able to achieve a superior statistical confidence of the results and to lead the system to a steady state. In particular, we apply our new model to the comparison of two recent proposals for key distribution in order to show the better quality of the results achieved by means of our model.