A Stochastic Analysis of Secure Joint Decision Processes in Peer-to-Peer Systems

Central trusted instances as well as predefined security policies are not available in spontaneously established peer-to-peer environments. The former can be addressed by joint decision processes based on threshold cryptography. To compensate the latter, users can be involved directly in security-relevant decisions. In this case, minimizing the number of users involved is a necessary optimization goal to keep user-based joint decisions feasible for real-world deployment. Still, a certain redundancy has to be introduced when taking into account users that do not provide their decision in a reasonable amount of time. In this paper we scrutinize different interaction schemes for joint decision processes. We develop stochastic models that describe the outcome subject to the number of users requested and the probability with which one user provides his decision in time. The derived closed-form representation of the models serves as a tool for governing the decision process, allowing for a real-time minimization of the number of users involved.