A Logic of Anonymity

Our project concerns anonymity, that is the ability of users in a system to transmit information without revealing their own identities. There are a number of protocols claiming to guarantee users’ anonymity in different situations, but there is no clear way to compare these protocols in terms of how anonymous their users really are. In order to develop a measure of anonymity, we need to be able to reason about the knowledge of the users in the system as well as the knowledge of agents outside of the system. Furthermore, many anonymity protocols use probabilistic aspects, so it is necessary to incorporate probability into our reasoning system. Thus, we developed a probabilistic, epistemic logic based on Kripke’s epistemic logic but also incorporating probability. I will present the syntax and semantics for this logic. In the future, we also hope to incorporate information theory and theory of evidence into our analysis of anonymity.