A geometric view of mutual information: Application to anonymity protocols

Anonymity protocols are a special type of security protocols that focus on protecting the identities of communicating entities in a network communication. In this research we explore the notion of anonymity from an information-theoretic point of view. We see a protocol as a noisy channel that links a set of anonymous events (inputs) to a set of observables (outputs). The degree of anonymity of the protocol can then be expressed in terms of how much information is being leaked by the channel. In information theory, the information leaked by a noisy channel is given by the notion of mutual information. We propose an alternative measure of information leakage based on the vector configuration of the noisy channel's matrix. We show that a variant of this new measure coincides with mutual information which gives an interesting geometric interpretation to mutual information.