Measuring Anonymity by Profiling Probability Distributions

We present a graphical framework containing certain infinite profiles of probability distributions resulting from attacks on anonymity systems. We represent all currently popular anonymity metrics within our framework to show that existing metrics base their decisions on just some small piece of information contained in a distribution, while ignoring much useful information. This explains the counter-intuitive, thus unsatisfactory, anonymity evaluation performed by any of these metrics for carefully constructed examples in literature. We then propose a new anonymity metric that takes entire profiles into consideration in arriving at the degree of anonymity associated with a probability distribution. The comprehensive approach of our metric results in correct measurement. A detailed comparison of our new metric, especially with the popular metrics based on Shannon entropy, gives the rationale and degree of disagreement between these approaches.