On the Fundamentals of Anonymity Metrics

In recent years, a handful of anonymity metrics have been proposed that are either based on (i) the number participants in the given scenario, (ii) the probability distribution in an anonymous network regarding which participant is the sender / receiver, or (iii) a combination thereof. In this paper, we discuss elementary properties of metrics in general and anonymity metrics in particular, and then evaluate the behavior of a set of state-of-the-art anonymity metrics when applied in a number of scenarios. On the basis of this evaluation and basic measurement theory, we also define criteria for anonymity metrics and show that none of the studied metrics fulfill all criteria. Lastly, based on previous work on entropy-based anonymity metrics, as well as on theories on the effective support size of the entropy function and on Huffman codes, we propose an alternative metric – the scaled anonymity set size – that fulfills these criteria.