In anonymity networks (e.g., Tor, Crowds, Mixmaster, I2P, etc.), it is important to be able to measure quantitatively the guarantee that is given to the system. The degree of anonymity is a device that was proposed at the 2002 Privacy Enhancing Technology (PET) conference. Two papers put forth the idea of using entropy as the basis for formally measuring anonymity: "Towards an Information Theoretic Metric for Anonymity", and "Towards Measuring Anonymity". The ideas presented are very similar with minor differences in the final definition of . Background Anonymity networks have been developed and many have introduced methods of proving the anonymity guarantees that are possible, originally with simple Chaum Mixes and Pool Mixes the size of the set of users was seen as the security that the system could provide to a user. This had a number of problems; intuitively if the network is international then it is unlikely that a message that contains only Urdu came from the United States, and vice versa. Information like this and via methods like the predecessor attack and intersection attack helps an attacker increase the probability that a user sent the message. Example With Pool Mixes As an example consider the network shown above, in here and are users (senders), , and are servers (receivers), the boxes are mixes, and , and where denotes the anonymity set. Now as there are pool mixes let the cap on the number of incoming messages to wait before sending be ; as such if , or is communicating with and receives a message then knows that it must have come from (as the links between the mixes can only have message at a time). This is in no way reflected in 's anonymity set, but should be taken into account in the analysis of the network. Degree of Anonymity The degree of anonymity takes into account the probability associated with each user, it begins by defining the entropy of the system (here is where the papers differ slightly but only with notation, we will use the notation from .): , where is the entropy of the network, is the number of nodes in the network, and is the probability associated with node . Now the maximal entropy of a network occurs when there is uniform probability associated with each node and this yields . The degree of anonymity (now the papers differ slightly in the definition