here, defines a bounded degree where it is compared to and gives an unbounded definition—using the entropy directly, we will consider only the bounded case here) is defined as . Using this anonymity systems can be compared and evaluated using a quantitatively analysis. Definition of Attacker These papers also served to give concise definitions of an attacker: Internal/External an internal attacker controls nodes in the network, whereas an external can only compromise communication channels between nodes. Passive/Active an active attacker can add, remove, and modify any messages, whereas a passive attacker can only listen to the messages. Local/Global a local attacker has access to only part of the network, whereas a global can access the entire network. Example In the papers there are a number of example calculations of ; we will walk through some of them here. Crowds In Crowds there is a global probability of forwarding (), which is the probability a node will forward the message internally instead of routing it to the final destination. Let there be corrupt nodes and total nodes. In Crowds the attacker is internal, passive, and local. Trivially , and overall the entropy is , is this value divided by . Onion routing In onion routing let's assume the attacker can exclude a subset of the nodes from the network, then the entropy would easily be , where is the size of the subset of non-excluded nodes. Under an attack model where a node can both globally listen to message passing and is a node on the path this decreases to , where is the length of the onion route (this could be larger or smaller than ), as there is no attempt in onion routing to remove the correlation between the incoming and outgoing messages. Applications of this metric In 2004, Diaz, Sassaman, and DeWitte presented an analysis of two anonymous remailers using the Serjantov and Danezis metric, showing one of them to provide zero anonymity under certain realistic conditions. See also Onion routing Tor (anonymity network) Entropy Crowds References See Towards Measuring Anonymity See Towards an Information Theoretic Metric for Anonymity See Comparison Between Two Practical Mix Designs Anonymity networks Computer network analysis Cryptographic software Internet privacy Routing software