A Combinatorial Enumeration Approach for Measuring Anonymity

A recent paper of Edman et al. has taken a combinatorial approach to measuring the anonymity of a threshold mix anonymous communications system. Their paper looks at ways of matching individual messages sent to individual messages received, irrespective of user, and determines a measure of the anonymity provided by the system. Here we extend this approach to include in the calculation information about how many messages were sent or received by a user and we define a new metric that can be computed exactly and efficiently using classical and elegant techniques from combinatorial enumeration.