A Combinatorial Enumeration Approach for Measuring Anonymity

TL;DR

This paper extends a combinatorial method for measuring anonymity in threshold mix systems by incorporating message counts per user, resulting in a new, efficiently computable anonymity metric.

Contribution

It introduces a novel combinatorial enumeration technique to accurately and efficiently measure anonymity considering user message counts.

Findings

New exact and efficient anonymity metric derived

Extension of previous combinatorial approach to include message counts

Provides a practical method for anonymity assessment

Abstract

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.