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Revisiting a combinatorial approach toward measuring anonymity

Recently, Edman et al. proposed the system's anonymity level [10], a combinatorial approach to measure the amount of additional information needed to reveal the communication pattern in a mix-based anonymous communication system as a whole. The metric is based on the number of possible bijective mappings between the inputs and the outputs of the mix. In this work we show that Edman et al.'s approach fails to capture the anonymity loss caused by subjects sending or receiving more than one message. We generalize the system's anonymity level in scenarios where user relations can be modeled as yes/no relations to cases where subjects send and receive an arbitrary number of messages. Further, we describe an algorithm to compute the redefined metric.