We first illustrate using examples that existing measures in literature are not sufficient to fully characterize the anonymity provided by an anonymous system. We then propose a new isolation measure, based upon presence of outliers in a distribution, and show that this measure is critical towards quantifying the overall anonymity provided by the system. We provide justification for three distinct aspects of anonymity, important from the perspectives of a user, a system designer, and an attacker, leading to a three-dimensional approach towards measuring sender anonymity. We further show how two anonymous systems can be compared in terms of the degree of anonymity provided, using the proposed 3-tuple metric and appropriate weights reflecting the attributes desired in the system. Finally, we apply the proposed metric to an existing anonymous system and discuss the insights gained.
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