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The Minimal-Hitting-Set attack (HS-attack) is a well-known, provably optimal exact attack against the anonymity provided by Chaumian Mixes (Threshold-Mixes). This attack allows an attacker to identify the fixed set of communication partners of a given user by observing all messages sent and received by a Chaum Mix. In contrast to this, the Statistical Disclosure attack (SDA) provides a guess of that user's contacts, based on statistical analyses of the observed message exchanges. We contribute<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-18467-8_3">doi:10.1007/978-3-319-18467-8_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ij32wlsgpvf7nbdljuxev7wgbm">fatcat:ij32wlsgpvf7nbdljuxev7wgbm</a> </span>
more »... he first closed formula that shows the influence of traffic distributions on the least number of observations of the Mix to complete the HS-attack. This measures when the Mix fails to hide a user's partners, such that the user cannot plausibly deny the identified contacts. It reveals that the HS-attack requires asymptotically less observations to identify a user's partners than the SDA, which guesses them with a given bias. This number of observations is O( 1 p ) for the HS-attack and O( 1 p 2 ) for the SDA, where p the probability that the attacked user contacts his least frequent partner.
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