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A Practical Complexity-Theoretic Analysis of Mix Systems

  • Dang Vinh Pham
  • Joss Wright
  • Dogan Kesdogan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6879)

Abstract

The Minimal-Hitting-Set attack[10] (HS-attack)  is a well-known passive intersection attack against Mix-based anonymity systems, applicable in cases where communication behaviour is non-uniform and unknown. The attack allows an observer to identify uniquely the fixed set of communication partners of a particular user by observing the messages of all senders and receivers using a Mix. Whilst the attack makes use of a provably minimal number of observations, it also requires solving an NP-complete problem. No prior research, to our knowledge, analyses the average complexity of this attack as opposed to its worst case.

We choose to explore the HS-attack, as opposed to statistical attacks, to provide a baseline metric and a practical attack for unambiguously identifying anonymous users. We show that the average complexity of the HS-attack can vary between a worst-case exponential complexity and a linear-time complexity according to the Mix parameters. We provide a closed formula for this relationship, giving a precise measure of the resistance of Mixes against the HS-attack in practice, and allowing adjustment of their parameters to reach a desired level of strength.

Keywords

Statistical Attack Attack Model Average Complexity Communication Round Choice Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dang Vinh Pham
    • 1
  • Joss Wright
    • 2
  • Dogan Kesdogan
    • 1
  1. 1.Siegen UniversitySiegenGermany
  2. 2.Oxford Internet InstituteUniversity of OxfordOxfordUnited Kingdom

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