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Measuring Anonymity Revisited

Nordsec 2004. Measuring Anonymity Revisited. Gergely Tóth Zoltán Hornák Ferenc Vajda Budapest University of Technology and Economics Department of Measurement and Information Systems. Outline. Our research group Anonymity in general Anonymous communication Measuring anonymity

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Measuring Anonymity Revisited

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  1. Nordsec 2004 Measuring Anonymity Revisited Gergely Tóth Zoltán Hornák Ferenc Vajda Budapest University of Technology and Economics Department of Measurement and Information Systems Gergely Tóth, 5 November 2004 1 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  2. Outline • Our research group • Anonymity in general • Anonymous communication • Measuring anonymity • past and present approaches • our suggestion • Summary and future plans Gergely Tóth, 5 November 2004 2 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  3. SEARCH-LAB at BUTE DMIS • Budapest University of Technology and Economics (BUTE) • Department of Measurement and Information Systems (DMIS) • Security Evaluation Analysis and Research Laboratory (SEARCH-LAB) • Core focus: Security in mobile networks • Current research areas: DRM, Biometrics & Anonymity Gergely Tóth, 5 November 2004 3 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  4. Summary of the Presentation & Paper • Anonymous communication is needed for several real-world scenarios • Different implementations provide different levels of anonymity • A theoretical, objective metric is needed to be able to compare them • After analyzing past approaches, we present our suggestion Gergely Tóth, 5 November 2004 4 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  5. Introduction Gergely Tóth, 5 November 2004 5 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  6. Anonymity in General • Anonymity means hiding the identity • actions are performed by subjects • aim is to hide the identity of these subjects from any possible adversary • Possible anonymity scenarios • hide the identity of the voter during e-voting • hide the identity of the buyer during e-payment • hide the identity of the sender of e-mails Gergely Tóth, 5 November 2004 6 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  7. Anonymous Communication • Several layers in the anonymity architecture with different functions • Focus of the presentation & paper: anonymous communication • systems that deliver messages so that they cannot be traced back to their sources • several such systems have been designed • aim is now to define metrics to be able to compare them Gergely Tóth, 5 November 2004 7 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  8. Need for Measuring Anonymity • Different systems • algorithms • network topologies • adversary models • Anonymity provided has to be measured • objective, theoretically based metrics • should be easy to understand by laymen • users should be able to definetheir required anonymity level Gergely Tóth, 5 November 2004 8 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  9. Anonymous Communication Gergely Tóth, 5 November 2004 9 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  10. Model of Anonymous Communication • Anonymous message transmission system • senders send encrypted messages to recipients through a channel • the channel alters, delays and reorders messages before delivery • an adversary tries to back-trace delivered messages to their senders Gergely Tóth, 5 November 2004 10 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  11. Anonymity Terminology • “Anonymity is the state of being not identifiable within a set of subjects, the anonymity set” • Sender anonymity means that • a particular message is not linkable to any sender and • to a particular sender no message is linkable. Gergely Tóth, 5 November 2004 11 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  12. Different Realizations • During the evolution of science several schemes have been proposed and implemented • batch systems: MIXes • continuous-time systems • peer-to-peer systems • systems with provable anonymity, such as DC networks • Let’s see some examples Gergely Tóth, 5 November 2004 12 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  13. MIXes I – Batched Operation • MIXes are network relays to make back-tracing messages to their senders hard • For this they buffer incoming messages and randomly reorder them upon delivery MIX Gergely Tóth, 5 November 2004 13 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  14. from sender to recipient MIX1 MIX2 MIX3 MIXes II – the MIX Network • They are furthermore organized in networks • There, special, onion-like messages are created and propagated M to MIX2 to MIX2 to MIX3 to Y to MIX3 M to Y to Y to Y to MIX3 M Gergely Tóth, 5 November 2004 14 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  15. Continuous Time Systems • MIXes did batching, in most cases they do not guarantee real-time delivery • On the other hand continuous-time systems process messages individually • message delay (d) in the channel is a probability variable with a given density f(d) • delay is not dependent on the actual message distribution Gergely Tóth, 5 November 2004 15 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  16. PROB-channel & SG-MIX • Two recent continuous-time systems: • SG-MIX (Stop-and-go MIX): exponential density function for non real-time scenarios • PROB-channel: uniform distribution with definite maximum for real-time use-cases Gergely Tóth, 5 November 2004 16 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  17. Challenge • The challenge: • with the evolution of science, newer and newer systems are constructed • different known systems are organized into networks of various topologies • Which architecture is better? • a theoretical metric is needed to objectively compare different systems • measuring should be easy to understand Gergely Tóth, 5 November 2004 17 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  18. MIX MIX MIX MIX MIX MIX MIX MIX More Complex Systems and Networks Gergely Tóth, 5 November 2004 18 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  19. Measuring Anonymity Gergely Tóth, 5 November 2004 19 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  20. Attempt #1 – Anonymity Set Size • Size of the anonymity set • the first attempt to quantity the level of anonymity • the bigger the anonymity set, the greater the level of anonymity • easy to calculate • easy to understand • you are anonymous as if one had to pick randomly from 500 equal possibilities Gergely Tóth, 5 November 2004 20 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  21. Problem with Anonymity Set Size • In some simple cases anonymity set size works well (e.g. for simple MIXes) • However a closer look reveals • in the anonymity set subjects have different probabilities, i.e. one is more likely to be the actual sender than the other according to the knowledge of the adversary • simply the size of the anonymity set is not definite enough Gergely Tóth, 5 November 2004 21 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  22. Attempt #2 – Entropy • The probabilities of the different subjects have to be considered • For this purpose in the information theory a fundamental construction had been defined: entropy • The improved approach: use the entropy of the probability distribution for quantifying anonymity Gergely Tóth, 5 November 2004 22 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  23. Entropy – Definitions • Determine the probabilities for a sender being the originator for a message • The anonymity set: • Simple entropy measure: • Normalized entropy measure: Gergely Tóth, 5 November 2004 23 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  24. Problems with Entropy • Entropy-based metrics aim to quantify the amount of information that is needed to totally break anonymity • Problem: non-desirable systems with arbitrarily high entropy exist • both for simple entropy and • for normalized entropy. Gergely Tóth, 5 November 2004 24 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  25. Example • 20 senders, uniform distribution, P=5% • 101 senders, non-uniform distribution • for one sender P=50% • for all the other 100 senders P=0.5% • For both cases entropy is the sameS=4.3219 bits • However, it is clear, that the two systems don’t achieve the same level of anonymity Gergely Tóth, 5 November 2004 25 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  26. Problems with Entropy – continued • In the paper for both simple and normalized entropy degenerate cases were shown • such measures neglect the local aspect of anonymity • the adversary does not necessarily want to totally compromise all messages • aim could be to locally guess forsome messages with a better probability than anticipated • Also easy understandability suffers Gergely Tóth, 5 November 2004 26 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  27. Our Suggestion – Maximal Probability • Use the maximal probability as a measure • If the above holds, a system is called source-hiding with parameter W • this approach is easy-to-understand • W=10% means that regardless what the adversary does, he won’t be able to compromise any of your messages with a probability greater than 10% Gergely Tóth, 5 November 2004 27 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  28. Maximal Probability – continued • Source-hiding property • it can be converted back to the entropy-based metrics • for both simple and normalized entropy equations were given • considers the local aspect of anonymity • for no messages can the threshold be exceeded • for some systems source-hiding property can be set as a requirement Gergely Tóth, 5 November 2004 28 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  29. Summary & Future Gergely Tóth, 5 November 2004 29 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  30. Summary • The field of anonymous communication is rapidly evolving • In order to be able to objectively compare different systems, a theoretical metric is needed • Our suggestion is to use the maximal probability from the probability distribution of the adversary to measure the achieved level of anonymity Gergely Tóth, 5 November 2004 30 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  31. Research Plans • For some scenarios the level of anonymity can be calculated • there are constructions where the anonymity has to be analyzed further • it has to be evaluated, how the combination of different systems behaves • Systems are needed, where the level of anonymity can be set as a requirement (QoS) Gergely Tóth, 5 November 2004 31 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

  32. Thank you for your attention Gergely Tóth Budapest University of Technology and Economics Department of Measurement and Information Systems gergely.toth@mit.bme.hu Gergely Tóth, 5 November 2004 32 Nordsec 2004, Helsinki, Finland, 4-5 November 2004

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