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Analyzing Anonymity in Social Network-Based Mix Topologies

Explore a mix network topology based on social networks to analyze the anonymity it provides under high-latency conditions. Theoretical bounds, path selection as random walk, mixing rates, and spectral graph theory applied to scale-free graphs are discussed. Conclusions highlight differences between expander and scale-free graphs in achieving network mixing. Exciting prospects for further evaluation of anonymous communication over social networks are proposed.

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Analyzing Anonymity in Social Network-Based Mix Topologies

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  1. Anonymous communication over social networks Shishir Nagaraja and Ross Anderson Security Group Computer Laboratory

  2. Basic aim • We present a mix network topology that is based on social networks • We would like to analyze the anonymity such networks provide under a high-latency assumption.

  3. A plausible setting – High latency mix network • consider the live-journal network of friendship ties. • assume that sometime in the future, users have a live-journal client that can run a mix. • users publish their mix keys on their site. • senders select routes from this topology.

  4. theoretical anonymity bounds in this case? • Path selection is abstracted as a random walk. • Mixing rate on scale-free graphs – steps in which the random walk converges to the Markov chain stationary distribution.

  5. Applying results from spectral graph theory of BA scale-free networks (Mihail et.al. 2005) we find that conductance is a constant for all scalefree graphs with dmin>=2.

  6. Example • Consider an expander graph of size 1000 with 40links per node (gives you good expansion properties) • The fundamental limit of how quickly a network can mix depends on 2>=0.3122 • In a social network using a BA-scalefree model we have for 1000 nodes with 4 edges per node 2 >=0.6363229 • 4-6 steps for expander vs 8-10 for a scalefree graph.

  7. Conclusions • RW on social networks based on BA scalefree graphs will take longer to converge, but you’ll get there. • We have applied results from graph theory of skewed degree topologies to throw light on how anonymity on these networks may be analyzed. • Further evaluation of anonymous communication over social networks should be exciting!

  8. Definitions

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