Anonymous communication over social networks

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Anonymous communication over social networks

• Shishir Nagaraja and Ross Anderson
• Security Group
• Computer Laboratory

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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.

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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.

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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.

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• 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 dmingt2.

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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 ?2gt0.3122
• In a social network using a BA-scalefree model we
  have for 1000 nodes with 4 edges per node ?2
  gt0.6363229
• 4-6 steps for expander vs 8-10 for a scalefree
  graph.

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Conclusions

• RW on social networks based on BA scalefree
  graphs will take longer to converge, but youll
  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!

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Definitions