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 d min >=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