Message Splitting Against the Partial Adversary

1. Message Splitting Against the Partial Adversary Andrei Serjantov The Free Haven Project (UK) Steven J Murdoch University of Cambridge Computer Laboratory

2. Outline • Mix Systems. Criticisms. • too strong threat model(!) • intersection attack when >1 msg (too much data) sent • Weaker threat model • Sending each message via random route • “non connection-based system” • Empirical observations about Mixmaster Mixminion • Characteristic delay function [Dan04] is difficult to esitmate

3. Mix Systems • Well known to this audience • Implemented • Mixmaster • Mixminion • Threat Model • Global Passive Adversary (GPA) • GPA with some (all but one?) compromised mixes

4. Criticisms • GPA does not exist • (a matter of some debate) • The mix system (Chaum 81) allows one fixed-sized message to be sent anonymously • Great for votes • Ok for email • Bad for Web Browsing • Awful for Bit Torrent • If >1 message (more than 32K data), anonymity is degraded

5. 1 1 1 D A Mix 3 Mix 1 1 1 E B 1 2 Mix 2 2 2 Mix 4 F C Intersection Attack Receivers Senders Attacker

6. Traffic

7. Intersection Attack • [BPS00] On the Disadvantages of Free Mix Routes (PET2001) • [WALS02] An Analysis of the Degradation of Anonymous Protocols (NDSS’02) • [KAP02] Limits of Anonymity in Open Environments (IH2002) • [Dan03] Statistical Disclosure (I-NetSec03) • [DS04] (IH2004) • [Dan04] The traffic analysis of continuous-time mixes (PET2004) etc

8. The Common Wisdom • Intersection attacks are: • Realistic • Powerful (reduce anonymity quickly) • Hard to protect against • Require lots of dummy traffic

9. Attacker observes: not all inputs not all outputs Not interesting A Weaker Model 1 1 1 A D Mix 1 2 Mix 2 2 2 E B Mix 3 Mix 4 F C

10. A Better Threat Model • A Partial Adversary • Does not observe all Sender to Mix links • (alternatively not all mixes which senders can send to) • Ignore compromised mixes

11. Observed Mix Attacker sends all his messages via one single route theough the mix system 1 1 1 A D Mix 1 Mix 2 2 2 2 B Mix 3 E Mix 4

12. Splitting Data Sender B splits his stream of data and sends each message via a randomly chosen route 1 1 1 A E Mix 1 Mix 2 2 1 1 2 Mix 3 1 Mix 4 B F 1 The problem: how do you choose the first mix? C

13. The Details • Problem: • mixes to send to • compromised, the rest not (but no idea which ones) • P packets • What are the s.t. a random subset (attacker) of size gives least information about • Note that (dummy traffic) • No proof or optimal solution in this paper! • See one possible solution next

14. One possible scheme • Pick (uniformly) at random a sequence of mixes • Pick from a geometric distribution with mean . Set • Pick from a geometric distribution with mean . Set • etc • Another in the paper (with some analysis)

15. Part II • (Looking at a particular intersection attack and finding it not as easy as it looks at first glance)

16. Another Intersection Attack • Danezis 2004 (thanks for the diagrams) • The Idea:

17. The Details

18. The Characteristic Delay Function • What is this for • Mixes • Mixmaster • Mixminion • Tor • This maybe unfair – Danezis intended his attack for lwo latency systems (Tor) • Nevertheless interesting

19. The Characteristic Delay Function • Theory: • What is the delay of a mix (cascade/network) • Can say not very much about it (as usual) • Details in the paper • Practice: • Steven wrote a disciplined pinger • Does not ping too often, hope not to affect the results by sampling

20. Results

21. Results

22. Comparing • Nothing surprising • Mixmaster has longer delay • Heavy tails

23. Conclusions I • It is well known that the intersection attack is powerful • No reason to abandon investigation! • New interesting, mathematically well defined threat model • Splitting traffic amongst first nodes • Does not have the efficiency of Tor or other connection-based systems • Does gain anonymity advantage (but only by means of a weaker threat model)

24. Conclusions II • Characteristic function of Mixmaster, Mixminion difficult to work out in theory or estimate empirically • Data at: • All references at “Anonymity Bibliography” Thank you

25. The Anonymity Advantage 100 The Network (Mixmaster) 17 Alice 10 87 5 Total observed packets 100 The Network (Mixmaster) 170 10 87 Alice 5

26. Attacker Intersection Attack Receivers Senders Mixes

27. Attacker observes: not all inputs not all outputs Not interesting A Weaker Model

28. Observed Mix Attacker sends all his messages via one single route theough the mix system

29. Splitting Data Attacker splits his stream of data and sends each message via a randomly chosen route The problem: how do you choose The first mix?

30. Results

31. Results

32. Comparing • Nothing surprising • Mixmaster has longer delay • Heavy tails