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

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

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

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 –Bad for Web Browsing –Awful for Bit Torrent If >1 message (more than 32K data), anonymity is degraded

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

Traffic

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

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

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

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

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

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

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

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

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

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

The Details

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

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

Results

Comparing Nothing surprising –Mixmaster has longer delay –Heavy tails

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)

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

The Anonymity Advantage The Network (Mixmaster) The Network (Mixmaster) Total observed packets Alice

Intersection Attack Senders Receivers Attacker Mixes

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

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

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?

Results

Comparing Nothing surprising –Mixmaster has longer delay –Heavy tails