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 email– Bad for Web Browsing– Awful for Bit Torrent

• If >1 message (more than 32K data), anonymity is degraded

Intersection Attack

A

B

C2 2 2

1

1

1

11

1D

E

F

Mix 1

Mix 4

Mix 3

Mix 2

Senders Receivers

Attacker

TrafficVolume of data dow nloaded through the anonymity system

0

5000

10000

15000

20000

25000

Volume of data, Kb

Nu

mb

er o

f u

sers

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 1Mix 2

D

E

F

1

2

1

2

Attacker observes:not all inputsnot all outputs

Notinteresting

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 3Mix 4

1

2

1

2

1

2

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 2E

F

1

2

2

11

1

1

11

Sender B splits his stream of data and sends each message via arandomly chosen route

The problem: how do you choosethe 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

MPP1

iPfM

fM

PPi

M

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)

1P

1' PPP 2P

2''' PPP 2/'P

2/P

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

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)

100

17

10

5

87

The Network(Mixmaster)

100

170

10

5

87

Total observed packets

Alice

Alice

Intersection Attack

SendersReceivers

AttackerMixes

A Weaker Model

Attacker observes:not all inputsnot all outputs

Notinteresting

Observed Mix

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

Splitting DataAttacker splits his stream of data and sends each message via arandomly chosen route

The problem: how do you chooseThe first mix?

Results

Results

Comparing

• Nothing surprising– Mixmaster has longer delay– Heavy tails