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Message Splitting Against the Partial Adversary

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Message Splitting Against the Partial Adversary

Andrei Serjantov

The Free Haven Project (UK)

Steven J Murdoch

University of Cambridge Computer Laboratory

- 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

- Well known to this audience
- Implemented
- Mixmaster
- Mixminion

- Threat Model
- Global Passive Adversary (GPA)
- GPA with some (all but one?) compromised mixes

- 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

1

1

1

D

A

Mix 3

Mix 1

1

1

E

B

1

2

Mix 2

2

2

Mix 4

F

C

Receivers

Senders

Attacker

- [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)

etc

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

Attacker observes:

not all inputs

not all outputs

Not

interesting

1

1

1

A

D

Mix 1

2

Mix 2

2

2

E

B

Mix 3

Mix 4

F

C

- A Partial Adversary
- Does not observe all Sender to Mix links
- (alternatively not all mixes which senders can send to)
- Ignore compromised mixes

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

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

- 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

- mixes to send to

- 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)

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

- Danezis 2004 (thanks for the diagrams)

- The Idea:

- What is this for
- Mixes
- Mixmaster
- Mixminion
- Tor

- This maybe unfair – Danezis intended his attack for lwo latency systems (Tor)
- Nevertheless interesting

- 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

- Steven wrote a disciplined pinger

- Nothing surprising
- Mixmaster has longer delay
- Heavy tails

- 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)

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

100

The Network

(Mixmaster)

17

Alice

10

87

5

Total observed packets

100

The Network

(Mixmaster)

170

10

87

Alice

5

Attacker

Receivers

Senders

Mixes

Attacker observes:

not all inputs

not all outputs

Not

interesting

Attacker sends all his messages via one single route theough

the mix system

Attacker splits his stream of data and sends each message via a

randomly chosen route

The problem: how do you choose

The first mix?

- Nothing surprising
- Mixmaster has longer delay
- Heavy tails