Giulia Fanti, Peter Kairouz, Sewoong Oh,Kannan Ramchandran, Pramod Viswanath

Spy vs. spy:Anonymous messagingover networks

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Some people have important,sensitive things to say.

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Others have less important,sensitive things to say.

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Privacy can help.

5

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Existing anonymous messaging apps

Alice

Thank you to all the blood donors…

6

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Centralized networks are not truly anonymous!

BobMary

Alice

Server

Existing anonymous messaging apps

7

/    54Avoid trusting servers to “do the right thing”

Compromises in anonymity

8

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Objective

9

Design a distributed messaging mechanism that:

(a) spreads content fast

(b) gives authors anonymity

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What can adversaries do?

10

Snapshot

Spy-based

Full oversight

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First-Order Solution: Distributed Messaging

Bob

Mary

Alice

Snapshot and spy-based adversaries can still infer the source!

11

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Information flow in social networks

Diffusion has statistical symmetry

message author

12

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Disease flow in populations

patient zero

13[Shah and Zaman 2011, Pinto et al. 2012, Zhu et al. 2013]

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Diffusion spreading = deanonymization

Low likelihood

High likelihood

[Shah, Zaman 2011] 14

Information flow in social networks

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Deanonymization on Social Networks

15Number of nodes with message (N)

Prob

abilit

y of

Det

ectio

n

DiffusionLower bound, 1/N

[Seo et al., 2012, SPIE]

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First-order solution doesn’t work.

Spreads fastJ

Bad anonymity properties L

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Lessons Learned

1) Diffusion = deanonymization

17

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Engineer the spread to hide authorship.

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Key idea:

19

Break the symmetry.

Direction Time

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Breaking symmetry: Adaptive diffusion

Low likelihood

High likelihood

Provides provable anonymity guarantees

[Spy vs. Spy: Rumor Source Obfuscation, ACM Sigmetrics 2015]20

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𝑑-regular trees: adaptive diffusion

Initially, the author is also the “virtual source”

21

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𝑑-regular trees: adaptive diffusion

22

Breakdirectionalsymmetry

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𝑑-regular trees: adaptive diffusion

chosen neighbor = new virtual source

23

Breakdirectionalsymmetry

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𝑑-regular trees: adaptive diffusion

24

Breakdirectionalsymmetry

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𝑑-regular trees: adaptive diffusion

keep the virtual source token pass the virtual source token 25

Breaktemporalsymmetry

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keep the virtual source token

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new  virtual  source

27

pass the virtual source token

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pass the virtual source token

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Results

29

[1] [2] [1]

[3] [3] [3]

Snapshot

Spy-based

𝑑-Regular trees Irregular trees Facebook graph

[1] Spy vs. Spy: Rumor Source Obfuscation, Sigmetrics 2015[2] Rumor Source Obfuscation on Irregular Trees, to appear in Sigmetrics 2016[3] Under review

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Snapshot adversary

Bob

Mary David

Alice

Craig

30

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When to keep the virtual source token?

Virtual source token is kept with probability 𝜶 = 𝒅 − 𝟏 '𝒉

distancefrom

source

31

nodedegree

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Maximum likelihood detection

Low likelihood

High likelihood

All nodes except for the final virtual source are equally likelyTHEOREM:  Probability of detection = )

*')32

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hop distancefrom source

ℎ = 1 ℎ = 2

Likelihood = %& ⋅ ( Likelihood = %& ⋅%)*&)%

treedegree

P(keep token)

Want these to be equal: ( = %&

ℎ = 1 ℎ = 2

Likelihood = ). ⋅ 𝛼

Pr(keep token)

Tree degree

Likelihood = ). ⋅

)'1.')

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Lessons Learned

1) Diffusion = deanonymization

2) For anonymity, break symmetry.

34

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Irregular trees

35

𝑑2 = 33          𝑤. 𝑝.      0.75            𝑤. 𝑝.      0.3

𝑑<=> = 3

𝑑<?@ = 5

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How do we analyze this?

36

𝑃 detection    snapshot) =1

min2∈PQRSQT

∏ 𝑑2�2∈W(2,2Z)

  min2∈PQRSQT

[ 𝑑2  ≈     𝑑<=> − 1 ]/_�

2∈W(2,2Z)

THEOREM: Probability of detection ≈ )(.`ab'))Z/c

Path from v to virtual source

Degree of node v

𝑑2 = 3 𝑑<=>          𝑤. 𝑝.      𝑝<=>𝑑<?@            𝑤. 𝑝.      𝑝<?@

If      𝑝<=> 𝑑<=> − 1 > 1

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Irregular trees

1 2 3 4 510-2

10-1

Adaptive Diffusion1-hop Preferential Attachment2-hop Preferential Attachment3-hop Preferential Attachment1/NT

37Timestep (T)

Prob

abilit

y of

Det

ectio

n

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Proof sketch for

38

𝑑2 = 33          𝑤. 𝑝.      0.75            𝑤. 𝑝.      0.3 𝑑2 = 33          𝑤. 𝑝.      0.71            𝑤. 𝑝.      0.3

If 𝑝<=> 𝑑<=> − 1 > 1  then the pruned process survives.

  min2∈PQRSQT

[ 𝑑2  ≈     𝑑<=> − 1 ]/_�

2∈W(2,2Z)

0.7 3

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Lessons Learned

1) Diffusion = deanonymization

2) For anonymity, break symmetry.

3) For more anonymity, hide in a crowd.

39

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Facebook graph

Adaptive diffusionDiffusionPerfect hiding

40Nodes Infected (N)

Prob

abilit

y of

Det

ectio

n

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Results

41

Optimal Near-optimal High anonymity

𝑑-Regular trees Irregular trees Facebook graphSnapshot

Spy-based

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Adversary sees metadata at spy nodes

Spy-based adversary

-message-T = 09/10/2015

@ 9:10 pm

-message-T = 09/10/2015

@ 8:40 pm

Bob

Mary

David

Alice

CraigWith probability 𝑝

42

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Result on 𝑑-regular trees

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

d=3d=4d=5d=15d=30d=100p

THEOREM:  Probability of detection = 𝑝 + 𝑜(𝑝)

Lower boundon detection

Spy probability, p

Prob

abilit

y of

det

ectio

n

43

𝑇 = ∞

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Spy Probability, p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Pr

obab

ility

of D

etec

tion,

PD

Lower bound, pAdaptive diffusionDiffusion, q=0.1Diffusion, q=0.5

Facebook Graph

Lower boundon detection

44Spy probability, p

Prob

abilit

y of

det

ectio

n

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Results

45

Optimal Near-optimal High anonymity

Asymptotically-Optimal ML Estimator High anonymity

𝑑-Regular trees Irregular trees Facebook graphSnapshot

Spy-based

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Adaptive Diffusion

Pros• Strong anonymity• Fast spreading• Distributed• Lightweight

Cons• No guarantees for

general graphs• Sub-optimal spreading• Passes around state

46

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Wildfire: P2P Anonymous Microblogging

Namespace resolution

Cyberbullying

47

https://github.com/gfanti/Wildfire

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Related Work

48

Waidner et al., `90,Golle and Juels, `04 Chaum `88

Statisticalanonymity

Robson et al. `03Corrigan-Gibbs et al. `10Wolinsky et al., `12

DiningCryptographer

Networks

Adve

rsar

y

Scalability

F. et al, `15F. et al, `16

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Ongoing Work

49

Physical Network Algorithms Social Science

AnonymousMessaging

CyberbullyingPrevention

Cellular LocationPrivacy

Vibration-basedBiometrics

Anonymous P2P Networking

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Cellular Location Privacy

50

Songbin Gong,Microwave Circuits

Pramod Viswanath,Wireless Comm.

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Anonymous P2P Messaging

51

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Cyberbullying Prevention

52Suma Bhat,NLP

Dorothy Espelage,Educational Psychology

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Ongoing Work

53

Physical Network Algorithms Social Science

AnonymousMessaging

CyberbullyingPrevention

Cellular LocationPrivacy

Vibration-basedBiometrics

Anonymous P2P Networking

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Acknowledgments

PramodViswanath

SewoongOh

KannanRamchandran

PeterKairouz

54

HongyuGong

Suma Bhat

SongbinGong

Romit RoyChoudhury

DorothyEspelage