LinkMirage: Enabling Privacy-preserving Analytics on Social - - PowerPoint PPT Presentation

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Outline Introduction LinkMirage Conclusion LinkMirage: Enabling Privacy-preserving Analytics on Social Relationships Changchang Liu, Prateek Mittal Email: cl12@princeton.edu, pmittal@princeton.edu Princeton University February 23, 2016 1 /

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Outline Introduction LinkMirage Conclusion

LinkMirage: Enabling Privacy-preserving Analytics

  • n Social Relationships

Changchang Liu, Prateek Mittal Email: cl12@princeton.edu, pmittal@princeton.edu Princeton University February 23, 2016

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

Social relationships

(a) (b)

Third party applications rely on users’ social relationships:

  • E-commerce
  • Spam detection
  • Anonymous communication
  • Sybil defenses

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

Social relationships are very sensitive!

Social relationships represent

  • Trusted friendships
  • Important interactions
  • Even more, business relations, etc.

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

How to balance utility and privacy?

Privacy Utility

Protect privacy of sensitive social relationships Preserve utility of obfuscated social relationships for real-world applications

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

Previous work of link privacy mechanisms

To protect link privacy, previous work

  • obfuscate social relationships through link additions/deletions

G G

add

p

del

p

However, previous work

  • only consider graph data where the links are redstatic

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

Limitations of previous link privacy mechanisms

To protect link privacy, previous work

  • obfuscate social relationships through link additions/deletions

G G

add

p

del

p

However, previous work

  • only consider graph data where the links are static

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

However, social networks are dynamic

Temporal Facebook dataset (every three months) with 46,952 users and 876,993 edges

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

However, social networks are dynamic

An adversary can combine the previously perturbed graphs together G¢ ...

1 t

G - ¢ G

...

1 t

G -

t

G¢

t

G

Adversary

  • bfuscation
  • bfuscation
  • bfuscation

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Outline Introduction LinkMirage Conclusion Social Relationships Privacy-utility tradeoff

Our Objective

  • Balance privacy and utility
  • Handle both the static and dynamic social network topologies
  • Provide rigorous privacy guarantees
  • Useful in real-world applications

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

LinkMirage LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Social Relationship based Applications

G

Original Graph

Untrusted Applications

Privacy-preserving graph analysis Sybil defenses Anonymous communication

Q ( )

Q G¢

...

OSN providers

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy-preserving Social Relationship based Applications

G

Original Graph

Untrusted Applications

Privacy-preserving graph analysis Sybil defenses Anonymous communication

Q ( )

Q G¢

...

OSN providers

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

LinkMirage Architecture

G G¢

Original Graph Obfuscated Graph

LinkMirage System (Trusted)

LinkMirage social link app User1 User2 User3 Obfuscation Algorithm

Untrusted Applications

Privacy-preserving graph analysis Sybil defenses Anonymous communication

Q ( )

Q G¢

...

OSN providers

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

LinkMirage LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Key intuitions

  • Naive method: independent perturbation

− more information is leaked to others

  • We need to

− incorporate graph evolution − leverage the information already released in previous graphs

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

1

C

2

C

  • 1. clustering

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

1

C

2

C

  • 1. clustering
  • 2. perturbation

1 t

G - ¢

1

C¢

2

C¢

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

t

G

  • 3. evolution

1

C

2

C

  • 1. clustering
  • 2. perturbation

1 t

G - ¢

1

C¢

2

C¢

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

t

G

  • 4. dynamic clustering
  • 3. evolution

1

C

2

C

  • 1. clustering
  • 2. perturbation

2

C

1

C

3

C

1 t

G - ¢

1

C¢

2

C¢

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

t

G

  • 5. selective perturbation
  • 4. dynamic clustering
  • 3. evolution

1

C

2

C

  • 1. clustering
  • 2. perturbation

2

C

1

C

3

C

t

G¢

1

C¢

2

C¢

3

C¢

1 t

G - ¢

1

C¢

2

C¢

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Algorithm Description

1 t

G -

t

G

Key step 2. selective perturbation Key step 1: dynamic clustering

  • 3. evolution

1

C

2

C

  • 1. clustering
  • 2. perturbation

2

C

1

C

3

C

t

G¢

1

C¢

2

C¢

3

C¢

1 t

G - ¢

1

C¢

2

C¢

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Two Key Steps in Our Algorithm

Two key steps

  • Dynamic Clustering

– find communities by simultaneously considering consecutive graphs – backtrack based on clustering result of the previous graph

  • Selective Perturbation

– perturb the minimal amount of edges – use a very high privacy parameter while preserving structural properties (utility)

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Facebook Temporal Dataset (46,952 users and 876,993 edges)

t=4 t=5

Original graphs

t=3 Superior utility, due to dynamic clustering Utility advantage even exists in static scenario

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Utility Advantage

t=4

Mittal et al.

t=5

LinkMirage Original graphs

t=3 Superior utility, due to dynamic clustering Utility advantage even exists in static scenario

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Utility Advantage

t=4

Mittal et al.

t=5

LinkMirage Original graphs

t=3 Superior utility, due to dynamic clustering Utility advantage even exists in static scenario

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy Advantage

Original graphs Overlapped edges (black) and Changed edges (yellow) between consecutive graphs

Superior privacy, due to selective perturbation

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy Advantage

Mittal et al. LinkMirage Original graphs Overlapped edges (black) and Changed edges (yellow) between consecutive graphs

Superior privacy, due to selective perturbation

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy Advantage

Mittal et al. LinkMirage Original graphs Overlapped edges (black) and Changed edges (yellow) between consecutive graphs

Superior privacy, due to selective perturbation

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

LinkMirage LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Anti-Inference Privacy

Assume the worst-case adversary knows

  • the obfuscated graphs {G′

i}t i=0

  • all the other links except for one link Lt
  • our obfuscation algorithm

The adversary computes the posterior probability P(Lt|{G′

i}t i=0,W) = P({G′ i}t i=0|Lt,W)× P(Lt|W)

P({G′

i}t i=0|W)

(1) and compare with the prior probability Higher similarity implies better anti-inference privacy

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Anti-Inference Privacy

Assume the worst-case adversary knows

  • the obfuscated graphs {G′

i}t i=0

  • all the other links except for one link Lt
  • our obfuscation algorithm

The adversary computes the posterior probability P(Lt|{G′

i}t i=0,W) = P({G′ i}t i=0|Lt,W)× P(Lt|W)

P({G′

i}t i=0|W)

(2) and compare with the prior probability Higher similarity implies better anti-inference privacy

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Anti-Inference Privacy

10

−3

10

−2

10

−1

10 0.2 0.4 0.6 0.8 1 Link Probability Cumulative distribution function Prior probability Mittal et al. LinkMirage

LinkMirage has higher anti-inference privacy!

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Anti-Inference Privacy

10

−3

10

−2

10

−1

10 0.2 0.4 0.6 0.8 1 Link Probability Cumulative distribution function Prior probability Mittal et al. LinkMirage

LinkMirage achieves higher anti-inference privacy!

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

LinkMirage LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy-preserving Graph Analytics

Facebook Original Graph LinkMirage Mittal et al. Modularity 0.488 0.487 0.415 LinkMirage preserves graph analytics better! Other graph analytics: pagerank, etc.

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Outline Introduction LinkMirage Conclusion LinkMirage Overview Algorithm Description Privacy Analysis Utility Analysis

Privacy-preserving Graph Analytics

Facebook Original Graph LinkMirage Mittal et al. Modularity 0.488 0.487 0.415 LinkMirage preserves graph analytics better! Other graph analytics: pagerank, etc. More applications:

  • Sybil defenses
  • Anonymous communication

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Outline Introduction LinkMirage Conclusion

Conclusion

Our LinkMirage system

  • Both static and temporal graphs
  • Provide rigorous privacy advantages
  • Show utility advantages theoretically and using real-world

applications

  • Generalizable to communication networks and web graphs

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Outline Introduction LinkMirage Conclusion

Appendix1: Indistinguishability

Definition

The indistinguishability for a link Lt that the adversary can infer from the perturbed graph G′

t under the adversary’s prior information

{

Gi(Lt)}t

i=0 is defined as

Privacyid = H(Lt|{G′

i}t i=0,{

Gi(Lt)}t

i=0)

(3)

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Outline Introduction LinkMirage Conclusion

Appendix1:Indistinguishability

1 2 3 4 5 6 7 8 0.1 0.2 0.3 0.4 0.5

(a) Timestamp t Indistinguishability k=5, Mittal et al. k=5, LinkMirage k=20, Mittal et al. k=20, LinkMirage Hay’s et al.

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Outline Introduction LinkMirage Conclusion

Appendix2:Anti-aggregation Privacy

Definition

The anti-aggregation privacy for a perturbed graph G′

t with respect to

the original graph Gt and the perturbation parameter k is

Privacyaa(Gt,G′

t,k) = Pk t − P′ tTV

(4)

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Outline Introduction LinkMirage Conclusion

Appendix2:Anti-aggregation Privacy

1 2 3 4 5 6 7 8 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

(b) Timestamp t Anti−aggregation Privacy K=2,Mittal et al. K=2,LinkMirage

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