measuring ocal opological anonymity in social …anonimized graph, g tar (anonimized export, e.g.,...

MEASURING LOCAL TOPOLOGICAL

Brussels

December 10, 2012

PinSoDa: Privacy in Social Data Workshopin conjunction with the 11th IEEE International Conference on Data Mining (ICDM 2012)

ANONYMITY IN SOCIAL NETWORKS

Gábor György Gulyás and Sándor Imre

Dept. of Telecommunications (BME)

{gulyasg, imre}@hit.bme.hu

Anonimized graph, Gtar

(anonimized export, e.g., Twitter)

Anonymous exports and private information?

Auxiliary information, Gsrc

(a public crawl, e.g., Flickr)

Measuring Local Topological Anonymity in Social Networks 2© Gábor György Gulyás, Sándor Imre

RepublicanDemocratic

Primary attack types

Active attacks1 Passive attacks2

Measuring Local Topological Anonymity in Social Networks 3© Gábor György Gulyás, Sándor Imre

1 Backstrom et al.: Wherefore Art Thou R3579X? Anonymized Social Networks,

Hidden Patterns, and Structural Steganography (2007) 2 Narayanan & Shmatikov: De-anonymizing social networks (2009)

Primary attack types

Active attacks1 Passive attacks2

Not always possible, e.g,

• data is unavailable prior to anonimization,

• creating links requires mutual confirmation.

Or it may not be feasible, e.g.,

• it is expensive to create new nodes, links (phone calls),

Measuring Local Topological Anonymity in Social Networks 4© Gábor György Gulyás, Sándor Imre

• it is expensive to create new nodes, links (phone calls),

• it is too slow to be done,

etc.

Plus it is more limited than identifying existing strutures.

1 Backstrom et al.: Wherefore Art Thou R3579X? Anonymized Social Networks,

Hidden Patterns, and Structural Steganography (2007) 2 Narayanan & Shmatikov: De-anonymizing social networks (2009)

Re-identification example

Gsrc: Gtar:

� The attacker uses nodedegrees.Anonymity sets:{D} {A, G} {C, H} {B, E, F}

� Dave is globally unique: Dave ↔ 3

� But what about Harry?• He is in {H, C}

• Relatively to Dave, i.e., (D,*)∈E, anon. sets:{A, G}, {B, E}, {H}

• Harry is locally unique:

Harry ↔ 1

Measuring Local Topological Anonymity in Social Networks 5© Gábor György Gulyás, Sándor Imre

Global re-identification phase(a.k.a. seed identification phase)

Gsrc: Gtar:

A B C D E F G H

d(vi) 1 3 2 5 3 3 1 2

A(vi) 1/2 2/3 1/2 0 2/3 2/3 1/2 1/2

� Problems:• Not feasible for large

networks

• Limited de-anonymizationrate

• Most of the nodes are notglobally outstanding

Measuring Local Topological Anonymity in Social Networks 6© Gábor György Gulyás, Sándor Imre

Anonymity sets: {D} {A, G} {C, H} {B, E, F}

Measuring anonymity:

Local re-identification phase(a.k.a. propagation identification phase)

Gsrc: Gtar:

� Local TopologicalAnonymity (LTA)• User: privacy status

estimation

• Data providers (and attackers): estimation of thesuccess of an attack

Measuring Local Topological Anonymity in Social Networks 7© Gábor György Gulyás, Sándor Imre

� Problem:anonymity sets depend onseed locations

� How to measure a priori anonymity?

How do propagation phases work?

� State-of-the-art algorithm:

Narayanan, A., Shmatikov, V.: De-anonymizing social networks.

In: 30th IEEE Symposium on Security and Privacy, pp. 173-187,

IEEE Computer Society, Washington (2009)

Measuring Local Topological Anonymity in Social Networks 8© Gábor György Gulyás, Sándor Imre

How do propagation phases work? (2)

� Need seeds as an initial mapping (Gsrc � Gtar)

� Round based: tries to extend mapping in each round

• Unmapped source nodes are structurally compared to

unmapped targed nodes

• Comparison involves their mapped neighbors and their

degree values

Measuring Local Topological Anonymity in Social Networks 9© Gábor György Gulyás, Sándor Imre

Gsrc Gtar

How do propagation phases work? (3)

� Need seeds as an initial mapping (Gsrc � Gtar)

� Round based: tries to extend mapping in each round

• Unmapped source nodes are structurally compared to

unmapped targed nodes

• Comparison involves their mapped neighbors and their

degree values

Measuring Local Topological Anonymity in Social Networks 10© Gábor György Gulyás, Sándor Imre

Gsrc Gtar

How do propagation phases work? (4)

� Need seeds as an initial mapping (Gsrc � Gtar)

� Round based: tries to extend mapping in each round

• Unmapped source nodes are structurally compared to

unmapped targed nodes

• Comparison involves their mapped neighbors and their

degree values

Measuring Local Topological Anonymity in Social Networks 11© Gábor György Gulyás, Sándor Imre

Gsrc Gtar

How do propagation phases work? (5)

� Future algorithms are likely to share these principles

� Node comparison yields success if

• a source node has an instance in the target graph,

• the source node and its target instance are similar enough,

• and the target instance is outstanding to its „competitors”.

⇒ this property can be captured by an a priori anonymity measure!

Measuring Local Topological Anonymity in Social Networks 12© Gábor György Gulyás, Sándor Imre

⇒ this property can be captured by an a priori anonymity measure!

Gsrc Gtar

Local Topological Anonymity

� Principle: how vi is

structurally hidden in its

2-neighborhood

• i.e., how similar vi is to its

neighbors of neighbors

� Proposed metrics:

vi

d(vi)=1

� Proposed metrics:

Measuring Local Topological Anonymity in Social Networks 13© Gábor György Gulyás, Sándor Imre

d(vi)=2

( )( )∑

∈∀

=2ik Vv i

kiiB

2,Vmax

v,vsim)v(LTA

( )∑∈∀

=2ik Vv

2i

kiiA

V

v,vsim)v(LTA

( )( )( )∑

∈∀ ∆σ⋅=

2ik Vv

2ideg

2i

kiiC

1,VmaxV

v,vsim)v(LTA

Local Topological Anonymity (2)

� Similarity metric?• State-of-the-art attack is

based on cosine similarity

• CosSim produced bestresults in the comparisonof similarity metrics

• (our comparison & Spertus et al, 2005)

vi

d(vi)=1

� Simulations: CosSim()

• For the state-of-the-artattack

• Other attack � differentmetric

Measuring Local Topological Anonymity in Social Networks 14© Gábor György Gulyás, Sándor Imre

d(vi)=2

Spertus et al.: Evaluating similarity measures:

a large-scale study in the orkut social network. (2005)

ki

kiki

VV

VV)v,v(CosSim

⋅=

I

Visual comparison for small nets

Measuring Local Topological Anonymity in Social Networks 15© Gábor György Gulyás, Sándor Imre

Evaluation methodology

� Simulational evaluation:attack results vs. LTA prediction• State-of-the-art attack (**)

• 10 rounds to avoid seeddependencies (e.g., location)

• Strong attacker

� Dataset sources:Slashdot, Wikivote, Epinions (*)LiveJournal (our crawl)

� Realistic test data (**)• Given overlap factors:

αV = Jacc(Vsrc, Vtar)αE = Jacc(Esrc, Etar)αE = Jacc(Esrc, Etar)

Measuring Local Topological Anonymity in Social Networks 16© Gábor György Gulyás, Sándor Imre

* Source: http://snap.stanford.edu/data/index.html

** Narayanan & Shmatikov: De-anonymizing social networks (2009)

V1 V2 V3

Dataset generation

Measuring Local Topological Anonymity in Social Networks 17© Gábor György Gulyás, Sándor Imre

Dataset generation (2)

Measuring Local Topological Anonymity in Social Networks 18© Gábor György Gulyás, Sándor Imre

Simulational results of LJ-10KvA

Scoring:

+1 for a TP

-1 for a FP

Measuring Local Topological Anonymity in Social Networks 19© Gábor György Gulyás, Sándor Imre

Simulational results of LJ-10KvA (2)

83.9% of the

overlapping

nodes!

Measuring Local Topological Anonymity in Social Networks 20© Gábor György Gulyás, Sándor Imre

Pearson correlation of LTA and results

avg(LTA )=-0.27945

Measuring Local Topological Anonymity in Social Networks 21© Gábor György Gulyás, Sándor Imre

avg(LTAA)=-0.27945

avg(LTAB)=-0.23164

avg(LTAC)=-0.17742

Corrected LTA evaluation

avg(LTA )=-0.42133

Measuring Local Topological Anonymity in Social Networks 22© Gábor György Gulyás, Sándor Imre

avg(LTAA)=-0.42133

avg(LTAB)=-0.34466

avg(LTAC)=-0.26988

Future work

� Attacker perspective:

network level LTA

predictions?

� Directed networks?

� Improving measures?

� Further LTA analysis

• Structural dependency

� LTA testing for other

algorithms

• E.g., seed-and-grow

� Combined global +

local metrics?

Measuring Local Topological Anonymity in Social Networks 23© Gábor György Gulyás, Sándor Imre

Questions?

THANK YOU FOR YOUR ATTENTION!

Measuring Local Topological Anonymity in Social Networks 24© Gábor György Gulyás, Sándor Imre

Gábor György Gulyás

assistant research fellow

Dept. of Telecommunications (BME)

gulyasg@hit.bme.hu