Anonymized Social Networks,Hidden Patterns, and Structural Stenography

Lars Backstrom, Cynthia Dwork, Jon Kleinberg

WWW 2007 – Best Paper

OUTLINE

Problem Some graph theory Walk-Based Attack Cut-Based Attack (Semi)-Passive Attacks

PROBLEM

Massive social network graphs exist MySpace

FaceBook

Phone Records

Email

Instant Messaging...

Social network structure is valuable

Just removing names isn't enough (we show this)

MOTIVATION

Privacy concerns – who talks to who Economic concerns – selling to marketers

AOL Search Data

GENERAL METHOD

Watermark the graph so that finding the watermark allows us to find individuals

Reveals the removed names Reveals edges between revealed names

WALK BASED ATTACK

Create a subgraph S to embed Desired Properties of Subgraph

Doesn't already exist in the graph

Can be easily found

No non-trivial automorphisms (can't be mapped to itself beyond the identity)

WALK BASED ATTACK

Let k = (2+d)logn be the number of nodes in the subgraph

x2 x3

x1 x4

WALK BASED ATTACK

Let k = (2+d)logn be the number of nodes in the subgraph

Pick W = {w1...wb} users to target

x2 x3

x1

w1

w2

w3

x4

WALK BASED ATTACK

Let k = (2+d)logn be the number of nodes in the subgraph

Pick W = {w1...wb} users to target

Pick a unique set of nodes in the subgraph to connect to each wi

x2 x3

x1

w1

w2

w3

x4

WALK BASED ATTACK

Let k = (2+d)logn be the number of nodes in the subgraph

Pick W = {w1...wb} users to target

Pick a unique set of nodes in the subgraph to connect to each wi

Pick an external degree for each xi

and create additional spurious edges

x2 x3

x1

w1

w2

w3

x4

WALK BASED ATTACK

Create the internal edges by including each edge (xi,xi+1).

Include all other edges with probability ½

Theoretical result guarantees that w.h.p. this subgraph doesn't exist in G and has no automorphisms.

x2 x3

x1

w1

w2

w3

x4

FINDING THE SUBGRAPH

Find all nodes with degree(x1)

Find all nodes connected to x1 with

degree(x2). Repeat by building a

tree With high probability the tree will be pruned to our embedded subgraph.

x2 x3

x1 w1

w2

w3

x4

d

b

c

a

e

deg(x1) = 5 deg(x2) = 4

x2

w3

x3

x4

x1

deg(x3) = 6 deg(x4) = 7

w2

QUESTION

What could we do to foil this attack?

Evaluation

LJ Data = 4.4 mil people, 77 mil edges

EVALUATION

Using 7 nodes the attack succeeds w.h.p

Can attack 34 - 70 nodes and ~560 - 2400 edges

Our subgraph is not 'obvious' in the graph without the degree sequence

CUT-BASED ATTACK

Requires O(√logn) nodes instead of O(logn) (theoretical lower bound)

Create a subgraph in a similar manner

Each x1 connects to one wi

Use min-cut methods to find H Walk-based attack is better

This subgraph is highly disconnected = sticks out

(SEMI)-PASSIVE ATTACKS

Walk and Cut based attacks are active

Groups of users could also collude to execute an attack on their neighbors

Experiments show this works for groups as small as 3 or 4 users

How do you defend against this?

Questions?