anonymized social networks, hidden patterns, and structural stenography lars backstrom, cynthia...
TRANSCRIPT
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
Phone Records
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?