Privacy issues with social networks

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Privacy issues with social networks
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Outline

• Introduction
• Attacks
• Methods countering attacks
• Summary

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Introduction

• Social networks become popular
• A lot of research can be done with the data from
  social networks
• Network structure
• Node information
• Edge information
• Releasing the SN data for research
• SN data are about people
• Privacy is a big issue
• No concrete examples for utilizing SN data for
  privacy attacks yet.
• However, well agreed that node identification is
  the big privacy threat

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Types of potential privacy breach
A Age Salary hobbies
Friends in messenger
Send emails
C Age Salary hobbies
B Age Salary hobbies
In the same club
Friends in facebook
D Age Salary hobbies

• Types of privacy threats
• Node identification
• Link disclosure
• Content disclosure

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Types of potential privacy breach

• Most papers focus on node identification
• Passive vs. active attacks
• Passive attacks do not change the network
  structure
• Active attacks may insert malicious nodes and
  links into the network.

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Passive attacks

• Need certain knowledge about the network
• Colluded users subgraph
• Compromised users
• Node degree
• Degree of the friends of the node (Linkedin)
• Papers 163-165

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Active attacks

• Paper 167
• Two active attacks are described
• Walk-based attack
• Cut-based attack
• Basic idea
• Plug in a set of fake nodes into the real SN,
  which have special interconnection structures
• These fake nodes are identifiable in the
  published/anonymized SN
• Then, the nodes connected by the fake nodes are
  identified

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Walk-based attack
w1,w2,wi,,wb
V1,v2,v3, vn
Original SN (G-H)
w1,w2,wi,,wb are targeted nodes
Subset Nb in fake SN All Ni are distinct
some random edges to the original SN
X1--x2--xi--,,--xk
fake SN (H)
½ prob to node xi
Xi should have ?i edges in total
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Theoretical results

• H can be efficiently recovered from G
• Degree test, xi has ?i degree
• Internal structure test we know the internal
  structure of xi

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Cut-based attack

• Let b be the number of users we wish to target,
  and k3b3
• Create H
• k fake users xi
• Generate edges between xi in a similar way
• Properties of H
• d(H) minimum degree in H
• r(H) minimum cut in H
• r(H) d(H) gtk/3 gt b, in high probability
• H has no non-trivial automorphisms
• Create links to G-H
• Choose b nodes x1,,xb in H, create edge(xi,wi)

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Theoretical results

• H can be efficiently recovered
• Using Gomory-Hu tree of G
• Minimum (v,w) cut minimum edge weight in the
  path from v to w in the tree T
• Remove edges of weight ltb from T
• T turns to a forest
• Check each component Si, with Si is isomorphic to
  H
• H has non-trivial automorphisms ? H can be
  uniquely recovered.

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Protect from passive attacks

• Attackers utilize
• Degree of nodes (paper 164)
• Neighborhood structures (paper 163,165)
• methods similar to k-anonymization

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K-degree anonymization

• Paper 164
• Definition
• At least k nodes that have the same node degree
  d.
• Address the attacks that depend on node degree to
  identify the node in the published SN

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The method

• Two-steps
• K-degree anonymization
• Construct graph with the modification of node
  degree

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K-degree anonymization

• Sort the node degrees d(1),,d(n)
• di,j d(i),d(i1),,d(j)
• Cost of anonymization
• DA(di,dj) di-dj
• I(di,j) sum(d(i)-d(j))
• DP Algorithm
• Change some node degree so that the k-degree
  anonymization is satisfied and the cost is
  minimized
• ilt2k, DA(d1,i I(d1,i)
• igt2k,

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Graph construction

• Check whether the degree sequence is relializable
  
• Lemma from Erdos and Gallai

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• Realizable with constraints
• Original G
• G with the sequence of degrees d
• E in E of G
• Another lemma states the condition for realizable
  subject to the input G
• Algorithms for graph constructions
• Probing
• Relaxed construction (greedy_swap)
• E of G contains almost all E

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Considering neighborhood structure

• Paper 165
• Attacks based on neighborhood structure

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Idea

• Describe the neighborhood structure of each node
• Definition of neighborhood
• Method for encoding the neighborhood
• For nodes with the same neighborhood structure,
  apply anonymization
• Minimize some cost

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definition

• d-neighbors
• d the distance from the node to its neighbor
• 1-neighbor all nodes directly connected to the
  target node

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Encoding the neighborhood

• Neighborhood components
• Encoding each component

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Encoding neighborhood component

• Using DFS-tree code
• minimum DFS code
• Unique for the same structure
• I.e. isomorphic graphs will have the same minimum
  DFS code.
• Check the referred paper

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Neighborhood Anonymization

• Sorting vertex degrees
• Same degree? check structure
• Cost Minimize the change to the structure
• Anonymize neighborhood components

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Summary

• Current research focuses on node identification
• Through node degree
• Through neighborhood structure
• Discover more attacks
• Design different methods countering the attacks
• Utility metric for SN