Computer Architecture Lab.
Hanbit Kim
2008. 12. 4
Contents
 Introduction
 Problem & Answer
 Network Model
 Problem Formulation
 Properties of Secure Graph
 Conclusion
 Discussion
2/17
Introduction
 Wireless Ad Hoc Networks (WANET)
 Wireless networks without the support
of centralized network management
3/17
Introduction
 Security architecture with selforganization
 Users prefer to join and leave the
network at random.
 Without the trusted third party
 How to exploit primary security
associations (SA) for secure connectivity
4/17
Question & Answer
 Question
 What is the minimum fraction of
primary SAs for securing all the links?
 Answer
 When the average number of
authenticated neighbors of each node is
Θ(1)
5/17
Network Model
Physical Graph
Local
TrustAugmented
Graph
G(Χ
,
Ε
)
Secure
G(Χn, ΕGraph
)
n
pl
SA
Isolated
G(Χn, Ε’sl)
node
Cluster
Cluster
Secure Graph
G(Χn, Εsl)
6/17
Network Model
 r
 Communication range
 Pf
 Probability that two nodes which meet as
neighbors will be friends
 k
 Pf • nπr2
 Expected value of the number of
neighboring friends
7/17
Assumptions
 Nodes are distributed uniformly at
random.
 SAs are always symmetric.
 Physical Graph G(Χn, Εpl) is connected.
 Trust Graph G(Χn, ΕSA) is connected.
8/17
Problem Formulation
 Constructing a secure path between
an arbitrary pair of nodes Χn  Χn
 What should k be?
 We must avoid routing-security
dependency loop.
9/17
Properties of Secure Graph
 Theorem 1:
 For secure graph G(Χn, Εsl), there is a
critical threshold kc = log(n).
 If k > kc then G(Χn, Εsl) is connected.
10/17
Properties of Secure Graph
 Theorem 2:
 For secure graph G(Χn, Εsl), there is a
percolation threshold kp .

pf  0.1
Approximately, kp  4.5 
1  0.1
 If k > kp then there is only one infinite-
order cluster.
11/17
Properties of Secure Graph
 Connected Phase
 k > kc
 The secure graph G(Χn, Εsl) is connected.
 There is only one cluster.
12/17
Properties of Secure Graph
 Supercritical Phase
 kp < k <= kc
 The secure graph G(Χn, Εsl) consist of one
infinite-order cluster and isolated nodes.
 Handling isolated nodes
13/17
Properties of Secure Graph
14/17
Properties of Secure Graph
 Subcritical phase
 k < kp = 4.5
 The network consists of small clusters.
 The network cannot achieve secure
connectivity.
15/17
Conclusion
 The secure graph is at least in the
supercritical phase.
 Achieve secure connectivity when the
average number of authenticated
neighbors is at least Ω(1).
16/17
Discussion
 Not uniform distribution
 Not connected trust graph
17/17