1. Chi Zhang, Yang Song and Yuguang Fang
Modeling Secure Connectivity of Self-Organized Wireless Ad Hoc Networks
Chi Zhang, Yang Song and Yuguang Fang
IEEE INFOCOM 2008
Computer Architecture Lab.
Hanbit Kim

2. Contents Introduction Problem & Answer Network Model
Problem Formulation
Properties of Secure Graph
Conclusion
Discussion

3. Introduction Wireless Ad Hoc Networks (WANET)
Wireless networks without the support of centralized network management

4. Introduction Security architecture with self- organization
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

5. Question & Answer Question Answer
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)

6. Physical Graph G(Χn, Εpl) Local Augmented Secure Graph
Network Model
Physical Graph G(Χn, Εpl)
Trust Graph G(Χn, ΕSA)
Local Augmented Secure Graph
G(Χn, Ε’sl)
Isolated node
Cluster
Secure Graph G(Χn, Εsl)
Cluster

7. Network Model r Pf Communication range
Probability that two nodes which meet as neighbors will be friends k
Pf • nπr2
Expected value of the number of neighboring friends

8. 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.

9. Problem Formulation
Constructing a secure path between an arbitrary pair of nodes
What should k be?
We must avoid routing-security dependency loop.

10. 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.

11. Properties of Secure Graph
Theorem 2:
For secure graph G(Χn, Εsl), there is a percolation threshold kp .
Approximately, kp
If k > kp then there is only one infinite-order cluster.

12. Properties of Secure Graph
Connected Phase
k > kc
The secure graph G(Χn, Εsl) is connected.
There is only one cluster.

13. 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

14. Properties of Secure Graph

15. Properties of Secure Graph
Subcritical phase
k < kp = 4.5
The network consists of small clusters.
The network cannot achieve secure connectivity.

16. 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).

17. Discussion
Not uniform distribution
Not connected trust graph