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 2008. 12. 4

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

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

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

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)

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

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

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.

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

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.

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.

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

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

Properties of Secure Graph

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

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).

Discussion Not uniform distribution Not connected trust graph