Abstract—Wireless sensor network (WSN) has a wide range of applications in various areas. Many time the environment in which these sensor were deployed are hostile in nature and sensors have continuous attacks from the adversary, in such environmental conditions we need a secure communication between the sensors. For secure communication, neighbors must posses a secret common key or there must exists a key-path among these nodes. In this paper, the object of study is a random graph induced by the random key pre-distribution scheme of Eschenauer and Gligor under the assumption of full visibility. Here we establish the threshold value of the parameters (Key pool size and key-ring of an individual node) for which the entire network is almost surely a single connected component. We prove that for a network having N nodes, is a single connected component almost surely, if size of the key-ring is m = √2 log N and the size of key pool is K = N log N.
Index Terms—Secure Sensor Networks, Random Key Pre-distribution Scheme, Secure Connectivity.
B.Gupta is with the Indian Institute of Information Technology, Design & Manufacturing Jabalpur, MP, India 482005.E-mail: gupta.bhupendra@gmail.com, http://www.iiitdmj.ac.in/ bhupen S.S.Lamba with Indian Institute of Information Technology, Design & Manufacturing Jabalpur, MP, India 482005.Email: subirs@gmail.com, http://www.iiitdmj.ac.in/ subirs
Cite: Bhupendra Gupta, and Subir Singh Lamba, "Connected Component in Secure Sensor Network Induced by a Random Key Pre-Distribution Scheme," International Journal of Machine Learning and Computing vol. 1, no. 3, pp. 247-252, 2011.