Analyzing connectivity of heterogeneous secure sensor networks
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We analyze connectivity of a heterogeneous secure sensor network that uses key predistribution to protect communications between sensors. For this network on a set V_n of n sensors, suppose there is a pool P_n consisting of P_n distinct keys. The n sensors in V_n are divided into m groups A_1, A_2, ..., A_m. Each sensor v is independently assigned to exactly a group according to the probability distribution with P[v ∈A_i]= a_i for i=1,2,...,m, where ∑_i=1^ma_i = 1. Afterwards, each sensor in group A_i independently chooses K_i,n keys uniformly at random from the key pool P_n, where K_1,n≤ K_2,n≤...≤ K_m,n. Finally, any two sensors in V_n establish a secure link in between if and only if they have at least one key in common. We present critical conditions for connectivity of this heterogeneous secure sensor network. The result provides useful guidelines for the design of secure sensor networks. This paper improves the seminal work [1] (IEEE Transactions on Information Theory 2016) of Yağan on connectivity in several aspects (omitted due to arxiv abstract's character limitation; see the paper for details).
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