Year: 2016
Type: article
Abstract: We analyze the connectivity of a heterogeneous secure sensor network that uses key predistribution to protect communications between sensors. For this network on a set Vnof n sensors, suppose there is a pool Pnconsisting of Pndistinct keys. The n sensors in Vnare divided into m groups A1, A2, . . . , Am. Each sensor v is independently assigned to exactly a group according to the probability distribution with P[v ∈ Ai] = aifor i = 1, 2, . . . , m, where Σi=1mai= 1. Afterwards, each sensor in group Aiindependently chooses Ki,nkeys uniformly at random from the key pool Pn, where K1,n≤ K2,n≤ . . . ≤ Km,n. Finally, any two sensors in Vnestablish 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 Yagan on connectivity in the following aspects. First, our result is more broadly applicable; specifically, we consider Km,n/K1,n= o(√n), while [1] requires Km,n/K1,n= o(ln n). Put differently, Km,n/K1,nin our paper examines the case of Θ(nx) for any xy) for any y > 0, while that of [1] does not cover any Θ(nx), and covers Θ((ln n)y) for only 0ndenoting Σj=1m{aj[1 - (Kj,nPn-K1,n)/(Kj,nPn)]} equals ln n/n, our paper considers any of bn= o(ln n/n), bn= Θ(ln n/n), and bn= ω(ln n/n), while [1] evaluates only bn= Θ(ln n/n). Third, in terms of characterizing the transitional behavior of connectivity, our scaling bn= ln n+ βn/n for a sequence βnis more fine-grained than the scaling bn~ c ln n/ n for a constant c ≠ 1 of [1]. In a nutshell, we add the case of c = 1 in bn~ c ln n/n, where the graph can be connected or disconnected asymptotically, depending on the limit of βn. Finally, although a recent study by Eletreby and Yagan [2] uses the fine-grained scaling discussed before for a more complex graph model, their result (just like [1]) also demands Km,n/K1,n= o(ln n), which is less general than Km,n/K1,n= o(√n) addressed in this paper.
Author: Jun Zhao
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2565036683