Connectivity of Wireless Sensor Networks Secured by the Heterogeneous Random Pairwise Key Predistribution Scheme

Eletreby, Rashad; Yağan, Osman

doi:10.1109/cdc.2018.8619814

Cited by 14 publications

(43 citation statements)

References 18 publications

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“…Our paper considers any of b n = o ln n n , b n = Θ ln n n , and b n = ω ln n n , while [1] evaluates only b n = Θ ln n n Improvements over Eletreby and Yagan [2], [22]. Although a recent research by Eletreby and Yagan [2] uses the fine-grained scaling discussed above for a more complex graph model (another work [22] by them uses the weaker scaling), both studies [2], [22] (just like [1]) also demand K m,n /K 1,n = o(ln n), which is less general than K m,n /K 1,n = o( √ n) addressed in this paper. Improvements over Zhao et al [3].…”

Section: Resultsmentioning

confidence: 99%

“…Compared with the seminal work [1] of Yagan (and its conference version [29]) on connectivity, our work has the following improvements, as already discussed in Section I-C above (we do not repeat the details here): more practical conditions by considering K m,n /K 1,n = o( √ n ) instead of just K m,n /K 1,n = o(ln n), more fine-grained zero-one law by considering the scaling ln n+βn n rather than c ln n n for a constant c = 1, and more general scaling condition. Although a recent work by Eletreby and Yagan [2] uses the finegrained scaling discussed above for a more complex graph model (other researches [22], [30] by them uses the weaker scaling), all these studies [2], [22], [30] (just like [1]) still demand K m,n /K 1,n = o(ln n), which is less general than K m,n /K 1,n = o( √ n) addressed in this paper. In addition,…”

Section: Related Workmentioning

confidence: 99%

“…Finally, we use (21) and (43) to derive lim n→∞ β * n = −∞, and use (22) and (43) to derive β * n = −o(ln n) so that |β * n | = o(ln n). Hence, result (i.5) is proved.…”

Section: (38)mentioning

confidence: 99%

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Analyzing Connectivity of Heterogeneous Secure Sensor Networks

Zhao¹

2018

IEEE Trans. Control Netw. Syst.

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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 Vn of n sensors, suppose there is a pool Pn consisting of Pn distinct keys. The n sensors in Vn are 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] = ai for i = 1, 2, . . . , m, where m i=1 ai = 1. Afterwards, each sensor in group Ai independently chooses Ki,n keys uniformly at random from the key pool Pn, where K1,n ≤ K2,n ≤ . . . ≤ Km,n. Finally, any two sensors in Vn 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 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,n in our paper examines the case of Θ(n x ) for any x < 1 2 and Θ (ln n) y for any y > 0, while that of [1] does not cover any Θ(n x ), and covers Θ (ln n) y ) for only 0 < y < 1. This improvement is possible due to a delicate coupling argument. Second, although both studies show that a critical scaling for connectivity is that the term bn denoting m j=1 aj 1 − Pn−K 1,n K j,n Pn K j,n 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 βn is 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 above 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.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Analyzing Connectivity of Heterogeneous Secure Sensor Networks

Zhao¹

2018

IEEE Trans. Control Netw. Syst.

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“…After deployment, two sensor nodes can communicate securely if they have at least one pairwise key in common. In Section II, we give the precise implementation details of this scheme and its heterogeneous variant proposed in [8]. The pairwise key predistribution scheme preserves the secrecy of rest of the network in case of node capture attacks, and also enables node-to-node authentication and quorum-based revocation [7].…”

Section: A Background and Motivationmentioning

confidence: 99%

“…From a theoretical stand point, this corresponds to advancing the literature pertaining to connectivity in inhomogeneous variants of classical random graph models. In order to model differing node capabilities, [8] introduced a heterogeneous pairwise key predistribution scheme in which each node is classified as type-1 (respectively, type-2) with probability µ (respectively, 1 − µ), 0 < µ < 1. Then, each type-1 (respectively, type-2) node selects one node (respectively, K n nodes) uniformly at random from all other nodes; see Figure 1.…”

Section: A Background and Motivationmentioning

confidence: 99%

Towards k-Connectivity in Heterogeneous Sensor Networks under Pairwise Key Predistribution

Sood

Yağan

2019

2019 IEEE Global Communications Conference (GLOBECOM)

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We study the secure and reliable connectivity of wireless sensor networks under the heterogeneous pairwise key predistribution scheme. This scheme was recently introduced as an extension of the random pairwise key predistribution scheme of Chan et al. to accommodate networks where the constituent sensors have different capabilities or requirements for security and connectivity. For simplicity, we consider a heterogeneous network where each of the n sensors is classified as type-1 (respectively, type-2) with probability µ (respectively, 1−µ) where 0 < µ < 1. Each type-1 (respectively, type-2) node selects 1 (respectively, Kn) other nodes uniformly at random to be paired with; according to the pairwise scheme each pair is then assigned a unique pairwise key so that they can securely communicate with each other. We establish critical conditions on n, µ, and Kn such that the resulting network has minimum node degree of at least k with high probability in the limit of large network size. Our result constitutes a zero-one law for the minimum node degree of the recently introduced inhomogeneous random K-out graph model. This constitutes a crucial step towards establishing a similar zeroone law for the k-connectivity of the graph; i.e., for the property that the network remains connected despite the failure of any k − 1 nodes or links. We present numerical results that indicate the usefulness of our results in selecting the parameters of the scheme in practical settings with finite number of sensors.

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A survey of key pre-distribution schemes based on combinatorial designs for resource-constrained devices in the IoT network

Esfehani

Javadi

2021

Wireless Netw

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Connectivity of Wireless Sensor Networks Secured by the Heterogeneous Random Pairwise Key Predistribution Scheme

Cited by 14 publications

References 18 publications

Analyzing Connectivity of Heterogeneous Secure Sensor Networks

Analyzing Connectivity of Heterogeneous Secure Sensor Networks

Towards k-Connectivity in Heterogeneous Sensor Networks under Pairwise Key Predistribution

A survey of key pre-distribution schemes based on combinatorial designs for resource-constrained devices in the IoT network

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