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arXiv:1001.3697

Secure Communication in Stochastic Wireless Networks

Pedro Pintó, João Barros, Moe Z. Win

Published Jan 21, 2010• 16 citations
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Abstract

Information-theoretic security -- widely accepted as the strictest notion of security -- relies on channel coding techniques that exploit the inherent randomness of the propagation channels to significantly strengthen the security of digital communications systems. Motivated by recent developments in the field, this paper aims at a characterization of the fundamental secrecy limits of wireless networks. Based on a general model in which legitimate nodes and potential eavesdroppers are randomly scattered in space, the intrinsically secure communications graph (iS-graph) is defined from the point of view of information-theoretic security. Conclusive results are provided for the local connectivity of the Poisson iS-graph, in terms of node degrees and isolation probabilities. It is shown how the secure connectivity of the network varies with the wireless propagation effects, the secrecy rate threshold of each link, and the noise powers of legitimate nodes and eavesdroppers. Sectorized transmission and eavesdropper neutralization are explored as viable strategies for improving the secure connectivity. Lastly, the maximum secrecy rate between a node and each of its neighbours is characterized, and the case of colluding eavesdroppers is studied. The results help clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks.

DOI
10.48550/arxiv.1001.3697

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Information-theoretic security -- widely accepted as the strictest notion of security -- relies on channel coding techniques that exploit the inherent randomness of the propagation channels to significantly strengthen the security of digital communications systems. Motivated by recent developments in the field, this paper aims at a characterization of the fundamental secrecy limits of wireless networks. Based on a general model in which legitimate nodes and potential eavesdroppers are randomly scattered in space, the intrinsically secure communications graph (iS-graph) is defined from the point of view of information-theoretic security. Conclusive results are provided for the local connectivity of the Poisson iS-graph, in terms of node degrees and isolation probabilities. It is shown how the secure connectivity of the network varies with the wireless propagation effects, the secrecy rate threshold of each link, and the noise powers of legitimate nodes and eavesdroppers. Sectorized transmission and eavesdropper neutralization are explored as viable strategies for improving the secure connectivity. Lastly, the maximum secrecy rate between a node and each of its neighbours is characterized, and the case of colluding eavesdroppers is studied. The results help clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks.
The ability to exchange secret information is critical to many commercial, governmental, and military networks. Information-theoretic security-widely accepted as the strictest notion of security-relies on channel coding techniques that exploit the inherent randomness of the propagation channels to strengthen the security of digital communications systems. Motivated by recent developments in the field, we aim to characterize the fundamental secrecy limits of wireless networks. The paper is comprised of two separate parts. In Part I, we define the intrinsically secure communications graph (iS-graph), a random graph which describes the connections that can be securely established over a large-scale network. We provide conclusive results for the local connectivity of the Poisson iS-graph, in terms of node degrees and isolation probabilities. We show how the secure connectivity of the network varies with the wireless propagation effects, the secrecy rate threshold of each link, and the noise powers of legitimate nodes and eavesdroppers. We then propose sectorized transmission and eavesdropper neutralization as viable strategies for improving the secure connectivity. Our results help clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks. In Part II of the paper, we study the achievable secrecy rates and the effect of eavesdropper collusion.
Motivated by recent developments in physical-layer security and stochastic geometry, we aim to characterize the fundamental limits of secure communication in wireless networks. Based on a general model in which legitimate nodes and potential eavesdroppers are randomly scattered in space, we define the secure communication graph (s-graph) from the point of view of information-theoretic security. For the Poisson s-graph, we provide conclusive results for: (a) the in-degree and out-degree of a node; (b) the isolation probability; and (c) the secrecy capacity between a node and each of its neighbours. Our analysis reveals the innate connections between information-theoretic security and the spatial densities of legitimate and eavesdropper nodes.
Information-theoretic security--widely accepted as the strictest notion of security--relies on channel coding techniques that exploit the inherent randomness of propagation channels to strengthen the security of communications systems. Within this paradigm, we explore strategies to improve secure connectivity in a wireless network. We first consider the intrinsically secure communications graph (iS-graph), a convenient representation of the links that can be established with information-theoretic security on a large-scale network. We then propose and characterize two techniques--sectorized transmission and eavesdropper neutralization--which are shown to dramatically enhance the connectivity of the iS-graph.
Information-theoretic security--widely accepted as the strictest notion of security--relies on channel coding techniques that exploit the inherent randomness of propagation channels to strengthen the security of communications systems. Within this paradigm, we explore strategies to improve secure connectivity in a wireless network. We first consider the intrinsically secure communications graph (iS-graph), a convenient representation of the links that can be established with information-theoretic security on a large-scale network. We then propose and characterize two techniques--sectorized transmission and eavesdropper neutralization--which are shown to dramatically enhance the connectivity of the iS-graph.
In Part I of this paper, we introduced the intrinsically secure communications graph (iS-graph)-a random graph which describes the connections that can be established with strong secrecy over a large-scale network, in the presence of eavesdroppers. We focused on the local connectivity of the iS-graph, and proposed techniques to improve it. In this second part, we characterize the maximum secrecy rate (MSR) that can be achieved between a node and its neighbors. We then consider the scenario where the eavesdroppers are allowed to collude, i.e., exchange and combine information. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncolluding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physical-layer security.
We consider the fundamental security limits of stochastic wireless networks in the presence of colluding eavesdroppers. By establishing a direct connection with the single-input multiple-output (SIMO) Gaussian wiretap channel, we are able to provide a complete characterization of the secrecy capacity for the case in which the eavesdroppers are scattered according to a spatial Poisson process. Our analysis, which includes the probabilities of existence and outage of secrecy capacity, helps clarify how the spatial density of eavesdroppers can jeopardize the success of wireless physical-layer security based on information-theoretic principles.