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IEEE Conference on Computer Communications (INFOCOM)

Impact of secrecy on capacity in large-scale wireless networks

Jinbei Zhang, Luoyi Fu, Xinbing Wang

Published Mar 1, 2012• 13 citations
Publisher

Abstract

Since wireless channel is vulnerable to eavesdroppers, the secrecy during message delivery is a major concern in many applications such as commercial, governmental and military networks. This paper investigates information-theoretic secrecy in large-scale networks and studies how capacity is affected by the secrecy constraint where the locations and channel state information (CSI) of eavesdroppers are both unknown. We consider two scenarios: 1) non-colluding case where eavesdroppers can only decode messages individually; and 2) colluding case where eavesdroppers can collude to decode a message. For the non-colluding case, we show that the network secrecy capacity is not affected in order-sense by the presence of eavesdroppers. For the colluding case, the per-node secrecy capacity of Θ(1/√n) can be achieved when the eavesdropper density ψe(n) is O(n-β), for any constant β >; 0 and decreases monotonously as the density of eavesdroppers increases. The upper bounds on network secrecy capacity are derived for both cases and shown to be achievable by our scheme when ψe(n) = O(n-β) or ψe(n) = Ω(log α-2/α n), where α is the path loss gain. We show that there is a clear tradeoff between the security constraints and the achievable capacity.

DOI
10.1109/infcom.2012.6195757

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Since wireless channel is vulnerable to eavesdroppers, the secrecy during message delivery is a major concern in many applications such as commercial, governmental and military networks. This paper investigates information-theoretic secrecy in large-scale networks and studies how capacity is affected by the secrecy constraint where the locations and channel state information (CSI) of eavesdroppers are both unknown. We consider two scenarios: 1) non-colluding case where eavesdroppers can only decode messages individually; and 2) colluding case where eavesdroppers can collude to decode a message. For the non-colluding case, we show that the network secrecy capacity is not affected in order-sense by the presence of eavesdroppers. For the colluding case, the per-node secrecy capacity of Θ(1/√n) can be achieved when the eavesdropper density ψe(n) is O(n-β), for any constant β >; 0 and decreases monotonously as the density of eavesdroppers increases. The upper bounds on network secrecy capacity are derived for both cases and shown to be achievable by our scheme when ψe(n) = O(n-β) or ψe(n) = Ω(log α-2/α n), where α is the path loss gain. We show that there is a clear tradeoff between the security constraints and the achievable capacity.
Due to the nature of a wireless medium, a wireless channel is susceptible to malicious nodes, which encourages the consideration of secrecy in many applications such as satellite networks, social networking services, etc. Motivated by the social characteristic that makes nodes more likely to communicate with nearby neighbors, we study the secrecy capacity of large-scale wireless networks with social relationships. We consider two distributions of legitimate nodes: They are homogeneously placed based on a Poisson point process (PPP), or they are inhomogeneously distributed as multiclustering topology. In particular, we consider two scenarios: 1) the noncolluding case, where each eavesdropper decodes its receiving message independently; and 2) the colluding case, where eavesdroppers can cooperate to decode the message. We adopt a rank-based model to describe the social characteristic and investigate its impact on the secrecy capacity using the technique of self-interference cancelation. We employ a passive attack model, where eavesdroppers can only listen to transmissions among legitimate nodes. Our important findings include the following: 1) In the noncolluding case, secrecy capacity is not influenced by eavesdroppers in order sense, but it varies with the density of eavesdroppers and social impacts in the colluding case. 2) The proposed scheme can achieve optimal secrecy throughput neglecting polylogarithmic factor in homogeneous wireless networks.
In a powerful secrecy attack, eavesdroppers can collude, i.e., they can share their observations. Securing information in such a scenario will be an even more challenging task compared to non-colluding case. We here analyze the effect of eavesdropper collusion on the achievable performance in both the path loss and ergodic multi-path fading models. We provide two results: 1) For the Poisson point process model in a random extended network, if the legitimate nodes have unit intensity (λ = 1) and the colluding eavesdroppers have an intensity of λe= O((log n)-(2+p)) for any p > 0, almost all of the nodes can achieve a secure rate of Ω(1/(√n)); I and 2) In the K-user Gaussian interference channel with E external colluding eavesdroppers, a secure degrees of freedom of η =[1/2-E/K]+per frequency-time slot is achievable for each user in the ergodic setting (in the absence of the eavesdropper channel state information).
We investigate the scalability of a class of algorithms that exploit the dynamics of wireless fading channels to achieve secret communication in a large wireless network of n randomly located nodes. We describe a construction in which nodes transmit artificial noise to suppress eavesdroppers whose locations are unknown and ensure secrecy of messages transported across the network. Under a model in which eavesdroppers operate independently and under appropriate conditions on the achievable per-node throughput Ψ(n), we show that the network can tolerate Ω((1⁄√n(n))2c) eavesdroppers while ensuring that the aggregate rate at which eavesdroppers intercept packets goes to 0, where c is a constant such that 0 0. We also establish sufficient conditions on the number of eavesdroppers to achieve a non-zero throughput in our construction.
We perform an analysis of the secrecy outage and transmission capacity of random networks under Nakagami-m fading with colluding eavesdroppers, in the asymptotic case of large reference signal-to-noise ratios. In literature, secrecy analysis from the perspective of collusion pool has still not been well characterized. Considering a network model that accounts for uncertainties both in node locations and channel coefficients, we approximate the distribution of the aggregate path gain received by a collusion of eavesdroppers. Using this result, the asymptotic secrecy rate distribution, the secrecy outage probability, and the secrecy transmission capacity of random networks with colluding eavesdroppers are obtained, with basic factors such as density of nodes, the guarding distance, and the fading figure all accounted for by explicit parameters. Since secrecy in low-outage random networks are found to be most significant when the density of active nodes is small, the expressions derived can be seen as upper-bounds on the three aforementioned secrecy performance metrics in random networks, offering particular insight on the impact of fading, density, and guarding distances, while taking into account cooperation among eavesdroppers. Furthermore, we give a bound on colluding pool size, which is pragmatic in creating a nonprotected communication zone for the typical destination.
Wireless networks provide flexible ubiquitous user communications but, at the same time, provide the same access to an attacker or eavesdropper trying to intercept private messages. Hence, security has become a primary concern in wireless networks, and there has been a resurgence of interest in physical layer forms of secrecy based on Shannon’s original information-theoretic formulation and Wyner’s consideration of the wiretap formulation of such. In this chapter, we venture beyond the prototypical three-node Alice-Bob-Eve security scenario to consider physical layer forms of secrecy in wireless networks, where the need to protect the message over multiple hops opens up system vulnerabilities, but the addition of system nodes beyond the communicating parties also offers opportunities. In particular, the scaling of secrecy in (asymptotically) large multihop networks will be considered, and we will focus, in particular, on how the flexibility offered by the large number of system nodes in the network can facilitate secure communication in the face of a large number of eavesdroppers, even if the location of those eavesdroppers is unknown. The transmission techniques that are employed in the conclusive results for secrecy scaling in large networks with noncollaborating eavesdroppers also have clear analogs that should prove effective in finite networks, but there are challenges to be addressed in such an adaptation.