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IEEE Transactions on Vehicular Technology

Secrecy Capacity Scaling of Large-Scale Networks With Social Relationships

Kechen Zheng, Jinbei Zhang, Xiaoying Liu, Luoyi Fu, Xinbing Wang, Xiaohong Jiang, Wenjun Zhang

Published Jun 23, 2016• 23 citations
Publisher

Abstract

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.

DOI
10.1109/tvt.2016.2582778

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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.
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.
Artificial noise has been considered as an effective and efficient way to improve the secrecy of wireless communications. However, most existing papers have been focused on the analysis of a single communication link between a transmitter and a legitimate receiver with some eavesdroppers. In this paper, we investigate the impact of artificial noise to the secrecy of a large scale decentralized wireless network where channels are modeled as Rayleigh fading and locations of legitimate nodes and eavesdroppers follow Poisson point processes. To study network throughput versus system parameters, we derive the secrecy transmission capacity and show how it is related to the number of transmitting antennas and the power allocation ratio between data and artificial noise. Analytical results provide insights on how system parameters can be designed to improve secrecy transmission capacity of a wireless network.
This work studies the achievable secure rate per source-destination pair in wireless networks. First, a path loss model is considered, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes with intensities λλλ and λeλ_eλe​, respectively. It is shown that, as long as λe/λ=o((log⁡n)−2)λ_e/λ=o((\log n)^{-2})λe​/λ=o((logn)−2), almost all of the nodes achieve a perfectly secure rate of Ω(1n)Ω(\frac{1}{\sqrt{n}})Ω(n​1​) for the extended and dense network models. Therefore, under these assumptions, securing the network does not entail a loss in the per-node throughput. The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Secondly, an ergodic fading model with nnn source-destination pairs and nen_ene​ eavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy pre-coding, each user is shown to achieve a constant positive secret rate for sufficiently large nnn. Remarkably, the scheme does not require eavesdropper CSI (only the statistical knowledge is assumed) and the secure throughput per node increases as we add more legitimate users to the network in this setting. Finally, the effect of eavesdropper collusion on the performance of the proposed schemes is characterized.
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).
Secure communication over large-scale decentralized wireless networks is an extremely challenging task due to the cost and difficulty in establishing secret keys among all the nodes in a distributed manner. For this reason, the notion of physical layer security has recently drawn significant attention, which may assist with key exchange and provide an additional layer of protection in such networks. In this paper, we investigate how the physical layer security constraints affect the network throughput. We consider a random network in which the legitimate and eavesdropper nodes are located according to independent Poisson point processes. We introduce a new metric "secrecy transmission capacity" to characterize the network throughput in terms of the area spectral efficiency of secure transmissions, subject to constraints on both the quality of service and the level of security. This capacity framework allows us to quantitatively study the throughput cost of physical layer security constraints. We observe that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network.
The co-channel interference modeling is vital for evaluating the secrecy performance in random wireless networks, where the legitimate nodes and eavesdroppers are randomly distributed. In this paper, a new interference model is proposed from the user-dominant perspective. The model can provide a better analytical assessment of secrecy performance with interference coordination for the presence of eavesdroppers. The typical legitimate is assumed to be located at the origin, and chooses the closest base station (BS) as its serving BS. The field of interferers is obtained by excluding the desired BSs (including the serving BS and its cooperative BS(s)). In contract with the exiting interference model, it is assumed that desired BSs and interferers belong to the same Poisson Point Process (PPP), and eavesdroppers are distributed according to another independent PPP. Based on this model, the average secrecy transmission capacity is derived in simply analytical forms with interference coordination. Analysis and simulation results show that the secrecy performance can be significantly enhanced by exploiting interference coordination. Furthermore, the average secrecy transmission capacity increases with increasing number of cooperative BSs.