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).
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).
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 λ and λe, respectively. It is shown that, as long as λe/λ=o((logn)−2), almost all of the nodes achieve a perfectly secure rate of Ω(n1) 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 n source-destination pairs and ne 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 n. 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.
This paper 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 λ and λe, respectively. It is shown that, as long as λe/λ =o((logn)-2), almost all of the nodes achieve a perfectly secure rate of Ω(1/√n) 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 multihop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Second, an ergodic fading model withnsource-destination pairs and neeavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy precoding, each user is shown to achieve a constant positive secret rate for sufficiently largen. 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.
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.
We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, ¿ = 1, and the eavesdroppers have an intensity of ¿e= O((log n)-2), almost all of the nodes achieve a perfectly secure rate of ¿ (1/¿n). 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). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.
In this paper, the physical-layer security for a three-node wiretap system model is studied. Under the threat of multiple eavesdroppers, it is presumed that a transmitter is communicating with a legitimate receiver. The channels are assumed to be following cascaded κ-μ fading distributions. In addition, two scenarios for eavesdroppers’ interception and information-processing capabilities are investigated: colluding and non-colluding eavesdroppers. The positions of these eavesdroppers are assumed to be random in the non-colluding eavesdropping scenario, based on a homogeneous Poisson point process (HPPP). The security is examined in terms of the secrecy outage probability, the probability of non-zero secrecy capacity, and the intercept probability. The exact and asymptotic expressions for the secrecy outage probability and the probability of non-zero secrecy capacity are derived. The results demonstrate the effect of the cascade level on security. Additionally, the results indicate that as the number of eavesdroppers rises, the privacy of signals exchanged between legitimate ends deteriorates. Furthermore, in this paper, regarding the capabilities of tapping and processing the information, we provide a comparison between colluding and non-colluding eavesdropping.