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.
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.
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.
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.
The wiretap channel model in a wireless scenario is analyzed where there is a transmitter, multiple legitimate receivers, non-colluding and colluding eavesdroppers; each of them is equipped with one antenna. Furthermore, all the channels are mutually independent and experiencing quasi-static Nakagami-m fading. We derive closed-form expressions for the exact secrecy outage probability as well as the average secrecy capacity with both non-colluding and colluding eavesdroppers. Such performance metrics are used to analyze the impacts of the number of receivers and eavesdroppers on the system. Remarkably, our results reveal that, for non-colluding eavesdroppers, increasing the number of users will cause greater secrecy degradation than the number of eavesdroppers, especially when the main channel is far superior to the wiretap channel or the value of the fading parameter is high. And for the colluding case, it turns out to be the opposite.
Intrigued by the rapid growth and expand of wireless devices, data security is increasingly playing a significant role in our daily transactions and interactions with different entities. Possible examples, including e-healthcare information and online shopping, are becoming vulnerable due to the intrinsic nature of wireless transmission medium and the widespread open access of wireless links. Traditionally, the communication security is mainly regarded as the tasks at the upper layers of layered protocol stack, security techniques, including personal access control, password protection, and end-to-end encryption, have been widely studied in the open literature. More recently, plenty of research interests have been drawn to the physical layer forms of secrecy. As a new but appealing paradigm at physical layer, physical layer security is based on two pioneering works: (i) Shannon’s information-theoretic formulation and (ii) Wyner’s wiretap formulation. \n \nOn account of the fundamental of physical layer security and the different nature of various wireless network, this dissertation is supposed to further fill the lacking of the existing research outcomes. To be specific, the contributions of this dissertation can be summarized as three-fold:(i) exploration of secrecy metrics to more general fading channels; (ii) characterization a new fading channel model and its reliability and security analysis in digital communication systems; and (iii) investigation of physical layer security over the random multiple-input multiple-output (MIMO) α −μ fading channels. \n \nTaking into account the classic Alice-Bob-Eve wiretap model, the first contribution can be divided into four aspects: (i) we have investigated the secrecy performance over single-input single-output (SISO) α −μ fading channels. The probability of non-zero (PNZ) secrecy capacity and the lower bound of secrecy outage probability (SOP) are derived for the special case when the main channel and wiretap channel undergo the same non-linearity fading parameter, i.e., α. Later on, for the purpose of filling the gap of lacking closed-form expression of SOP in the open literature and extending the obtained results in chapter 2 to the single-input multiple-output (SIMO) α − μ wiretap fading channels, utilizing the fact that the received signal-tonoise ratios (SNRs) at the legitimate receiver and eavesdropper can be approximated as new α −μ distributed random variables (RVs), the SOP metric is therefore derived, and given in terms of the bivariate Fox’s H-function; (ii) the secrecy performance over the Fisher-Snedecor F wiretap fading channels is initially considered. The SOP, PNZ, and ASC are finalized in terms of Meijer’s G-function; (iii) in order to generalize the obtained results over α −μ and Fisher-Snedecor F wiretap fading channels, a more flexible and general fading channel, i.e., Fox’s H-function fading model, are taken into consideration. Both the exact and asymptotic analysis of SOP, PNZ, and average secrecy capacity (ASC), are developed with closed-form expressions; and (iv) finally, motivated by the fact that the mixture gamma (MG) distribution is an appealing tool, which can be used to model the received instantaneous SNRs over wireless fading channels, the secrecy metrics over wiretap fading channels are derived based on the MG approach. \n \nDue to the limited transmission power and communication range, cooperative relays or multi-hop wireless networks are usually regarded as two promising means to address these concerns. Inspired by the obtained results in Chapters 2 and 3, the second main contribution is to propose a novel but simple fading channel model, namely, the cascaded α −μ. This new distribution is advantageous since it encompasses the existing cascaded Rayleigh, cascaded Nakagami-m, and cascaded Weibull with ease. Based on this, both the reliability and secrecy performance of a digital system over cascaded α −μ fading channels are further evaluated. Closed-form expressions of reliability metrics (including amount of fading (AF), outage probability, average channel capacity, and average symbol error probability (ABEP).) and secrecy metrics (including SOP, PNZ, and ASC) are respectively provided. Besides, their asymptotic behaviors are also performed and compared with the exact results. \n \nConsidering the impacts of users’ densities, spatial distribution, and the path-loss exponent on secrecy issue, the third aspect of this thesis is detailed in Chapter 8 as the secrecy investigation of stochastic MIMO system over α −μ wiretap fading channels. Both the stochastic geometry and conventional space-time transmission (STT) scheme are used in the system configuration. The secrecy issue is mathematically evaluated by three metrics, i.e., connection outage, the probability of non-zero secrecy capacity and the ergodic secrecy capacity. Those three metrics are later on derived regarding two ordering scheme, and further compared with Monte-Carlo simulations.
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.
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.