Unlike the traditional key-exchange based cryptography, physical layer security is built on information theory and aims to achieve unconditional security by exploiting the physical characteristics of wireless channels. With the growth of the number of wireless devices, physical layer security has been gradually emphasized by researchers. Various physical layer security protocols have been proposed for different communication scenarios. Since these protocols are based on information-theoretic security and the formalization work for information theory were not complete when these protocols were proposed, the security of these protocols lacked formal proofs. In this paper, we propose a formal definition for the secrecy capacity in non-degraded wiretap channel model and a formal proof for the secrecy capacity in binary symmetric channel with the help of SSReflect/Coq theorem prover.
Unlike the traditional key-exchange based cryptography, physical layer security is built on information theory and aims to achieve unconditional security by exploiting the physical characteristics of wireless channels. With the growth of the number of wireless devices, physical layer security has been gradually emphasized by researchers. Various physical layer security protocols have been proposed for different communication scenarios. Since these protocols are based on information-theoretic security and the formalization work for information theory were not complete when these protocols were proposed, the security of these protocols lacked formal proofs. In this paper, we propose a formal definition for the secrecy capacity in non-degraded wiretap channel model and a formal proof for the secrecy capacity in binary symmetric channel with the help of SSReflect/Coq theorem prover.
In this chapter, we develop the notion of secrecy capacity , which plays a central role in physical-layer security. The secrecy capacity characterizes the fundamental limit of secure communications over noisy channels, and it is essentially the counterpart to the usual point-to-point channel capacity when communications are subject not only to reliability constraints but also to an information-theoretic secrecy requirement. It is inherently associated with a channel model called the wiretap channel , which is a broadcast channel in which one of the receivers is treated as an adversary. This adversarial receiver, which we call the eavesdropper to emphasize its passiveness, should remain ignorant of the messages transmitted over the channel. The mathematical tools, and especially the random-coding argument, presented in this chapter are the basis for most of the theoretical research in physical-layer security, and we use them extensively in subsequent chapters. We start with a review of Shannon's model of secure communications (Section 3.1), and then we informally discuss the problem of secure communications over noisy channels (Section 3.2). The intuition we develop from loose arguments is useful to grasp the concepts underlying the proofs of the secrecy capacity and motivates a discussion of the choice of an information-theoretic secrecy metric (Section 3.3). We then study in detail the fundamental limits of secure communication over degraded wiretap channels (Section 3.4) and broadcast channels with confidential messages (Section 3.5).
Abstract Physical layer security (PLS) has been proposed to afford an extra layer of security on top of the conventional cryptographic techniques. Unlike the conventional complexity-based cryptographic techniques at the upper layers, physical layer security exploits the characteristics of wireless channels, e.g., fading, noise, interference, etc., to enhance wireless security. It is proved that secure transmission can benefit from fading channels. Accordingly, numerous researchers have explored what fading can offer for physical layer security, especially the investigation of physical layer security over wiretap fading channels. Therefore, this paper aims at reviewing the existing and ongoing research works on this topic. More specifically, we present a classification of research works in terms of the four categories of fading models: (i) small-scale, (ii) large-scale, (iii) composite, and (iv) cascaded. To elaborate these fading models with a generic and flexible tool, three promising candidates, including the mixture gamma (MG), mixture of Gaussian (MoG), and Fox’sH-function distributions, are comprehensively examined and compared. Their advantages and limitations are further demonstrated via security performance metrics, which are designed as vivid indicators to measure how perfect secrecy is ensured. Two clusters of secrecy metrics, namely (i) secrecy outage probability (SOP), and the lower bound of SOP; and (ii) the probability of nonzero secrecy capacity (PNZ), the intercept probability, average secrecy capacity (ASC), and ergodic secrecy capacity, are displayed and, respectively, deployed in passive and active eavesdropping scenarios. Apart from those, revisiting the secrecy enhancement techniques based on Wyner’s wiretap model, the on-off transmission scheme, jamming approach, antenna selection, and security region are discussed.
In physical-layer security, communication secrecy is commonly achieved by providing the legitimate receiver a physical-layer advantage over the eavesdropper or, equivalently, by making the eavesdropper's channel more degraded than the legitimate receiver's, a setting traditionally known as the degraded wiretap channel. There may be situations, however, where such advantages cannot be guaranteed. One example is the wireless channel where the legitimate receiver's channel may be more degraded than the eavesdropper's owing to a deep fade (outage), additive interference at the edge of a network cell, etc. To our knowledge, such scenarios have not been remedied in the related literature. Thus, we propose in this work the first physical-layer security scheme that achieves communication in a setting where the eavesdropper has the physical-layer advantage over the legitimate receiver, a scenario that we call the reversely-degraded wiretap channel. Precisely, we show that by constraining the transmitter's input to be discrete uniformly distributed (such as an on-off keying modulation) and by using nonlinear threshold-based signal detection, the legitimate receiver is guaranteed to have a positive secrecy capacity even though the eavesdropper has a better signal-to-noise ratio (SNR). The former requirement on the input distribution is to limit the capacity gains of the eavesdropper at high SNR. The latter requirement allows the communication channel to exhibit supra-threshold stochastic resonance, a phenomenon whereby noise improves signal detection and increases the mutual information. A numerical example is provided to confirm our claims.
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.
The location-specific channel state information can be exploited to generate secret keys for wireless system services, In the multipath wireless environment. Its secrecy capacity was usually studied with the wiretap channel model. This paper proposes a side channel model which is even more threatening to the security of the physical layer randomness based secret keys. We present the information-theoretic analysis of the side channel model, and compare it with the wire-tap model. The analysis indicates that the secret key capacity of the side-channel will be lower than that of the wire-tap channel, especially with a fading scenario. We conduct MATLAB simulation of physical layer randomness based key generation and SPICE simulation of key extraction to observe the side channel leakage of the circuit. The simulation results confirm the consistency of the key bits, thus verifying the feasibility of our proposed side-channel attack scheme against the physical layer security.
The inherent openness of wireless medium makes information security one of the most important and difficult problems in wireless networks.Physical layer security, which achieves the information-theoretic security by exploiting the differences between the physical properties of signal channels such that a degraded signal at an eavesdropper is always ensured and thus the original data can be hardly recovered regardless of how the signal is processed at the eavesdropper, has been studied as a promising approach to providing a strong form of security.By now, many research works have been devoted to understand the fundamental performance limits of physical layer security under different wire-tap channel models.It is notable that among different wire-tap channel models, the fading channel model has been an important model to efficiently capture the basic time-varying properties of wireless channels.Available works related to physical layer security study of the fading wire-tap channel are mainly based on the assumption that the channel from a transmitter to a legitimate receiver is independent of the one from the transmitter to an eavesdropper.In practice, however, the correlation among channels from a transmitter to different receivers has been frequently observed.Therefore, understanding the performance of physical layer security under the more practical correlated fading channels is of great importance for practical applications of physical layer security in wireless networks.In this thesis, we aim to provide a comprehensive study on the fundamental performance limits of physical layer security under a fading wire-tap channel, where the channel from transmitter to legitimate receiver is correlated with the one from transmitter to eavesdropper.We start the study from the scenario when the transmission power is asymptotically infinite.In particular, we first provide an informationtheoretic formulation of secure transmission over wireless fading channels at one realization of coherence interval in the high transmission power regime and show that the secrecy capacity is limited by the channel gain ratio of the main and eavesdropper channels rather than the transmission power, which is different from the Shannon's capacity that increases with transmission power.We next characterize the asymptotic outage probability and also asymptotic outage secrecy capacity for the correlated fading wire-tap channel as the transmission power goes to infinity.We then analyze the performance of physical layer security under correlated fading wire-tap channel with a limited transmission power, a more complicate scenario compared with the one with asymptotic-infinite power.Specifically, we provide theoretical modeling for the secrecy capacity, transmission outage probability and secrecy outage probability of such systems.In particular, we first derive a simple closedform expression of secrecy capacity based on the typical Marcum Q function.This is achieved by exploring the symmetry property between the main channel and eavesdropper channel such that some complicated integration operations involved in the secrecy capacity analysis can be significantly simplified.We then derive the transmission outage probability and secrecy outage probability to depict the reliability and security performances of the concerned wire-tap channel.Finally, extensive numerical results are provided to illustrate the inherent performance tradeoffs under i I am truly and deeply indebted to so many people that there is no way to acknowledge them all, or even any of them properly.Without their support, help and encouragement, this work would not and could not haven been done.I extend my deepest gratitude to all.