Physical-layer security offers an alternative to cryptology, where instead of using the secrecy keys, randomness of the wireless channel is utilized to conceal information. In this chapter, we give an overview of different state-of-the-art multi-terminal information theoretic models to secure information with varying quality of channel state information at the transmitter. We first introduce the essential elements of information theoretic security, and later on discuss its application from a degrees of freedom viewpoint. In particular, we focus our attention on the models in which the topology of the network is known at the transmitter. Introduction Wireless communication has completely revolutionized the lives of common users. Modern communication systems provide high data rates, which allow users to perform different day-to-day tasks wirelessly. For example, users can access their bank account details and monitor their home security remotely. However, due to the broadcast nature of the medium, the information exchange between these communication nodes can be overheard by unintended users in the network. The leakage of information to unintended users may have serious consequences. In this chapter, we intend to answer this fundamental question of how to secure wireless communication. State of the Art and Preliminaries In conventional systems, cryptographic encryption is used to conceal information from adversaries. Figure 7.1 shows a simple example which sheds light on the problem of secret key sharing studied in cryptology. The source message at Alice is converted to ciphertext with the help of a secret key which is shared between Alice and the legitimate receiver, Bob. The ciphertext is then communicated over the wireless channel and is received by both Bob and Eve. Upon getting the ciphertext and having access to the secret key, Bob can easily recover Alice's message [1]. It is assumed that Eve, the eavesdropper, is of limited computational complexity or has limited resources. Thus, it is unable to generate all combinations of secret key, and consequently cannot recover Alice's message. In this framework, secrecy relies on the difficulty level of some hard mathematical problem which the eavesdropper is unable to solve due to limited computational resources.
Physical-layer security offers an alternative to cryptology, where instead of using the secrecy keys, randomness of the wireless channel is utilized to conceal information. In this chapter, we give an overview of different state-of-the-art multi-terminal information theoretic models to secure information with varying quality of channel state information at the transmitter. We first introduce the essential elements of information theoretic security, and later on discuss its application from a degrees of freedom viewpoint. In particular, we focus our attention on the models in which the topology of the network is known at the transmitter. Introduction Wireless communication has completely revolutionized the lives of common users. Modern communication systems provide high data rates, which allow users to perform different day-to-day tasks wirelessly. For example, users can access their bank account details and monitor their home security remotely. However, due to the broadcast nature of the medium, the information exchange between these communication nodes can be overheard by unintended users in the network. The leakage of information to unintended users may have serious consequences. In this chapter, we intend to answer this fundamental question of how to secure wireless communication. State of the Art and Preliminaries In conventional systems, cryptographic encryption is used to conceal information from adversaries. Figure 7.1 shows a simple example which sheds light on the problem of secret key sharing studied in cryptology. The source message at Alice is converted to ciphertext with the help of a secret key which is shared between Alice and the legitimate receiver, Bob. The ciphertext is then communicated over the wireless channel and is received by both Bob and Eve. Upon getting the ciphertext and having access to the secret key, Bob can easily recover Alice's message [1]. It is assumed that Eve, the eavesdropper, is of limited computational complexity or has limited resources. Thus, it is unable to generate all combinations of secret key, and consequently cannot recover Alice's message. In this framework, secrecy relies on the difficulty level of some hard mathematical problem which the eavesdropper is unable to solve due to limited computational resources.
In this chapter, we will discuss how the quality and availability of channel state information (CSI) affects secrecy in wireless networks. In particular, we study how the delay in the availability of CSI affects secrecy in the context of the two-user broadcast channel with confidential messages. We adopt a secure degrees of freedom perspective and investigate various CSI scenarios, including cases when the availability of CSI at the transmitter varies across users and with time. We discuss how to leverage such variabilities in CSI for secrecy and highlight the differences between the optimal degrees of freedom with or without secrecy constraints. Introduction The availability of channel state information at the transmitters (CSIT) plays a crucial role in securing wireless communication at the physical layer. Various well-known physical-layer security techniques such as coding for the fading wiretap channel [1–4], coding for the multiple-antenna wiretap channel [5–8], artificial noise injection [9], cooperative jamming [10, 11], cooperation for secrecy [12–18], secure signal alignment [19–22], and other related techniques rely upon the assumption of timely availability of precise CSIT; see also a recent review article in [23]. In most practical scenarios, the channel gains are measured by the receivers and then fed back to the transmitters. The measurement and feedback process necessarily introduces imprecision and delay into the CSI. Motivated by this fact, in this chapter we explore the fundamental limits of physical layer security when the CSIT is imperfect. For concreteness, we will focus on a particular wireless network model: the multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM). This effectively models practical systems such as a cellular downlink network where each user wants not only reliability but also confidentiality of the information intended for it. The focus of this chapter is on the secure degrees of freedom (s.d.o.f.) region of the fading two-user MISO BCCM, in which the transmitter with two antennas has two confidential messages, one for each of the single antenna users (see Fig. 8.1). The secrecy capacity region of the MISO broadcast channel (BC) for the case of perfect and instantaneous CSI at all terminals (transmitter and the receivers) has been characterized in [24, 25]. Using these results, it follows that for the two-user MISO BCCM, the sum s.d.o.f. is 2 with perfect and instantaneous CSIT.
Recent years have been marked by an enormous growth of wireless communication networks and an extensive use of wireless applications. In return, this phenomenal expansion induced more concerns about the privacy and the security of the users. Physical layer security is one of the most promising solutions that were proposed to enhance the security of next generation wireless systems. The fundamental idea behind this technique is to exploit the randomness and the fluctuations of the wireless channel to achieve security without conditional assumptions on the computational capabilities of the eavesdropper. In fact, while these elements have traditionally been associated with signal deterioration, physical layer security uses them to ensure the confidentiality of the users. Nevertheless, these technical virtues rely heavily on perhaps idealistic channel state information assumptions. In that regard, the aim of this thesis is to look at the physical layer security paradigm from the channel uncertainty perspective. In particular, we discuss the ergodic secrecy capacity of different wiretap channels when the transmitter is hampered by the imperfect knowledge of the channel state information (CSI). We consider two prevalent causes of uncertainty for the CSI at transmitter (CSIT); either an error of estimation occurs at the transmitter and he can only base his coding and the transmission strategies on a noisy version of the CSI, or the CSI feedback link has a limited capacity and the legitimate receivers can only inform the transmitter about the quantized CSI. We investigate both the single-user multiple-input multiple-output (MIMO) wiretap channel and the multi-user broadcast wiretap channel. In the latter scenario, we distinguish between two situations: multiple messages transmission and common message transmission. We also discuss the broadcast channel with confidential messages (BCCM) where the transmitter has one common message to be transmitted to two users and one secret message intended to only one of them. In all cases, we show that by appropriately designing the coding and the transmission schemes, a secure communication can still be achieved even with an imperfect knowledge of the CSIT.
Introduction Future communication systems will be decentralized and ad-hoc, hence allowing various types of network mobile terminals to join and leave. This makes the whole system vulnerable and susceptible to attacks. Anyone within communication range can listen to and possibly extract information. While these days we have numerous cryptographic methods to ensure high-level security, there is no system with perfect security on the physical layer. Therefore, the physical layer security is attracting renewed attention. Of special interest is so-called information-theoretic security since it concerns the ability of the physical layer to provide perfect secrecy of the transmitted data. In this chapter, we present different scenarios of a decentralized system that protects the broadcasted data on the physical layer and makes it impossible for the eavesdropper to receive the packets no matter how computationally powerful the eavesdropper is. In approaches where information-theoretic security is applied, the main objective is to maximize the rate of reliable information from the source to the intended destination, while all malicious nodes are kept ignorant of that information. This maximum reliable rate under which a perfectly secret communication is possible is known as the secrecy capacity . This line of work was pioneered by Aaron Wyner, who defined the wiretap channel and established the possibility of secure communication links without relying on private (secret) keys.
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective. First, we study the Gaussian multiple-input multiple-output (MIMO) wiretap channel. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner. Next, we study the secure broadcasting problem, where a transmitter wants to have secure communication with multiple legitimate users in the presence of an external eavesdropper. We study several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region. Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message. Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region. Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel. Next, we focus on the multiple access wiretap (MAC-WT) channel whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where each user's link to the legitimate receiver is stronger than its link to the eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable region in an n-letter form. We evaluate a looser version of our outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT. Then, we investigate the effects of user cooperation on the secrecy of broadcast channels by considering the cooperative relay broadcast channel (CRBC). We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation. We further investigate the effects of user cooperation on secrecy by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC. We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF. Next, we study the two-user one-eavesdropper discrete memoryless compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel, and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users. Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and the transmitter sends a confidential message to each group of legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group. Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading, both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain. Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation. Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.
Achieving secure transmission in wireless network is a significantly important research topic. Classic cryptography encrypts a confidential message to an unreadable cipher message. Thus only the authentic receiver with correct secrecy key is able to decrypt the message. However, with the growing computational capability of adversaries, the requirement of secrecy key generation and distribution is getting stringent. Another method to achieve wireless security, which has attracted much attention in recent years, is through physical layer processing, named physical layer security. In a typical wiretap channel model consisting of a transmitter, a legal receiver and an adversary (illegal receiver), early works have proven that it is possible to achieve positive secrecy rate using multiple antenna techniques, such as beamforming, at the transmitter. In this thesis, we focus on two types of malicious behaviors of the adversary: passive eavesdropping and active attack. For the passive eavesdropping, we first consider the multi-input-single-output (MISO) wiretap channel, in which the legitimate transmitter utilizes the artificial noise aided precoding strategy to maximize the achievable secrecy rate of the channel. Both scenarios of known and unknown channel state information (CSI) for the eavesdropper channels are considered. By deriving the closed-form expression of ergodic secrecy rate, we prove that there exists an optimal power ratio between the information signal and the artificial noise. We then extend our study to a four-node fading channel model in a wireless relay network, which includes two single-antenna users, one single-antenna eavesdropper and one relay node equipped with multiple antennas. By studying the decode-and-forward (DF) scheme, cooperative jamming (CJ) scheme and one proposed hybrid relay scheme, relay-and-jamming (RJ), we aims to find the optimal relay scheme with the condition that the transmitter and the relay node are under individual power constraints and the CSI of the illegitimate channel is only statistically known. Our analysis shows that the hybrid RJ scheme is optimal when the transmitter has a relatively small power budget and/or the transmitter is far away from the intended receiver. Besides the passive eavesdropping, the adversary could also choose the active attack. The pilot spoofing attack is one active attack conducted by the adversary during the channel estimation phase of the legitimate transmission. In practical systems, the pilot signals are usually known \textit{a priori} and repeatedly used information. In this attack, an intelligent adversary spoofs the transmitter on the estimation of CSI by sending the identical pilot signal as the legitimate receiver. By doing so, the adversary could obtain a larger channel rate in the data transmission phase, and also drastically weaken the strength of the received signal at the legitimate receiver if the adversary utilizes large enough power. Due to the serious consequences caused by such an attack, we first propose an energy ratio detector (ERD) that explores the asymmetry of received signal power levels at the transmitter and the legitimate receiver when the attack occurs. Our analysis shows that the ERD could provide very high probability of detection with certain requirement on the false alarming probability. Furthermore, we design a two-way training based scheme to provide not only attack detection but also secure transmission. The two-way training based detector (TWTD) exploits the intrusive component created by the adversary, followed by a secure beamforming-assisted data transmission. In addition to the good detection performance, our scheme could estimate both legitimate and illegitimate channels, with which the beamforming could be designed for data transmission.