The past decade has witnessed significant effort towards establishing reliable and information theoretically secure rates in communication networks, taking advantage of the properties of the communication medium. Such efforts include those in the wireless medium where simultaneous transmissions and the ensuing interference can prove advantageous from an information theoretic secrecy point of view. With the goal of obtaining a secrecy rate that scales with transmit power, structured signaling with simultaneous favorable signal alignment at the legitimate receiver(s) and unfavorable signal alignment at the eavesdropper(s) has proven particularly useful in multi-terminal Gaussian channels. Many challenges remain however in realizing the vision of absolute security provided by the wireless physical layer including handling more realistic models. In this paper, we provide a brief overview of the state of the art, the forward look and argue for an additional asset that could be utilized for secrecy, i.e., bidirectional signaling. Taking the bidirectional wiretap channel as an example, Gaussian signaling is demonstrated to be as good as structured signaling from the degrees of freedom point of view, while observed to be performing better with finite transmit power. Moreover, taking bidirectional signals explicitly into account for encoding performs even better and provides a way forward to synergistically combine physical layer based secrecy and encryption.
The past decade has witnessed significant effort towards establishing reliable and information theoretically secure rates in communication networks, taking advantage of the properties of the communication medium. Such efforts include those in the wireless medium where simultaneous transmissions and the ensuing interference can prove advantageous from an information theoretic secrecy point of view. With the goal of obtaining a secrecy rate that scales with transmit power, structured signaling with simultaneous favorable signal alignment at the legitimate receiver(s) and unfavorable signal alignment at the eavesdropper(s) has proven particularly useful in multi-terminal Gaussian channels. Many challenges remain however in realizing the vision of absolute security provided by the wireless physical layer including handling more realistic models. In this paper, we provide a brief overview of the state of the art, the forward look and argue for an additional asset that could be utilized for secrecy, i.e., bidirectional signaling. Taking the bidirectional wiretap channel as an example, Gaussian signaling is demonstrated to be as good as structured signaling from the degrees of freedom point of view, while observed to be performing better with finite transmit power. Moreover, taking bidirectional signals explicitly into account for encoding performs even better and provides a way forward to synergistically combine physical layer based secrecy and encryption.
This dissertation studies the security of wireless interference networks from an information-theoretic point of view. In this setting, several transmitter-receiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework based on information-theoretic principles to determine the complete solutions for the signaling schemes in different wireless interference networks with large transmit powers, and derive the corresponding fundamental limits in terms of the secure degrees of freedom (s.d.o.f.). Next, we study one-hop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian broadcast channel (BC) with confidential messages, Gaussian interference channel (IC) with confidential messages, and Gaussian multiple access (MAC) wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the s.d.o.f. of the Gaussian wiretap channel with no helpers is zero. We show that the exact s.d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact s.d.o.f. in this case is M/(M+1). We then generalize this approach to more general network structures with multiple messages. We show that the sum s.d.o.f. of the Gaussian BC with confidential messages and M helpers is 1, the sum s.d.o.f. of the two-user IC with confidential messages is 2/3, the sum s.d.o.f. of the two-user IC with confidential messages and M helpers is 1, and the sum s.d.o.f. of the K-user MAC wiretap channel is K(K-1)/(K(K-1)+1). Then, we study the sum s.d.o.f. of multi-receiver networks. In this dissertation, we determine the exact sum s.d.o.f. of the K-user Gaussian IC. We consider three different secrecy constraints: 1) K-user IC with one external eavesdropper (IC-EE), 2) K-user IC with confidential messages (IC-CM), and 3) K-user IC with confidential messages and one external eavesdropper (IC-CM-EE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K-1)/(2K-1). We show converses for IC-EE and IC-CM, which imply a converse for IC-CM-EE. We show achievability for IC-CM-EE, which implies achievability for IC-EE and IC-CM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers' observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller sub-space at every receiver, in order to attain the optimum sum s.d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly. Next, we study the entire s.d.o.f. regions of multi-user network structures. In this dissertation, we determine the entire s.d.o.f. regions of the K-user MAC wiretap channel and the K-user IC with secrecy constraints. The converse for the MAC follows from a middle step in the converse of the sum s.d.o.f. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. As a byproduct of determining the entire s.d.o.f. regions of MAC and IC channels, we show that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models. Then, we determine the sum s.d.o.f. of two-unicast layered wireless networks. Without any secrecy constraints, the sum d.o.f. of this class of networks was shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where, in addition to being reliably transmitted, each message is required to be kept information-theoretically secure from the unintended receiver. We show that the sum s.d.o.f. can only take one of five possible values: 0, 2/3, 1, 3/2,2, for all network configurations. To determine the sum s.d.o.f., we divide the class of two-unicast layered networks into several sub-classes, and propose an achievable scheme based on the specific structure of the networks in each sub-class. Our achievable schemes are based on real interference alignment, cooperative jamming, interference neutralization and cooperative jamming neutralization techniques. Next, we consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. One of the key ingredients of our optimal achievable scheme with perfect CSI is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This requires perfect eavesdropper CSI at the transmitters. We propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same s.d.o.f. of M/(M+1) but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper. Then, we study the separability of the parallel MAC wiretap channel. Separability, when exists, is useful as it enables us to code separately over parallel channels, and still achieve the optimum overall performance. It is well-known that the parallel single-user channel, parallel MAC and parallel BC are all separable, however, the parallel IC is not separable in general. In this dissertation, we show that, while MAC is separable MAC wiretap channel is not separable in general. We prove this via a specific linear deterministic MAC wiretap channel. We then show that even the Gaussian MAC wiretap channel is inseparable in general. Finally, we show that, when the channel gains are drawn from continuous distributions, and when the s.d.o.f. region is considered, then the Gaussian MAC wiretap channel is almost surely separable. Finally, we study the two-user one-sided IC with confidential messages. In this IC, in addition to the usual selfishness of the users, the relationship between the users is adversarial in the sense of both receivers' desires to eavesdrop on the communication of the other pair. We develop a game-theoretic model for this setting. We start with a model where each pair's payoff is their own secrecy rate. We then propose a refinement for the payoff function by explicitly accounting for the desire of the receiver to eavesdrop on the other party's communication. This payoff function captures the adversarial relationship between the users better. We determine the Nash equilibria for the binary deterministic channel for both payoff functions.
The study of the physical layer has offered a new perspective to the problem of communication security. This led to the development of a vast set of ideas and techniques rooted in information theory which can be employed in practice to provide unbreakable security. The information-theoretic approach relies mainly on the physical nature of the communication medium. In a wireless medium, the unique features of the wireless communication channel, such as its fading and broadcast nature, can be exploited to achieve higher secure information rates. In this dissertation, we study the secure transmission problem in wireless channels from an information-theoretic perspective. We first consider the fading multiple access wiretap channel. We give two new achievable schemes that use the time-varying (fading) nature of the channel to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher-dimensional space for the interfering signals at the legitimate receiver hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling based alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme (ergodic secret alignment). For each scheme, we show that the achievable secrecy rates scale logarithmically with the signal-to-noise ratio (SNR). Next, we study the security gains that can be achieved in a wireless network by employing cooperation among the nodes which is possible due to the broadcast nature of the wireless channel. We investigate the role of passive (also known as deaf) cooperation in improving the achievable secrecy rates in a Gaussian multiple relay network with an external eavesdropper. We distinguish between two modes of deaf cooperation, namely, cooperative jamming (CJ) and noise forwarding (NF). We derive the conditions in which each mode of deaf cooperation achieves secrecy rates that are higher than the secrecy capacity of the original Gaussian wiretap channel. As a result, we show that a deaf helper cannot be a useful cooperative jammer and noise forwarder at the same time. We derive the optimal power control policy for each mode. We consider the deaf helper selection problem where a fixed-size set of deaf helpers (possibly operating in different modes) are to be selected from the set of available relays so that the achievable secrecy rate is maximized. We propose a simple and efficient suboptimal strategy for selection which is shown to be optimal when only one helper is selected. Furthermore, we study the role of a multi-antenna deaf helper. Unlike the single antenna case, we show that, in general, it is useful to split the helper's power between cooperative jamming and noise forwarding. Hence, we propose a deaf cooperation strategy for this model and derive its optimal power control policy. We also show, for specific class of relay-eavesdropper channels, that a simple cooperative jamming strategy yields a secrecy rate that approaches the secrecy capacity as the helper's power is increased. Finally, we consider the role of active cooperation for secrecy in the multiple relay networks. We propose several relaying strategies for secure communication and derive the achievable secrecy rate for each strategy. In our strategies the relays decode the source signal and then forward it to the destination either in a single-hop or a multi-hop fashion. Each relay scales its transmitted signal in a way that ensures that signal components from different relays are canceled out at the eavesdropper.
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.
Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel.
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.
This work investigates providing information theoretically secure communication in a scenario where the eavesdropper is more powerful as compared to models considered to date. Specifically, we consider the setting where the eavesdropper, based on signals it received in the past, modifies its channel state in order to benefit its reception of the legitimate parties' messages. Natural to this setting is that the legitimate parties do not have any knowledge of the eavesdropper's channel state. In this setting, we study the Gaussian two-way wiretap channel, namely two legitimate nodes connected by a bi-directional link in the presence of an eavesdropper that receives the superposition of signals from both nodes. We show that a positive secrecy rate in the sense of strong secrecy is achievable even under these assumptions. The secrecy rate obtained scales with transmit power. The achievable strategy involves cooperative jamming pointing out to its robustness to the adaptive nature of the eavesdropper channel.