Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Cambridge University Press eBooks

Modeling malicious behavior in cooperative cellular wireless networks

Ninoslav Marina, Walid Saad, Zhu Han, Are Hjørungnes

Published Mar 10, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1017/cbo9780511667008.015

Related papers

Relaying Techniques for Improving the Physical Layer Security

Fathi E. Abd El-Samie, Faisal S. Al-kamali, Azzam Y. Al-nahari +1 more

Security issues for traditional wireless networks have been considered as a very important research area, and have taken a considerable attention for several years due to the broadcast nature of the wireless medium, which makes attacks more likely to happen than in wireline systems. Most of the studies in this area focus on the security in the higher layers in the protocol stack via the use of cryptography and key management. The main idea of these security approaches is based on the limited computational power of the eavesdroppers. With the advent of the infrastructureless networks such as mobile ad hoc networks (MANETs), further challenges have appeared which make the nodes more vulnerable to attacks. Among these challenges are the absence of centralized hardware for security problems, the multihop routes that the transmitted information should follow, and the power-limited terminals [152]. Therefore, to cope with these limitations, physical layer security (or informationtheoretic security) has gained a considerable attention in the last few years. The goal of physical layer security is to allow the source to confidentially communicate with the legitimate destination, while the eavesdropper cannot interpret the source information, without any assumption for the eavesdropper nodes such as the computational power, or the available information. From an information-theoretic standpoint, the achieved source-destination confidential rate is called the achievable secrecy rate.

CRC Press eBooks•Jun 19, 2013•0 citations

Characterization of the Secrecy Region of a Single Relay Cooperative System

Ninoslav Marina, Are Hjørungnes

Security is an important aspect for the future wireless networks. Since the number of network nodes increases constantly, and, in addition, the networks are decentralized and ad-hoc in nature, it becomes more challenging to apply the current cryptographic methods that require exchange of keys between the communicating parties. Information-theoretic secrecy is an emerging security field that explores the possibility of achieving perfect secrecy data transmission between the intended network nodes, while possible malicious nodes (also called eavesdroppers) are kept ignorant of the transmitted information. In other words, that is the ability of the physical layer to provide security (beside the reliability) of the transmitted (broadcasted) data. For that reason, it is often called physical layer security. In this paper we observe how a simple cooperative network with one relay node can improve the physical layer security by decreasing the area in which the eavesdropper can reside and listen to the information transmitted to the destination. This region is called vulnerability region and we provide its characterization. Under certain conditions, the vulnerability region vanishes, which makes our wireless system perfectly secure for any position of the eavesdropper within the wireless network.

IEEE Wireless Communications and Networking Conference•Apr 1, 2010•17 citations

On physical layer security in cooperative networks

Zohaib Hassan Awan

With the advent of mobile telephony, complemented by the availability of economic infrastructure devices has provided users the freedom to communicate and perform everyday tasks wirelessly. The access to information anywhere anytime provide users more flexibility to communicate, nonetheless it also makes communication more vulnerable to eavesdropping. Security is now considered as an important issue in the design of modern wireless communication system. In contrast to the conventional systems where security issues are dealt in the upper\nlayers of the protocol stack, in this thesis we focus our attention to construct security schemes by exploiting the attributes of the physical layer. \nIn the first part of the thesis, we consider a two-user multiacces channel where the two encoders, Encoder 1 and Encoder 2, are allowed to communicate with each other over a unidirectional noiseless bit-pipe of finite capacity in the presence of an adversary. In this model, the role of Encoder 2 is restricted to only help Encoder 1 in securing information from adversary. For this model, we\nestablish fundamental performance limits on secure communication and characterizes the secrecy capacity in some extreme cases of cooperation between the encoders. The second part of the thesis considers an elementary\nnetwork, which consists of four nodes – a source, a relay, a legitimate receiver and a passive eavesdropper. In this network, the link between two nodes consists of multiple parallel channels as subchannel. Towards this end, we establish bounds on secure communication. We show that for the case in which the relay does not listens to the source, under certain conditions secrecy capacity is established. In the last part of the thesis, we studied a two-user multi-input multioutput X-channel with local feedback and delayed channel state information\navailable at the transmitter in high signal-to-noise ratio regimes. In this setting each transmitter transmits independent messages to both receivers that need to be kept secret from each other. We characterize the optimal sum secure degrees of freedom region of this model.

•Jan 1, 2013•0 citations

MISO Wiretap Channel with Strictly Causal CSI: A Topological Viewpoint

Zohaib Hassan Awan, Aydin Sezgin

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.

Cambridge University Press eBooks•Jun 16, 2017•0 citations

Information-theoretic Secrecy in Multi-user Channels

Ersen Ekrem

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.

•Jan 1, 2012•0 citations

Physical Layer Security in Wireless Networks

Emad S. Hassan

Due to the broadcast nature of wireless communications, it is difficult to shield transmitted signals from adversarial users in the coverage area of the transmission. This chapter highlights many issues concerned with achieving secrecy in the physical layer. It discusses overview of the foundations dating back to the pioneering key-based Shannon and keyless Wyner–Ziv works on information-theoretic security. In 1978, Leung-Yang-Cheong and Hellman considered the Gaussian wiretap channel. The chapter introduces multiformity of cooperative jamming techniques to show the effectiveness of jamming signals transmitted by some legitimate transmitters in a network of multiple transmitters and receivers in achieving physical layer security for a certain legitimate pair. It gives the idea of employing cooperative jammers in a multiple trusted/untrusted relay networks in order to improve security, and the interactions arising between cooperation and secrecy in the presence of untrusted relays are adopted. A resurgence of interest in aspects of secrecy at the physical layer has been experienced.

CRC Press eBooks•Apr 27, 2018•2 citations
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.
Security issues for traditional wireless networks have been considered as a very important research area, and have taken a considerable attention for several years due to the broadcast nature of the wireless medium, which makes attacks more likely to happen than in wireline systems. Most of the studies in this area focus on the security in the higher layers in the protocol stack via the use of cryptography and key management. The main idea of these security approaches is based on the limited computational power of the eavesdroppers. With the advent of the infrastructureless networks such as mobile ad hoc networks (MANETs), further challenges have appeared which make the nodes more vulnerable to attacks. Among these challenges are the absence of centralized hardware for security problems, the multihop routes that the transmitted information should follow, and the power-limited terminals [152]. Therefore, to cope with these limitations, physical layer security (or informationtheoretic security) has gained a considerable attention in the last few years. The goal of physical layer security is to allow the source to confidentially communicate with the legitimate destination, while the eavesdropper cannot interpret the source information, without any assumption for the eavesdropper nodes such as the computational power, or the available information. From an information-theoretic standpoint, the achieved source-destination confidential rate is called the achievable secrecy rate.
Security is an important aspect for the future wireless networks. Since the number of network nodes increases constantly, and, in addition, the networks are decentralized and ad-hoc in nature, it becomes more challenging to apply the current cryptographic methods that require exchange of keys between the communicating parties. Information-theoretic secrecy is an emerging security field that explores the possibility of achieving perfect secrecy data transmission between the intended network nodes, while possible malicious nodes (also called eavesdroppers) are kept ignorant of the transmitted information. In other words, that is the ability of the physical layer to provide security (beside the reliability) of the transmitted (broadcasted) data. For that reason, it is often called physical layer security. In this paper we observe how a simple cooperative network with one relay node can improve the physical layer security by decreasing the area in which the eavesdropper can reside and listen to the information transmitted to the destination. This region is called vulnerability region and we provide its characterization. Under certain conditions, the vulnerability region vanishes, which makes our wireless system perfectly secure for any position of the eavesdropper within the wireless network.
With the advent of mobile telephony, complemented by the availability of economic infrastructure devices has provided users the freedom to communicate and perform everyday tasks wirelessly. The access to information anywhere anytime provide users more flexibility to communicate, nonetheless it also makes communication more vulnerable to eavesdropping. Security is now considered as an important issue in the design of modern wireless communication system. In contrast to the conventional systems where security issues are dealt in the upper\nlayers of the protocol stack, in this thesis we focus our attention to construct security schemes by exploiting the attributes of the physical layer. \nIn the first part of the thesis, we consider a two-user multiacces channel where the two encoders, Encoder 1 and Encoder 2, are allowed to communicate with each other over a unidirectional noiseless bit-pipe of finite capacity in the presence of an adversary. In this model, the role of Encoder 2 is restricted to only help Encoder 1 in securing information from adversary. For this model, we\nestablish fundamental performance limits on secure communication and characterizes the secrecy capacity in some extreme cases of cooperation between the encoders. The second part of the thesis considers an elementary\nnetwork, which consists of four nodes – a source, a relay, a legitimate receiver and a passive eavesdropper. In this network, the link between two nodes consists of multiple parallel channels as subchannel. Towards this end, we establish bounds on secure communication. We show that for the case in which the relay does not listens to the source, under certain conditions secrecy capacity is established. In the last part of the thesis, we studied a two-user multi-input multioutput X-channel with local feedback and delayed channel state information\navailable at the transmitter in high signal-to-noise ratio regimes. In this setting each transmitter transmits independent messages to both receivers that need to be kept secret from each other. We characterize the optimal sum secure degrees of freedom region of this model.
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.
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.
Due to the broadcast nature of wireless communications, it is difficult to shield transmitted signals from adversarial users in the coverage area of the transmission. This chapter highlights many issues concerned with achieving secrecy in the physical layer. It discusses overview of the foundations dating back to the pioneering key-based Shannon and keyless Wyner–Ziv works on information-theoretic security. In 1978, Leung-Yang-Cheong and Hellman considered the Gaussian wiretap channel. The chapter introduces multiformity of cooperative jamming techniques to show the effectiveness of jamming signals transmitted by some legitimate transmitters in a network of multiple transmitters and receivers in achieving physical layer security for a certain legitimate pair. It gives the idea of employing cooperative jammers in a multiple trusted/untrusted relay networks in order to improve security, and the interactions arising between cooperation and secrecy in the presence of untrusted relays are adopted. A resurgence of interest in aspects of secrecy at the physical layer has been experienced.