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Physical-Layer Security in Wireless Communication Systems

Ghadamali Bagherikaram

Published May 17, 2010• 0 citations
OpenAlex

Abstract

The use of wireless networks has grown significantly in contemporary \ntimes, and continues to develop further. The broadcast nature of \nwireless communications, however, makes them particularly vulnerable \nto eavesdropping. Unlike traditional solutions, which usually handle \nsecurity at the application layer, the primary concern of this \ndissertation is to analyze and develop solutions based on coding \ntechniques at the physical-layer. \n \nFirst, in chapter $2$, we consider a scenario where a source node \nwishes to broadcast two confidential messages to two receivers, \nwhile a wire-tapper also receives the transmitted signal. This model \nis motivated by wireless communications, where individual secure \nmessages are broadcast over open media and can be received by any \nillegitimate receiver. The secrecy level is measured by the \nequivocation rate at the eavesdropper. We first study the general \n(non-degraded) broadcast channel with an eavesdropper, and present \nan inner bound on the secrecy capacity region for this model. This \ninner bound is based on a combination of random binning, and the \nGelfand-Pinsker binning. We further study the situation in which the \nchannels are degraded. For the degraded broadcast channel with an \neavesdropper, we present the secrecy capacity region. Our achievable \ncoding scheme is based on Cover's superposition scheme and random \nbinning. We refer to this scheme as the Secret Superposition Scheme. \nOur converse proof is based on a combination of the converse proof \nof the conventional degraded broadcast channel and Csiszar Lemma. We \nthen assume that the channels are Additive White Gaussian Noise and \nshow that the Secret Superposition Scheme with Gaussian codebook is \noptimal. The converse proof is based on Costa's entropy power \ninequality. Finally, we use a broadcast strategy for the slowly \nfading wire-tap channel when only the eavesdropper's channel is \nfixed and known at the transmitter. We derive the optimum power \nallocation for the coding layers, which maximizes the total average \nrate. \n \n \nSecond, in chapter $3$ , we consider the \nMultiple-Input-Multiple-Output (MIMO) scenario of a broadcast \nchannel where a wiretapper also receives the transmitted signal via \nanother MIMO channel. First, we assume that the channels are \ndegraded and the wiretapper has the worst channel. We establish the \ncapacity region of this scenario. Our achievability scheme is the \nSecret Superposition Coding. For the outerbound, we use notion of \nthe enhanced channels to show that the secret superposition of \nGaussian codes is optimal. We show that we only need to enhance the \nchannels of the legitimate receivers, and the channel of the \neavesdropper remains unchanged. We then extend the result of the \ndegraded case to a non-degraded case. We show that the secret \nsuperposition of Gaussian codes, along with successive decoding, \ncannot work when the channels are not degraded. We develop a Secret \nDirty Paper Coding scheme and show that it is optimal for this \nchannel. We then present a corollary generalizing the capacity \nregion of the two receivers case to the case of multiple receivers. \nFinally, we investigate a scenario which frequently occurs in the \npractice of wireless networks. In this scenario, the transmitter and \nthe eavesdropper have multiple antennae, while both intended \nreceivers have a single antenna (representing resource limited \nmobile units). We characterize the secrecy capacity region in terms \nof generalized eigenvalues of the receivers' channels and the \neavesdropper's channel. We refer to this configuration as the MISOME \ncase. We then present a corollary generalizing the results of the \ntwo receivers case to multiple receivers. In the high SNR regime, we \nshow that the capacity region is a convex closure of rectangular \nregions. \n \n \nFinally, in chapter $4$, we consider a $K$-user secure Gaussian \nMultiple-Access-Channel with an external eavesdropper. We establish \nan achievable rate region for the secure discrete memoryless MAC. \nThereafter, we prove the secrecy sum capacity of the degraded \nGaussian MIMO MAC using Gaussian codebooks. For the non-degraded \nGaussian MIMO MAC, we propose an algorithm inspired by the \ninterference alignment technique to achieve the largest possible \ntotal Secure-Degrees-of-Freedom . When all the terminals are \nequipped with a single antenna, Gaussian codebooks have shown to be \ninefficient in providing a positive S-DoF. Instead, we propose a \nnovel secure coding scheme to achieve a positive S-DoF in the single \nantenna MAC. This scheme converts the single-antenna system into a \nmultiple-dimension system with fractional dimensions. The \nachievability scheme is based on the alignment of signals into a \nsmall sub-space at the eavesdropper, and the simultaneous separation \nof the signals at the intended receiver. We use tools from the field \nof Diophantine Approximation in number theory to analyze the \nprobability of error in the coding scheme. We prove that the total \nS-DoF of $\\frac{K-1}{K}$ can be achieved for almost all channel \ngains. For the other channel gains, we propose a multi-layer coding \nscheme to achieve a positive S-DoF. As a function of channel gains, \ntherefore, the achievable S-DoF is discontinued.

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Secrecy Rate Region of the Broadcast Channel with an Eavesdropper

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper. We present an inner bound on the secrecy capacity region for this model. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. We further study the situation in which the channels are degraded. For the degraded broadcast channel with an eavesdropper, we present the secrecy capacity region. Our achievable coding scheme is based on Covers superposition scheme and random binning. We refer to this scheme as the Secret Superposition Scheme. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise (AWGN) and show that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costas entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdroppers channel is fixed and known at the transmitter. We derive the optimum power allocation for the coding layers, which maximizes the total average rate.

arXiv:0910.3658•Oct 19, 2009•13 citations

The Secrecy Rate Region of the Broadcast Channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.

arXiv:0806.4200•Jun 25, 2008•33 citations

Secure broadcasting : The secrecy rate region

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as secret superposition scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma.

Allerton Conference on Communication, Control, and Computing•Sep 1, 2008•40 citations

Secrecy capacity region of Gaussian broadcast channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as secret superposition coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.

Conference on Information Sciences and Systems•Mar 1, 2009•29 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. 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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

The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to non-degraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channels are not degraded. we develop a Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, we investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.

arXiv:0903.3261•Mar 19, 2009•15 citations
The use of wireless networks has grown significantly in contemporary \ntimes, and continues to develop further. The broadcast nature of \nwireless communications, however, makes them particularly vulnerable \nto eavesdropping. Unlike traditional solutions, which usually handle \nsecurity at the application layer, the primary concern of this \ndissertation is to analyze and develop solutions based on coding \ntechniques at the physical-layer. \n \nFirst, in chapter 222, we consider a scenario where a source node \nwishes to broadcast two confidential messages to two receivers, \nwhile a wire-tapper also receives the transmitted signal. This model \nis motivated by wireless communications, where individual secure \nmessages are broadcast over open media and can be received by any \nillegitimate receiver. The secrecy level is measured by the \nequivocation rate at the eavesdropper. We first study the general \n(non-degraded) broadcast channel with an eavesdropper, and present \nan inner bound on the secrecy capacity region for this model. This \ninner bound is based on a combination of random binning, and the \nGelfand-Pinsker binning. We further study the situation in which the \nchannels are degraded. For the degraded broadcast channel with an \neavesdropper, we present the secrecy capacity region. Our achievable \ncoding scheme is based on Cover's superposition scheme and random \nbinning. We refer to this scheme as the Secret Superposition Scheme. \nOur converse proof is based on a combination of the converse proof \nof the conventional degraded broadcast channel and Csiszar Lemma. We \nthen assume that the channels are Additive White Gaussian Noise and \nshow that the Secret Superposition Scheme with Gaussian codebook is \noptimal. The converse proof is based on Costa's entropy power \ninequality. Finally, we use a broadcast strategy for the slowly \nfading wire-tap channel when only the eavesdropper's channel is \nfixed and known at the transmitter. We derive the optimum power \nallocation for the coding layers, which maximizes the total average \nrate. \n \n \nSecond, in chapter 333 , we consider the \nMultiple-Input-Multiple-Output (MIMO) scenario of a broadcast \nchannel where a wiretapper also receives the transmitted signal via \nanother MIMO channel. First, we assume that the channels are \ndegraded and the wiretapper has the worst channel. We establish the \ncapacity region of this scenario. Our achievability scheme is the \nSecret Superposition Coding. For the outerbound, we use notion of \nthe enhanced channels to show that the secret superposition of \nGaussian codes is optimal. We show that we only need to enhance the \nchannels of the legitimate receivers, and the channel of the \neavesdropper remains unchanged. We then extend the result of the \ndegraded case to a non-degraded case. We show that the secret \nsuperposition of Gaussian codes, along with successive decoding, \ncannot work when the channels are not degraded. We develop a Secret \nDirty Paper Coding scheme and show that it is optimal for this \nchannel. We then present a corollary generalizing the capacity \nregion of the two receivers case to the case of multiple receivers. \nFinally, we investigate a scenario which frequently occurs in the \npractice of wireless networks. In this scenario, the transmitter and \nthe eavesdropper have multiple antennae, while both intended \nreceivers have a single antenna (representing resource limited \nmobile units). We characterize the secrecy capacity region in terms \nof generalized eigenvalues of the receivers' channels and the \neavesdropper's channel. We refer to this configuration as the MISOME \ncase. We then present a corollary generalizing the results of the \ntwo receivers case to multiple receivers. In the high SNR regime, we \nshow that the capacity region is a convex closure of rectangular \nregions. \n \n \nFinally, in chapter 444, we consider a KKK-user secure Gaussian \nMultiple-Access-Channel with an external eavesdropper. We establish \nan achievable rate region for the secure discrete memoryless MAC. \nThereafter, we prove the secrecy sum capacity of the degraded \nGaussian MIMO MAC using Gaussian codebooks. For the non-degraded \nGaussian MIMO MAC, we propose an algorithm inspired by the \ninterference alignment technique to achieve the largest possible \ntotal Secure-Degrees-of-Freedom . When all the terminals are \nequipped with a single antenna, Gaussian codebooks have shown to be \ninefficient in providing a positive S-DoF. Instead, we propose a \nnovel secure coding scheme to achieve a positive S-DoF in the single \nantenna MAC. This scheme converts the single-antenna system into a \nmultiple-dimension system with fractional dimensions. The \nachievability scheme is based on the alignment of signals into a \nsmall sub-space at the eavesdropper, and the simultaneous separation \nof the signals at the intended receiver. We use tools from the field \nof Diophantine Approximation in number theory to analyze the \nprobability of error in the coding scheme. We prove that the total \nS-DoF of fracK−1K\\frac{K-1}{K}fracK−1K can be achieved for almost all channel \ngains. For the other channel gains, we propose a multi-layer coding \nscheme to achieve a positive S-DoF. As a function of channel gains, \ntherefore, the achievable S-DoF is discontinued.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper. We present an inner bound on the secrecy capacity region for this model. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. We further study the situation in which the channels are degraded. For the degraded broadcast channel with an eavesdropper, we present the secrecy capacity region. Our achievable coding scheme is based on Covers superposition scheme and random binning. We refer to this scheme as the Secret Superposition Scheme. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise (AWGN) and show that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costas entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdroppers channel is fixed and known at the transmitter. We derive the optimum power allocation for the coding layers, which maximizes the total average rate.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as secret superposition scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma.
In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as secret superposition coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.
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.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to non-degraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channels are not degraded. we develop a Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, we investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.