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10
Secure Transmission with Multiple Antennas: The MISOME Wiretap Channel
, 2007
"... The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and t ..."
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Cited by 240 (19 self)
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The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacityachieving. In addition, we show that in the high signaltonoise (SNR) ratio regime the penalty for not knowing eavesdropper’s channel is small—a simple “secure spacetime code ” that can be thought of as masked beamforming and radiates power isotropically attains nearoptimal performance. In the limit of large number of antennas, we obtain a realizationindependent characterization of the secrecy capacity as a function of the number β: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when β < 1, but that for β≥2 the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.
Secure communication over fading channels
, 2007
"... The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from rec ..."
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Cited by 186 (21 self)
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The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an informationtheoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established. This result is then specialized to give the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then
Wireless informationtheoretic security  part I: Theoretical aspects
 IEEE Trans. on Information Theory
, 2006
"... In this twopart paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an informationtheoretic problem formulation in which two legitimate partners communicate over a quasistatic fading channel and an eavesdropper observes their transmissi ..."
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Cited by 162 (12 self)
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In this twopart paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an informationtheoretic problem formulation in which two legitimate partners communicate over a quasistatic fading channel and an eavesdropper observes their transmissions through another independent quasistatic fading channel. We define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading informationtheoretic security is achievable even when the eavesdropper has a better average signaltonoise ratio (SNR) than the legitimate receiver — fading thus turns out to be a friend and not a foe. The issue of imperfect channel state information is also addressed. Practical schemes for wireless informationtheoretic security are presented in Part II, which in some cases comes close to the secrecy capacity limits given in this paper.
Secure broadcasting over fading channels
 IEEE Transactions on Information Theory
, 2008
"... Abstract—We study a problem of broadcasting confidential messages to multiple receivers under an informationtheoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are ..."
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Cited by 66 (9 self)
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Abstract—We study a problem of broadcasting confidential messages to multiple receivers under an informationtheoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fastfading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sumcapacity for transmitting independent messages. For the case of fastfading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers. Index Terms—Confidential messages, cryptography, fading channels, informationtheoretic secrecy, key distribution, multicasting, multiuser diversity, parallel channels, wiretap channel. I.
Secrecy Capacity over Correlated Ergodic Fading Channel
, 2008
"... We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eave ..."
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Cited by 5 (0 self)
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We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss of the secrecy capacity due to the correlation. In addition, we study the asymptotic behavior of the secrecy capacity as SignaltoNoise Ratio (SNR) tends to infinity. The capacity of an ordinary fading channel logarithmically increases with SNR. On the contrary, the secrecy capacity converges into a limit which can be an upper bound on the secrecy capacity over the fading wiretap channel. We find a closed form of the upper bound for the correlated Rayleigh wiretap channel which also includes the independent case as a special one. Our work shows that the upper bound is determined by only two channel parameters; the correlation coefficient and the ratio of the main to the eavesdropper channel gains that will be called PCC and CGR respectively. The analysis of the upper bound tells how the two channel parameters affect the secrecy capacity and leads to the conclusion that the excessively large signal power does not provide any advantage in the secrecy capacity, and the loss due to the correlation is especially serious in low CGR regime.
Algorithms and Architectures for Multiuser, Multiterminal, Multilayer Information Theoretic Security
, 2008
"... As modern infrastructure systems become increasingly more complex, we are faced with many new challenges in the area of information security. In this thesis we examine some approaches to security based on ideas from information theory. The protocols considered in this thesis, build upon the “wiretap ..."
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Cited by 4 (0 self)
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As modern infrastructure systems become increasingly more complex, we are faced with many new challenges in the area of information security. In this thesis we examine some approaches to security based on ideas from information theory. The protocols considered in this thesis, build upon the “wiretap channel, ” a model for physical layer security proposed by A. Wyner in 1975. At a higher level, the protocols considered here can strengthen existing mechanisms for security by providing a new location based approach at the physical layer. In the first part of this thesis, we extend the wiretap channel model to the case when there are multiple receivers, each experiencing a time varying fading channel. Both the scenario when each legitimate receiver wants a common message as well as the scenario when they all want separate messages are studied and capacity results are established in several special cases. When each receiver wants a separate independent message, an opportunistic scheme that transmits to the strongest user at each time, and uses Gaussian codebooks is shown to achieve the sum secrecy capacity in the
On Ergodic Secrecy Rate for MISO Wiretap Broadcast Channels with Opportunistic Scheduling
"... Abstract—In this letter, we study onoff opportunistic beamforming for the multiuser downlink channel with a passive eavesdropper. Two opportunistic scheduling schemes exploiting multiuser diversity are investigated which require limited feedback of the effective signaltonoise ratio (SNR) from t ..."
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Cited by 1 (1 self)
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Abstract—In this letter, we study onoff opportunistic beamforming for the multiuser downlink channel with a passive eavesdropper. Two opportunistic scheduling schemes exploiting multiuser diversity are investigated which require limited feedback of the effective signaltonoise ratio (SNR) from the legitimate users. For the two scheduling schemes, we derive new closedform expressions for the ergodic secrecy rate with onoff beamforming over Rayleigh fading channels. Numerical results are provided to verify our analytical results and illustrate the impact of multiuser diversity on the secrecy performance. Index Terms—Opportunistic beamforming, multiuser scheduling, multiuser diversity, physical layer security. I.
Secure Broadcasting over Fading Channels Ashish Khisti, Student Member, IEEE, Aslan Tchamkerten,
"... Motivated by the keydistribution application, we study the information theoretic problem of broadcasting confidential messages to multiple receivers. Two scenarios are considered: all receivers want a common message and each receiver needs an independent message. For the case of reversely degraded ..."
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Motivated by the keydistribution application, we study the information theoretic problem of broadcasting confidential messages to multiple receivers. Two scenarios are considered: all receivers want a common message and each receiver needs an independent message. For the case of reversely degraded parallel channels with one sender, one eavesdropper and arbitrary number of legitimate receivers we determine the commonmessagesecrecycapacity and the secrecysumcapacity for independent messages. For the case of fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while the channel state information of the eavesdropper is only known to the eavesdropper. For the case of common message our proposed scheme achieves a rate independent of the number of receivers, in contrast to naive schemes that achieve a rate which vanishes with the number of receivers. For the case of independent messages, an opportunistic transmission scheme is proposed and shown to be optimal in the limit of large number of receivers.
1 Secure Broadcasting
"... Wyner’s wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the s ..."
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Wyner’s wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the sender broadcasts either a common message or independent messages to the intended receivers. We derive upper and lower bounds on the commonmessagesecrecy capacity, which coincide when the users are reversely degraded. For the case of independent messages we establish the secrecy sumcapacity when the users are reversely degraded. In the second part of the paper we apply our results to fading channels: perfect channel state information of all intended receivers is known globally, whereas the eavesdropper channel is known only to her. For the common message case, a somewhat surprising result is proven: a positive rate can be achieved independently of the number of intended receivers. For independent messages, an opportunistic transmission scheme is presented that achieves the secrecy sumcapacity in the limit of large number of receivers. Our results are stated for a fast fading channel model. Extensions to the block fading model are also discussed.