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26
Cooperative jamming for secure communications in MIMO relay networks
 IEEE Trans. Signal Process
, 2011
"... Abstract—Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for twohop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the rel ..."
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Cited by 29 (12 self)
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Abstract—Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for twohop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decodeandforward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closedform jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVDbased cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming. Index Terms—Interference, jamming, physical layer security, relay networks, secrecy, wiretap channel. I.
Secure Degrees of Freedom of Onehop Wireless Networks
, 2012
"... We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple a ..."
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Cited by 19 (12 self)
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We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple access wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1 2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M M+1. We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the twouser interference channel with confidential messages is 2 3, the sum secure d.o.f. of the twouser interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the Kuser multiple access wiretap channel is
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
"... This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without rely ..."
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Cited by 16 (1 self)
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This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higherlayer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on informationtheoretic security. We then describe the evolution of secure transmission strategies from pointtopoint channels to multipleantenna systems, followed by generalizations to multiuser broadcast, multipleaccess, interference, and relay networks. Secretkey generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of interdisciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area.
MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper: Secrecy degrees of freedom
 IEEE TRANSACTIONS ON INFORMATION THEORY, FEBRUARY
, 2013
"... A twotransmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known t ..."
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Cited by 13 (5 self)
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A twotransmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a singleuser wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weightedsumrate expression. This is accomplished by using induction, where at each step one combines the secrecy and multipleaccess constraints associated with an adversary eavesdropping a carefully selected group of subchannels.
MIMO Broadcast Channel with Arbitrarily Varying Eavesdropper Channel: Secrecy Degrees of Freedom
 IN IEEE GLOBAL TELECOMMUNICATION CONFERENCE
, 2011
"... A tworeceiver MIMO broadcastwiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper exp ..."
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Cited by 8 (6 self)
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A tworeceiver MIMO broadcastwiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a commonconfidential message as well as a privateconfidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular structured binning across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.
Secrecy from Resolvability
, 2011
"... We investigate an approach to physicallayer security based on the premise that the coding mechanism for secrecy over noisy channels is fundamentally tied to the notion of resolvability. Instead of considering capacitybased constructions, which associate to each message a subcode whose rate approa ..."
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Cited by 4 (0 self)
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We investigate an approach to physicallayer security based on the premise that the coding mechanism for secrecy over noisy channels is fundamentally tied to the notion of resolvability. Instead of considering capacitybased constructions, which associate to each message a subcode whose rate approaches the capacity of the eavesdropper’s channel, we consider resolvabilitybased constructions, which associate to each message a subcode whose rate is beyond the resolvability of the eavesdropper’s channel. We provide evidence that resolvability is a more powerful and perhaps more fundamental coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that, at least for binary symmetric wiretap channels, random capacitybased constructions fail to approach the strong secrecy capacity while resolvabilitybased constructions achieve it. We then obtain the secrecycapacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics, which generalizes existing results. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information, compound and mixed channels, as well as the secretkey capacity of source models for secretkey agreement. By tying secrecy to resolvability, we obtain achievable rates for stronger secrecy metrics and with simpler proofs than previously derived.
MIMO Broadcast Channel with an Unknown Eavesdropper: Secrecy Degrees of Freedom
"... Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secr ..."
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Cited by 3 (1 self)
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Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secrecy degrees of freedom for the broadcast channel with common and private messages. We show that a direct extension of the singleuser wiretap codebook does not achieve the secrecy degrees of freedom. Our proposed optimal scheme involves decomposing the signal space into a common subspace, which can be observed by both receivers, and private subspaces which can be observed by only one of the receivers, and carefully transmitting a subset of messages in each subspace. We also consider the case when each user’s private message must additionally remain confidential from the other legitimate receiver and characterize the s.d.o.f. region in this case. Index Terms—Information theoretic security, broadcast channels, wiretap channels, generalized singular value decomposition, MIMOME channel. I.
Secrecy when the eavesdropper controls its channel states
 in Proc. IEEE Int. Symp. Information Theory
, 2011
"... Abstract—This work investigates providing information theoretically secure communication in a scenario where the eavesdropper is more powerful as compared to models considered to date. Specifically, we consider the setting where the eavesdropper, based on signals it received in the past, modifies ..."
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Cited by 3 (3 self)
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Abstract—This work investigates providing information theoretically secure communication in a scenario where the eavesdropper is more powerful as compared to models considered to date. Specifically, we consider the setting where the eavesdropper, based on signals it received in the past, modifies its channel state in order to benefit its reception of the legitimate parties ’ messages. Natural to this setting is that the legitimate parties do not have any knowledge of the eavesdropper’s channel state. In this setting, we study the Gaussian twoway wiretap channel, namely two legitimate nodes connected by a bidirectional link in the presence of an eavesdropper that receives the superposition of signals from both nodes. We show that a positive secrecy rate in the sense of strong secrecy is achievable even under these assumptions. The secrecy rate obtained scales with transmit power. The achievable strategy involves cooperative jamming pointing out to its robustness to the adaptive nature of the eavesdropper channel. I.
A Broadcast Approach for Fading Wiretap Channels. Submitted to
 IEEE Transactions on Information Theory
"... A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding respectively, are developed to encode information into a number of layers and use stochast ..."
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Cited by 2 (0 self)
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A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding respectively, are developed to encode information into a number of layers and use stochastic encoding to keep the corresponding information secret from an eavesdropper. The layers that can be successfully and securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The advantage of these broadcast approaches is that the transmitter does not need to know the CSI to the legitimate receiver and the eavesdropper, but the scheme still adapts to the channel states of the legitimate receiver and the eavesdropper. Three scenarios of block fading wiretap channels with a stringent delay constraint are studied, in which either the legitimate receiver’s channel, the eavesdropper’s channel, or both channels are fading. For each scenario, the secrecy rate that can be achieved via the broadcast approach developed in this paper is derived, and the optimal power allocation over the layers (or the conditions on the optimal power
The Gaussian Interference Wiretap Channel When the Eavesdropper Channel is Arbitrarily Varying
"... Abstract—In this work we considered the Gaussian twouser interference channel where the eavesdropper channel is arbitrarily varying, all channel matrices have rank less than or equal to 2, and the eavesdropper has 1 antenna. We identify a class of these channel models for which the secrecy degrees o ..."
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Cited by 1 (1 self)
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Abstract—In this work we considered the Gaussian twouser interference channel where the eavesdropper channel is arbitrarily varying, all channel matrices have rank less than or equal to 2, and the eavesdropper has 1 antenna. We identify a class of these channel models for which the secrecy degrees of freedom (s.d.o.f.) region is achieved by letting only one user transmit a time. We also provided a nontrivial example for which such a transmission strategy is suboptimal in terms of s.d.o.f. region. The achievable scheme for this example introduces a new technique to achieve secrecy for MIMO wiretap channels, in which the transmitterreceiver pair uses linear precoding so that effectively the signals are beamformed toward a direction that can not be attained by the eavesdropper and is at the same time orthogonal to interference from the other user. I.