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Cooperation with an untrusted relay: a secrecy perspective
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2010
"... We consider the communication scenario where a sourcedestination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untr ..."
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Cited by 52 (13 self)
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We consider the communication scenario where a sourcedestination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show, by means of the achievable secrecy rate based on compressandforward, that by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover–Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the sourcedestination link is not worse than the sourcerelay link, by matching with achievable rate we present.
Providing Secrecy With Structured Codes: Tools and Applications to TwoUser Gaussian Channels
, 2009
"... Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured c ..."
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Cited by 45 (17 self)
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Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in twouser Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the twouser multiple access wiretap channel, the twouser interference channel with confidential messages and the twouser interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.
MIMO Wiretap Channels with Arbitrarily Varying Eavesdropper Channel States. Arxiv.org:1007.4801
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Degraded Compound Multireceiver Wiretap Channels
, 2009
"... In this paper, we study the degraded compound multireceiver wiretap channel. The degraded compound multireceiver wiretap channel consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a ..."
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Cited by 22 (11 self)
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In this paper, we study the degraded compound multireceiver wiretap channel. The degraded compound multireceiver wiretap channel consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the general discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multipleinput multipleoutput (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario we study, the transmitter sends a confidential message to users in the first group which needs to be kept confidential from the second group of users and the eavesdroppers. Furthermore, the transmitter sends a different confidential message to users in the second group which needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. As in the first scenario, we obtain the secrecy capacity region for the general discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we establish the secrecy capacity region when there is only one user in the second group.
Capacity region of Gaussian MIMO broadcast channels with common and confidential messages. submitted to
 IEEE Trans. Inf. Theory
, 2010
"... Abstract—We study the twouser Gaussian multipleinput multipleoutput (MIMO) broadcast channel with common and confidential messages. In this channel, 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 ..."
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Cited by 18 (2 self)
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Abstract—We study the twouser Gaussian multipleinput multipleoutput (MIMO) broadcast channel with common and confidential messages. In this channel, 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 the capacity region we obtain for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its nonconfidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private messages, which is not known completely. Index Terms—Gaussian multipleinput multipleoutput (MIMO) broadcast channel, secrecy capacity region. Gaussian MIMO broadcast channel with common and confidential mesFig. 1. sages. I.
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 18 (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.
Secured Communication over FrequencySelective Fading Channels: A Practical Vandermonde Precoding
, 2009
"... In this paper, we study the frequencyselective broadcast channel with confidential messages (BCC) in which the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of N symbols followed by a guard interval of L symbols ..."
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Cited by 17 (8 self)
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In this paper, we study the frequencyselective broadcast channel with confidential messages (BCC) in which the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of N symbols followed by a guard interval of L symbols, the frequencyselective channel can be modeled as a N × (N + L) Toeplitz matrix. For this special type of multipleinput multipleoutput (MIMO) channels, we propose a practical Vandermonde precoding that consists of projecting the confidential messages in the null space of the channel seen by receiver 2 while superposing the common message. For this scheme, we provide the achievable rate region, i.e. the ratetuple of the common and confidential messages, and characterize the optimal covariance inputs for some special cases of interest. It is proved that the proposed scheme achieves the optimal degree of freedom (d.o.f) region. More specifically, it enables to send l ≤ L confidential messages and N − l common messages simultaneously over a block of N + L symbols. Interestingly, the proposed scheme can be applied to secured multiuser scenarios such as the K + 1user frequencyselective BCC with K confidential messages and the twouser frequencyselective BCC with two confidential messages. For
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.
Secrecy Capacity Region of the Gaussian MultiReceiver Wiretap Channel
"... Abstract — We consider the Gaussian multireceiver wiretap channel and evaluate its secrecy capacity region. This evaluation requires the identification of underlying auxiliary random variables. For this purpose, we first visit the converse proof of the scalar Gaussian broadcast channel, and show th ..."
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Cited by 12 (1 self)
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Abstract — We consider the Gaussian multireceiver wiretap channel and evaluate its secrecy capacity region. This evaluation requires the identification of underlying auxiliary random variables. For this purpose, we first visit the converse proof of the scalar Gaussian broadcast channel, and show that this proof cannot be extended to this secrecy context. The failure of this extension comes from the insufficiency of the entropypower inequality to resolve the ambiguity regarding the auxiliary random variables. Instead, we provide two converse proofs. The first one uses the alternative representation of the mutual information as an integration of the minimummeansquareerror (MMSE) along with the properties of the MMSE. The second one uses the relationship between the differential entropy and the Fisher information via the de Bruin identity along with the properties of the Fisher information. I.