We study a multi-antenna 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 single-user 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.

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 Gaussian random codes. In this paper, we advocate that structure in random code generation is useful for providing secrecy as well. In particular, a Gaussian wiretap channel in the presence of a cooperative jammer is studied. Previously, the achievable secrecy rate for this channel was derived using Gaussian signaling, which saturated at high signal-to-noise ratio (SNR), owing to the fact that the cooperative jammer simultaneously helps by interfering with the eavesdropper, and hurts by interfering with the intended receiver. In this paper, a new achievable rate is derived through imposing a lattice structure on the signals transmitted by both the source and the cooperative jammer, which are aligned at the eavesdropper but remain separable at the intended receiver. We prove that the achieved secrecy rate does not saturate at high SNR for all values of channel gains except when the channel is degraded.

In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.

A two-transmitter 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 single-user wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.

We consider a Gaussian two-hop network where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine adversary. Both the source and the destination nodes are allowed to transmit, and the relay receives a superposition of their transmitted signals. We propose a new coding scheme that satisfies two requirements simultaneously: the transmitted message must be kept secret from the relay node, and the destination must be able to detect any Byzantine attack that the relay node might launch reliably and fast. The three main components of the proposed scheme are the nested lattice code, the privacy amplification scheme, and the algebraic manipulation detection (AMD) code. Specifically, for the Gaussian two-hop network, we show that lattice coding can successfully pair with AMD codes enabling its first application to a noisy channel model. We prove, using this new coding scheme, that the probability that the Byzantine attack goes undetected decreases exponentially fast with respect to the number of channel uses, while the loss in the secrecy rate, compared to the rate achievable when the relay is honest, can be made arbitrarily small. In addition, in contrast with prior work in Gaussian channels, the notion of secrecy provided here is strong secrecy.

Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.

A multi-hop line network is considered, where each node can receive signals transmitted by its two neighbors. As such, the model embodies both the interference and broadcast aspects of wireless networks. The leftmost node wishes to send messages to the rightmost node, while keeping these messages confidential from all the intermediate relay nodes. In this setting where any or all of the relay nodes can be eavesdroppers, it is shown that end-to-end secure and reliable communication is possible. Notably, it is shown that an end-to-end secrecy rate that is independent of the number of hops, i.e., intermediate eavesdroppers, is achievable by means of a carefully designed transmission schedule, compute-and-forward relaying and coding strategy utilizing nested lattice codes. The achievable rate obtained indicates that imposing secrecy constraints penalizes the capacity by at most 1 bit per channel use. Therefore, it is concluded that information theoretic secrecy can be guaranteed for this model irrespective of eavesdropping relays and a fixed modest cost for the end-to-end rate.

In this work we considered the Gaussian two-user 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 non-trivial example for which such a transmission strategy is sub-optimal 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 transmitter-receiver pair uses linear precoding so that effectively the signals are beam-formed toward a direction that can not be attained by the eavesdropper and is at the same time orthogonal to interference from the other user.

A two-receiver MIMO broadcast-wiretap 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 common-confidential message as well as a private- confidential 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 \emph{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.

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 two-way wiretap channel, namely two legitimate nodes connected by a bi-directional 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.

The many-to-one interference channel has received interest by virtue of embodying the essence of an interference network while being more tractable than the generalK-user interference channel. In this paper, we introduce information theoretic secrecy to this model and consider the many-to-one interference channel with confidential messages, in which each receiver, in particular, the one subject to interference, is also one from which the interfering users' messages need to be kept secret from. We derive the achievable secrecy sum rate for this channel using nested lattice codes, as well as an upper bound on the secrecy sum rate for all possible channel gain configurations. We identify several nontrivial cases where the gap between the upper bound and the achieved secrecy sum rate is only a function of the number of the usersK, and is uniform over all possible channel gain configurations in each case. In addition, we identify the secure degrees of freedom for this channel and show it to be equivalent to its degrees of freedom, i.e., the secrecy in high SNR comes for free.

A usual concern against physical layer security is that the legitimate parties would need to have (partial) channel state information (CSI) of the eavesdropper in order to design transmission schemes that provide secrecy. In this work, to overcome this concern, we consider the model where the eavesdropper's CSI is completely unknown at the legitimate transmitter(s) and the receiver. A static channel setting, and multiple antennas are considered for all parties, and it is assumed that the eavesdropper has perfect self-CSI. In this setting, assuming that the legitimate parties can employ a larger number of antennas than the eavesdropper, we provide a positive secure communication rate in the sense of strong secrecy. The achievable (guaranteed) secrecy rate we derive for the MIMO wiretap channel matches its converse in terms of secure degrees of freedom. As a side result of our approach, we also derive the secure degrees of freedom region for the MIMO MAC-wiretap channel where the transmitters and the intended receiver have the same number of antennas.

We investigate the fundamental communication limits when messages are sent via a Gaussian two-way channel, which must at the same time be kept secret from an external eavesdropper. In this two-way wiretap channel that models two legitimate transceivers and an eavesdropping receiver, there are two techniques to provide confidentiality for the messages: one entails the legitimate nodes to jam the eavesdropper, i.e., cooperative jamming, while the other entails generating keys from the feedback signals received by the two legitimate nodes and using them to encrypt the messages. Previous work has shown that both methods can be used concurrently to improve the secrecy rates of a channel with a degradedness condition. In this work, we consider the general case, and derive a new outer bound for the secrecy capacity region of this channel. A case is identified where the loss in secrecy rate, due to ignoring the backward (feedback) link at each legitimate transmitter from the other, is bounded by a constant which only depends on the channel gains. This is the case when the power of the two legitimate nodes increases proportionally. In all other cases, we show that ignoring feedback signals causes unbounded loss in the secrecy rate. The loss is measured as the gap between the achievable rate when the feedback signals are taken into account, and the upper bound when the feedback is not used, and hence is not affected by the choice of the achievable scheme. This result therefore establishes that, for the Gaussian two-way channel with an external eavesdropper, the encoders need to be designed with memory. This is in contrast to the result for this channel in the absence of an eavesdropper.

In this work, we investigate secret key generation from channel states. We point out, by means of a packet-delay-based attack, that observing its own channel states is not the only way an adversary can learn about the channel states of the legitimate communicating parties. The attack suggests that it is not secure to transmit data via the channel whose states generate secret keys. However, not using the channel at all would result in a waste of bandwidth. Hence, we propose using this channel to transmit the bits needed to reconcile the channel state estimates at the transmitter and the receiver. This is a necessary step in secret key generation that required a separate channel in previous work. Although the scheme proposed here in effect prohibits the use of an adaptive transmitter, we show, for the Rayleigh fading channel, that a decent key rate that outperforms existing schemes is obtained. This is due to the fact that collection of the channel state information and transmission of the reconciliation bits are performed concurrently rather than via time sharing.

We consider the communication scenario where a source-destination 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 compress-and-forward, 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 source-destination link is not worse than the source-relay link, by matching with achievable rate we present.

In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.

We investigate the K-user many-to-one interference channel with confidential messages in which the Kth user experiences interference from all other K - 1 users, and is at the same time treated as an eavesdropper to all the messages of these users. We derive achievable rates and an upper bound on the sum rate for this channel and show that the gap between the achievable sum rate and its upper bound is log2(K - 1) bits per channel use under very strong interference, when the interfering users have equal power constraints and interfering link channel gains. The main contributions of this work are: (i) nested lattice codes are shown to provide secrecy when interference is present, (ii) a secrecy sum rate upper bound is found for strong interference regime and (iii) it is proved that under very strong interference and a symmetric setting, the gap between the achievable sum rate and the upper bound is constant with respect to transmission powers.

We consider a communication scenario where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine attacker. Hence for secure communication, two requirements must be met simultaneously: the transmitted message must be kept secret, and a Byzantine attack must be detected reliably. Both a discrete noiseless adder model with the relay receiving the real sum of two signals and a Gaussian model are considered. In both models, the loss in rate due to Byzantine detection can be made arbitrarily small. For the discrete adder model, we show that the probability that the adversary wins decreases exponentially with the number of channel uses. For the Gaussian model, we show that this probability decreases exponentially with the square root of the number of channel uses. The rate derived in this paper is the strong secrecy rate, and the rate loss incurred due to the untrusted and Byzantine relay is measured with respect to the achievable secrecy rate when the relay is untrusted but honest. The result is obtained via a careful combination of the algebraic manipulation detection (AMD) code, the linear wire-tap code constructed from low density parity check (LDPC) code, randomly generated wire-tap code and for the Gaussian model the lattice code.

In this work, we consider achievable secrecy rates for symmetric K-user (K ges 3) interference channels with confidential messages. We find that nested lattice codes and layered coding are useful in providing secrecy for these channels. Achievable secrecy rates are derived for very strong interference. In addition, we derive the secure degrees of freedom for a range of channel parameters. As a by-product of our approach, we also demonstrate that nested lattice codes are useful for K-user symmetric interference channels without secrecy constraints in that they yield higher degrees of freedom than previous results.

We consider a source-destination pair that can communicate only through an unauthenticated intermediate relay node. In this two-hop communication scenario, where the cooperation from the relay node is essential, we investigate whether achieving non-zero secrecy rate is possible. Specifically, we treat the relay node as an eavesdropper from whom the source information needs to be kept secret, despite the fact that its cooperation in relaying this information is needed. We find that a positive secrecy rate is indeed achievable, with the aid of the destination node or an external node that jams the relay, i.e., by cooperative jamming. We derive an upper bound on the secrecy rate by means of an eavesdropper-relay separation argument. We remark that this upper bound is the first of its kind in Gaussian channels with cooperative jamming. The upper bound is strictly smaller than the channel capacity without secrecy constraints. The achievable secrecy rates are found using stochastic encoding and compress-and-forward at the relay. Numerical results show that the gap between the bound and the achievable rate is small when the relay's power is larger than the power of the jammer and the source. In essence, this paper shows that a cooperative jammer enables secure communication to take place using an untrusted relay which would be otherwise impossible.

This paper addresses the joint estimator and power optimization problem for a sensor network whose mission is to estimate an unknown parameter. We assume a two-hop network where each sensor collects observations from the source that transmits the quantity to be estimated, then amplifies and forwards its observations to a fusion center. The fusion center combines the observations using a Linear Minimum Mean Squared Error (LMMSE) estimator. We study the scenario where multiple parallel channels are available between the source and each sensor as well as between the sensors and the fusion center. We find the global optimal power allocation and estimator design for this network model. We present two practical scenarios of interest that utilize spatial and temporal diversity for which this solution applies, namely, a clustered network model and a single cluster model with an ergodic fading channel.

We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. A class of relay channels with orthogonal components is considered and an upper bound on the secrecy rate is derived. For the class of relay channels in consideration, we prove the relay and the eavesdropper can be separated to obtain an ‘enhanced’ channel in terms of secrecy capacity. We then consider two special cases of this channel model: (i) the Gaussian orthogonal relay channel, and (ii) the Gaussian Cover-Kim deterministic relay channel. For the former, the upper bound found is tighter than the previously known bound. For the latter, we show that the bound yields the secrecy capacity when the source-destination link is not worse than the source-relay link. This second case also provides the first example where secrecy capacity is achieved with compress and-forward at the relay.