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The topological interference management (TIM) problem refers to the study of the $K$ -user partially connected interference networks with no channel state information at the transmitters (CSIT), except for the knowledge of network topology. In this paper, we study the TIM problem with confidential messages (TIM-CM), where message confidentiality must be satisfied in addition to reliability constraints. In particular, each transmitted message must be decodable at its intended receiver and remain confidential at the remaining $(K-1)$ receivers. Our main contribution is to present a comprehensive set of results for the TIM-CM problem by studying the symmetric secure degrees of freedom (SDoF). To this end, we first characterize necessary and sufficient conditions for feasibility of positive symmetric SDoF for any arbitrary topology. We next present two achievable schemes for the TIM-CM problem: For the first scheme, we use the concept of secure partition and, for the second one, we use the concept of secure independent sets. We also present outer bounds on symmetric SDoF for any arbitrary network topology. Using these bounds, we characterize the optimal symmetric SDoF of all $K=2$ -user and $K=3$ -user network topologies. [ABSTRACT FROM AUTHOR]

Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El Gamal and the method of output statistics of random binning. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that derives an inner bound on the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels. [ABSTRACT FROM AUTHOR]

Delivering confidential messages in wireless network is gaining continuous attraction as a fundamental building block for the Internet of things (IoT). This paper overviews the confidential message transmission techniques in broadcast channel (BC) where a transmitter serves multiple users by delivering confidential messages to their intended users. Each confidential message must be prevented from extracting its information by any unintended users. First, we consider a basic network consisting of two users. In the two-user BC, the secret dirty paper coding (S-DPC) achieves the secrecy capacity region. However, since the DPC requires a high computational complexity for characterizing the capacity region, two sub-optimal transmission techniques with low complexities are explained. Second, we extend our discussion to the network including more than two users. For $K$ -user BC with confidential messages, the optimal transmission scheme and the secrecy capacity region have not yet been derived. Instead of presenting the optimal scheme, we explain two sub-optimal transmission techniques and compare their features and performances. In conclusion, we discuss the open problems in the confidential message transmission for networks with more than two users.

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$. For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM. [ABSTRACT FROM AUTHOR]

We consider the two-user multiple-input multiple-output (MIMO) interference channel with confidential messages (ICCM). We determine the exact secure degrees of freedom (s.d.o.f.) region for the symmetric case of $M$ antennas at both transmitters and $N$ antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the interference channel with no secrecy constraints, and vector extensions of the secrecy penalty and role of a helper lemmas. For the achievability, we first show that the s.d.o.f. region is a four-vertex polytope. For the sum s.d.o.f. point, we propose a novel achievable scheme for the $2 \times 2$ ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any $M$ and $N$ by proper vector space operations. We achieve the other non-trivial extreme polytope points by employing one of the transmitters as a deaf helper for assisting the secure transmission of the other user. We present simplified achievable schemes for the special case of time-varying MIMO ICCM. The achievable schemes, in this case, make use of the time-varying nature of the channel to construct vector-space alignment counterpart of the real interference alignment used in the static channel case. [ABSTRACT FROM AUTHOR]

We consider the multiple-input multiple-output (MIMO) wiretap channel under a minimum receiver-side power constraint in addition to the usual maximum transmitter-side power constraint. This problem is motivated by energy harvesting communications with wireless energy transfer, where an added goal is to deliver a minimum amount of energy to a receiver in addition to delivering secure data to another receiver. In this paper, we characterize the exact secrecy capacity of the MIMO wiretap channel under transmitter and receiver-side power constraints. We first show that solving this problem is equivalent to solving the secrecy capacity of the wiretap channel under a double-sided correlation matrix constraint on the channel input. We show the converse by extending the channel enhancement technique to our case. We present two achievable schemes that achieve the secrecy capacity: the first achievable scheme uses a Gaussian codebook with a fixed mean, and the second achievable scheme uses artificial noise (or cooperative jamming) together with a Gaussian codebook. The role of the mean or the artificial noise is to enable energy transfer without sacrificing from the secure rate. This is the first instance of a channel model where either the use of a mean signal or the use of channel prefixing via artificial noise is strictly necessary for the MIMO wiretap channel. We then extend our work to consider a maximum receiver-side power constraint instead of a minimum receiver-side power constraint. This problem is motivated by cognitive radio applications, where an added goal is to decrease the received signal energy (interference temperature) at a receiver. We further extend our results to: requiring receiver-side power constraints at both receivers; considering secrecy constraints at both receivers to study broadcast channels with confidential messages; and removing the secrecy constraints to study the classical broadcast channel. [ABSTRACT FROM PUBLISHER]

We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the effects of a trusted relay node on the secrecy of the broadcast channel by considering the model of relay broadcast channel with confidential messages (RBC-CM). Inner and outer bounds on the capacity-equivocation region of the RBC-CM are provided, and the capacity results are further explained via a degraded Gaussian example, which we call the degraded Gaussian relay broadcast channel with one common and one confidential messages. Numerical results show that this trusted relay node helps to enhance the security of the Gaussian broadcast channel with one common and one confidential messages. [ABSTRACT FROM PUBLISHER]

In coding schemes for the wire-tap channel or for broadcast channels with confidential messages, it is well-known that the sender needs to use stochastic encoding to avoid information about the transmitted confidential message from being leaked to an eavesdropper. In this paper, we investigate the tradeoff between the rate of random numbers needed to realize the stochastic encoding and the rates of common, private, and confidential messages. For the direct theorem, we use the superposition coding scheme for the wire-tap channel, recently proposed by Chia and El Gamal, and its strong security is proved. The matching converse theorem is also established. Our result clarifies that a combination of ordinary stochastic encoding and channel prefixing by channel simulation is suboptimal. [ABSTRACT FROM AUTHOR]

The cognitive interference channel with confidential messages (CICC) proposed by Liang et al. is investigated. When the security is considered in coding systems, it is well-known that the sender needs to use a stochastic encoding to avoid the information about the transmitted confidential message to be leaked to an eavesdropper. For the CICC, the tradeoff between the rate of the random number to realize the stochastic encoding and the communication rates is investigated, and the optimal tradeoff is completely characterized. [ABSTRACT FROM AUTHOR]

The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner's random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the two-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper, or the K-receiver BC without a wiretapper. [ABSTRACT FROM PUBLISHER]

Like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. It is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the noncognitive receiver (receiver 1) should decode only message 1. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. In this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. The capacity-equivocation region for the Gaussian cognitive interference channel is also obtained explicitly. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem. [ABSTRACT FROM AUTHOR]

The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is. seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy "jam" the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system. [ABSTRACT FROM AUTHOR]

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic 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 fast-fading 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 sum-capacity for transmitting independent messages. For the case of fast-fading 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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a secure cognitive radio network (CRN), which deploys non-orthogonal multiple access (NOMA) to deliver a mixed multicast and unicast traffic to the intended receivers, while keeping them secret from the eavesdroppers. This model represents a cognitive interference channel with an external eavesdropper (CIC-EE). In this model, there are one pair of primary nodes, one pair of secondary nodes, and an external eavesdropper. The primary transmitter multicasts a confidential message to both primary and secondary receivers, while trying to keep it secret from the eavesdropper. The secondary transmitter helps the primary user to deliver its message in exchange of transmission opportunity. The secondary message is unicasted to the secondary receiver, while concealing it from both primary receiver and the eavesdropper. This scenario models a NOMA-based overlay cognitive radio paradigm with an external eavesdropper. For this scenario, the achievable rate-equivocation region is obtained and its optimality is shown for a class of degraded channels. Then, the results obtained for the discrete memoryless channel are extended to the Gaussian channel model. Furthermore, by deploying numerical examples, a comparison is made between the proposed secure NOMA-based scheme, its orthogonal multiple access (OMA) based counterpart, and a cognitive interference channel without an external eavesdropper. It is shown that the NOMA-based method achieves significantly higher rates than its OMA based counterpart. [ABSTRACT FROM AUTHOR]