Secrecy Constraints Research Articles

Maximum Secrecy Throughput of MIMOME FSO Communications With Outage Constraints

In this paper, we consider a scenario where two multiple-aperture legitimate nodes (Alice and Bob) communicate by means of free-space optical communication in the presence of a multiple-aperture eavesdropper (Eve), which is subject to pointing errors. Two different schemes are considered depending on the availability of channel state information (CSI) at Alice: 1) the adaptive scheme, where Alice possesses the instantaneous CSI with respect to Bob and 2) the fixed-rate scheme, where such information is not available at Alice. The performance of the aforementioned schemes is evaluated in terms of a recently proposed metric named effective secrecy throughput (EST), which encompasses both the reliability and secrecy constraints. By constraining the system to operate below a given maximum allowed secrecy outage probability, we evaluate the EST analytically and through numerical results, showing that the use of multiple apertures at Alice is very important toward achieving the optimal EST.

Secure Communications for the Two-User Broadcast Channel With Random Traffic

In this paper, we study the stability region of the two-user broadcast channel (BC) with bursty data arrivals and security constraints. It is assumed that one of the receivers has a secrecy constraint, i.e., its packets need to be kept secret from the other receiver, which is defined based on signal to interference noise ratio. The receiver with secrecy constraint has full-duplex capability to send a jamming signal for improving its service rate. The stability region of the two-user BC with secrecy constraint is characterized for the general decoding case. Then, assuming two different decoding schemes, the respective stability regions are derived. The full-duplex operation of receiver results in self-interference, and the effect of imperfect self-interference cancelation on the stability region is also investigated. The stability region of the BC with a secrecy constraint, where the receivers do not have full duplex capability can be obtained as a special case of the results derived in this paper. In addition, the paper considers the problem of maximizing the saturated throughput of the queue for which there is no secrecy constraint under minimum service guarantees for the other queue. The results provide new insights on the effect of the secrecy constraint on the stability region of the BC. It is found that the stability region with secrecy constraint is sensitive to the degree of self-interference cancelation.

Strong Secrecy for Interference Channels Based on Channel Resolvability

Interference channels with confidential messages are studied under strong secrecy constraints, based on the framework of channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is above the resolution of its corresponding wiretapped channel, strong secrecy can be guaranteed. The information-spectrum method introduced by Han and Verdu is generalized to an arbitrary interference channel to obtain a direct channel resolvability result as a first step. For stationary and memoryless channels with discrete output alphabets, the results show that the achievable rates under weak and strong secrecy constraints are the same. This result is then generalized to channels with continuous output alphabets by deriving a reverse direction of Pinsker’s inequality to bound the secrecy measure from above by a function of the variational distance of relevant distributions. As an application, Gaussian interference channels are studied in which the agreement between the best known weak and strong secrecy rate regions also appear. Following the footsteps of Csiszar, Hayashi and of Bloch and Laneman, these results provide further evidence that channel resolvability is a powerful and general framework for strong secrecy analysis in multiuser networks.

Energy Efficient Beamforming for Multi-User Transmission in Cognitive Radio Networks With Secrecy Constraints

This paper investigates the energy efficiency (EE) maximization problem with secrecy constraints for a multi-user underlay cognitive radio network (CRN), where each single-antenna cognitive user is surrounded by a multi-antenna eavesdropper user. Specifically, we aim to maximize the EE of the cognitive base station (CBS), which is defined as the ratio of the achievable rate to total power consumption, under the quality-of-service requirement of primary user, the secrecy rate (SR) constraint of CRN and the transmit power limitation of CBS. The formulated optimization problem is nonconvex and nontrivial due to the fractional form of EE and the subtractive form of SR. To solve this complex non-convex problem, we first convert the original fractional form of the EE into an equivalent subtractive form, and then adopt the difference of two-convex functions (D.C.) method to approximate the subtractive form of SR into a convex one. Finally, a convergent iterative algorithm is proposed to obtain the optimal solution of the considered EE maximization problem. Numerical results showing the effectiveness of the proposed algorithm are given.

Secure Transmission on the Two-Hop Relay Channel With Scaled Compute-and-Forward

In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

On the Tradeoff Region of Secure Exact-Repair Regenerating Codes

We consider the $(n,k,d,\ell )$ secure exact-repair regenerating code problem, which generalizes the $(n,k,d)$ exact-repair regenerating code problem with the additional constraint that the stored file needs to be kept information-theoretically secure against an eavesdropper, who can access the data transmitted to regenerate a total of $\ell $ different failed nodes. For all known results on this problem, the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi, and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general, these existing results suggest a phase-change-like behavior, i.e., enforcing a secrecy constraint ( $\ell \geq 1$ ) immediately reduces the tradeoff region to one with a single corner point. In this paper, we first show that when the secrecy parameter $\ell $ is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when $\ell $ is small, we show that the tradeoff region can in fact have multiple corner points. In particular, we establish a precise characterization of the tradeoff region for the (7, 6, 6, 1) problem, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened.

Optimal Parameter Encoding Based on Worst Case Fisher Information Under a Secrecy Constraint

In this letter, optimal deterministic encoding of a uniformly distributed scalar parameter is performed in the presence of an eavesdropper. The objective is to maximize the worst case Fisher information of the parameter at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain level. The eavesdropper is modeled to employ the linear minimum MSE estimator based on the encoded version of the parameter. First, the optimal encoding function is derived when there exist no secrecy constraints. Next, to obtain the solution of the problem in the presence of the secrecy constraint, the form of the encoding function that maximizes the MSE at the eavesdropper is explicitly derived for any given level of worst case Fisher information. Then, based on this result, a low-complexity algorithm is provided to calculate the optimal encoding function for the given secrecy constraint. Finally, numerical examples are presented.

On the Design of Secure Non-Orthogonal Multiple Access Systems

This paper proposes a new design of non-orthogonal multiple access (NOMA) under secrecy considerations. We focus on a NOMA system where a transmitter sends confidential messages to multiple users in the presence of an external eavesdropper. The optimal designs of decoding order, transmission rates, and power allocated to each user are investigated. Considering the practical passive eavesdropping scenario where the instantaneous channel state of the eavesdropper is unknown, we adopt the secrecy outage probability as the secrecy metric. We first consider the problem of minimizing the transmit power subject to the secrecy outage and quality of service constraints, and derive the closed-form solution to this problem. We then explore the problem of maximizing the minimum confidential information rate among users subject to the secrecy outage and transmit power constraints, and provide an iterative algorithm to solve this problem. We find that the secrecy outage constraint in the studied problems does not change the optimal decoding order for NOMA, and one should increase the power allocated to the user whose channel is relatively bad when the secrecy constraint becomes more stringent. Finally, we show the advantage of NOMA over orthogonal multiple access in the studied problems both analytically and numerically.

Individual Secrecy for Broadcast Channels With Receiver Side Information

This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two receivers which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) are characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a square with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate; making secrecy more affordable but still acceptable to the end user.

Multi-Slot Spectrum Sensing Schedule and Transmitted Energy Allocation in Harvested Energy Powered Cognitive Radio Networks Under Secrecy Constraints

Herein, the authors consider harvested energy powered cognitive radio networks (CRNs) in which harvested energy is stored in a rechargeable battery which has finite capacity. In addition, a practical scenario in which the amount of harvested power is finite is taken into account. Cognitive users (CUs) opportunistically access a licensed channel (or primary channel); meanwhile, it should be ensured that their confidential communications are not leaked to an eavesdropper. We investigate an optimal spectrum sensing schedule and the optimal amount of transmission energy for the CUs in each processing time slot. In particular, at the beginning of each time slot, based on the remaining energy in the battery, CU transmitter decides either: 1) to be active to sense the channel and transmit its data if the channel is found vacant or 2) to stay inactive during the current time slot in order to save energy and wait for more incoming energy for use in the next time slots. The decision is based on expected secrecy transmission rate calculated for both cases over subsequent $K$ time slots. The proposed scheme aims to improve long-term secrecy transmission rate of CRNs in comparison with a conventional scheme where the decision for the current time slot is made to maximize current secrecy transmission rate without considering any future reward.

On the Secrecy Capacity Region of the Two-User Symmetric Z Interference Channel With Unidirectional Transmitter Cooperation

In this paper, the role of unidirectional limited rate transmitter cooperation is studied for the two-user symmetric Z interference channel (Z-IC) with secrecy constraints at the receivers, in achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy . First, the problem is studied under the linear deterministic model. A novel scheme for partitioning the encoded messages and outputs based on the relative strengths of the signal and interference is proposed. The partitioning reveals the side information that needs to be provided to the receiver and facilitates the development of tight outer bounds on the secrecy capacity region. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings. The insights obtained from the deterministic model are used to derive inner and outer bounds on the secrecy capacity region of the two-user Gaussian symmetric Z-IC. The achievable scheme for the Gaussian model uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. For the Gaussian case, the secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.

Coding Schemes for Achieving Strong Secrecy at Negligible Cost

We study the problem of achieving strong secrecy over wiretap channels at negligible cost , in the sense of maintaining the overall communication rate of the same channel without secrecy constraints. Specifically, we propose and analyze two source-channel coding architectures, in which secrecy is achieved by multiplexing public and confidential messages. In both cases, our main contribution is to show that secrecy can be achieved without compromising communication rate and by requiring only randomness of asymptotically vanishing rate. Our first source-channel coding architecture relies on a modified wiretap channel code, in which randomization is performed using the output of a source code. In contrast, our second architecture relies on a standard wiretap code combined with a modified source code termed uniform compression code , in which a small shared secret seed is used to enhance the uniformity of the source code output. We carry out a detailed analysis of uniform compression codes and characterize the optimal size of the shared seed.

Improving the Physical Layer Security in Cooperative Networks with Multiple Eavesdroppers

Physical layer security is an efficient technique to realize security in wireless network without relying on conventional cryptographic techniques. In cooperative networks with secrecy constraints, joint relay and jammer selection is a promising approach for improving the security of wireless communications. We need to apply more techniques in order to achieve more effective security in contrast to the mentioned method. In this paper, we propose three techniques to increase the secrecy as follows: Firstly, we introduce a new criterion which decreases the rate at the eavesdroppers. Next, a new relay selection schemes are proposed, where two of the available relays are selected for data transmission. Therefore, the secrecy rate is increased considerably. Finally, we propose a sub-optimal power allocation solution for jammer nodes. Sub-optimal power of the jammer nodes vary according to the type of scenario, location of the eavesdroppers, and the destination. The sub-optimal power allocation to the jammer nodes causes more eavesdroppers confusion. As a result, the total secrecy rate is increased. Simulation and analytical results demonstrate the performance improvement of the proposed techniques.

Achieving Secrecy Capacity of the Wiretap Channel and Broadcast Channel With a Confidential Component

The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a “strong secrecy constraint” can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csiszar and Korner, achieving the entire capacity region of this communication model.

Individual Secrecy for the Broadcast Channel

This paper studies the problem of secure communications over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system.

Strong Secrecy for Cooperative Broadcast Channels

A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semi-deterministic and physically degraded BCs, and the results are compared with those of the corresponding BCs without a secrecy constraint. Blackwell and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.

Arbitrarily Varying Wiretap Channels With Type Constrained States

Determining a single-letter secrecy-capacity formula for the arbitrarily varying wiretap channel (AVWTC) is an open problem largely because of two main challenges. Not only does it capture the difficulty of the compound wiretap channel (another open problem), it also requires that secrecy is ensured with respect to exponentially many possible channel state sequences. By extending the strong soft-covering lemma, recently derived by the authors, to the heterogeneous scenario, this paper accounts for the exponential number of secrecy constraints while only imposing single-letter constraints on the communication rate. Through this approach, we derive a single-letter characterization of the correlated-random (CR)-assisted semantic-security (SS) capacity of an AVWTC with a type constraint on the allowed state sequences. The allowed state sequences are the ones in a typical set around a single constraining type. The stringent SS requirement is established by showing that the mutual information between the message and the eavesdropper’s observations is negligible even when maximized over all message distributions, choices of state sequences, and realizations of the CR-code. Both the achievability and the converse proofs of the type-constrained coding theorem rely on stronger claims than actually required. The direct part establishes a novel single-letter lower bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained by any convex and closed set of state probability mass functions. This bound achieves the best known single-letter secrecy rates for a corresponding compound wiretap channel over the same constraint set. In contrast to other single-letter results in the AVWTC literature, this paper does not assume the existence of a best channel to the eavesdropper. Instead, SS follows by leveraging the heterogeneous version of the strong soft-covering lemma and a CR-code reduction argument. Optimality is a consequence of a max-inf upper bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained to any collection of type-classes. When adjusted to the aforementioned compound WTC, the upper bound simplifies to a max–min structure, thus strengthening the previously best known single-letter upper bound by Liang et al. that has a min–max form. The proof of the upper bound uses a novel distribution coupling argument. The capacity formula shows that the legitimate users effectively see an averaged main channel, while security must be ensured versus an eavesdropper with perfect channel state information. An example visualizes our single-letter results, and their relation to the past multi-letter secrecy-capacity characterization of the AVWTC is highlighted.

On the Capacity of the Two-User Symmetric Interference Channel With Transmitter Cooperation and Secrecy Constraints

This paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy, in the two-user Gaussian symmetric interference channel (IC). First, the problem is studied in the symmetric linear deterministic IC (SLDIC) setting, and achievable schemes are proposed, based on interference cancelation, relaying of the other user's data bits, and transmission of random bits. In the proposed achievable scheme, the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model parameters. Outer bounds on the secrecy rate are also derived, using a novel partitioning of the encoded messages and outputs depending on the relative strength of the signal and the interference. The partitioning helps to bound certain negative entropy terms, leading to a tractable outer bound. The inner and outer bounds are derived under all possible parameter settings. It is found that, for some parameter settings, the inner and outer bounds match, yielding the capacity of the SLDIC under transmitter cooperation and secrecy constraints. In some other scenarios, the achievable rate matches with the capacity region of the two-user SLDIC without secrecy constraints derived by Wang and Tse; thus, the proposed scheme offers secrecy for free, in these cases. Inspired by the achievable schemes and outer bounds in the deterministic case, achievable schemes and outer bounds are derived in the Gaussian case. The proposed achievable scheme for the Gaussian case is based on Marton's coding scheme and stochastic encoding along with dummy message transmission. One of the key techniques used in the achievable scheme for both the models is interference cancelation, which simultaneously offers two seemingly conflicting benefits: it cancels interference and ensures secrecy. Many of the results derived in this paper extend to the asymmetric case also. The results show that limited transmitter cooperation can greatly facilitate secure communications over two-user ICs.

Wireless Power Transfer and Cooperative Jamming for Secrecy Throughput Maximization

This letter studies the secure communication between a wireless powered source node and a destination node in the presence of multiple eavesdroppers. We propose a hybrid base station (BS) scheme where the hybrid BS first transfers wireless power to the source and then performs cooperative jamming while the source transmits the information signal using the harvested energy. We maximize the secrecy throughput by jointly optimizing the time allocation, source transmit power, and redundancy rate under the secrecy constraint and transmit power constraint. We transform the secrecy throughput maximization problem into a convex optimization problem and obtain the optimal solutions efficiently. Numerical results illustrate that our solution is superior to other benchmark schemes.

An Analysis on Secure Communication in Millimeter/Micro-Wave Hybrid Networks

The secrecy outage of millimeter wave (mmWave) overlaid micro-wave ( $\mu $ Wave) networks under the impact of blockages is analyzed, and closed form as well as integral expressions are provided. Specifically, using a network model that accounts for uncertainties both in node locations and blockages, we characterize the conditional connection outage probability and the secrecy outage probability of hybrid networks with multiple eavesdroppers under basic factors, such as density of eavesdropping nodes, antenna gain, and blockage density. The upper and lower bounds of the conditional secrecy outage probability for both the line-of-sight and non-line-of-sight links are derived. As a desirable side effect, certain factors, such as blockages and reduced antenna gain, can decrease the secrecy outage probability in mmWave networks. This can be considered as a tradeoff between outage capacity and secrecy outage capacity with respect to blockages. Hence, blockages that have been proved to be detrimental to achieving higher data rates in mmWave systems, can be helpful for systems with secrecy constraints. Finally, we have shown the coexistence of mmWave and $\mu $ Wave networks from a secrecy perspective.