Legitimate Receiver Research Articles

Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels

In this paper, we study the secrecy precoding problem for a cognitive multiple-input–multiple-output multiple-eavesdropper (MIMOME) wiretap system. The problem is studied with an artificial noise (AN)-aided precoding scheme. First, we place AN in the null space of the legitimate receiver's channel matrix and formulate a secrecy rate maximization (SRM) problem, which is subject to both an interference power constraint imposed to protect the primary user (PU) and a maximum transmit power constraint available for the secondary transmitter. Second, we drop the null space constraint and reformulate the SRM problem. Because the formulated SRM problems naturally constitute difference-convex-type programming problems, we solve them by employing a successive convex approximation method, where the nonconvex parts of each problem are approximated by their first-order Taylor expansion. Thus, the SRM problems can be iteratively solved through successive convex programming of their convexified versions. Results show that our algorithms can achieve a satisfactory solution with guaranteed convergence.

Secure robust relay beamforming: a convex conic approximation approach

In this study, the problem of secure robust relay beamforming for peer-to-peer networks in the presence of eavesdroppers has been optimised and relaxed by assuming the imperfect knowledge of eavesdroppers’ channel state information (CSI). Since the wiretap CSI is imperfect at its legitimate transmitter and receiver, it is a critical issue to make the optimisation problem robust against the channel uncertainty. The authors’ optimisation problem aims to maximise the probabilistic secrecy rate that is subject to keeping the probability of the transmission power of the relays below a specific threshold. The problem is shown to be non-convex in its original form since the outage probability constraint does not admit a closed-form expression and it is a non-deterministic polynomial complete problem. They have presented three novel stochastic methods to handle the outage probability constraint. It has been shown that after some relaxation and randomisation, the problem can be represented as a convex optimisation problem which can be efficiently solved using interior point methods. Simulation results have been presented to verify the advantages of their methods.

Strong Secrecy Capacity of a Class of Wiretap Networks

This paper considers a special class of wiretap networks with a single source node and K sink nodes. The source message is encoded into a binary digital sequence of length N, divided into K subsequences, and sent to the K sink nodes respectively through noiseless channels. The legitimate receivers are able to obtain subsequences from arbitrary μ 1 = K α 1 sink nodes. Meanwhile, there exist eavesdroppers who are able to observe subsequences from arbitrary μ 2 = K α 2 sink nodes, where 0 ≤ α 2 < α 1 ≤ 1 . The goal is to let the receivers be able to recover the source message with a vanishing decoding error probability, and keep the eavesdroppers ignorant about the source message. It is clear that the communication model is an extension of wiretap channel II. Secrecy capacity with respect to the strong secrecy criterion is established. In the proof of the direct part, a codebook is generated by a randomized scheme and partitioned by Csiszár’s almost independent coloring scheme. Unlike the linear network coding schemes, our coding scheme is working on the binary field and hence independent of the scale of the network.

Secrecy Outage Probability of a Distributed Multi-Antenna Cooperative Communication System

A distributed multi-antenna cooperative communication system with amplify-and-forward mode for secure communication in the presence of an eavesdropper is considered. In the communication system, there is no direct communication link between the transmitter and the intended receiver, and all nodes except relay nodes are equipped with multi-antenna. The secrecy capacity of this multiple input multiple output multiple eavesdropper system is investigated. The communication security depends on whether the noise on wiretap channel is stronger than that on main channel or not. The secrecy outage behavior of the flat Rayleigh fading channel is discussed and a relation between the strength of the channel noise and the secrecy outage probability is obtained. It is demonstrated that the secrecy outage probability is closely related to the channel noise strength and the number of the relay nodes. The thresholds for the noises received by legitimate receiver and eavesdropper are suggested, which is useful to design the secure distributed multi-antenna cooperative communication system.

Secret-Key Agreement With Public Discussion Subject to an Amplitude Constraint

This paper considers the problem of secret-key agreement with public discussion subject to a peak power constraint $A$ on the channel input. The optimal input distribution is proved to be discrete with finite support. The result is obtained by first transforming the secret-key channel model into an equivalent Gaussian wiretap channel with better noise statistics at the legitimate receiver and then using the fact that the optimal distribution of the Gaussian wiretap channel is discrete. To overcome the computationally heavy search for the optimal discrete distribution, several suboptimal schemes are proposed and shown numerically to perform close to the capacity. Moreover, lower and upper bounds for the secret-key capacity are provided and used to prove that the secret-key capacity converges for asymptotic high values of $A$, to the secret-key capacity with an average power constraint $A^2$. Finally, when the amplitude constraint A is small ($A \to 0$), the secret-key capacity is proved to be asymptotically equal to the capacity of the legitimate user with an amplitude constraint A and no secrecy constraint.

Achievable Rates of Secure Transmission in Gaussian MISO Channel With Imperfect Main Channel Estimation

A Gaussian multiple-input single-output (MISO) fading channel is considered. We assume that the transmitter, in addition to the statistics of all channel gains, is aware instantaneously of a noisy version of the channel to the legitimate receiver. On the other hand, the legitimate receiver is aware instantaneously of its channel to the transmitter, whereas the eavesdropper instantaneously knows all channel gains. We evaluate an achievable rate using a Gaussian input without indexing an auxiliary random variable. A sufficient condition for beamforming to be optimal is provided. When the number of transmit antennas is large, beamforming also turns out to be optimal. In this case, the maximum achievable rate can be expressed in a simple closed form and scales with the logarithm of the number of transmit antennas. Furthermore, in the case when a noisy estimate of the eavesdropper’s channel is also available at the transmitter, we introduce the SNR difference and the SNR ratio criterions and derive the related optimal transmission strategies and the corresponding achievable rates.

A Half-Duplex Self-Protection Jamming Approach for Improving Secrecy of Block Transmissions in Underwater Acoustic Channels

Block transmissions are commonly used in underwater acoustic communications due to the large delay spread of the underlying channels. In this paper, we propose a novel jamming protocol based on the half-duplex nature of the underwater transceivers and the block-based transmission structure, taking advantage of the large propagation delays of underwater acoustic channels to create interference at the eavesdropper without affecting the reception of the intended user. This half-duplex jamming protocol acts like a self-protection scheme, which does not need any helpers but instead relies on the legitimate receiver itself to transmit jamming signals for the improvement of secrecy rate. The simulation results evaluate the secrecy rate improvement as a function of the eavesdropper locations.

The Henchman Problem: Measuring Secrecy by the Minimum Distortion in a List

We introduce a new measure of information-theoretic secrecy based on rate-distortion theory and study it in the context of the Shannon cipher system. Whereas rate-distortion theory is traditionally concerned with a single reconstruction sequence, in this paper, we suppose that an eavesdropper produces a list of $2^{nR_{\sf L}}$ reconstruction sequences and measure secrecy by the minimum distortion over the entire list. We show that this setting is equivalent to one in which an eavesdropper must reconstruct a single sequence, but also receives side information about the source sequence and public message from a rate-limited henchman (a helper for an adversary). We characterize the optimal tradeoff of secret key rate, list rate, and eavesdropper distortion. The solution hinges on a problem of independent interest: lossy compression of a codeword uniformly drawn from a random codebook. We also characterize the solution to the lossy communication version of the problem in which distortion is allowed at the legitimate receiver. The analysis in both the settings is greatly aided by a recent technique for proving source coding results with the use of a likelihood encoder.

Swift Jamming Attack on Frequency Offset Estimation: The Achilles’ Heel of OFDM Systems

Frequency offset (FO) refers to the difference in the operating frequencies of two radio oscillators. Failure to compensate for the FO may lead to decoding errors, particularly in OFDM systems. To correct the FO, wireless standards append a publicly known preamble to every frame before transmission. In this paper, we demonstrate how an adversary can exploit the known preamble structure of OFDM-based wireless systems, particularly IEEE802.11a/g/n/ac, to launch a very stealth (low energy/duty cycle) reactive jamming attack against the FO estimation mechanism. In this attack, the adversary quickly detects a transmitted OFDM frame and subsequently jams a tiny part of the preamble that is used for FO estimation at the legitimate receiver. By optimizing the energy and structure of the jamming signal and accounting for frame detection timing errors and unknown channel parameters, we empirically show that the adversary can induce a bit error rate close to $0.5$ , making the transmission practically irrecoverable. Such vulnerability to FO jamming exists even when the frame is shielded by efficient channel coding. We evaluate the FO estimation attack through simulations and USRP experimentation. We also propose three approaches to mitigate such an attack.

Secure Transmission Against Pilot Spoofing Attack: A Two-Way Training-Based Scheme

The pilot spoofing attack is one kind of active eavesdropping activities conducted by a malicious user during the channel training phase. By transmitting the identical pilot (training) signals as those of the legal users, such an attack is able to manipulate the channel estimation outcome, which may result in a larger channel rate for the adversary but a smaller channel rate for the legitimate receiver. With the intention of detecting the pilot spoofing attack and minimizing its damages, we design a two-way training-based scheme. The effective detector exploits the intrusive component created by the adversary, followed by a secure beamforming-assisted data transmission. In addition to the solid detection performance, this scheme is also capable of obtaining the estimations of both legitimate and illegitimate channels, which allows the users to achieve secure communication in the presence of pilot spoofing attack. The detection probability is evaluated based on the derived test threshold at a given requirement on the probability of false alarming. The achievable secrecy rate is utilized to measure the security level of the data transmission. Our analysis shows that even without any pre-assumed knowledge of eavesdropper, the proposed scheme is still able to achieve the maximal secrecy rate in certain cases. Numerical results are provided to show that our scheme could achieve a high detection probability as well as secure transmission.

Free-space optical channel estimation for physical layer security.

We present experimental data on message transmission in a free-space optical (FSO) link at an eye-safe wavelength, using a testbed consisting of one sender and two receiver terminals, where the latter two are a legitimate receiver and an eavesdropper. The testbed allows us to emulate a typical scenario of physical-layer (PHY) security such as satellite-to-ground laser communications. We estimate information-theoretic metrics including secrecy rate, secrecy outage probability, and expected code lengths for given secrecy criteria based on observed channel statistics. We then discuss operation principles of secure message transmission under realistic fading conditions, and provide a guideline on a multi-layer security architecture by combining PHY security and upper-layer (algorithmic) security.

Location-Based Beamforming for Enhancing Secrecy in Rician Wiretap Channels

We propose a new optimal Location-Based Beamforming (LBB) scheme for the wiretap channel, where both the main channel and the eavesdropper's channel are subject to Rician fading. In our LBB scheme the two key inputs are the location of the legitimate receiver and the location of the potential eavesdropper. Notably, our scheme does not require as direct inputs any channel state information of the main channel or the eavesdropper's channel, making it easy to deploy in a host of application settings in which the location inputs are known. Our beamforming solution assumes a multiple-antenna transmitter, a multiple-antenna eavesdropper, and a single-antenna receiver, and its aim is to maximize the physical layer security of the channel. To obtain our solution we first derive the secrecy outage probability of the LBB scheme in a closed-form expression that is valid for arbitrary values of the Rician K-factors of the main channel and the eavesdropper's channel. Using this expression we then determine the location-based beamformer solution that minimizes the secrecy outage probability. To assess the usefulness of our new scheme, and to quantify the value of the location information to the beamformer, we compare our scheme to other schemes, some of which do not utilize any location information. Our new beamformer solution provides optimal physical layer security for a wide range of location-based applications.

A reliable group key management scheme for broadcast encryption

A major challenge achieving scalable access control for a large number of subscribers in a public broadcast is to distribute key update messages reliably to all stateless receivers. However, in a public broadcast, the rekeying messages can be dropped or compromised during transmission over an insecure broadcast channel, or transmitted to receivers while they were off-line. In this study, we propose a novel group key management scheme. It features a mechanism to allow legitimate receivers to recover the current group key, even if they lose key update messages for long-term sessions. The scheme uses short hint messages and member computation. Performance analysis shows that the proposed scheme has the advantages of scalability and efficient rekeying compared to previous reliable group key distribution schemes. The proposed key management scheme targets a conditional access system in a media broadcast in which there is no feedback channel from receivers to the broadcasting station.

Physical-layer secrecy outage of spectrum sharing CR systems over fading channels

In this paper, we investigate the physical-layer secrecy outage performance of underlay spectrum sharing systems over Rayleigh and log-normal fading channels in the presence of one eavesdropper. In particular, the secondary transmitter sends data to the legitimate receiver under the constraints of the interference temperature at the primary receiver, while suffering the wiretap from the eavesdropper. Closed-form and approximated expressions are derived for the secrecy outage probability over Rayleigh and log-normal fading channels, respectively. The accuracy of our performance analysis is verified by simulation results.

Worst-Case Cooperative Jamming for Secure Communications in CIoT Networks.

The Internet of Things (IoT) is a significant branch of the ongoing advances in the Internet and mobile communications. Yet, the use of a large number of IoT devices can severely worsen the spectrum scarcity problem. The usable spectrum resources are almost entirely occupied, and thus, the increasing demands of radio access from IoT devices cannot be met. To tackle this problem, the Cognitive Internet of Things (CIoT) has been proposed. In a CIoT network, secondary users, i.e., sensors and actuators, can access the licensed spectrum bands provided by licensed primary users (such as cellular telephones). Security is a major concern in CIoT networks. However, the traditional encryption method at upper layers (such as symmetric and asymmetric ciphers) may not be suitable for CIoT networks since these networks are composed of low-profile devices. In this paper, we address the security issues in spectrum-leasing-based CIoT networks using physical layer methods. Considering that the CIoT networks are cooperative in nature, we propose to employ cooperative jamming to achieve secure transmission. In our proposed cooperative jamming scheme, a certain secondary user is employed as the helper to harvest energy transmitted by the source and then uses the harvested energy to generate an artificial noise that jams the eavesdropper without interfering with the legitimate receivers. The goal is to minimize the Signal to Interference plus Noise Ratio (SINR) at the eavesdropper subject to the Quality of Service (QoS) constraints of the primary traffic and the secondary traffic. We formulate the minimization problem into a two-stage robust optimization problem based on the worst-case Channel State Information of the Eavesdropper (ECSI). By using Semi-Definite Programming (SDP), the optimal solutions of the transmit covariance matrices can be obtained. Moreover, in order to build an incentive mechanism for the secondary users, we propose an auction framework based on the cooperative jamming scheme. The proposed auction framework jointly formulates the helper selection and the corresponding energy allocation problems under the constraint of the eavesdropper's SINR. By adopting the Vickrey auction, truthfulness and individual rationality can be achieved. Simulation results demonstrate the effective performance of the cooperative jamming scheme and the auction framework.

Secure Broadcasting With Imperfect Channel State Information at the Transmitter

We investigate the problem of secure broadcasting over fast fading channels with imperfect main channel state information (CSI) at the transmitter. In particular, we analyze the effect of the noisy estimation of the main CSI on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. Besides, we consider the realistic case where the transmitter is only aware of the statistics of the eavesdropper’s CSI and not of its channel’s realizations. First, we discuss the common message transmission case where the source broadcasts the same information to all the receivers, and we provide an upper and a lower bound on the ergodic secrecy capacity. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link and we prove that a nonzero secrecy rate can still be achieved even when the CSI at the transmitter is noisy. Then, we look at the independent messages case where the transmitter broadcasts multiple messages to the receivers, and each intended user is interested in an independent message. For this case, we present an expression for the achievable secrecy sum-rate and an upper bound on the secrecy sum-capacity and we show that, in the limit of large number of legitimate receivers $K$ , our achievable secrecy sum-rate follows the scaling law $\textbf{log} \left((1{-}\alpha)\textbf{log}(K)\right)$ , where $\alpha$ is the estimation error variance of the main CSI. The special cases of high SNR, perfect and no-main CSI are also analyzed. Analytical derivations and numerical results are presented to illustrate the obtained expressions for the case of independent and identically distributed Rayleigh fading channels.

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate $R_f$ . We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded , the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszar, and Korner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.

Cooperative jamming polar codes for multiple‐access wiretap channels

The authors study cooperative security in the physical layer of wireless systems based on the recently developed polar codes for multiple access channel (MAC). Specifically, the authors first consider the case of a m-user MAC with external eavesdropper. Using polar alignment, the authors formulate a discrete optimisation problem where security and reliability criteria can be handled separately over the bases of a set of deterministic binary matrices. A discrete algorithm with incrementally polynomial complexity is used to maximise the uniform sum secrecy rate of users. Moreover, the proposed coding scheme is shown to achieve strong security for any subset of users. The authors next examine the case of minimum number of cooperative helpers to fulfil a feasible secrecy rate requirement at the legitimate user. Here, a low-complexity suboptimal algorithm is presented with at most one helper more than the optimal solution. Using Tal–Sharov–Vardy implementation of MAC polar codes, secure polar coding is implemented for a 2-user Gaussian wiretap MAC channel. The upper and lower bound of block error probability are compared, respectively, at the legitimate receiver and the eavesdropper. The results demonstrate clearly that with sufficiently long block length, strong secrecy with respect to the eavesdropper is achieved, while block error probability approaches 0.5.

Interleaved Concatenated Coding for Secrecy in the Finite Blocklength Regime

We propose a systematic concatenated coding scheme based on the combination of interleaving with powerful channel codes and jamming for wireless secrecy under the practical assumption of codes in the finite blocklength regime. The basic idea lies in generating a short random key that is used to shuffle/interleave information at the source, Alice. This key is then sent to the legitimate receiver, Bob, during a brief period of advantageous communication over the eavesdropper Eve (e.g., due to more interference from a jammer). Finally, the key is decoded at Bob to properly deinterleave the original information. Bob receives a better quality version of the interleaving key, therefore having the needed advantage over Eve. Information reliability is provided by a strong inner code, while security against Eve results from the proper selection of the outer code and interference levels over the key. We propose a methodology for selection of the outer code with reliability and security constraints. For that, we introduce bit error complementary cumulative distribution function metrics, suitable for security and reliability analysis of error correcting codes.

Secrecy performance of MIMO Nakagami‐m wiretap channels with optimal TAS and different antenna schemes

AbstractTransmit antenna selection (TAS) in wiretap channels has arisen as a simple promising scheme to improve physical layer security. However, up to now, TAS schemes have aimed at maximising the instantaneous signal‐to‐noise ratio of the legitimate receiver, which by its essence is a sub‐optimal strategy from a secrecy point of view. In this paper, unlike previous works, we propose a novel TAS scheme for multiple‐input multiple‐output wiretap channels by exploiting full channel state information. The proposed scheme achieves higher secrecy performance by selecting an antenna that maximises the secrecy rate. In our analysis, we assume that the receiver (Rx) and the eavesdropper employ either selection combining (SC) or maximal‐ratio combining (MRC) to combine the received signals, and this results in four different receiver combining arrangements. By considering Nakagami‐m fading, secrecy performance is analysed. Specifically, closed‐form expressions for the secrecy outage probability are derived, which can be used as a quality of service metric. Moreover, an asymptotic analysis is carried out and the respective diversity/array gains are obtained. The ergodic secrecy rate is also investigated for the case of multiple‐input single‐output wiretap channels. Insightful discussions are attained from our analysis. For instance, it is shown that the performance gain of MRC over SC at the Rx does not depend on the number of antennas and combining scheme at the eavesdropper. More interestingly, we observe that such a performance gain is independent of the TAS scheme used at the transmitter (Tx). On the other hand, it is shown that the secrecy gap between SC and MRC at the eavesdropper is independent of the number of antennas at the Tx, but it depends on the number of antennas at the Rx. Finally, it is demonstrated that the diversity gain is the same for all antenna configurations. Copyright © 2016 John Wiley & Sons, Ltd.