Secrecy Constraints Research Articles

Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback.

For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key. By secret sharing, any capacity-achieving coding scheme for the AWGN channel without feedback can be secure by itself, which indicates that the capacity of the same model without the secrecy constraint also affords an achievable secrecy rate to the AWGN channel with an eavesdropper and feedback. Then it is natural to ask: is the secret key-based feedback scheme still the optimal scheme for the AWGN multiple-access channel (MAC) with an external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose the optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. This paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of an external eavesdropper and channel feedback.

Secretive Coded Caching With Nonuniform Demands in Fog Radio Access Networks

In this letter, we investigate the problem of secretive coded caching in fog radio access networks (F-RANs), aiming at minimizing the average backhaul rate under nonuniform file popularity distribution. Firstly, a two-layer placement scheme which jointly considers secrecy constraints and cache resources in the network is designed. Next, a two-stage delivery scheme which utilizes the network architecture characteristics and exploits the redundancy in user demands is designed. By integrating the above two schemes, a novel secretive coded caching scheme is proposed. Finally, we derive the expression of the average backhaul rate and evaluate the performance of the proposed scheme via simulations. Simulation results show that our proposed scheme outperforms the state of the art in terms of backhaul rate reduction.

Deep-Reinforcement-Learning-Based IRS for Cooperative Jamming Networks Under Edge Computing

Effective energy design and secure communications are critical in the Internet of Things (IoT). A cooperative jamming (CJ) scheme based on deep reinforcement learning (DRL) is proposed for intelligent reflecting surface (IRS) aided secure cooperative network with eavesdroppers. Our goal is to maximize the average secrecy rate, or energy efficiency with secrecy constraints by jointly optimising the transmit, jamming beamforming matrices and IRS phase-shift matrix. In order to figure out the challenging non-convex optimization problem, the deep deterministic policy gradient (DDPG) optimization algorithm is proposed to solve the energy efficiency maximization problem. In order to speed up task processing and reduce service delay, the edge computing server is employed for DRL training to improve computing speed and promote secure communication efficiency. By taking advantages of the features of proximity to end devices and computing resources, the edge devices provide a low latency efficient training support to the legal users and real-time control to the IRS units. By this way, a high security and low energy consumption IoT system is built. Numerical results show that the novel scheme improves the secrecy rate and energy efficiency compared with the benchmark scheme.

Optimal signal design for coherent detection of binary signals in Gaussian noise under power and secrecy constraints

The problem of optimal signal design for coherent detection of binary signals in Gaussian noise is revisited under power and secrecy constraints. In particular, the aim is to select the binary transmitted signals in an optimal manner so that the probability of error is minimized at an intended receiver while the probability of error at an eavesdropper is maintained above a threshold value and the signal powers are limited. It is shown that an optimal solution exists in the form of antipodal signaling along the eigenvector corresponding to the solution of a maximum (possibly generalized) eigenvalue problem, which is specified explicitly based on the channel coefficient matrices and the noise covariance matrices at the intended receiver and the eavesdropper. Furthermore, optimal signal design can be performed in an efficient manner by solving a semidefinite programming (SDP) relaxation followed by a matrix rank-one decomposition. Numerical examples are provided to illustrate optimal solutions for three different but exhaustive cases.

Secrecy Outage Analysis of Pilot-Assisted URLLC Systems With Randomly Distributed Eavesdroppers

In this letter, we focus on the secrecy outage analysis of ultra-reliable low-latency communication (URLLC) systems in the presence of randomly located eavesdroppers and imperfect channel state information (CSI). To be specific, the secrecy outage probability (SOP) of pilot-assisted URLLC system is investigated, which is defined as the probability that either the reliability const-raint or the secrecy constraint cannot be satisfied when the packet is delivered with a target data rate and blocklength. In fact, the definition of SOP in URLLC scenarios with short-packet feature is evidently different from that in the infinite blocklength regime. Inspired by this, we first propose a novel analytical framework to approximate the SOP in a tractable manner. Then, the asymptotic behaviours of SOP in the high-SNR and large-antenna cases are also analyzed to gain a comprehensive insight. Numerical results illustrate how the SOP of our pilot-assisted URLLC system varies with specific transmission parameters.

Short Blocklength Wiretap Channel Codes via Deep Learning: Design and Performance Evaluation

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

Three-Dimensional Trajectory Design for Unmanned Aerial Vehicle-Based Secure and Energy-Efficient Data Collection

Fixed-wing unmanned aerial vehicles (UAVs) provide a practical means for data collection in many Internet-of-Things (IoT) applications. Secrecy and energy efficiency are crucial to the data collection, but have never been well addressed in the lack of appropriate propulsion energy models for three-dimensional (3D) flights of fixed-wing UAVs. This paper delivers a new approach to the joint optimization of the 3D flight trajectory and data collection schedule of a fixed-wing UAV for secure and energy-efficient data collection under an eavesdropping attack. A critical aspect is that we derive a new propulsion energy model for fixed-wing UAVs flying 3D trajectories. By using equivalent transformation, difference-of-convex techniques, and successive convex approximation, we convexify the model and demonstrate its viability to the design of energy-efficient 3D trajectories. Another key aspect is that we further optimize the trajectory and schedule of the UAV for secure and energy-efficient collection of secret data from sensor nodes on the ground. This is non-trivial due to the convexification of the non-smooth secrecy constraints in addition to the new 3D propulsion energy model. Simulations validate the new model and demonstrate considerable energy saving of 3D trajectories, compared to two-dimensional (2D) trajectories optimized based on the state-of-the-art 2D propulsion energy model.

Performance enhancement in the cell-free massive MIMO SWIPT system with active eavesdropping

This paper investigates the secure transmission for simultaneous wireless information and power transfer (SWIPT) in the cell-free massive multiple-input multiple-output (MIMO) system. To develop green communication, legitimate users harvest energy by the hybrid time switching (TS) and power splitting (PS) strategy in the downlink phase, and the harvested energy can provide power to send uplink pilot sequences for the next time slot. By in-built batteries, the active eavesdropper can send the same pilots with the wiretapped user, which results in undesirable correlations between the channel estimates. Under these scenarios, we derive the closed-form expressions of average harvested energy and achievable rates, and propose an iterative power control (PC) scheme based on max–min fairness algorithm with energy and secrecy constraints (MMF-ESC). This scheme can ensure the uniform good services for all users preserving the distributed architecture advantage of cell-free networks, while meeting the requirements of energy harvested by legitimate users and network security against active eavesdroppers. Besides, continuous approximation, bisection and path tracking are jointly applied to cope with the high-complexity and non-convex optimization. Numerical results demonstrate that MMF-ESC PC scheme can effectively increase the achievable rate and the average harvested energy of each user, and decrease the eavesdropping rate below the threshold. Moreover, the results also reveal that PS strategy is superior in harvesting energy in terms of more stringent network requirements for average achievable rates or security.

Secrecy Rate Region Enhancement in Multiple Access Wiretap Channel

It is commonly known that physical layer security is achieved with a trade-off in terms of the achievable rate. Hence, security constraints generate rate losses in wiretap channels. To mitigate such rate losses in multi-user channels, we propose a coding/decoding scheme for multi-user multiple access wiretap channel (MAC-WT), where previously transmitted messages are used as a secret key to enhance the secrecy rates of the transmitting users, until the usual Shannon capacity region of a multiple access channel (MAC) is achieved without the secrecy constraint. With this coding scheme, all messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal, we introduce secret key buffers at both the users and the legitimate receiver. Finally, we consider a fading MAC-WT and show that with this coding/decoding scheme, we can achieve the capacity region of a fading MAC channel (in the ergodic sense).

Physical Layer Security in Large-Scale Random Multiple Access Wireless Sensor Networks: A Stochastic Geometry Approach

This paper investigates physical layer security for a large-scale WSN with random multiple access, where each fusion center in the network randomly schedules a number of sensors to upload their sensed data subject to the overhearing of randomly distributed eavesdroppers. We propose an uncoordinated random jamming scheme in which those unscheduled sensors send jamming signals with a certain probability to defeat the eavesdroppers. With the aid of stochastic geometry theory and order statistics, we derive analytical expressions for the connection outage probability and secrecy outage probability to characterize transmission reliability and secrecy, respectively. Based on the obtained analytical results, we formulate an optimization problem for maximizing the sum secrecy throughput subject to both reliability and secrecy constraints, considering a joint design of the wiretap code rates for each scheduled sensor and the jamming probability for the unscheduled sensors. We provide both optimal and low-complexity sub-optimal algorithms to tackle the above problem, and further reveal various properties on the optimal parameters which are useful to guide practical designs. In particular, we demonstrate that the proposed random jamming scheme is beneficial for improving the sum secrecy throughput, and the optimal jamming probability is the result of trade-off between secrecy and throughput. We also show that the throughput performance of the sub-optimal scheme approaches that of the optimal one when facing a stringent reliability constraint or a loose secrecy constraint.

Secure GDoF of the Z-Channel With Finite Precision CSIT: How Robust are Structured Codes?

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.

Artificial-noise aided secure transmission over visible light communication system under coexistent passive and active eavesdroppers.

In this paper, secure transmission over multiple-input single-output visible light communication system under coexistent passive and active eavesdroppers (Eves) is studied. To enhance the achievable secrecy rate of this system given statistical channel state information (CSI) error model for the passive Eves-related channels, a robust artificial-noise (AN) based transmit strategy is proposed and a secrecy rate maximization problem subject to secrecy-outage-probability constraint, sum power constraint, and peak amplitude constraint is formulated. To solve this non-convex problem, a conservative approximation is presented to replace the probabilistic constraint and unbounded CSI error with worst-case secrecy constraints and spherically-bounded CSI errors, respectively. Then, semi-definite relaxation, S-procedure, and a Golden search-based algorithm are proposed to solve the approximated problem with fast convergence and low complexity. Simulation results show that the proposed method outperforms the other AN-aided and non-AN method for the coexistent active and passive Eves case, especially when the power budget is high.

Role of Shared Key for Secure Communication Over 2-User Gaussian Z-Interference Channel

In this paper, the role of secret key with finite rate is studied to enhance the secrecy performance of the system when users are operating in interference limited scenarios. To address this problem, a 2-user Gaussian Z-interference channel with secrecy constraint at the receiver is considered. The paper proposes novel achievable schemes, where the schemes differ from each other based on how the key has been used in the encoding process. The first achievable scheme uses a combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">key rate splitting</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one-time pad</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stochastic encoding</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">superposition coding</i> . In this scheme, one part of the key is used for one-time pad and the remaining part of the key is used for stochastic encoding. The encoding is performed such that the receiver experiencing interference can decode some part of the interference without violating the secrecy constraint. As a special case of the derived result, one can obtain the secrecy rate region when the key is completely used for one-time pad or part of the stochastic encoding. The second scheme uses the shared key to encrypt the message using one-time pad and in contrast to the previous case no interference is decoded at the receiver. The paper also derives outer bound on the sum rate and secrecy rate. The main novelty of deriving outer bound lies in the selection of side information provided to the receiver and using the secrecy constraint. The derived outer bounds are found to be tight for certain channel conditions and rate of the key. The scaling behaviour of key rate is also explored for different schemes using the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secure generalized degrees of freedom</i> . The optimality of different schemes are characterized for some specific cases. The developed results show the importance of key rate splitting in enhancing the secrecy performance of the system.

Impact of Self-Energy Recycling and Cooperative Jamming on SWIPT-Based FD Relay Networks With Secrecy Constraints

This paper investigates the secrecy performance of a power splitting-based simultaneous wireless information and power transfer cooperative relay network in the presence of an eavesdropper. The relay is considered to operate in full-duplex (FD) mode to perform both energy harvesting and information decoding simultaneously. To accomplish that, the relay is assumed to employ two rechargeable batteries, which switch between power supplying mode and charging mode at each transmission block. We also assume that the self-interference inherent of the FD mode is not completely suppressed. Therefore, it is assumed that, after some stages of passive and active self-interference cancellation, there is still a residual self-interference (RSI). A portion of this RSI (remaining after passive cancellation) is recycled for energy harvesting. In order to improve the system secrecy performance, it is considered that the relay can split its transmit power to send the information signal and to emit a jamming signal to degrade the eavesdropper&#x2019;s channel. The secrecy performance is evaluated in terms of the secrecy outage probability and the optimal secrecy throughput. Tight-approximate and asymptotic expressions are obtained for the secrecy outage probability, and the particle swarm optimization method is employed for addressing the secrecy throughput optimization problem. From numerical results, we show that the secrecy performance can be increased depending on the self-energy recycling channel condition. Finally, our derived expressions are validated via Monte Carlo simulations.

A Method Exploiting the Channel-Training Phase to Achieve Secrecy in a Fading Broadcast Channel

This work considers a time-varying Rayleigh block fading broadcast channel formed by two users and an eavesdropper, external to the legitimate network. One of the users is the legitimate/trusted user and the other an untrusted user. The transmitter uses superposition coding to broadcast information to both users. The aim is to ensure the confidentiality of the legitimate user information against the untrusted user and eavesdropper. To satisfy these secrecy constraints, this work proposes an innovative secure channel-training method applied to a cooperative jamming scenario. The jammer uses interference alignment to achieve secrecy against the untrusted user; meanwhile, the developed channel-training method is designed exploiting the time-varying nature of the channel to extend the system secrecy also to the external eavesdropper. An information theoretical evaluation of the proposed scheme demonstrates that (1/4, 1/4) positive secure degrees of freedom are achievable in the presence of both untrusted users and external eavesdroppers.

Relay-assisted secure short-packet transmission in cognitive IoT with spectrum sensing

Cognitive Internet of Things (IoT) has attracted much attention due to its high spectrum utilization. However, potential security of the short-packet communications in cognitive IoT becomes an important issue. This paper proposes a relay-assisted maximum ratio combining/zero forcing beamforming (MRC/ZFB) scheme to guarantee the secrecy performance of dual-hop short-packet communications in cognitive IoT. This paper analyzes the average secrecy throughput of the system and further investigates two asymptotic scenarios with the high signal-to-noise ratio (SNR) regime and the infinite blocklength. In addition, the Fibonacci-based alternating optimization method is adopted to jointly optimize the spectrum sensing blocklength and transmission blocklength to maximize the average secrecy throughput. The numerical results verify the impact of the system parameters on the tradeoff between the spectrum sensing blocklength and transmission blocklength under a secrecy constraint. It is shown that the proposed scheme achieves better secrecy performance than other benchmark schemes.

Secretive Coded Caching With Shared Caches

We consider the problem of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secretive coded caching</i> in a shared cache setup where the number of users accessing a particular <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">helper cache</i> is more than one, and every user can access exactly one helper cache. In secretive coded caching, the constraint of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perfect secrecy</i> must be satisfied. It requires that the users should not gain, either from their caches or from the transmissions, any information about the content of the files that they did not request from the server. In order to accommodate the secrecy constraint, our problem setup requires, in addition to a helper cache, a dedicated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user cache</i> of minimum capacity of 1 unit to every user. This is where our formulation differs from the original work on shared caches (“Fundamental Limits of Coded Caching With Multiple Antennas, Shared Caches and Uncoded Prefetching” by E. Parrinello, A. Ünsal and P. Elia in Trans. Inf. Theory, 2020). In this work, we propose a secretively achievable coded caching scheme with shared caches under centralized placement. When our scheme is applied to the dedicated cache setting, it matches the scheme by Ravindrakumar <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (“Private Coded Caching”, in Trans. Inf. Forensics and Security, 2018).

Intelligent Reflecting Surface Assisted NOMA With Heterogeneous Internal Secrecy Requirements

The intelligent reflecting surface (IRS) technology can significantly enhance the flexibility of non-orthogonal multiple access (NOMA) by reconfiguring the channel gains according to the users’ communication requirements. We propose to use IRS to enhance the internal secrecy among NOMA users in the multiple-input-single-output downlink networks. The objective is to minimize the total transmit power under heterogeneous secrecy constraints, by jointly optimizing the beamforming vectors and the IRS reflecting factors. To efficiently solve this non-convex problem, an alternating optimization based iterative algorithm is proposed by leveraging the successive convex approximation and the semi-definite relaxation techniques. Simulation results show that our proposed IRS-assisted NOMA can effectively guarantee the internal secrecy of users with significantly reduced transmit power compared to the convectional NOMA without IRS and the orthogonal multiple access with or without IRS.

Joint Buffer-Aided Hybrid-Duplex Relay Selection and Power Allocation for Secure Cognitive Networks With Double Deep Q-Network

This paper applies the reinforcement learning in the joint relay selection and power allocation in the secure cognitive radio (CR) relay network, where the data buffers and full-duplex jamming are applied at the relay nodes. Two cases are considered: maximizing the throughput with the delay and secrecy constraints, and maximizing the secrecy rate with the delay constraint, respectively. In both cases, the optimization relies on the buffer states, the interference to/from the primary user, and the constraints on the delay and/or secrecy. This makes it mathematically intractable to apply the traditional optimization methods. In this paper, the double deep Q-network (DDQN) is used to solve the above two optimization problems. We also apply the a-priori information in the CR network to improve the DDQN learning convergence. Simulation results show that the proposed scheme outperforms the traditional algorithm significantly.

Optimal Secure GDoF of Symmetric Gaussian Wiretap Channel With a Helper

We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper, under a weak notion of secrecy constraint. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.