In smart grids, smart meters periodically collect users' fine-grained multi-dimensional energy data, which poses great concerns on users' privacy and security. Existing privacy preserving multi-dimensional aggregation schemes suffer from heavy computational burdens, especially for smart meters with limited computational resources. To address these limitations, in this paper we propose an efficient and flexible multi-dimensional data aggregation scheme called MDA-SMuSha, by which smart meters employ the Shamir's multi-secret sharing to generate a set of shared secrets, with the first one kept locally, while the remained ones are packaged and then uploaded to a control center via an aggregator. By the MDA-SMuSha scheme, aggregation results of smart meters' multi-dimensional energy data during multiple periods can be obtained, with only one time of Paillier encryption conducted on the smart meters. In addition, it allows the control center to send query requests flexibly, i.e., at a pre-specified frequency or whenever it wants to obtain statistical data of interests. Rigorous security analyses show that the MDA-SMuSha scheme satisfies security requirements of privacy-preservation, authenticity and data integrity as well as fault-tolerance. Both theoretical analyses and experiment results show that the MDA-SMuSha scheme outperforms state-of-the art methods in terms of computation costs, with comparable communication costs.

While multi-label learning has shown excellent performance in False Data Injection Attack (FDIA) locational detection, it has also exposed some potential security risks and vulnerabilities. However, unlike the image domain, the vulnerabilities of multi-label learning in the field of power grid have just received attention and urgently need to be explored and addressed. In this paper, to achieve a better understanding for the security risks of deep learning-based multi-label FDIA detectors, we propose two Alternating Direction Method of Multipliers (ADMM) based adversarial attacks, which are applicable to two different scenarios. The proposed two ADMM-based attacks aim to reduce additional attack costs while seeking suitable adversarial perturbations, making the attacks more realistic and feasible. The experimental results verify the effectiveness of the proposed ADMM-based attacks, making noteworthy strides in fostering a profound comprehension of the vulnerabilities in the unique field of deep multi-label learning for power systems.

Shadow characteristics are of great importance for scene understanding. Existing works mainly consider shadow regions as binary masks, often leading to imprecise detection results and suboptimal performance for scene understanding. We demonstrate that such an assumption oversimplifies light-object interactions in the scene, as the scene details under either hard or soft shadows remain visible to a certain degree. Based on this insight, we aim to reformulate the shadow detection paradigm from the opacity perspective, and introduce a new fine-grained shadow detection method. In particular, given an input image, we first propose a shadow opacity augmentation module to generate realistic images with varied shadow opacities. We then introduce a shadow feature separation module to learn the shadow position and opacity representations separately, followed by an opacity mask prediction module that fuses these representations and predicts fine-grained shadow detection results. In addition, we construct a new dataset with opacity-annotated shadow masks across varied scenarios. Extensive experiments demonstrate that our method outperforms the baselines qualitatively and quantitatively, enhancing a wide range of applications, including shadow removal, shadow editing, and 3D reconstruction.

Blockchain-based vehicular edge computing (VEC) is regarded as a promising computing paradigm that can enhance the computing capabilities of mobile vehicles while ensuring security during task offloading. However, the blockchain consensus for secure task offloading inevitably increases the communication and computation resource consumption. More importantly, the frequent handover among roadside units during the fast movement of vehicles also raises the communication cost for blockchain consensus. To address these issues, this article proposes intelligent secure task offloading and caching (ISTOC) scheme for VEC networks. Specifically, we first establish a digital twin-assisted VEC network that migrates the blockchain consensus process from the physical space to the cyber space, supporting the dynamic handover of vehicles. Correspondingly, we propose a lightweight blockchain scheme named diffused delegated Byzantine fault tolerance (d2BFT). Then, aiming at simultaneously reducing the task processing latency and improving the blockchain transaction throughput, we formulate the joint blockchain, communication, computation, and caching (B3C) optimization problem subject to task division, communication bandwidth, computing frequency, cache storage, task deadline, and blockchain stability. Due to the nonconvexity of B3C, we transform it into a Markov decision process, and propose a multiagent double actor-critic (MADAC) algorithm in light of the distributed characteristic of blockchain. Through offline training and online execution, we jointly optimize the task division, communication bandwidth, computing frequency and cache storage allocation, block size, and block generation interval for ISTOC. Experimental results show that the proposed MADAC-based ISTOC scheme can stably converge with a much higher reward than the benchmark schemes based on MADDPG, soft actor-critic, deep deterministic policy gradient, and TD3. The improvement of MADAC-ISTOC over SAC-ISTOC is more than 25.93%.

Integrating Unmanned Aerial Vehicles (UAVs) and autonomous vehicles within the crowdsensing paradigm offers a promising approach to collecting environment-relevant data over large spatial areas, particularly in disaster-stricken or high-risk regions. However, deploying crowdsensing systems in emergency response scenarios presents substantial challenges. The lack of prior environmental knowledge complicates the selection of optimal sensing locations and strategy optimization, often relying on costly trial-and-error methods. Additionally, realtime decision-making is critical in such scenarios, requiring the rapid identification of optimal deployment strategies. Yet, the absence of prior knowledge further complicates the assessment of the optimality of these strategies. This gap remains inadequately addressed in existing research. To address this, we present the first framework that frames these challenges as a rapid online strategy optimization problem for mobile agent-based crowdsensing systems operating in unknown environments during emergency response scenarios. We propose DGap-UCB, a novel approach within the multi-armed bandit (MAB) framework, which efficiently identifies the optimal sensing strategy with highconfidence guarantees. Leveraging the Upper-Confidence Bound (UCB) technique, DGap-UCB iteratively refines strategy selection based on reward feedback. To accelerate learning, we introduce a gap-confidence pair (Δt, δt)-based Quick Stopping Criterion, enabling rapid and high-confidence identification of the optimal strategy. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of DGap-UCB over stateof-the-art techniques

Although conventional false data injection attacks can circumvent the detection of bad data detection (BDD) in sustainable power grid cyber physical systems, they are easily detected by well-trained deep learning-based detectors. Still, state estimation models with deep leaning-based detectors are not secure due to the vulnerabilities and fragility of deep learning models. Using the related laws of conventional false data injection attacks and adversarial sample attacks, this paper proposes the targEted adVersarial fAlse Data injEction (EVADE) strategy to explore targeted adversarial false data injection attacks for state estimation in Smart Grid. The proposed EVADE attack strategy selects key state variables based on adversarial saliency maps to improve the attack efficiency and perturbs as few state variables as possible to reduce the attack cost. In this way, the EVADE attack strategy can bypass the detection of BDD and neural attack detection (NAD) methods (that is, maintaining deep stealthy) with a high success rate and achieve the attack target simultaneously. Experimental results demonstrate the effectiveness of the proposed strategy, posing serious and pressing concerns for sustainable cyber physical power system security.

Deep learning methods can not only detect false data injection attacks (FDIA) but also locate attacks of FDIA. Although adversarial false data injection attacks (AFDIA) based on deep learning vulnerabilities have been studied in the field of single-label FDIA detection, the adversarial attack and defense against multi-label FDIA locational detection are still not involved. To bridge this gap, this paper first explores the multi-label adversarial example attacks against multi-label FDIA locational detectors and proposes a general multi-label adversarial attack framework, namely muLti-labEl adverSarial falSe data injectiON attack (LESSON). The proposed LESSON attack framework includes three key designs, namely Perturbing State Variables, Tailored Loss Function Design, and Change of Variables, which can help find suitable multi-label adversarial perturbations within the physical constraints to circumvent both Bad Data Detection (BDD) and Neural Attack Location (NAL). Four typical LESSON attacks based on the proposed framework and two dimensions of attack objectives are examined, and the experimental results demonstrate the effectiveness of the proposed attack framework, posing serious and pressing security concerns in smart grids.

Industrial Wireless Sensor Networks (IWSNs) have been widely used in industrial applications that require highly reliable and real-time wireless transmission. A lot of works have been done to optimize the Relay Node Placement (RNP), which determines the underlying topology of IWSNs and hence impacts the network performance. However, existing RNP algorithms use a fixed communication radius to compute the deployment result at once offline, while ignoring that the radio environment may vary drastically across different locations, also known as radio irregularity. To address this limitation, we propose a Voronoi diagram and Q-learning based RNP (VQRNP) method in this article. Instead of using a fixed communication radius, VQRNP employs the Q-learning algorithm to dynamically update the radio environment of measured areas, uses a Voronoi diagram based method to estimate the radio environment of unmeasured areas, and proposes a coverage extension location selection algorithm to place RNs so as to extend the coverage of the deployed network based on the results estimated by Voronoi diagram based Graph Generating (VGG). In this way, the VQRPN method can adapt itself well to the variation of radio environment and largely speed up the deployment process. Extensive simulations verify that VQRNP significantly outperforms existing RNP algorithms in terms of reliability.

Temporal recommendation systems aim to suggest items to users at the optimal time. However, the significant imbalance of items in the training data poses a major challenge to predictive accuracy. Existing approaches attempt to alleviate this issue by modifying the loss function or utilizing resampling techniques, but such approaches may inadvertently amplify the specificity of certain behaviors.

In various multi-party cooperations data stored on blockchains (i.e., on-chain data) should be decentralized consistent, verifiable, traceable, and immutable. Online analytical processing (OLAP) services are critical requirements in these applications. However, OLAP performances of existing blockchain systems are much worse than those of relational databases due to the lack of SQL support. In this paper, we propose a novel SQL-empowered analytical blockchain framework, aChain. It fully provides SQL-based OLAP services, while keeping the secure characteristics. Specifically, aChain relationally reorganizes on-chain data to support full SQL executions. Then, a relational versioning scheme is designed to ensure the atomicity and consistency of transactions. Furthermore, SQL-based APIs are designed based on an execute-order-validate architecture. Finally, we demonstrate that the performance of aChain and MySQL (in both cluster and non-cluster models) is at the same level on a typical OLAP benchmark, TPC-H.

Transportation networks are essential to the operation of societies and economies. Protecting the privacy of sensitive information is a meaningful conception in sustainable transport when mining the transportation data. In data mining, differential privacy (DP) has provable privacy guarantees for releasing sensitive data by introducing randomness into query results. However, it suffers from significant accuracy loss of outputs when the query has high sensitivity (e.g., triangle counting). The reason is that the range of random perturbation to each query result in DP is too large. It consists of all possible output values for a query that forms a large or even unbounded interval. However, when impose perturbation only in a small neighborhood of the true query result, the similarity measure based on randomness in DP fails. Thereupon, we introduce fuzziness into DP to formulate new models which have smaller disturbance via fuzzy similarity measures. In this article, we establish a novel and general theory of private data analysis, fuzzy differential privacy (FDP). The new theory FDP aims to acquire a more flexible tradeoff between the accuracy of outputs and the privacy-preserving level of data. FDP combines DP with fuzzy set theory by introducing fuzziness into the query results and characterizing similarities between outputs via multiple fuzzy similarity measures. From this perspective, DP can be viewed as a special case of FDP with probabilistic similarity measure. Compared with DP, FDP has three superiorities: 1) most fuzzy similarity measures in FDP support sliding window perturbation strategies we proposed, which refer to perturbation in a small neighborhood of the query results; 2) FDP adds noise to the query results only according to a fraction of all possible neighboring datasets; and 3) the fuzzy similarity with valued in [0,1] quantifies the privacy protection level intuitively. These three points enable more accurate outputs while providing provable and intuitive privacy guarantees. As for subgraph counting, the state-of-the-art method is ladder framework in DP. We illustrate FDP mechanisms by applying them to a common application in subgraph counting–triangle/4-cliques counting. Experiments show that FDP is effective and efficient with smaller output errors than DP.

In smart grids, various Internet-of-Things-based (IoT-based) components are massively deployed across the power systems. However, most of these IoT-based components have their own vulnerabilities, leveraging which malicious users can launch different cyber/physical attacks to steal electricity. Economic losses caused by electricity theft amount to $96 billion in 2017. Most existing electricity theft detection techniques suffer from either a high deployment cost or a low detection accuracy. To address these concerns, we propose a novel Electricity Theft Detector based upon Convolutional Long Short Term Memory neural networks, called ETD-ConvLSTM. By installing a central observer meter in each community, we can know which communities have malicious users. For these communities, users’ time series of electricity consumptions with temporal correlations are transformed into spatio-temporal sequence data, mainly by constructing a two-dimensional matrix containing both consumptions and consumption differences among several adjacent days. This matrix is then divided into a sequence of sub-matrices, which are then fed into a ConvLSTM network consisting of multiple stacked ConvLSTM layers, with each layer formed by several temporarily concatenated ConvLSTM nodes. When capturing the periodicity in users’ consumption patterns, the ETD-ConvLSTM method considers both global and local knowledge, and hence the detection accuracy improves significantly. Simulations results show that compared with existing state-of-the-art detectors, the proposed ETD-ConvLSTM method can obtain better or comparable performance in terms of detection accuracy, false negative rates and false positive rates within much shorter detection time.

The popularization of unmanned aerial vehicles (UAVs) has boosted various civil applications such as traffic monitoring, in which the effective coordination of the UAV swarm plays a significant role in expanding the monitoring range and enhancing the execution efficiency. However, due to the isolated local environments as well as the heterogeneous execution capabilities, it is challenging to achieve highly consistent actions. In this article, we incorporate the federated learning framework with the imitation learning technique to coordinate the UAVs' maneuvers by interactively imitating the leader UAV's operations. During the interagent global model download phase, we utilize the generative adversarial imitation learning (GAIL) model to accurately follow the leader UAV's operations by removing the biased estimates of imitation parameters. While in the intraagent local model training phase, we utilize the self-imitation learning (SIL) model to correct delicate imitation errors by virtue of the follower UAVs' own historical valuable experiences. In order to achieve more efficient distributed parameter interactions, we regularize the federated gradient updates and eventually yield coordinated swarm policies. We evaluate the proposed algorithm in the UAV-based traffic monitoring scenario. Evaluation results demonstrate the superiorities on training and execution efficiencies.

For achieving the goal of two-way communication and power flows, smart grids are integrated with much state-of-the-art hardware and software. However, these newly added components also introduce a lot of vulnerabilities into the power systems, which results in that malicious users can launch various cyber–physical attacks to steal electricity. The existing electricity theft detection techniques suffer from an implicit assumption that malicious users tamper with smart meter readings to values much less than their actual electricity consumptions. These are called large-amount electricity theft (LET) attacks. Nevertheless, in the real world, some malicious users may be cautious enough to deliberately launch small-amount electricity theft (SET) attacks, where smart meter readings are manipulated to numbers slightly lower than the actual values, mainly to escape detection. To address this limitation, we propose a detector that is able to deal with both LET and SET attacks effectively. This detector applies a cumulative sum (CUSUM) control chart and a Shewhart control chart together to analyze users’ reported readings and measurements of a central observer meter. It consists of an electricity theft detection phase, which aims to detect the existence of LET/SET attacks timely and a malicious user identification phase, which aims to identify malicious users exactly. Extensive experiments are conducted to evaluate the proposed detector, and the results show that it has good performance in terms of several metrics.

For accommodating rapidly increasing power demands, power systems are transitioning from analog systems to systems with increasing digital control and communications. Although this modernization brings many far-reaching benefits, the hardware and software newly incorporated into the power systems also incur many vulnerabilities. By taking advantage of these vulnerabilities, adversaries can launch various cyber/physical attacks to tamper with electricity meter readings, i.e., to steal electricity. It is reported that total worldwide annual economic losses caused by electricity theft reached up to almost one hundred billion dollars in recent years. With methods to tamper with meter readings becoming more versatile, secret, and flexible, electricity theft tends to get even more serious in modernized power systems. For preventing adversaries from stealing electricity, researchers have done a lot of works. Although some related surveys on these works exist, they are not updated or just discuss electricity theft in a specific region. This survey aims to gain a comprehensive and in-depth understanding of the electricity theft issue. After investigating how adversaries tamper with meter readings, we systematically survey all existing detection methods up to date, which is classified into machine learning- and measurement mismatch-based methods. Adverse effects and political and socioeconomic factors of electricity theft are also provided. This survey can help relevant researchers to shape future research directions, especially in the area of developing new effective electricity theft detection methods.

The ongoing coronavirus disease 2019 (COVID-19) is a pandemic causing millions of deaths, devastating social and economic disruptions. Testing individuals for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the pathogen of COVID-19, is critical for mitigating and containing COVID-19. Many countries are implementing group testing strategies against COVID-19 to improve testing capacity and efficiency while saving required workloads and consumables. A group of individuals’ nasopharyngeal/oropharyngeal (NP/OP) swab samples is mixed to conduct one test. However, existing group testing methods neglect the fact that mixing samples usually leads to substantial dilution of viral ribonucleic acid (RNA) of SARS-CoV-2, which seriously impacts the sensitivity of tests. In this paper, we aim to screen individuals infected with COVID-19 with as few tests as possible, under the premise that the sensitivity of tests is high enough. To achieve this goal, we propose an Adaptive Group Testing (AdaGT) method. By collecting information on the number of positive and negative samples that have been identified during the screening process, the AdaGT method can estimate the ratio of positive samples in real-time. Based on this ratio, the AdaGT algorithm adjusts its testing strategy adaptively between an individual testing strategy and a group testing strategy. The group size of the group testing strategy is carefully selected to guarantee that the sensitivity of each test is higher than a predetermined threshold and that this group contains at most one positive sample on average. Theoretical performance analysis on the AdaGT algorithm is provided and then validated in experiments. Experimental results also show that the AdaGT algorithm outperforms existing methods in terms of efficiency and sensitivity.Note to Practitioners—Real-time reverse transcription-polymerase chain reaction (rRT-PCR) tests provide scope for automation and are one of the most widely used laboratory methods for detecting the SARS-CoV-2 virus. This paper is motivated by the following challenges: (1) Many countries are experiencing an acute shortage of professionals and consumables for conducting rRT-PCR tests; (2) Group sizes of existing group testing methods against COVID-19 may not be optimal, which adversely impacts the efficiency of the screening of the SARS-CoV-2 virus; (3) Existing group testing methods do not consider the fact that the sensitivity of rRT-PCR tests usually decreases with the group size. The objective of this paper is to improve the efficiency and sensitivity of large-scale screening against COVID-19. For achieving this goal, we propose an Adaptive Group Testing (AdaGT) algorithm, which has the following advantages: (1) It can improve the efficiency for screening the SARS-CoV-2 virus, mainly by adaptively adjusting its testing strategy between an individual testing strategy and a group testing strategy based upon an estimated ratio of positive samples during the screening process; (2) It can guarantee a high sensitivity of the rRT-PCR tests by determining the group sizes of the group testing strategy based upon some constraints; (3) We derive an appropriate threshold for the estimated ratio of positive samples such that the AdaGT algorithm can achieve a minimum average number of rRT-PCR tests and can be directly employed in practical applications.

The pathogen of the ongoing coronavirus disease 2019 (COVID-19) pandemic is a newly discovered virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Testing individuals for SARS-CoV-2 plays a critical role in containing COVID-19. For saving medical personnel and consumables, many countries are implementing group testing against SARS-CoV-2. However, existing group testing methods have the following limitations: (1) The group size is determined without theoretical analysis, and hence is usually not optimal. This adversely impacts the screening efficiency. (2) These methods neglect the fact that mixing samples together usually leads to substantial dilution of the SARS-CoV-2 virus, which seriously impacts the sensitivity of tests. In this paper, we aim to screen individuals infected with COVID-19 with as few tests as possible, under the premise that the sensitivity of tests is high enough. We propose an eXpectation Maximization based Adaptive Group Testing (XMAGT) method. The basic idea is to adaptively adjust its testing strategy between a group testing strategy and an individual testing strategy such that the expected number of samples identified by a single test is larger. During the screening process, the XMAGT method can estimate the ratio of positive samples. With this ratio, the XMAGT method can determine a group size under which the group testing strategy can achieve a maximal expected number of negative samples and the sensitivity of tests is higher than a user-specified threshold. Experimental results show that the XMAGT method outperforms existing methods in terms of both efficiency and sensitivity.

Contact tracing is a critical tool in containing epidemics such as COVID-19. Researchers have carried out a lot of work on contact tracing. However, almost all of the existing works assume that their clients and authorities have large storage space and powerful computation capability and clients can implement contact tracing on their own mobile devices such as mobile phones, tablet computers, and wearable computers. With the widespread outbreaks of the epidemics, these approaches are of less robustness to a larger scale of datasets when it comes to resource-constrained clients. To address this limitation, we propose a publicly verifiable contact tracing algorithm in cloud computing (PvCT), which utilizes cloud services to provide storage and computation capability in contact tracing. To guarantee the integrity and accuracy of contact tracing results, PvCT applies a novel set accumulator-based authentication data structure whose computation is outsourced, and the client can check whether returned results are valid. Furthermore, we provide rigorous security proof of our algorithm based on the q -Strong Bilinear Diffie–Hellman assumption. Detailed experimental evaluation is also conducted on three real-world datasets. The results show that our algorithm is feasible within milliseconds of client CPU time and can significantly reduce the storage overhead from the size of datasets to a constant 128 bytes.

Integrated with cutting-edge equipment and technologies, smart grid takes prominent advantages over traditional power systems. However, hardware and software techniques also bring smart grid numerous security concerns, especially various cyberattacks. Malicious users can launch cyberattacks to tamper with smart meters anytime and anywhere, mainly for the purpose of stealing electricity. This makes electricity theft much easier to commit and more difficult to detect. Researchers have devised many approaches to identify malicious users. However, these approaches suffer from either poor accuracy or expensive cost of deploying monitoring devices. This paper aims to locate malicious users using a limited number of monitoring devices (called inspectors) within the shortest detection time. Before inspectors conduct any inspection, suspicions that users steal electricity are comprehensively assessed, mainly through analyzing prior records of electricity theft as well as deviations between the reported and predicted normal consumptions. On the basis of these suspicions, we further propose a suspicion assessment-based inspection (SAI) algorithm, in which the users with the highest suspicions will be first probed individually. Then, the other users will be probed by a binary tree-based inspection strategy. The binary tree is built according to users' suspicions. The inspection order of the nodes on the binary tree is also determined by the suspicions. The experiment results show that the SAI algorithm outperforms the existing methods.

Electricity theft is a widespread problem that causes tremendous economic losses for all utility companies around the globe. As many countries struggle to update their antique power systems to emerging smart grids, more and more smart meters are deployed throughout the world. Compared with analog meters which can be tampered with by only physical attacks, smart meters can be manipulated by malicious users with both physical and cyber-attacks for the purpose of stealing electricity. Thus, electricity theft will become even more serious in a smart grid than in a traditional power system if utility companies do not implement efficient solutions. The goal of this paper is to identify all malicious users in a neighborhood area in a smart grid within the shortest detection time. We propose an adaptive binary splitting inspection (ABSI) algorithm which adopts a group testing method to locate the malicious users. There are two considered inspection strategies in this paper: a scanning method in which users will be inspected individually, and a binary search method by which a specific number of users will be examined as a whole. During the inspection process of our proposed scheme, the inspection strategy as well as the number of users in the groups to be inspected are adaptively adjusted. Simulation results show that the proposed ABSI algorithm outperforms existing methods.

As the smart meters are vulnerable to physical attacks as well as cyber attacks, electricity theft in smart grids is much easier to commit and more difficult to detect than that in traditional power grids. In this paper, to facilitate the inspection of the malicious meters, a full and complete binary inspection tree whose leaves stand for smart meters is employed as a logical structure. We can logically configure an inspector (a meter for detection) at any node on the tree. By calculating the difference between the inspector’s reading and the summation of the readings reported from the smart meters on the subtree of one node, as well as the difference between the total amount of stolen electricity on the subtrees of an internal node and its left child, we propose a difference-comparison-based inspection algorithm which allows the inspector to skip a large number of nodes on the tree and hence accelerates the detection speed of the malicious meters remarkably. Furthermore, for quickly identifying a complete set of malicious meters, we propose an adaptive reporting mechanism which adopts much shorter reporting periods during the inspection process. Analysis with proofs about the performance bounds of the proposed algorithm in terms of the number of inspection steps is provided. Simulations not only validate the theoretical analysis, but also show the superiority of the proposed algorithm over the existing works in terms of inspection steps, regardless of the ratio and the permutation of malicious meters.

To detect the malicious meters committing electricity theft in a neighborhood area smart grid, in this paper, a novel inspection algorithm, termed as the Binary-Coded Grouping-based Inspection (BCGI) algorithm, is proposed. In the proposed algorithm, each meter is identified with a unique binary-coded number. The BCGI algorithm can locate the unique malicious meter (if any) by one inspection step under the assumption that at most one meter becomes malicious in one reporting period. Furthermore, by controlling the reporting periods of meters, we could make the probability of the event that at most one meter becomes malicious in one reporting period arbitrarily close to 1 under some assumptions. We further extend the algorithm into a Generalized BCGI algorithm (G-BCGI) to deal with the case that there are two or more meters which happen to commit the theft of electricity in one reporting period. Simulation results demonstrate the inspection efficiency of the BCGI and G-BCGI algorithms.

In this paper, we explore the malicious meter inspection (MMI) problem in neighborhood area smart grids. By exploiting a binary inspection tree, we propose a Difference-Comparison-based Inspection (DCI) algorithm to quickly target the malicious meters. Different from existing algorithms, the DCI algorithm is designed based on three rules that are derived according to the difference comparison results in each local subtree. An attractive feature of the DCI algorithm is that it manages to skip a large number of nodes on the binary inspection tree and thus accelerates the detection of malicious nodes. Both analysis and simulation results show that DCI outperforms the existing inspection algorithms in terms of inspection speed, regardless of the ratio and permutation of malicious meters.