Securing the Internet of Health Things with Certificateless Anonymous Authentication Scheme

Internet of Health Things(IoHT)is a subset of Internet of Things(IoT)technology that includes interconnected medical devices and sensors used in medical and healthcare information systems.However,IoHT is susceptible to cybersecurity threats due to its reliance on low-power biomedical devices and the use of open wireless channels for communication.In this article,we intend to address this shortcoming,and as a result,we propose a new scheme called,the certificateless anonymous authentication(CAA)scheme.The proposed scheme is based on hyperelliptic curve cryptography(HECC),an enhanced variant of elliptic curve cryptography(ECC)that employs a smaller key size of 80 bits as compared to 160 bits.The proposed scheme is secure against various attacks in both formal and informal security analyses.The formal study makes use of the Real-or-Random(ROR)model.A thorough comparative study of the proposed scheme is conducted for the security and efficiency of the proposed scheme with the relevant existing schemes.The results demonstrate that the proposed scheme not only ensures high security for health-related data but also increases efficiency.The proposed scheme’s computation cost is 2.88 ms,and the communication cost is 1440 bits,which shows its better efficiency compared to its counterpart schemes.

Assessing the Spatial Equality of COVID Testing Sites Maintaining Zero COVID Policy

Rapid and timely testing is essential to minimize the COVID-19 spread. Decision makers and policy planners need to determine the equal distribution and accessibility of testing sites. This study mainly examines the spatial equality of COVID-19 testing sites that maintain a zero COVID policy in Guangzhou City. The study has identified the spatial disparities of COVID testing sites, characteristics of testing locations, and accessibility. The study has obtained information on COVID testing sites in Guangzhou City and population data. Point pattern analyses, Euclidian distance and allocation, and network analyses are the main methods used to achieve the research objectives, and 1183 total COVID testing sites can be recognized in Guangzhou City. Results revealed that spatial disparities could be noticed over the study area. Testing locations of Guangzhou City are highly clustered. The most significant testing sites are located in Haizhu District, which has the third largest population. The highest population density can be identified in Yuexiu District. However, only 94 testing sites are located there. According to all the results, higher disparities can be identified, and a lack of testing sites is located in the north part of the study area. Some people in the northern part have to travel more than 10 km to reach a testing site. Finally, this paper suggests increasing the number of testing sites in the north and south parts of the study area and keeping the same distribution, considering the area, total population, and population density. This kind of research will be helpful to decision-makers in making proper decisions to maintain a zero COVID policy.

A Hybrid and Lightweight Device-to-Server Authentication Technique for the Internet of Things

The Internet of Things(IoT)is a smart networking infrastructure of physical devices,i.e.,things,that are embedded with sensors,actuators,software,and other technologies,to connect and share data with the respective server module.Although IoTs are cornerstones in different application domains,the device’s authenticity,i.e.,of server(s)and ordinary devices,is the most crucial issue and must be resolved on a priority basis.Therefore,various field-proven methodologies were presented to streamline the verification process of the communicating devices;however,location-aware authentication has not been reported as per our knowledge,which is a crucial metric,especially in scenarios where devices are mobile.This paper presents a lightweight and location-aware device-to-server authentication technique where the device’s membership with the nearest server is subjected to its location information along with other measures.Initially,Media Access Control(MAC)address and Advance Encryption Scheme(AES)along with a secret shared key,i.e.,λ_(i) of 128 bits,have been utilized by Trusted Authority(TA)to generate MaskIDs,which are used instead of the original ID,for every device,i.e.,server and member,and are shared in the offline phase.Secondly,TA shares a list of authentic devices,i.e.,server S_(j) and members C_(i),with every device in the IoT for the onward verification process,which is required to be executed before the initialization of the actual communication process.Additionally,every device should be located such that it lies within the coverage area of a server,and this location information is used in the authentication process.A thorough analytical analysis was carried out to check the susceptibility of the proposed and existing authentication approaches against well-known intruder attacks,i.e.,man-in-the-middle,masquerading,device,and server impersonations,etc.,especially in the IoT domain.Moreover,proposed authentication and existing state-of-the-art approaches have been simulated in the real environment of IoT to verify their performance,particularly in terms of various evaluation metrics,i.e.,processing,communication,and storage overheads.These results have verified the superiority of the proposed scheme against existing state-of-the-art approaches,preferably in terms of communication,storage,and processing costs.

Internet of Things Authentication Protocols: Comparative Study

Nowadays, devices are connected across all areas, from intelligent buildings and smart cities to Industry 4.0 andsmart healthcare. With the exponential growth of Internet of Things usage in our world, IoT security is still thebiggest challenge for its deployment. The main goal of IoT security is to ensure the accessibility of services providedby an IoT environment, protect privacy, and confidentiality, and guarantee the safety of IoT users, infrastructures,data, and devices. Authentication, as the first line of defense against security threats, becomes the priority ofeveryone. It can either grant or deny users access to resources according to their legitimacy. As a result, studyingand researching authentication issues within IoT is extremely important. As a result, studying and researchingauthentication issues within IoT is extremely important. This article presents a comparative study of recent researchin IoT security;it provides an analysis of recent authentication protocols from2019 to 2023 that cover several areaswithin IoT (such as smart cities, healthcare, and industry). This survey sought to provide an IoT security researchsummary, the biggest susceptibilities, and attacks, the appropriate technologies, and the most used simulators. Itillustrates that the resistance of protocols against attacks, and their computational and communication cost arelinked directly to the cryptography technique used to build it. Furthermore, it discusses the gaps in recent schemesand provides some future research directions.

Enhancing Internet of Things Intrusion Detection Using Artificial Intelligence

Escalating cyber security threats and the increased use of Internet of Things(IoT)devices require utilisation of the latest technologies available to supply adequate protection.The aim of Intrusion Detection Systems(IDS)is to prevent malicious attacks that corrupt operations and interrupt data flow,which might have significant impact on critical industries and infrastructure.This research examines existing IDS,based on Artificial Intelligence(AI)for IoT devices,methods,and techniques.The contribution of this study consists of identification of the most effective IDS systems in terms of accuracy,precision,recall and F1-score;this research also considers training time.Results demonstrate that Graph Neural Networks(GNN)have several benefits over other traditional AI frameworks through their ability to achieve in excess of 99%accuracy in a relatively short training time,while also capable of learning from network traffic the inherent characteristics of different cyber-attacks.These findings identify the GNN(a Deep Learning AI method)as the most efficient IDS system.The novelty of this research lies also in the linking between high yielding AI-based IDS algorithms and the AI-based learning approach for data privacy protection.This research recommends Federated Learning(FL)as the AI training model,which increases data privacy protection and reduces network data flow,resulting in a more secure and efficient IDS solution.

ResNeSt-biGRU: An Intrusion Detection Model Based on Internet of Things

The rapid expansion of Internet of Things (IoT) devices across various sectors is driven by steadily increasingdemands for interconnected and smart technologies. Nevertheless, the surge in the number of IoT device hascaught the attention of cyber hackers, as it provides them with expanded avenues to access valuable data. Thishas resulted in a myriad of security challenges, including information leakage, malware propagation, and financialloss, among others. Consequently, developing an intrusion detection system to identify both active and potentialintrusion traffic in IoT networks is of paramount importance. In this paper, we propose ResNeSt-biGRU, a practicalintrusion detection model that combines the strengths of ResNeSt, a variant of Residual Neural Network, andbidirectionalGated RecurrentUnitNetwork (biGRU).Our ResNeSt-biGRUframework diverges fromconventionalintrusion detection systems (IDS) by employing this dual-layeredmechanism that exploits the temporal continuityand spatial feature within network data streams, a methodological innovation that enhances detection accuracy.In conjunction with this, we introduce the PreIoT dataset, a compilation of prevalent IoT network behaviors, totrain and evaluate IDSmodels with a focus on identifying potential intrusion traffics. The effectiveness of proposedscheme is demonstrated through testing, wherein it achieved an average accuracy of 99.90% on theN-BaIoT datasetas well as on the PreIoT dataset and 94.45% on UNSW-NB15 dataset. The outcomes of this research reveal thepotential of ResNeSt-biGRU to bolster security measures, diminish intrusion-related vulnerabilities, and preservethe overall security of IoT ecosystems.

Interworking between Modbus and internet of things platform for industrial services

In the era of rapid development of Internet of Things(IoT),numerous machine-to-machine technologies have been applied to the industrial domain.Due to the divergence of IoT solutions,the industry is faced with a need to apply various technologies for automation and control.This fact leads to a demand for an establishing interworking mechanism which would allow smooth interoperability between heterogeneous devices.One of the major protocols widely used today in industrial electronic devices is Modbus.However,data generated by Modbus devices cannot be understood by IoT applications using different protocols,so it should be applied in a couple with an IoT service layer platform.oneM2M,a global IoT standard,can play the role of interconnecting various protocols,as it provides flexible tools suitable for building an interworking framework for industrial services.Therefore,in this paper,we propose an interworking architecture between devices working on the Modbus protocol and an IoT platform implemented based on oneM2M standards.In the proposed architecture,we introduce the way to model Modbus data as oneM2M resources,rules to map them to each other,procedures required to establish interoperable communication,and optimization methods for this architecture.We analyze our solution and provide an evaluation by implementing it based on a solar power management use case.The results demonstrate that our model is feasible and can be applied to real case scenarios.

Vector Dominance with Threshold Searchable Encryption (VDTSE) for the Internet of Things

The Internet of Medical Things(IoMT)is an application of the Internet of Things(IoT)in the medical field.It is a cutting-edge technique that connects medical sensors and their applications to healthcare systems,which is essential in smart healthcare.However,Personal Health Records(PHRs)are normally kept in public cloud servers controlled by IoMT service providers,so privacy and security incidents may be frequent.Fortunately,Searchable Encryption(SE),which can be used to execute queries on encrypted data,can address the issue above.Nevertheless,most existing SE schemes cannot solve the vector dominance threshold problem.In response to this,we present a SE scheme called Vector Dominance with Threshold Searchable Encryption(VDTSE)in this study.We use a Lagrangian polynomial technique and convert the vector dominance threshold problem into a constraint that the number of two equal-length vectors’corresponding bits excluding wildcards is not less than a threshold t.Then,we solve the problem using the proposed technique modified in Hidden Vector Encryption(HVE).This technique makes the trapdoor size linear to the number of attributes and thus much smaller than that of other similar SE schemes.A rigorous experimental analysis of a specific application for privacy-preserving diabetes demonstrates the feasibility of the proposed VDTSE scheme.

Deep Learning-Based Secure Transmission Strategy with Sensor-Transmission-Computing Linkage for Power Internet of Things

The automatic collection of power grid situation information, along with real-time multimedia interaction between the front and back ends during the accident handling process, has generated a massive amount of power grid data. While wireless communication offers a convenient channel for grid terminal access and data transmission, it is important to note that the bandwidth of wireless communication is limited. Additionally, the broadcast nature of wireless transmission raises concerns about the potential for unauthorized eavesdropping during data transmission. To address these challenges and achieve reliable, secure, and real-time transmission of power grid data, an intelligent security transmission strategy with sensor-transmission-computing linkage is proposed in this paper. The primary objective of this strategy is to maximize the confidentiality capacity of the system. To tackle this, an optimization problem is formulated, taking into consideration interruption probability and interception probability as constraints. To efficiently solve this optimization problem, a low-complexity algorithm rooted in deep reinforcement learning is designed, which aims to derive a suboptimal solution for the problem at hand. Ultimately, through simulation results, the validity of the proposed strategy in guaranteed communication security, stability, and timeliness is substantiated. The results confirm that the proposed intelligent security transmission strategy significantly contributes to the safeguarding of communication integrity, system stability, and timely data delivery.

Behaviour recognition based on the integration of multigranular motion features in the Internet of Things

With the adoption of cutting-edge communication technologies such as 5G/6G systems and the extensive development of devices,crowdsensing systems in the Internet of Things(IoT)are now conducting complicated video analysis tasks such as behaviour recognition.These applications have dramatically increased the diversity of IoT systems.Specifically,behaviour recognition in videos usually requires a combinatorial analysis of the spatial information about objects and information about their dynamic actions in the temporal dimension.Behaviour recognition may even rely more on the modeling of temporal information containing short-range and long-range motions,in contrast to computer vision tasks involving images that focus on understanding spatial information.However,current solutions fail to jointly and comprehensively analyse short-range motions between adjacent frames and long-range temporal aggregations at large scales in videos.In this paper,we propose a novel behaviour recognition method based on the integration of multigranular(IMG)motion features,which can provide support for deploying video analysis in multimedia IoT crowdsensing systems.In particular,we achieve reliable motion information modeling by integrating a channel attention-based short-term motion feature enhancement module(CSEM)and a cascaded long-term motion feature integration module(CLIM).We evaluate our model on several action recognition benchmarks,such as HMDB51,Something-Something and UCF101.The experimental results demonstrate that our approach outperforms the previous state-of-the-art methods,which confirms its effective-ness and efficiency.

Artificial intelligence in physiological characteristics recognition for internet of things authentication

Effective user authentication is key to ensuring equipment security,data privacy,and personalized services in Internet of Things(IoT)systems.However,conventional mode-based authentication methods(e.g.,passwords and smart cards)may be vulnerable to a broad range of attacks(e.g.,eavesdropping and side-channel attacks).Hence,there have been attempts to design biometric-based authentication solutions,which rely on physiological and behavioral characteristics.Behavioral characteristics need continuous monitoring and specific environmental settings,which can be challenging to implement in practice.However,we can also leverage Artificial Intelligence(AI)in the extraction and classification of physiological characteristics from IoT devices processing to facilitate authentication.Thus,we review the literature on the use of AI in physiological characteristics recognition pub-lished after 2015.We use the three-layer architecture of the IoT(i.e.,sensing layer,feature layer,and algorithm layer)to guide the discussion of existing approaches and their limitations.We also identify a number of future research opportunities,which will hopefully guide the design of next generation solutions.

Power-Domain Collision-Tolerant Random Access Method with Auxiliary Beam for Satellite Internet of Things:A New Solution

There are numerous terminals in the satellite Internet of Things(IoT).To save cost and reduce power consumption,the system needs terminals to catch the characteristics of low power consumption and light control.The regular random access(RA)protocols may generate large amounts of collisions,which degrade the system throughout severally.The near-far effect and power control technologies are not applicable in capture effect to obtain power difference,resulting in the collisions that cannot be separated.In fact,the optimal design at the receiving end can also realize the condition of packet power domain separation,but there are few relevant researches.In this paper,an auxiliary beamforming scheme is proposed for power domain signal separation.It adds an auxiliary reception beam based on the conventional beam,utilizing the correlation of packets in time-frequency domain between the main and auxiliary beam to complete signal separation.The roll-off belt of auxiliary beam is used to create the carrier-to-noise ratio(CNR)difference.This paper uses the genetic algorithm to optimize the auxiliary beam direction.Simulation results show that the proposed scheme outperforms slotted ALOHA(SA)in terms of system throughput per-formance and without bringing terminals additional control burden.

The Machine Learning Ensemble for Analyzing Internet of Things Networks:Botnet Detection and Device Identification

The rapid proliferation of Internet of Things(IoT)technology has facilitated automation across various sectors.Nevertheless,this advancement has also resulted in a notable surge in cyberattacks,notably botnets.As a result,research on network analysis has become vital.Machine learning-based techniques for network analysis provide a more extensive and adaptable approach in comparison to traditional rule-based methods.In this paper,we propose a framework for analyzing communications between IoT devices using supervised learning and ensemble techniques and present experimental results that validate the efficacy of the proposed framework.The results indicate that using the proposed ensemble techniques improves accuracy by up to 1.7%compared to singlealgorithm approaches.These results also suggest that the proposed framework can flexibly adapt to general IoT network analysis scenarios.Unlike existing frameworks,which only exhibit high performance in specific situations,the proposed framework can serve as a fundamental approach for addressing a wide range of issues.

Privacy-Preserving Information Fusion Technique for Device to Server-Enabled Communication in the Internet of Things:A Hybrid Approach

Due to the overwhelming characteristics of the Internet of Things(IoT)and its adoption in approximately every aspect of our lives,the concept of individual devices’privacy has gained prominent attention from both customers,i.e.,people,and industries as wearable devices collect sensitive information about patients(both admitted and outdoor)in smart healthcare infrastructures.In addition to privacy,outliers or noise are among the crucial issues,which are directly correlated with IoT infrastructures,as most member devices are resource-limited and could generate or transmit false data that is required to be refined before processing,i.e.,transmitting.Therefore,the development of privacy-preserving information fusion techniques is highly encouraged,especially those designed for smart IoT-enabled domains.In this paper,we are going to present an effective hybrid approach that can refine raw data values captured by the respectivemember device before transmission while preserving its privacy through the utilization of the differential privacy technique in IoT infrastructures.Sliding window,i.e.,δi based dynamic programming methodology,is implemented at the device level to ensure precise and accurate detection of outliers or noisy data,and refine it prior to activation of the respective transmission activity.Additionally,an appropriate privacy budget has been selected,which is enough to ensure the privacy of every individualmodule,i.e.,a wearable device such as a smartwatch attached to the patient’s body.In contrast,the end module,i.e.,the server in this case,can extract important information with approximately the maximum level of accuracy.Moreover,refined data has been processed by adding an appropriate nose through the Laplace mechanism to make it useless or meaningless for the adversary modules in the IoT.The proposed hybrid approach is trusted from both the device’s privacy and the integrity of the transmitted information perspectives.Simulation and analytical results have proved that the proposed privacy-preserving information fusion technique for wearable devices is an ideal solution for resource-constrained infrastructures such as IoT and the Internet ofMedical Things,where both device privacy and information integrity are important.Finally,the proposed hybrid approach is proven against well-known intruder attacks,especially those related to the privacy of the respective device in IoT infrastructures.

Dynamics modeling and optimal control for multi-information diffusion in Social Internet of Things

As an ingenious convergence between the Internet of Things and social networks,the Social Internet of Things(SIoT)can provide effective and intelligent information services and has become one of the main platforms for people to spread and share information.Nevertheless,SIoT is characterized by high openness and autonomy,multiple kinds of information can spread rapidly,freely and cooperatively in SIoT,which makes it challenging to accurately reveal the characteristics of the information diffusion process and effectively control its diffusion.To this end,with the aim of exploring multi-information cooperative diffusion processes in SIoT,we first develop a dynamics model for multi-information cooperative diffusion based on the system dynamics theory in this paper.Subsequently,the characteristics and laws of the dynamical evolution process of multi-information cooperative diffusion are theoretically investigated,and the diffusion trend is predicted.On this basis,to further control the multi-information cooperative diffusion process efficiently,we propose two control strategies for information diffusion with control objectives,develop an optimal control system for the multi-information cooperative diffusion process,and propose the corresponding optimal control method.The optimal solution distribution of the control strategy satisfying the control system constraints and the control budget constraints is solved using the optimal control theory.Finally,extensive simulation experiments based on real dataset from Twitter validate the correctness and effectiveness of the proposed model,strategy and method.

An Optimized Approach to Deep Learning for Botnet Detection and Classification for Cybersecurity in Internet of Things Environment

The recent development of the Internet of Things(IoTs)resulted in the growth of IoT-based DDoS attacks.The detection of Botnet in IoT systems implements advanced cybersecurity measures to detect and reduce malevolent botnets in interconnected devices.Anomaly detection models evaluate transmission patterns,network traffic,and device behaviour to detect deviations from usual activities.Machine learning(ML)techniques detect patterns signalling botnet activity,namely sudden traffic increase,unusual command and control patterns,or irregular device behaviour.In addition,intrusion detection systems(IDSs)and signature-based techniques are applied to recognize known malware signatures related to botnets.Various ML and deep learning(DL)techniques have been developed to detect botnet attacks in IoT systems.To overcome security issues in an IoT environment,this article designs a gorilla troops optimizer with DL-enabled botnet attack detection and classification(GTODL-BADC)technique.The GTODL-BADC technique follows feature selection(FS)with optimal DL-based classification for accomplishing security in an IoT environment.For data preprocessing,the min-max data normalization approach is primarily used.The GTODL-BADC technique uses the GTO algorithm to select features and elect optimal feature subsets.Moreover,the multi-head attention-based long short-term memory(MHA-LSTM)technique was applied for botnet detection.Finally,the tree seed algorithm(TSA)was used to select the optimum hyperparameter for the MHA-LSTM method.The experimental validation of the GTODL-BADC technique can be tested on a benchmark dataset.The simulation results highlighted that the GTODL-BADC technique demonstrates promising performance in the botnet detection process.

An Efficient and Provably Secure SM2 Key-Insulated Signature Scheme for Industrial Internet of Things

With the continuous expansion of the Industrial Internet of Things(IIoT),more andmore organisations are placing large amounts of data in the cloud to reduce overheads.However,the channel between cloud servers and smart equipment is not trustworthy,so the issue of data authenticity needs to be addressed.The SM2 digital signature algorithm can provide an authentication mechanism for data to solve such problems.Unfortunately,it still suffers from the problem of key exposure.In order to address this concern,this study first introduces a key-insulated scheme,SM2-KI-SIGN,based on the SM2 algorithm.This scheme boasts strong key insulation and secure keyupdates.Our scheme uses the elliptic curve algorithm,which is not only more efficient but also more suitable for IIoT-cloud environments.Finally,the security proof of SM2-KI-SIGN is given under the Elliptic Curve Discrete Logarithm(ECDL)assumption in the random oracle.

Ultra reliability and massive connectivity provision in integrated internet of military things(IoMT)based on tactical datalink

One of the major challenges arising in internet of military things(IoMT)is accommodating massive connectivity while providing guaranteed quality of service(QoS)in terms of ultra-high reliability.In this regard,this paper presents a class of code-domain nonorthogonal multiple accesses(NOMAs)for uplink ultra reliable networking of massive IoMT based on tactical datalink such as Link-16 and joint tactical information distribution system(JTIDS).In the considered scenario,a satellite equipped with Nr antennas servers K devices including vehicles,drones,ships,sensors,handset radios,etc.Nonorthogonal coded modulation,a special form of multiple input multiple output(MIMO)-NOMA is proposed.The discussion starts with evaluating the output signal to interference-plus-noise(SINR)of receiver filter,leading to the unveiling of a closed-form expression for overloading systems as the number of users is significantly larger than the number of devices admitted such that massive connectivity is rendered.The expression allows for the development of simple yet successful interference suppression based on power allocation and phase shaping techniques that maximizes the sum rate since it is equivalent to fixed-point programming as can be proved.The proposed design is exemplified by nonlinear modulation schemes such as minimum shift keying(MSK)and Gaussian MSK(GMSK),two pivotal modulation formats in IoMT standards such as Link-16 and JITDS.Numerical results show that near capacity performance is offered.Fortunately,the performance is obtained using simple forward error corrections(FECs)of higher coding rate than existing schemes do,while the transmit power is reduced by 6 dB.The proposed design finds wide applications not only in IoMT but also in deep space communications,where ultra reliability and massive connectivity is a keen concern.

Federated Learning on Internet of Things:Extensive and Systematic Review

The proliferation of IoT devices requires innovative approaches to gaining insights while preserving privacy and resources amid unprecedented data generation.However,FL development for IoT is still in its infancy and needs to be explored in various areas to understand the key challenges for deployment in real-world scenarios.The paper systematically reviewed the available literature using the PRISMA guiding principle.The study aims to provide a detailed overview of the increasing use of FL in IoT networks,including the architecture and challenges.A systematic review approach is used to collect,categorize and analyze FL-IoT-based articles.Asearch was performed in the IEEE,Elsevier,Arxiv,ACM,and WOS databases and 92 articles were finally examined.Inclusion measures were published in English and with the keywords“FL”and“IoT”.The methodology begins with an overview of recent advances in FL and the IoT,followed by a discussion of how these two technologies can be integrated.To be more specific,we examine and evaluate the capabilities of FL by talking about communication protocols,frameworks and architecture.We then present a comprehensive analysis of the use of FL in a number of key IoT applications,including smart healthcare,smart transportation,smart cities,smart industry,smart finance,and smart agriculture.The key findings from this analysis of FL IoT services and applications are also presented.Finally,we performed a comparative analysis with FL IID(independent and identical data)and non-ID,traditional centralized deep learning(DL)approaches.We concluded that FL has better performance,especially in terms of privacy protection and resource utilization.FL is excellent for preserving privacy becausemodel training takes place on individual devices or edge nodes,eliminating the need for centralized data aggregation,which poses significant privacy risks.To facilitate development in this rapidly evolving field,the insights presented are intended to help practitioners and researchers navigate the complex terrain of FL and IoT.

GENDER EQUALITY IN THE CHINESE WORKPLACE

Gender equality is a significant issue in the economic and social sectors.A McKinsey study found that promoting gender equality in the workplace could contribute US$13 trillion to global GDP growth.And if China reaches the forefront of gender equality in the workplace in the Asia-Pacific region,it would generate about US$3 trillion in GDP.