Reinforcement learning (RL) has been increasingly adopted in IoT systems for tasks such as resource allocation and control. However, in privacy-critical and resource-constrained environments, existing privacy-preserving RL schemes suffer from high computational cost, slow convergence, and limited scalability due to the use of homomorphic encryption or differential privacy. We propose a distributed privacy-preserving Q-learning framework that enables secure and efficient policy updates across multiple clients. Each client independently trains a local Q-table and encrypts it using a sparse matrix transformation combined with additive secret sharing of structured perturbations. The encrypted Q-tables are uploaded to a cloud server for aggregation and averaging without decryption. The encrypted global Q-table is then returned and decrypted locally using the inverse sparse matrix. Experimental results on four benchmark environments (CartPole-v1, MountainCar-v0, Acrobot-v1, and LunarLander-v3) show that our scheme achieves up to 92% reduction in computation time compared to the FHE-based method, while maintaining comparable reward performance and faster convergence.

Machine learning algorithm for multi-modal image segmentation is extensively employed in medical analysis and diagnosis. Clustering represents a mainstream approach for image segmentation, with the fuzzy c-means and particle swarm optimization (FCM-PSO) algorithm garnering significant attention. As image segmentation tasks have substantial computational costs, the outsourcing scheme offers an effective solution by leveraging cloud servers to execute complex computations. Given that medical images contain sensitive patient information, the image segmentation outsourcing scheme must ensure data privacy and confidentiality. In this paper, we propose a secure outsourcing scheme for the FCM-PSO based image segmentation algorithm through a novel sparse matrix encryption method. By analyzing each stage of the image segmentation algorithm, we delegate the computationally intensive task of calculating the Euclidean distance to an untrusted cloud server. We utilize sparse matrices to obscure the private image data. These matrices are created by incorporating multiple small-sized random invertible matrices, thereby circumventing the local storage of generation factors. Additionally, we implement a lightweight verification method to verify the correctness of returned results. Experimental results show that our scheme improves the efficiency of the image segmentation task by 29.99% to 49.50% with the increasing of image set, compared to the original algorithm executed locally.

As a fundamental operation, Matrix Inversion Computation (MIC) plays an important role in various applications. Nevertheless, it is difficult for resource-constrained devices to independently compute large-scale MIC. A good choice of the user is to leverage the cloud for large-scale MIC computation under the condition of privacy protection. Recently, some privacy-preserving protocols for large-scale MIC have been proposed. In the paper, we show these existing protocols perform well in protecting dense matrices but fail to sufficiently safeguard the privacy of sparse matrices. For the applications based on sparse matrices, these protocols suffer from security vulnerabilities, which may leak privacy information through the zero elements or linear relationships in the blinded matrices. To circumvent such vulnerabilities, we firstly design a novel triangular matrix blinding technique that can well protect the sparse matrices. This blinding technique, however, has an$O(n^{3})$computational complexity, unable to be applied to secure outsourcing MIC directly. Then, we further construct an optimization algorithm that transforms the matrix multiplications involved in the designed triangular matrix blinding technique into matrix-chain multiplications and additions, thereby reducing the computational complexity from$O(n^{3})$to$O(n^{2})$. Based on above blinding technique and optimization algorithm, we finally propose an enhanced privacy-preserving protocol for large-scale MIC. Theoretical analysis shows that the proposed protocol satisfies privacy, correctness, verifiability, and high-efficiency. Experimental results demonstrate the performance advantage of the enhanced privacy-preserving protocol.

As a combination of digital twin and edge computing, the digital twin edge networks (DITENs) have gained significant interest due to their bridging roles between physical edge networks and digital systems. The Device-to-Device (D2D) communication acts as an ongoing transmission paradigm for DITENs since it facilitates interoperability between nearby wireless entities and enhances the spectrum utilization and overall throughput via direct link. However, most existing works on the D2D communication are related to the centralized ones, and consider the mobility and interference management separately, which cannot be used for the dynamic scenarios in DITENs. In this paper, we consider the D2D communication problem in dynamic DITENs in the context of the SINR model, and propose a dynamicity-tolerant D2D communication algorithm in a distributed manner. Using an oblivious transmission strategy, our algorithm can complete the D2D communication among$n$entities within$O(\log n)$time steps despite the various dynamic factors, which achieves asymptotically optimal time complexity. It is asserted that the D2D communication algorithm is asymptotically optimal, given that the lower bound for successful message dissemination is$\Omega (\log n)$. Rigorous theoretical analyses and empirical results are conducted to show the correctness and efficiency of our proposed algorithm.

The linkschedulingis to determine which links should be scheduled at what times, each of which is a (sender, receiver) communication pair used to realize wireless transmission of a message. It is an appealing solution to fulfill the resource-constrained and latency requirements of unmanned aerial vehicle (UAV) swarms. However, most existing link scheduling algorithms primarily focus on the throughput or latency in wireless communication, neglecting the protection against the eavesdropping attack due to the openness of UAV swarms, thereby leading to unsafe message dissemination. To address this issue, we consider integrating the covert communication into the link scheduling by concealing the very existence of message transmission. We first present a successive interference cancellation-based link diversity partition (SIC-LDP) algorithm in the context of the physical interference model, to maximize the number of concurrently transmitting links in a single time round, also called the maximum link scheduling (MLS) issue. Then, using a friendly jammer, we further propose a covertness-aware SIC-LDP algorithm (named SIC-CLDP) to resolve the MLS, as well as to defend against the eavesdropping attack. Both SIC-LDP and SIC-CLDP algorithms are proven to have constant approximation ratios. Next, implementing SIC-LDP and SIC-CLDP repeatedly can minimize the number of time rounds schedulingnparticipating links, termed the shortest link scheduling (SLS) issue, with an approximation ratio ofO(lnn). Lastly, theoretical proofs and simulation results demonstrate the correctness, covertness, and efficiency of our proposed algorithms under the eavesdropping attack.

With the rapid development of artificial intelligence and big data technologies, gait recognition has become a key method for identity authentication. As a unique biometric characteristic, gait is difficult to counterfeit and supports long-distance, non-contact authentication, making it ideal for security, surveillance, and health monitoring. However, traditional gait authentication faces privacy and efficiency challenges. This paper presents a privacy-preserving gait authentication scheme based on partial Euclidean distance calculation, and the scheme encrypts gait features using block-diagonal orthogonal matrices and random perturbation vectors, enabling efficient encrypted computation on the cloud. Experimental results demonstrate that the proposed scheme improves processing efficiency and matching accuracy while protecting privacy. For instance, on the CASIA-B dataset, it reduces computation time by approximately 30% without compromising accuracy.

Graph matching, as an important query technology, has been widely applied in various fields. With the increasing of graph data, users choose to encrypt a large number of graphs and store them in the cloud. Existing solutions to graph matching query over encrypted graphs require the user to execute a lot of time-consuming subgraph isomorphism (NP-complete problem) operations to extract the matched graphs, which inevitably brings heavy computational burden to the user. Therefore, how to reduce the number of subgraph isomorphisms is crucial for releasing the user from the heavy workload in a graph matching query scheme over encrypted graphs. In this paper, we propose a secure and efficient scheme for graph matching query over encrypted graphs. The main idea is to classify the query graph into frequent subgraph and infrequent subgraph, and adopt different strategies to perform the matching query. We design the novel secure index based on the frequent subgraphs and the edge labels to reduce the number of subgraph isomorphisms. When the query graph is a frequent subgraph, the proposed scheme can directly produce the exact result owing to this secure index. The user does not need to perform any subgraph isomorphism in this case. When the query graph is an infrequent subgraph, the proposed scheme can return a set of data graphs very close to the exact result. As a result, the proposed scheme reduces the number of subgraph isomorphisms substantially. Formal security proof is provided. Extensive experiments on real-world data sets show that the proposed scheme reduces nearly 90% subgraph isomorphism.

Privacy-preserving federated learning can protect the privacy of model gradients/parameters in the model aggregation phase. Most existing schemes only consider the scenario where user models have the same weight in model aggregation. However, users often hold different numbers of training samples in practice. This makes the model convergence speed of existing schemes very slow. To solve this problem, we propose a privacy-preserving federated learning scheme with secure weighted aggregation. It is able to allocate appropriate user weights based on the user’s local data size with privacy protection. In addition, it is impossible for the cloud server to obtain the user’s original model parameters and local data size in the proposed scheme. Specifically, we use Lagrange interpolation to combine the model parameters and local data size into a set of ciphertexts. The cloud server can smoothly perform weighted aggregation based on these ciphertexts. Leveraging the Chinese Remainder Theorem, we convert the local data size into a series of verification values. This enables the user to verify the correctness of results returned from the server. We provide a theoretical analysis for the proposed scheme, demonstrating its effectiveness, privacy, and verifiability. We perform extensive experiments on the MNIST dataset. Experimental results demonstrate its model performance, computation overhead, and communication overhead.

Community search on attributed graphs has gained significant attention in recent years for its ability to provide meaningful and personalized results. Given a query community, a similar community search aims to identify the communities that are similar in structural and attributed characteristics to the query community. As real-world networks continue to grow in complexity and size, outsourcing graph data and search tasks to cloud servers not only saves local storage space but also significantly enhances search efficiency. Nonetheless, this inevitably raises concerns about data privacy since cloud servers are not completely trustworthy. In this paper, we research on privacy-preserving similar community search on graphs. We propose a privacy-preserving closest similar community search scheme for attributed graphs that leverages cloud servers to enhance search efficiency while safeguarding the sensitive information in the graph. We consider packaging communities using center vertices to evaluate relationships across communities without accessing details within the communities. To achieve this, we design a centrality score function that integrates attribute contribution and closeness centrality to identify the center vertex of a community. To ensure the security of sensitive information in the attribute graph, we construct three secure indexes for the original graph utilizing diverse cryptographic primitives. By searching secure indexes, cloud servers can answer the closest similar community searches without possessing any sensitive information about the attribute graph. We employ Paillier homomorphic cryptosystem and related protocols to support efficient and secure evaluation of the distance and similarity between two communities on secure indexes. The security analysis confirms that the proposed scheme can be against adaptive chosen-query attacks so as to achieve CQA2-security and experimental results demonstrate the efficiency of the proposed scheme.

The top-k Hamming distance query is to find the k optimal objects with the smallest Hamming distance to the query data. It has a wide range of applications in many domains such as social networks, image retrieval and biological recognition. The existing privacy-preserving protocols do not support the top-k Hamming distance query in practice. To address this issue, we consider letting the user securely query the top-k Hamming distance on the cloud in a secure outsourcing manner. We propose two protocols to realize the privacy-preserving top-k Hamming distance query on the cloud. In the first protocol, two cloud servers are introduced to cooperatively complete the privacy-preserving top-k Hamming distance query. To preserve data privacy, the Paillier encryption and randomization techniques are leveraged to blind the user data, and the ciphertext data is stored on the first cloud server. The second cloud server calculates the Hamming distance on the ciphertexts. After that, the encrypted query results are returned to the query user for recovering the top-k query results. In the second protocol, we adopt the data aggregation strategy to further enhance the efficiency. By packaging data, the computation overhead of each participant is reduced and the communication overhead of the protocol is decreased, remarkably. Security analysis demonstrates that the data privacy is guaranteed in the proposed protocols. Experimental results evaluate the performance of the proposed protocols and confirm the superiority of the second protocol.

Lattice-based Post-Quantum Cryptography (PQC) can effectively resist the quantum threat to blockchain's underlying cryptographic algorithms. Blockchain node decryption is one of the most commonly used cryptographic computations in blockchain systems, and polynomial multiplication, a time-consuming operation for decryption, is one of the factors limiting blockchain efficiency. This paper proposes a novel distributed computing algorithm for polynomial multiplication, applicable in blockchain decryption. By splitting polynomials into lower-degree terms and delegating tasks to distributed nodes, our approach reduces computation time. A novel verification strategy based on the Karatsuba algorithm ensures result accuracy. The experimental results demonstrate that our proposed scheme improves the execution efficiency of NTT and INTT operations by approximately 47.8% and 52.4%, and reduces Kyber decryption time by up to 23.5%.

Abstract According to Menger’s theorem, connectivity and edge connectivity are closely related to node-disjoint paths and edge-disjoint paths, respectively. Node- and edge-disjoint paths can keep the effective transmission of information and confidentiality. Therefore, node-disjoint paths and edge-disjoint paths are two important parameters to measure the reliability of a network. For a faulty node (resp. edge) set $S\subset V$ (resp. $S\subset E$), a connected graph $G=(V,E)$ is $S$-strongly Menger-node-connected (resp. Menger-edge-connected) if any two distinct nodes $x$ and $y$ in $G-S$ are connected by $\min \{\deg _{G-S}(x),\deg _{G-S}(y)\}$ internally node-disjoint (resp. edge-disjoint) paths in $G-S$, where $\deg _{G-S}(x)$ and $\deg _{G-S}(y)$ are the degrees of $x$ and $y$ in $G-S$, respectively. And most of the previous studies are based on networks that are triangle-free. In this paper, we consider the strongly Menger (edge) connectedness of a class of $r$-dimensional recursive networks RNCG $G_{r}$ with triangles. Moreover, we show that $G_{r}$ is $(rl-l-1)$-strongly Menger-node-connected. And then we show that $G_{r}$ is $[k+(r-1)l-2]$-strongly Menger-edge-connected of order 1 and $[2k+2(r-1)l-6]$-strongly Menger-edge-connected of order 2. Since the class of $r$-dimensional recursive networks RNCG $G_{r}$ includes not only data center networks DCell and generalized DCell but also interconnection network dragonfly, etc., all the results are appropriate for these networks.

With the advancement of the Internet of Things (IoT), numerous machine learning applications on IoT are encountering performance bottlenecks. Graph embedding is an emerging type of machine learning that has achieved commendable results in areas such as network anomaly detection, malware detection, IoT device management, and service recommendation within the Internet of Things. However, for some resource-constrained IoT devices, computing graph embedding algorithms is highly complex and time-consuming. In this paper, we introduce an efficient and secure distributed outsourcing scheme, employing four non-colluding cloud servers to facilitate the computation of graph embedding for IoT devices. Our scheme utilizes a novel blinding factor generated through QR decomposition to blind matrices containing sensitive information. We partition the blinded matrix into several segments, distributing different small matrix blocks across four servers, each of which executes only a portion of the computational tasks. The proposed outsourcing solution ensures the privacy of input and output information is not compromised. In our scheme, we utilize an effective verification method that can detect the erroneous behaviors of cloud servers with a probability close to one. Theoretical analysis and experimental results indicate that our solution achieves a computational efficiency of (35m2+2m)/(3m3) compared to the original algorithm.

With the rapid development of IoT technology, a vast quantity of spatial data with text information is generated, because of the explosive growth of the spatial data, users usually encrypt these data and outsource them to the cloud for enjoying the storage and computing capability. Privacy-preserving Boolean k Nearest Neighbor (kNN) query is a typical query technique over the spatial data. It finds k objects that exactly match the query keyword and are nearest to the query point upon encrypted spatial data. We propose a scheme which supports the privacy-preserving Boolean kNN query over the cloud-based spatial data in this article. In order to efficiently obtain the spatial objects containing the query keywords, we ask the cloud to pick the objects containing the query keyword with the lowest frequency. Then, the cloud filters out the objects that do not contain other query keywords. Since the number of objects containing the query keyword with the lowest frequency is minimal, the number of objects to filter is also minimal. In this way, the query efficiency is improved. In order to realize convenient and safe distance comparison over the encrypted spatial data, we convert the coordinates to the vectors. The distance between the two points can be expressed as the inner product of the two vectors. Furthermore, we use the enhanced asymmetric scalar-product-preserving encryption algorithm to protect the data privacy. We prove that the proposed scheme satisfies the CQA2-security. Meanwhile, we conduct experiments using the real data sets to show the performance of the proposed scheme.

Linear regression is a classical statistical model with a wide range of applications. The function of linear regression is to predict the value of a dependent variable (the output) given an independent variable (the input). The training of a linear regression model is to find a linear relationship between the input and the output based on data samples. IoT applications usually require real-time data processing. Nonetheless, the existing schemes about privacy-preserving outsourcing of linear regression cannot fully meet the rapid response requirement for computation. To address this issue, we consider employing multiple edge servers to accomplish privacy-preserving parallel computation of linear regression. We propose two novel solutions based on edge servers in edge computing networks and construct two efficient schemes for linear regression. In the first scheme, we present a new blinding technique for data privacy protection. Two edge servers are employed to execute the encrypted linear regression task in parallel. To further enhance the efficiency, we design an adaptive parallel algorithm, which is adopted in the second scheme. Multiple edge servers are employed in the second scheme to achieve higher efficiency. We analyze the correctness, privacy, and verifiability of the proposed schemes. Finally, we assess the computational overhead of the proposed schemes and conduct experiments to validate the performance advantages of the proposed schemes.

Cloud-assisted computation empowers resource-constrained clients to efficiently tackle computationally intensive tasks by outsourcing them to resource-rich cloud servers. In the current era of Big Data, the widespread need to solve large-scale modular linear systems of equations ($\mathcal {LMLSE}$) of the form$\mathbf {A}\mathbf {x}\equiv \mathbf {b}\;{\rm mod}\;{q}$poses a significant challenge, particularly for lightweight devices. This paper delves into the secure outsourcing of$\mathcal {LMLSE}$under a malicious single-server model and, to the best of our knowledge, introduces the inaugural protocol tailored to this specific context. The cornerstone of our protocol lies in the innovation of a novel matrix encryption method based on sparse unimodular matrix transformations. This novel technique bestows our protocol with several key advantages. First and foremost, it ensures robust privacy for all computation inputs, encompassing$\mathbf {A},\mathbf {b}, q$, and the output$\mathbf {x}$, as validated by thorough theoretical analysis. Second, the protocol delivers optimal verifiability, enabling clients to detect cloud server misbehavior with an unparalleled probability of 1. Furthermore, it boasts high efficiency, requiring only a single interaction between the client and the cloud server, significantly reducing local-client time costs. For an$m$-by-$n$matrix$\mathbf {A}$, a given parameter$\lambda =\omega (\log q)$, and$\rho =2.371552$, the time complexity is diminished from$O(\max \lbrace m n^{\rho -1}, m^{\rho -2} n^{2}\rbrace \cdot (\log q)^{2})$to$O((mn+m^{2})\lambda \log q+mn(\log q)^{2})$. The comprehensive results of our experimental performance evaluations substantiate the protocol's practical efficiency and effectiveness.

Graph matching, as one of the most fundamental problems in graph database, has a wide range of applications. Due to the large scale of graph database and the hardness of graph matching, graph user tends to outsource the encrypted graphs to the cloud. The complex graph matching is performed by the cloud. Several schemes have been proposed to support graph matching query over encrypted graphs. However, none of them can realize efficient subgraph extraction when the matched subgraph needs to be exactly located at the data graph. The graph user has to perform the complex subgraph isomorphism (NP-complete problem) operation to extract the isomorphic subgraph from the matched data graph in state-of-the-art schemes. In order to solve this problem, we propose a privacy-preserving graph matching query scheme supporting quick subgraph extraction in this paper. In our design, two non-colluding cloud servers are adopted to accomplish the matching operation jointly. Neither of them can infer the plaintexts of graphs. Two cloud servers jointly get a matched matrix to represent the matching relationship between vertices in data graph and query graph. Graph user can directly and quickly extract the subgraph isomorphic to query graph from data graph based on the matched matrix. No subgraph isomorphism operation is involved for graph user. The time complexity of subgraph extraction is$O(m^{2})$in our scheme, where$m$is the number of vertices in query graph. The extensive experiments with real-world database demonstrate the efficiency of the proposed privacy-preserving graph matching scheme.

The minimum community search is used to identify a minimum dense community that includes a specified vertex in a large network. It has gained significant attention because of its various applications in social-network analysis, e-commerce transactions, biological network modeling, and other areas. Nevertheless, how to realize privacy-preserving minimum community search remains unexplored up to now. In this paper, we initiate the first research on privacy-preserving approximate minimum community search. We propose an effective scheme that allows cloud servers to identify the smallest possible community while safeguarding the private information of the network. To ensure the privacy of sensitive information in the network, we employ obfuscation technology and graph encryption technology to construct two secure indexes instead of the original graph. To strike a balance between safeguarding private information and maintaining search efficiency, our scheme incorporates Bloom filters into the index and implements a two-step strategy on the secure indexes to achieve privacy-preserving approximate minimum community searches. Furthermore, to secure the privacy of the search result, we carefully design an array comparison protocol based on the BGN cryptosystem. This protocol enables cloud servers to perform privacy-preserving heuristic searches from the initial community without exposing any details about the approximate minimum community. The security analysis confirms that our scheme achieves CQA2-security for two non-colluding cloud servers. The experimental results based on real social networks show that the proposed scheme can efficiently handle approximate minimum community searches on large networks.

Cloud storage auditing mechanism is used to check whether the data of users stored in the cloud is intact. Most existing auditing schemes for secure cloud storage are designed to check the integrity for specified files based on file identities. In some scenarios, the user would like to check the integrity of the files generated and uploaded to the cloud in a certain time period. Existing cloud storage auditing schemes cannot work well for supporting this practical requirement because the private information will be exposed. To satisfy this requirement, we propose a brand-new paradigm termed as privacy-preserving time-based auditing for secure cloud storage. The proposed paradigm allows the user to check whether the files generated and uploaded in a certain time period are intactly stored in the cloud. When intending to check the integrity of the files uploaded in this time period, the user only provides the challenged time period t to the Third Party Auditor (TPA). The TPA can verify the integrity of all the files based on this time period, but cannot know how many files and which files the user has generated and uploaded to the cloud in this time period. To decrease the complex overhead associated with certificate management, we introduce an identity-based auditing mechanism. We provide a specific security analysis to show the correctness, auditing soundness and privacy preserving of this scheme. The experiments demonstrate the efficiency of the proposed scheme.

As the Internet of Medical Things booms, the cloud-assisted health monitoring service has attracted extensive attention. The medical institutions often use the Naïve Bayesian classification technology to establish the medical inference models. These models can be outsourced to cloud servers, allowing the remote users without models to utilize well-performing models for medical diagnosis. Existing Naïve Bayesian secure outsourcing schemes mostly use heavy cryptographic primitives or pure additive secret sharing (ASS) technology. In this article, we use searchable encryption technology combined with ASS to design a privacy-preserving Naïve Bayesian classification scheme that can protect the medical institutions' models, the users' medical data, and the final inference result made by cloud servers. Compared with the state-of-the-art, our scheme further reduces the number of communications between the user and the cloud server and reduces the computation complexity of cloud servers from$O(dtf)$to$O(dt)$. We provide the formal security analysis to show that our scheme ensures the necessary security. Through experiments on multiple datasets, we show that our scheme can efficiently handle the classification requests in the test dataset in less than 100 ms.

Remote data integrity auditing, as a key technology for cloud storage, allows verifier to check cloud data integrity without downloading entire file from cloud server (CS). In practice, user might only concern the integrity of the files containing the specific keyword and would like to perform data dynamic operations on data. In this paper, we construct a practical keyword-based remote data integrity auditing scheme supporting full data dynamics. In such a scheme, a novel construction called keyword tag is designed. Using the keyword tag, TPA is able to simultaneously check whether CS correctly keeps all files containing the specific keyword. TPA can detect CS's misbehaviors once CS does not keep these files correctly. Furthermore, our scheme supports full data dynamics, including file-level updates and block-level updates. The keyword tag is updated when the user performs the file-level updates. To support block-level updates, we introduce an index switcher set to maintain the relationship between the block index and the authenticator index. We can avoid the recalculation of the authenticators by using authenticator indexes to generate authenticators. After cloud data are updated, data integrity still can be guaranteed. Security analysis and experimental results show that our scheme is provably secure and efficient.

K-hop Reachability Query (KRQ) is one of fundamental graph queries, which can answer whether a node u can reach a node v within K hops. With the scale of graph data increasing, data owner desires to outsource the local graphs to cloud server. To protect the graph privacy, data owner encrypts graphs before outsourcing them to the cloud server. It imposes a great challenge to KRQ over encrypted graphs. How to realize Privacy-Preserving K-hop Reachability Query (PPKRQ) over encrypted graphs is still an unexplored problem. In this paper, we explore this problem and propose a practical scheme. In order to efficiently answer KRQ over encrypted graphs, we construct the encrypted Breadth-First Spanning Tree table and adjacent list D (BFST-D). Based on encrypted BFST table, we can directly judge whether two query nodes are reachable within K hops when they are in one spanning tree. The encrypted adjacent list D can help answer that two query nodes in different spanning trees. To protect the privacy, we utilize the Paillier cryptographic and Order-Revealing Encryption (ORE) to support the comparison and computation over ciphertexts. As a result, our scheme achieves the sensitive information privacy without losing the ability of querying over encrypted graphs. The security analysis shows that our proposed scheme is secure based on semi-honest cloud server. The extensive experiments show the efficiency of our scheme.

With the rapid development of 5 G and 6 G technologies, vast amounts of data are being generated. To save costs and ensure data security, these data are typically uploaded to multiple cloud servers. For handling massive data, distributed storage is necessary. Additionally, remote data integrity checking is essential. To achieve this, the PDP paradigm (Provable Data Possession) has been proposed. Unfortunately, existing PDP schemes suffer from inefficiencies. The main cause is that the data must be divided into small blocks with a limited size, such as 160 bits for bilinear pairings-based PDP schemes. This approach incurs significant computation and communication costs.To address this issue, we propose a new model called synchronous blockchain-based DPDP (Distributed Provable Data Possession) with forward-security in multi-cloud storage. This new concept leverages blockchain, which is the foundation of cryptocurrency. The paper formalizes the system model and security model for the new concept. Furthermore, a concrete blockchain-based DPDP scheme is designed using blockchain and RSA. The proposed scheme is provably secure, and its performance is analyzed from both theoretical and implementation perspectives. Our analysis demonstrates that the proposed DPDP scheme is provably secure, synchronous, forward-secure, efficient, and practical.

Large-scale matrix multiplication is a computational bottleneck in various applications including artificial intelligence and machine learning. Given the time complexity of O(n3) for matrix multiplication, large matrix computation is exceedingly time-consuming for the client-side user. By outsourcing this task to cloud servers with substantial computational resources, we can significantly reduce the client-side computational time. This paper presents a parallel matrix multiplication outsourcing scheme based on Cannon’s algorithm. By distributing the matrix across multiple cloud servers for parallel computation, we can get a significant efficiency speedup. Our scheme employs multiple cloud servers to perform parallel matrix computation, reducing the computational load by 89-97% when utilizing 4-16 servers as opposed to using a single server. We provide a comprehensive analysis of the scheme’s correctness, security, and verifiability, substantiating the benefits of our approach through the experimental data.

The proliferation of Internet of Things (IoT) devices has led to the generation of massive amounts of data that require efficient aggregation for analysis and decision-making. However, multi-tier IoT systems, which involve multiple layers of devices and gateways, face more complex security challenges in data aggregation compared to ordinary IoT systems. In this paper, we propose an efficient privacy-preserving multi-functional data aggregation scheme for multi-tier IoT architecture. The scheme supports privacy-preserving calculation of mean, variance, and anomaly proportion. The scheme uses the Paillier cryptosystem and the BLS algorithm for encryption and signature, and uses blinding techniques to keep the size of the IoT system secret. In order to make the Paillier algorithm more suitable for the IoT scenario, we also improve its efficiency of encryption and decryption. The performance evaluation shows that the scheme improves encryption efficiency by 43.7% and decryption efficiency by 45% compared to the existing scheme.

Public auditing is a significant technique in cloud-based Internet of Things (IoT) systems, which enables the verifier to check the integrity of IoT data stored in the cloud. Nowadays, data become a core property for owners. Once the data of one owner are sold to another one, the ownership of these data has to be transferred. However, the existing public auditing schemes with data transfer require all the authenticators corresponding to the transferred data to be transformed to the new ones for integrity auditing. It incurs significant computation cost because of recomputing the new authenticators for all transferred data, especially when a vast quantity of data is being transferred. In addition, the data privacy and the identity privacy of the data owner cannot be protected for the verifier in such schemes. Thus, how to achieve efficient data transfer and privacy protection are key challenges in public auditing with data transfer for cloud-based IoT data. In this article, we propose a privacy-preserving identity-based public auditing scheme with efficient data transfer for cloud-based IoT data (PPADT). In PPADT, all the authenticators corresponding to the transferred data blocks do not need to be transformed. We only need to transform an aggregated authenticator in the integrity auditing phase. It means that the computation cost of data transfer is independent of the number of transferred data blocks. Furthermore, the data owner’s identity privacy can be ensured with the assistance of the private key generator. The data privacy can also be guaranteed by employing the random masking technique.

Face recognition is one of the key technologies in intelligent security systems. Data privacy and identification efficiency have always been concerns about face recognition. Existing privacy-preserving protocols only focus on the training phase of face recognition. Since intelligent security systems mainly complete the calculation of large-scale face data in the identification phase, existing privacy-preserving protocols cannot be well applied to intelligent security systems. In this article, we propose the first privacy-preserving face recognition protocol for the calculations in the identification phase for intelligent security systems. We introduce the Householder matrix to blind user data including model data and face data, which enables the proposed protocol to support privacy-preserving face recognition on semi-trusted edge servers. Utilizing edge computing, fast response for large-scale face recognition can be achieved. The user can offload heavy calculations of matrix multiplication and Euclidean distances to edge servers simultaneously. The proposed protocol supports parallel computing based on multiple edge servers and thus enhances the efficiency of face recognition in intelligent security systems. Moreover, the recognition accuracy in the proposed protocol is the same as that in the original PCA-based face recognition algorithm. The security analysis demonstrates that the protocol protects the privacy of user data. The numerical analysis and simulation experiments are carried out to show the efficiency and feasibility of the proposed protocol.

The key exposure is a serious threat for the security of data integrity auditing. Once the user's private key for auditing is exposed, most of the existing data integrity auditing schemes would inevitably become unable to work. To deal with this problem, we construct a novel and efficient identity-based data integrity auditing scheme with key-exposure resilience for cloud storage. This is achieved by designing a novel key update technique, which is fully compatible with BLS signature used in identity-based data integrity auditing. In our design, the Third Party Auditor (TPA) is responsible for generating update information. The user can update his private key based on the private key in one previous time period and the update information from the TPA. Furthermore, the proposed scheme supports real lazy update, which greatly improves the efficiency and the feasibility of key update. Meanwhile, the proposed scheme relies on identity-based cryptography, which makes certificate management easy. The security proof and the performance analysis demonstrate that the proposed scheme achieves desirable security and efficiency.

Aggregate signatures enable the sensor nodes of Industrial Internet of Things to send their signatures to the aggregator to realize signature compression. Before being stored in the data center, sensitive data and non-sensitive data should adopt different data processing methods in the process of sensor data fusion. In the high security analysis scenario of Industrial Internet of Things, only the verifier with a specified high security level can verify the resulting aggregate signature. So far, no one has explored how to ensure sensitive data privacy in the designated-verifier aggregate signatures. Motivated by it, this paper proposes a designated-verifier aggregate signature scheme (named DVAS) based on permissioned blockchain to achieve sensitive data privacy. In this scheme, the aggregator can be used not only to aggregate signatures, but also to sanitize data. Through smart contracts, the aggregator can sanitize the sensitive data according to the contract, and convert the original signature of the sensitive data into a valid signature. Therefore, DVAS can achieve elastic sensitive data privacy, not limited to encryption operations. The security attributes of DVAS include conditional anonymity, unforgeability, immutability and protecting data privacy. At the same time, DVAS realizes accountability through signature verification. Finally, the formal security proof, performance evaluation and experiments indicate that DVAS is secure, effective and practical for Industrial Internet of Things.

With the widespread deployment of secure outsourcing computation, the resource-constrained client can delegate intensive computation tasks to powerful servers. Matrix determinant computation is a fundamental mathematical operation that has been widely used in IoT applications. This operation is computationally expensive. Nevertheless, the existing secure outsourcing protocols for matrix determinant are all designed based on one cloud server, which cannot well meet the low-latency and real-time computing requirements for the client. To address this issue, we explore accelerating the computation of matrix determinant by parallel outsourcing based on two nearby edge servers and propose the first practical protocol. We use the matrix blocking technique to split the computation task into multiple subtasks, which are parallel outsourced to edge servers for accelerating the computation. Moreover, we propose a privacy-preserving matrix transformation technique for data privacy protection. This technique only involves the operations of matrix-vector multiplication and matrix-matrix addition. It achieves the lightweight computation for the client and supports computational indistinguishability for the blinded input and a uniform distribution. The correctness, privacy and verifiability of the proposed protocol are analyzed. Finally, the performance advantage of the proposed protocol is demonstrated through simulation experiments.

Edge computing can help the resource-constrained Internet of Things (IoT) devices to perform some complex tasks. Edge computing has many advantages, such as the distributed architecture, low interaction latency, and good resilience. It can provide fast response and reliable service for the IoT applications. There exists an important application in the edge computing environment is to outsource the computationally intensive problems to nearby edge servers, which has become a research hotspot in the area of industry and academia. In this article, we propose a distributed and secure system DSOS for seeking the least squares solution to the overdetermined system of linear equations (OSLE) with the assistance of multiple nearby noncolluding edge servers. Solving this type of linear equations is one of the most common problems for statistics and data mining in IoT. In our system, the coefficient matrix is divided into multiple blocks according to rows. The different blocks are distributed to the different edge servers. All edge servers can help the user to obtain the correct solution to the OSLE by the interactive computation. Our system can ensure the private information about input parameters and final results is not leaked to the participating edge servers. In addition, the mutual verification between the edge servers can ensure the validity of the final results. The experimental evaluations show that the designed system outperforms the existing ones in terms of fast response between the edge server and the user, low computation overload on the edge server side, and high efficiency on the user side.

With the popularity of Internet of Things (IoT) and 5G, privacy-preserving message transmission and authentication have become an indispensable part in the field of data collection and analysis. There exist many protocols based on the public key cryptosystem, which allow the users to utilize their own identity as the public key to carry out data encryption and digital signature, which is very suitable for applying in the IoT environment with a large number of terminal devices. However, these protocols usually involve some complex cryptographic operations, which hinder their application on the resource-constrained IoT devices. In this paper, we design a privacy-preserving and verifiable outsourcing message transmission and authentication protocol, which allows the resource-constrained users to delegate some complex operations to the two untrusted edge servers and reduce the computational burden on the users side. The designed protocol contains several secure and novel outsourcing algorithms for modular exponentiation, bilinear pairing and scalar multiplication. For the different operations in the different situations, we design several different blinding techniques and verification methods, which not only protect the users’ private information, but also ensure the users can verify the correctness of results. Finally, we carry out some experiments to show that our proposed protocol is efficient.

Abstract Connectivity and diagnosability are two crucial subjects for a network’s ability to tolerate and diagnose faulty processors. The $r$-component connectivity $c\kappa _{r}(G)$ of a network $G$ is the minimum number of vertices whose deletion results in a graph with at least $r$ components. The $r$-component diagnosability $ct_{r}(G)$ of a network $G$ is the maximum number of faulty vertices that the system can guarantee to identify under the condition that there exist at least $r$ fault-free components. This paper first establishes that the $(r+1)$-component connectivity of $k$-ary $n$-cube $Q^{k}_{n}$ is $c\kappa _{r+1}(Q^{k}_{n})=-\frac{1}{2}r^{2}+\Big(2n-\frac{1}{2}\Big)r+1$ for $n\geq 2$, $k\geq 4$ and $1\leq r\leq n$. In view of $c\kappa _{r+1}(Q^{k}_{n})$, we prove that the $(r+1)$-component diagnosabilities of $k$-ary $n$-cube $Q^{k}_{n}$ under the PMC model and MM* model are $ct_{r+1}(Q^{k}_{n})=-\frac{1}{2}r^{2}+\Big(2n-\frac{3}{2}\Big)r+2n$ for $n\geq 4$, $k\geq 4$ and $1\leq r\leq n-1$.

Abstract Connectivity is a significant metric to assess the fault tolerance of a network. For a faulty vertex set $H$, the $h$-extra connectivity is defined under the assumption that every component of the network removing $H$ has at least $h+1$ fault-free vertices. Compared to the traditional connectivity, which is defined under the assumption that the network removing $H$ is disconnected or trivial, the $h$-extra connectivity can better reflect the true fault tolerance of the network. The $BCube$ is an important server-centric data center network; it has good fault tolerance and scalability. In this paper, our research focuses on the logical structure of $BCube$, named $BC_{n,k}$, which is actually a specific type of generalized hypercubes. We prove that the 3-extra connectivity of $BC_{n,k}$ is $4(k+1)(n-1)-4n$ for $k\geq 4$ and $n\geq 4$.

With the rapid development of Internet of Things (IoT), edge computing has been widely applied as a novel computing paradigm. Securely outsourcing intensive tasks to edge servers is becoming increasingly pervasive. It is a nice approach for resource-limited IoT devices to accomplish heavy computing tasks. Matrix inversion is a basic but time-consuming operation, which has a wide range of applications in IoT. The current privacy-preserving outsourcing schemes for matrix inversion cannot support parallel computing based on multiple edge servers. As a result, they cannot well satisfy the requirement of fast response for computation in IoT. In order to deal with this problem, we propose two privacy-preserving parallel outsourcing schemes for matrix inversion in IoT. In the first scheme, we design a novel method to generate a random matrix, which is used to blind the inputted original matrix. In this scheme, two edge servers compute the inversion of the encrypted matrix in parallel to improve the computational efficiency. To further improve the efficiency, we design a novel subtasks partitioning and assignment strategy and propose the second scheme by balancing the computing load of edge servers. We analyze the correctness, security, and verifiability of the proposed schemes. And we provide theoretical analysis and experimental results to demonstrate the performance advantages of the proposed schemes.

Solving quadratic congruence equations is an expensive operation widely employed in cryptographic constructions for secure Internet of Things applications. Recently, two outsourcing algorithms were proposed by Zhanget al.to solve quadratic congruence equations by employing Cippolla’s algorithm. It was claimed that all the inputs and outputs can be obscured in these two algorithms. However, we present two passive attacks in this article to show that all the inputs and outputs can be recovered efficiently by just a curious server, which implies the two outsourcing algorithms are insecure. To fix them, we further propose an improved outsourcing algorithm to solve quadratic congruence equations, which is more efficient and the privacy of actual inputs and outputs can be protected very well.

With popularity and growth of cloud computing, outsourcing computation, as an important cloud service, has been applied in the field of academic and industry. It allows the resource-constrained IoT devices to outsource the computationally intensive problems to the cloud server. The smallest normalized cuts of the large-scale graph is a fundamental issue in graph theory, which is often used in various fields, such as community discovery, image segmentation, and network partition. Minimizing the normalized cuts of graph, as an NP-hard problem, can be approximately solved by the spectral decomposition. However, carrying out the spectral decomposition is very time-consuming and complicated for some IoT devices. In this article, we design a secure and efficient algorithm for outsourcing the spectral decomposition to an untrusted cloud server. We utilize a series of elementary matrices to protect both the input’s privacy and the output’s privacy from being disclosed to the cloud server. In order to ensure the correctness of the returned results, we design an efficient verification algorithm, which allows the client to detect the invalid results with a probability approximately 1. Our proposed algorithm not only reduces computational overhead on the client side, but also does not bring extra computational overhead on the cloud server side. Then, we give a theoretical analysis about correctness and privacy. Finally, we also provide some experimental results to show the feasibility of our proposed algorithm.

The Internet of Things (IoT) devices possessed by individuals produce massive amounts of data. The private data onto specific IoT devices can be combined with intelligent platform to provide help for future research and prediction. As an important digital asset, individuals can sell private data to get rewards. Problems, such as privacy, security, and access control prevent individuals from sharing their private data. The blockchain technology is widely used to build an anonymous trading system. In this article, we construct a blockchain-based privacy-preserving and rewarding private data-sharing scheme (BPRPDS) for IoT. A privacy issue worth considering is that the malicious cloud server may establish a behavior profile database of data users (DUs). In the case of anonymity, the transactions of private data sharing are easy to cause disputes. When anonymous DUs are framed, it is hard to protect their rights. With the help of the deniable ring signature and Monero, we realize the behavior profile building prevention and nonframeability of BPRPDS. At the same time, we utilize the licensing technology executed by smart contracts to ensure flexible access control of multisharing. The proposed BPRPDS is provably secure. Performance analysis and experimental results show that BPRPDS is efficient and practical.

With the development of cloud computing and the advent of Internet of Things(IoT), outsourcing computation, as an important application of cloud computing, has been widely researched in the field of academic and industry. The convex optimization problem, as a most common mathematical problem, often appears in some machine learning algorithms and smart grid designs. However, the process of solving the convex optimization problem is very complicated and time-consuming. For some resource-constrained IoT devices, there are no enough computation resources and storage resources to deal with this problem. In this paper, we proposed an efficient and secure outsourcing algorithm for solving the large-scale convex optimization problem with equality constraints in IoT. Our proposed algorithm can not only reduce the computational complexity on the client side, but also protect the client’s sensitive data from being disclosed to the dishonest cloud server. In addition, the client can detect the malicious behavior from the cloud server with probability approximately 1. Finally, we give a theoretical analysis about correctness and security, and conduct experiments to show the feasibility of our proposed algorithm.

With the vigorous development and gradual maturity of machine learning (ML) technologies, the AI-assisted disease diagnosis and prediction ($\mathcal {AADP}$) system has been extensively studied and can be expected to be intensively deployed in the real world. However, as the scale of ML data increases exponentially, the training and application of ML models impose a great burden on resource-constrained terminals. Designing cloud/edge server-aided$\mathcal {AADP}$protocols is becoming a popular topic. Whereas, the sensitivity of ML data, the intellectual property of ML models, and the uncontrollability of servers bring great security challenges to this promising computing paradigm. In this article, we initialize a new four-party framework for the$\mathcal {AADP}$system which consists of users, third-party test institution, AI doctor, and cloud/edge server. With this framework, we design two high-efficiency and secure outsourcing$\mathcal {AADP}$protocols under two different security models. By comprehensively employing secure hash functions, Householder transformations, and random permutations, we realize the following design objectives: 1) user’s actual identification is invisible to the other parties; 2) user’s feature vector is blinded to the AI doctor and the server; 3) the ML model of the AI doctor is confidential to the server; 4) AI doctor can obtain decent computational savings compared with achieving the diagnosis task by itself; and 5) AI doctor can verify the server’s misbehaviors with a nonnegligible probability under the security model with a fully malicious server. We argue these claims with rigid theoretical proofs and corroborate them with extensive experimental analysis.

Devices in the Internet-of-Things (IoT) are networked and perform massive computations to support various social IoT systems. Applications in social IoT systems often involve complicated computations that are out of the computation capacity of some resource-constrained IoT devices. Thus, how to enable resource-constrained IoT devices to accomplish complex computations efficiently and securely is of significant importance. To address this problem, we develop a secure edge-aided computation scheme for the social IoT systems. We scope the framework of edge-aided computations and identify the security threats in such a system. We define the security requirements that the outsourcing algorithms should meet. Then, we provide two examples of secure outsourcing algorithms (matrix multiplication and modular exponentiation) that meet the given security requirements. The efficiency and security of the proposed algorithms are supported through the theoretical analysis and experimental results.

The public cloud data integrity auditing technique is used to check the integrity of cloud data through the Third Party Auditor (TPA). In order to make it more practical, we propose a new paradigm called integrity auditing based on the keyword with sensitive information privacy for encrypted cloud data. This paradigm is designed for one of the most common scenario, that is, the user concerns the integrity of a portion of encrypted cloud files that contain his/her interested keywords. In our proposed scheme, the TPA who is only provided with the encrypted keyword, can audit the integrity of all encrypted cloud files that contain the user’s interested keyword. Meanwhile, the TPA cannot deduce the sensitive information about which files contain the keyword and how many files contain this keyword. These salient features are realized by leveraging a newly proposed Relation Authentication Label (RAL). The RAL can not only authenticate the relation that files contain the queried keyword, but also be used to generate the auditing proof without sensitive information exposure. We give concrete security analysis showing that the proposed scheme satisfies correctness, auditing soundness and sensitive information privacy. We also conduct the detailed experiments to show the efficiency of our scheme.

In the digital twin environment, the fusion data onto physical entities in the physical space are mapped to multiple virtual spaces for digital modeling and intelligent simulation in different dimensions. In real intelligent manufacturing scenarios, heterogeneous multi-source fusion data are collected at the same time period. So they are consistent in time state. For the autonomous digital twin system, time states verification and integrity checking are basic security factors. Provable data possession technology can check the integrity of data onto virtual spaces. The blockchain can provide the synchronization interface to make distributed entities to obtain the trusted time state value. Considering the privacy, the blockchain can also provide anonymous services for entities. Therefore, we propose the blockchain-based synchronized provable data possession scheme (named BSPDP) for digital twin. In our scheme, the selection of verifier is flexible. Since virtual spaces may be maliciously framed to pay compensation, we use tag verification to prevent honest virtual spaces from being framed. Under the assumption of RSA, the proposed BSPDP is provably secure. Finally, the performance analysis demonstrates that BSPDP is practical. The experimental results show that BSPDP is effective and attractive for digital twin.

With the integration of the healthcare system, Internet of Things, and cloud storage service, more and more medical institutions upload their electronic medical records (EMRs) to the cloud to reduce the local storage burden and realize data sharing among external researchers. To secure the sensitive information, EMRs usually should be encrypted before being stored on the cloud. However, the existing searchable encryption schemes that encrypt the entire EMRs can hide the sensitive information, but this results in the shared EMRs being unable to be used by researchers. In addition, if the queried and extracted EMRs are incorrect, it will lead to misdiagnosis and even endanger the patient’s life. In order to solve the aforementioned problems, in this article, we propose a verifiable keyword search scheme supporting sensitive information hiding for the cloud-based healthcare sharing system. The sensitive information is encrypted, while other contents in EMR can be shared among users in this scheme. Doctors and researchers can quickly perform search operations based on keywords to extract the EMRs they require. This time complexity is$O(n)$, where$n$is the number of attribute values in the record. But the sensitive information is hidden for the researchers. Furthermore, the correctness of EMRs can be verified when they are extracted from the cloud. This time complexity is max$\lbrace O(n^{\prime }),O(N^{\prime })\rbrace$, where$n^{\prime }$is the number of query keywords and$N^{\prime }$is the number of the retrieved records. We expound the security and carry out experiments to estimate the efficiency of the proposed scheme.

As the product of combining Internet of Things (IoT), cloud computing, and traditional healthcare, Intelligent IoT Healthcare (IIoTH) brings us a lot of convenience, meanwhile security and privacy issues have attracted great attention. Dynamic searchable symmetric encryption (DSSE) technique can make the user search the dynamic healthcare information from IIoTH system under the condition that the privacy is protected. In this article, a novel privacy-preserving DSSE scheme for IIoTH system is proposed. It is the first DSSE scheme designed for personal health record (PHR) files database with forward security. We construct the secure index based on hash chain and realize trapdoor updates for resisting file injection attacks. In addition, we realize fine-grained search over encrypted PHR files database of attribute-value type. When the user executes search operations, he/she gets only a matched attribute value instead of the whole file. As a result, the communication cost is reduced and the disclosure of patient's privacy is minimized. The proposed scheme also achieves attribute access control, which allows users have different access authorities to attribute values. The specific security analysis and experiments show the security and the efficiency of the proposed scheme.

In cryptography and algorithmic number theory, modular inversion is viewed as one of the most common and time-consuming operations. It is hard to be directly accomplished on resource-constrained clients (e.g., mobile devices and IC cards) since modular inversion involves a great amount of operations on large numbers in practice. To address the above problem, this paper proposes a novel unimodular matrix transformation technique to realize secure outsourcing of modular inversion. This technique makes our algorithm achieve several amazing properties. First, to the best of our knowledge, it is the first secure outsourcing computation algorithm that supports arbitrary and variable modulus, which eliminates the restriction in previous work that the protected modulus has to be a fixed composite number. Second, our algorithm is based on the single untrusted program model, which avoids the non-collusion assumption between multiple servers. Third, for each given instance of modular inversion, it only needs one round interaction between the client and the cloud server, and enables the client to verify the correctness of the results returned from the cloud server with the (optimal) probability 1. Furthermore, we propose an extended secure outsourcing algorithm that can solve modular inversion in multi-variable case. Theoretical analysis and experimental results show that our proposed algorithms achieve remarkable local-client’s computational savings. At last, as two important and helpful applications of our algorithms, the outsourced implementations of the key generation of RSA algorithm and the Chinese Reminder Theorem are given.

In recent years, Industrial Internet of Things (IIoT) has gradually attracted the attention of the industry owing to its accurate time synchronization, communication accuracy, and high adaptability. As an important data structure, graphs are widely used in IIoT applications, where entities and their relationships can be expressed in the form of graphs. With the widespread adoption of IIoT and cloud computing, an increasing number of individuals or organizations are outsourcing their IIoT graph data to cloud servers to enjoy the unlimited storage space and fast computing service. To protect the privacy of graph data, graphs are usually encrypted before being outsourced. In this article, we propose a search pattern privacy system for approximate shortest distance query of encrypted graphs in IIoT. To realize search pattern privacy, we adopt two noncolluded cloud servers to accomplish different tasks. We leverage the first server to store the encrypted data and perform query operations, and use the second one to rerandomize the contents and shuffle the locations of the queried records. Before queries, we generate the trapdoors by using different random numbers. After queries, we ask the second server to rerandomize the contents of the records that the first server touched. In addition, we shuffle the physical locations of original records by inserting some fake records. In this way, all contents and physical locations of the touched records change, so that the first server cannot distinguish whether two queries are the same or not. To enhance the efficiency on the user side, we further improve this system by moving some heavy workloads from the user to the cloud. The security analysis and the performance evaluation show that our work is secure and efficient.

Data security and privacy have become an important problem while big data systems are growing dramatically fast in various application fields. Paillier additive homomorphic cryptosystem is widely used in information security fields such as big data security, communication security, cloud computing security, and artificial intelligence security. However, how to improve its computational performance is one of the most critical problems in practice. In this paper, we propose two modifications to improve the performance of the Paillier cryptosystem. Firstly, we introduce a key generation method to generate the private key with low Hamming weight, and this can be used to accelerate the decryption computation of the Paillier cryptosystem. Secondly, we propose an acceleration method based on Hensel lifting in the Paillier cryptosystem. This method can obtain a faster and improved decryption process by showing the mathematical analysis of the decryption algorithm.

Abstract As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, $g$-restricted connectivity and $h$-extra connectivity, which are two crucial subjects for a DCN’s ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the $g$-restricted connectivity and $h$-extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the $g$-restricted connectivity of BCDC is 4 for $n=3$ and $2n+g(n-2)-2$ for $n\geq 4$, where $0\leq g\leq n-3$, and the $h$-extra connectivity of BCDC is 4 for $n=3$ and $2n+h(n-2)-2$ for $n\geq 4$, where $0\leq h\leq n-3$.

Object recognition of hyperspectral remote sensing images based on machine learning is widely applied in many industries. However, the efficiency of the training and recognizing process of object recognition on hyperspectral remote sensing images is a critical issue since it involves complex matrix operations and large scale training data sets, especially for resource-constrained devices. One solution is to outsource the heavy workload of object recognition on hyperspectral remote sensing images to a cloud server. Nonetheless, it may bring some security problems when the cloud server is untrustworthy. Therefore, how to enable resource-constrained devices to securely and efficiently accomplish the training and recognizing process of object recognition on hyperspectral remote sensing images is of significant importance. In this article, we propose a secure and efficient scheme to outsource the object recognition on hyperspectral remote sensing images to the untrustworthy cloud server. The proposed scheme can protect the privacy of the computation input and output. Also, we develop an effective verification approach in our scheme that can detect the misbehavior of cloud server with the optimal probability 1. The theoretical analysis and experimental results indicate that our proposed scheme is secure and efficient.

Phrase search encryption, as an important technique in cloud-based IoT system, allows users to retrieve encrypted IoT data that contains a set of consecutive keywords. It plays an important role in cloud-based e-healthcare diagnosis system, machine learning applications for cloud-based IoT system, etc. However, to the best of our knowledge, the existing phrase search encryption schemes cannot achieve the complete verification for search results. They either cannot verify whether the returned files correctly containing the query phrase or cannot verify whether all files containing this query phrase are returned. Result verification is very important for some cloud-based IoT applications. If the search result is incorrect in the cloud-based e-healthcare diagnosis system, it will lead to misdiagnosis even endanger the patient's life. In order to deal with this problem, this article explores how to achieve verifiable phrase search over encrypted cloud-based IoT data. Specifically, we design novel look-up tables which can be utilized to determine and verify the position relationship among keywords. Meanwhile, we adopt a two-phase query strategy. In the first query phase, the data user can know the identifiers of files containing the keywords in the query phrase, and generate the search trapdoor based on these identifiers for the next phase. In the second query phase, the data user can obtain the verification information to check whether all files containing the query phrase are correctly returned. We present the security analysis of our scheme and conduct extensive experiments. The results prove the high security and efficiency of our proposed scheme.

For large-scale data transmission of the Industrial Internet of Things (IIoT), aggregate signature is an effective approach. It can compress the signatures of different senders to save bandwidth. In order to maintain the autonomous management of IIoT, massive sensing data are sent to the data center for intelligent analysis. The reliability of data is an important guarantee of the autonomous management of IIoT. Tracing abnormal senders is a challenge when hiding their real identity. Therefore, we design the first permissioned blockchain-based anonymous and traceable aggregate signature (PBATAS) scheme for IIoT. Smart contracts are used to authenticate anonymous sources and share cryptographic materials among entities, providing reliable regulatory support for IIoT. The regulator can quickly trace the abnormal data sources recorded on the blockchain, which is practical for the anonymous IIoT environment. Through the formal security proof of conditional anonymity, unforgeability, traceability, and resistance to coalition attacks, the proposed PBATAS is provably secure. Performance analysis demonstrates that PBATAS is effective.

Bilinear pairing is a fundamental operation that is widely used in cryptographic algorithms (e.g., identity-based cryptographic algorithms) to secure IoT applications. Nonetheless, the time complexity of bilinear pairing is$O(n^{3})$, making it a very time-consuming operation, especially for resource-constrained IoT devices. Secure outsourcing of bilinear pairing has been studied in recent years to enable computationally weak devices to securely outsource the bilinear pairing to untrustworthy cloud servers. However, the state-of-art algorithms often require to precompute and store some values, which results in storage burden for devices. In the Internet of Things, devices are generally with very limited storage capacity. Thus, the existing algorithms do not fit the IoT well. In this article, we propose a secure outsourcing algorithm of bilinear pairings, which does not require precomputations. In the proposed algorithm, the outsourcer side’s efficiency is significantly improved compared with executing the original bilinear pairing operation. At the same time, the privacy of the input and output is ensured. Also, we apply the Ethereum blockchain in our outsourcing algorithm to enable fair payments, which ensures that the cloud server gets paid only when he correctly accomplished the outsourced work. The theoretical analysis and experimental results show that the proposed algorithm is efficient and secure.

Using cloud storage services, users can store their data in the cloud to avoid the expenditure of local data storage and maintenance. To ensure the integrity of the data stored in the cloud, many data integrity auditing schemes have been proposed. In most, if not all, of the existing schemes, a user needs to employ his private key to generate the data authenticators for realizing the data integrity auditing. Thus, the user has to possess a hardware token (e.g., USB token, smart card) to store his private key and memorize a password to activate this private key. If this hardware token is lost or this password is forgotten, most of the current data integrity auditing schemes would be unable to work. In order to overcome this problem, we propose a new paradigm called data integrity auditing without private key storage and design such a scheme. In this scheme, we use biometric data (e.g., iris scan, fingerprint) as the user’s fuzzy private key to avoid using the hardware token. Meanwhile, the scheme can still effectively complete the data integrity auditing. We utilize a linear sketch with coding and error correction processes to confirm the identity of the user. In addition, we design a new signature scheme which not only supports blockless verifiability, but also is compatible with the linear sketch. The security proof and the performance analysis show that our proposed scheme achieves desirable security and efficiency.

Verifiable Searchable Symmetric Encryption, as an important cloud security technique, allows users to retrieve the encrypted data from the cloud through keywords and verify the validity of the returned results. Dynamic update for cloud data is one of the most common and fundamental requirements for data owners in such schemes. To the best of our knowledge, the existing verifiable SSE schemes supporting data dynamic update are all based on asymmetric-key cryptography verification, which involves time-consuming operations. The overhead of verification may become a significant burden due to the sheer amount of cloud data. Therefore, how to achieve keyword search over dynamic encrypted cloud data with efficient verification is a critical unsolved problem. To address this problem, we explore achieving keyword search over dynamic encrypted cloud data with symmetric-key based verification and propose a practical scheme in this paper. In order to support the efficient verification of dynamic data, we design a novel Accumulative Authentication Tag (AAT) based on the symmetric-key cryptography to generate an authentication tag for each keyword. Benefiting from the accumulation property of our designed AAT, the authentication tag can be conveniently updated when dynamic operations on cloud data occur. In order to achieve efficient data update, we design a new secure index composed by a search table ST based on the orthogonal list and a verification list VL containing AATs. Owing to the connectivity and the flexibility of ST, the update efficiency can be significantly improved. The security analysis and the performance evaluation results show that the proposed scheme is secure and efficient.

Provable Data Possession is viewed as an important technique to check the integrity of the data stored in remote servers. Recently, a new provable data possession scheme [Secure and Efficient Privacy Preserving Provable Data Possession in Cloud Storage, IEEE Transactions on Services Computing, (2018) DOI: 10.1109/TSC.2018.2820713] was proposed. The authors claimed this scheme can guarantee the storage correction. In this paper, we show this scheme cannot satisfy this fundamental security. Specifically, we demonstrate the malicious cloud can generate a proof to pass the third party auditor's verification even if it does not store the user's whole file.

With the development of Internet of Things (IoT) and 5G, edge computing, as a new computing paradigm, has been widely popularized in academia and industry. Due to the distributed architecture and being close to the user, edge computing can faster respond to the IoT device's request and provide a better quality of service for IoT applications. An important application of edge computing is to outsource the complicated computation task to the nearby edge nodes. Modular exponentiation is widely considered as one of the most common and expensive operations in cryptographic protocols. As far as we know, all secure outsourcing algorithms of modular exponentiation are based on the centralized cloud server, but not based on multiple edge nodes. In this article, we propose the first secure and distributed outsourcing algorithm for modular exponentiation (fixed base and variable exponent) under the multiple noncolluding edge node model. In our algorithm, the exponent is divided into a certain number of parts. In addition, we propose another secure and distributed outsourcing algorithm of modular exponentiation (variable base and variable exponent). The user can protect the privacy in the process of outsourcing and detect the invalid results from edge nodes with high probability. Finally, we provide the experimental evaluation to support that our proposed algorithms are efficient on both the user side and the edge node side.

Rivest-Shamir-Adleman (RSA) is one of the widely deployed public-key algorithms. Yet, its decryption facet is very time consuming for resource-constrained Internet-of-Thing (IoT) devices, as it is based on the modular exponentiation of a large number. Although several variants of RSA have been designed to accelerate decryption, the outcomes have been far from satisfactory. Therefore, it is of imminent importance to investigate how to securely outsource RSA decryption to computational powerful parties as an alternative solution. In this article, we introduce the first efficient and secure outsourcing scheme for RSA decryption in IoT. Though RSA decryption is achieved via modular exponentiation, existing secure outsourcing schemes for modular exponentiation either assume the modulus to be prime and are not applicable to RSA or incur massive computation costs and are heavy laden in practice. To address these issues, we have designed our scheme based on the Chinese remainder theorem (CRT). In our scheme, the private keys (including the exponent and the modulus) and the plaintext are concealed concurrently, and the proposed scheme is highly efficient for both client and cloud. In addition, our scheme enables the client to detect any misbehavior of the cloud server with a probability of 99.17%. To validate the effectiveness of our proposed scheme, we provide rigorous proofs of security and verifiability, as well as efficiency analysis. The effectiveness and efficiency of our scheme are further confirmed based on experimental results.

Solving quadratic congruences is a widely applied operation in cryptographic protocols to ensure the data secrecy in the Internet of Things (IoT). Yet it requires unaffordable computation resource for resource-constrained IoT devices when bulk of this type of operations need to be performed. How to efficiently and effectively solve quadratic congruences on IoT devices becomes a challenging issue. To address this problem, in this article, we propose two practical and secure outsourcing algorithms for solving quadratic congruences. Our proposed algorithms enable the IoT devices to outsource the heavy computation of solving quadratic congruences to a single cloud server, and therefore, achieve high efficiency for IoT devices. Meanwhile, we obscure the input and the output so that the outsourcing process does not leak the privacy of the computation, and the IoT devices in our algorithms can detect any misbehavior of the cloud server with a probability of 1. In addition, we take the Rabin encryption algorithm as an example to show how our proposed algorithms can be applied to IoT applications. The theoretical analysis and experimental results support the fact that our proposed algorithms are secure and efficient.

Cloud storage auditing schemes for shared data refer to checking the integrity of cloud data shared by a group of users. User revocation is commonly supported in such schemes, as users may be subject to group membership changes for various reasons. Previously, the computational overhead for user revocation in such schemes is linear with the total number of file blocks possessed by a revoked user. The overhead, however, may become a heavy burden because of the sheer amount of the shared cloud data. Thus, how to reduce the computational overhead caused by user revocations becomes a key research challenge for achieving practical cloud data auditing. In this paper, we propose a novel storage auditing scheme that achieves highly-efficient user revocation independent of the total number of file blocks possessed by the revoked user in the cloud. This is achieved by exploring a novel strategy for key generation and a new private key update technique. Using this strategy and the technique, we realize user revocation by just updating the non-revoked group users' private keys rather than authenticators of the revoked user. The integrity auditing of the revoked user's data can still be correctly performed when the authenticators are not updated. Meanwhile, the proposed scheme is based on identity-base cryptography, which eliminates the complicated certificate management in traditional Public Key Infrastructure (PKI) systems. The security and efficiency of the proposed scheme are validated via both analysis and experimental results.

Finding min-cut is a fundamental operation in graph theory. It has been widely used in many applications such as image segmentation and network partition. However, solving the min-cut problem is time-consuming for resource-constrained devices, especially when the graph is large and dense. In this paper, we explore how to securely solve the min-cut problem in the cloud environment, and propose two secure outsourcing schemes for the min-cut of undirected edge-weighted graphs. The first scheme is based on two non-colluded untrusted cloud servers, and the second one is under the single untrusted cloud server model. In the designed schemes, we develop a new technique that contains merging vertices and edges, inserting fake vertices and edges, shuffling vertices and randomizing weights of edges to protect the privacy of graphs. In order to realize the checkability of result from a single untrusted cloud server, we design a novel verification mechanism by outsourcing the min-cut of two related graphs. Besides, we also provide security analysis and the experimental evaluation. To the best of our knowledge, it is the first research on secure outsourcing of graph algorithm.

With cloud storage services, users can remotely store their data to the cloud and realize the data sharing with others. Remote data integrity auditing is proposed to guarantee the integrity of the data stored in the cloud. In some common cloud storage systems such as the electronic health records system, the cloud file might contain some sensitive information. The sensitive information should not be exposed to others when the cloud file is shared. Encrypting the whole shared file can realize the sensitive information hiding, but will make this shared file unable to be used by others. How to realize data sharing with sensitive information hiding in remote data integrity auditing still has not been explored up to now. In order to address this problem, we propose a remote data integrity auditing scheme that realizes data sharing with sensitive information hiding in this paper. In this scheme, a sanitizer is used to sanitize the data blocks corresponding to the sensitive information of the file and transforms these data blocks' signatures into valid ones for the sanitized file. These signatures are used to verify the integrity of the sanitized file in the phase of integrity auditing. As a result, our scheme makes the file stored in the cloud able to be shared and used by others on the condition that the sensitive information is hidden, while the remote data integrity auditing is still able to be efficiently executed. Meanwhile, the proposed scheme is based on identity-based cryptography, which simplifies the complicated certificate management. The security analysis and the performance evaluation show that the proposed scheme is secure and efficient.

When the data is stored in public clouds, provable data possession (for short, PDP) is of crucial importance in cloud storage. PDP can make the users verify whether their outsourced data is kept intact without downloading the whole data. In some application scenarios, anonymity is very important in order to protect the user identity privacy. In order to encourage users to disclose bad event, the government or organization or individual may pay for the user who provides the precious data. Thus, incentive and unconditionally anonymous identity-based public PDP (for short, IAID-PDP) is a very important security concept. From the above requirements, for the first time, we propose the concept of IAID-PDP. We formalize its system model and security model. Based on the bilinear pairings, a concrete IAID-PDP protocol is presented. Based on the standard hard problems, the proposed IAID-PDP protocol is provably secure. IAID-PDP protocol eliminates the complex certificate management since it is designed in the identity-based public key cryptography. Through the performance analysis and security analysis, our IAID-PDP protocol satisfies the following properties: certification elimination, incentive, unconditional anonymity and remote data integrity checking.

Key exposure is one serious security problem for cloud storage auditing. In order to deal with this problem, cloud storage auditing scheme with key-exposure resilience has been proposed. However, in such a scheme, the malicious cloud might still forge valid authenticators later than the key-exposure time period if it obtains the current secret key of data owner. In this paper, we innovatively propose a paradigm named strong key-exposure resilient auditing for secure cloud storage, in which the security of cloud storage auditing not only earlier than but also later than the key exposure can be preserved. We formalize the definition and the security model of this new kind of cloud storage auditing and design a concrete scheme. In our proposed scheme, the key exposure in one time period doesn’t affect the security of cloud storage auditing in other time periods. The rigorous security proof and the experimental results demonstrate that our proposed scheme achieves desirable security and efficiency.

Key-exposure resistance has always been an important issue for in-depth cyber defence in many security applications. Recently, how to deal with the key exposure problem in the settings of cloud storage auditing has been proposed and studied. To address the challenge, existing solutions all require the client to update his secret keys in every time period, which may inevitably bring in new local burdens to the client, especially those with limited computation resources, such as mobile phones. In this paper, we focus on how to make the key updates as transparent as possible for the client and propose a new paradigm called cloud storage auditing with verifiable outsourcing of key updates. In this paradigm, key updates can be safely outsourced to some authorized party, and thus the key-update burden on the client will be kept minimal. In particular, we leverage the third party auditor (TPA) in many existing public auditing designs, let it play the role of authorized party in our case, and make it in charge of both the storage auditing and the secure key updates for key-exposure resistance. In our design, TPA only needs to hold an encrypted version of the client's secret key while doing all these burdensome tasks on behalf of the client. The client only needs to download the encrypted secret key from the TPA when uploading new files to cloud. Besides, our design also equips the client with capability to further verify the validity of the encrypted secret keys provided by the TPA. All these salient features are carefully designed to make the whole auditing procedure with key exposure resistance as transparent as possible for the client. We formalize the definition and the security model of this paradigm. The security proof and the performance simulation show that our detailed design instantiations are secure and efficient.

Proofs-of-Retrievability enables a client to store his data on a cloud server so that he executes an efficient auditing protocol to check that the server possesses all of his data in the future. During an audit, the server must maintain full knowledge of the client’s data to pass, even though only a few blocks of the data need to be accessed. Since the first work by Juels and Kaliski, many PoR schemes have been proposed and some of them can support dynamic updates. However, all the existing works that achieve public verifiability are built upon traditional public-key cryptosystems which imposes a relatively high computational burden on low-power clients (e.g., mobile devices). In this work we explore indistinguishability obfuscation for building a Proof-of-Retrievability scheme that provides public verification while the encryption is based on symmetric key primitives. The resulting scheme offers light-weight storing and proving at the expense of longer verification. This could be useful in apations where outsourcing files is usually done by low-power client and verifications can be done by well equipped machines (e.g., a third party server). We also show that the proposed scheme can support dynamic updates. At last, for better assessing our proposed scheme, we give a performance analysis of our scheme and a comparison with several other existing schemes which demonstrates that our scheme achieves better performance on the data owner side and the server side.

Cloud storage auditing is viewed as an important service to verify the integrity of the data in public cloud. Current auditing protocols are all based on the assumption that the client's secret key for auditing is absolutely secure. However, such assumption may not always be held, due to the possibly weak sense of security and/or low security settings at the client. If such a secret key for auditing is exposed, most of the current auditing protocols would inevitably become unable to work. In this paper, we focus on this new aspect of cloud storage auditing. We investigate how to reduce the damage of the client's key exposure in cloud storage auditing, and give the first practical solution for this new problem setting. We formalize the definition and the security model of auditing protocol with key-exposure resilience and propose such a protocol. In our design, we employ the binary tree structure and the preorder traversal technique to update the secret keys for the client. We also develop a novel authenticator construction to support the forward security and the property of blockless verifiability. The security proof and the performance analysis show that our proposed protocol is secure and efficient.

A mobile ad hoc network (MANET) is a self-configuring network of mobile nodes connected by wireless links without fixed infrastructure, which is originally designed for a cooperative environment. However, MANETs are subjected to a variety of attacks by malicious nodes, in particular for attacks on the packet routing. Compared with traditional cryptosystem based security mechanisms, trust-enhanced routing protocol could provide a better quality of service. In this study, we abstract a basic decentralized effective trust inference model based on node's behavior assessment, where each peer assigns a trust value for a set of peers of interest. In this model, we introduce the 'voting' mechanism to access the recommending experience (or ratings), in order to reduce the cost of the algorithm design and the system overhead. Then combined with this trust model, a novel trust-enhanced multicast routing protocol (TeMR) is proposed. This new protocol introduces the group-shared tree strategy, which establishes more efficient multicast routes since it uses 'trust' factor to improve the efficiency and robustness of the forwarding tree. Moreover, it provides a flexible and feasible approach in routing decision making with trust constraint and malicious node detection. Experiments have been conducted to evaluate the effectiveness of the proposed protocol.

In traditional identity-based encryption schemes, security will be entirely lost once secret keys are exposed. However, with more and more use of mobile and unprotected devices, key exposure seems unavoidable. To deal with this problem, we newly propose a forward-secure identity-based public-key encryption scheme. In this primitive, the exposure of the secret key in one period doesn't affect the security of the ciphertext generated in previous periods. Any parameter in our scheme has at most log-squared complexity in terms of the total number of time periods. We also give the semantic security notions of forward-secure identity-based public-key encryption. The proposed scheme is proven semantically secure in the standard model. As far as we are concerned, it is the first forward-secure identity-based public-key encryption scheme without random oracles.

Y. D. Lyuu and M. L. Wu had proposed an improved multi-proxy multi-signature scheme, which was claimed to resist the forge attack. Lately, L. Guo and G. Wang found an inside attack on the Lyuu-Wu's scheme. In this paper, we propose a new attack on Lyuu-Wu's scheme, which can factor the parameter N and Q by using efficient number-theoretic algorithms when Q is roughly larger than the square root of N. It follows that Lyuu-Wu's scheme suffers from the forge attack from the proxy signers in that case.

How to protect the security of vital data is one of the most important issues of the database security. An efficient method is to divide the vital data into multiple parts that are stored among a group of servers by secret sharing technique. In this paper, we propose a publicly verifiable dynamic sharing protocol for data secure storage. In this protocol, the important data can be publicly verifiably shared among multiple servers, at the same time, the protocol can dynamically recover the bad shares in the system if some servers are attacked. Different from previous protocols, the new protocol is not only efficient but also practical in many circumstances because all operations can be verified by everyone not only shareholders.