With the development of sensor network, mobile computing, and web applications, data are now collected from many distributed sources to form big datasets. Such datasets can be hosted in the cloud to achieve economical processing. However, these data might be highly sensitive requiring secure storage and processing. We envision a cloud-based data storage and processing framework that enables users to economically and securely share and handle big datasets. Under this framework, we study the matrix-based data mining algorithms with a focus on the secure top-k eigenvector algorithm. Our approach uses an iterative processing model in which the authorized user interacts with the cloud to achieve the result. In this process, both the source matrix and the intermediate results keep confidential and the client-side incurs low costs. The security of this approach is guaranteed by using Paillier Encryption and a random perturbation technique. We carefully analyze its security under a cloud-specific threat model. Our experimental results show that the proposed method is scalable to big matrices while requiring low client-side costs.
@cite_17 use a more directed approach and present secure outsourcing solutions that are specific to large scale systems of linear equations and matrix multiplication applications. These solutions fall short in that they leak private information, depend on multiple non-colluding servers, and require a large communication overhead, respectively. @cite_4 use an iterative approach for solving linear equations via client-cloud collaboration. However, their approach has several weaknesses. First, their approach requires that the entire unencrypted matrix be present at the client side. Secondly, the client side must perform a problem transformation step with a computation cost of @math . These weaknesses render the approach impractical for big matrices and do not fully utilize the benefit of the cloud.
@cite_4 @cite_17
2136624667 1975199330
We give improved protocols for the secure and private outsourcing of linear algebra computations, that enable a client to securely outsource expensive algebraic computations (like the multiplication of large matrices) to a remote server, such that the server learns nothing about the customer's private input or the result of the computation, and any attempted corruption of the answer by the server is detected with high probability. The computational work performed at the client is linear in the size of its input and does not require the client to locally carry out any expensive encryptions of such input. The computational burden on the server is proportional to the time complexity of the current practically used algorithms for solving the algebraic problem (e.g., proportional to n3 for multiplying two n x n matrices). The improvements we give are: (i) whereas the previous work required more than one remote server and assumed they do not collude, our solution works with a single server (but readily accommodates many, for improved performance); (ii) whereas the previous work required a server to carry out expensive cryptographic computations (e.g., homomorphic encryptions), our solution does not make use of any such expensive cryptographic primitives; and (iii) whereas in previous work collusion by the servers against the client revealed to them the client's inputs, our scheme is resistant to such collusion. As in previous work, we maintain the property that the scheme enables the client to detect any attempt by the server(s) at corruption of the answer, even when the attempt is collusive and coordinated among the servers. Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LE problems would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach -- iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design. Cloud computing paradigm provides an alternative and economical service for resource-constrained clients to perform large-scale data computation. Since large matrix determinant computation (DC) is ubiquitous in the fields of science and engineering, a first step is taken in this paper to design a protocol that enables clients to securely, verifiably, and efficiently outsource DC to a malicious cloud. The main idea to protect the privacy is employing some transformations on the original matrix to get an encrypted matrix which is sent to the cloud; and then transforming the result returned from the cloud to get the correct determinant of the original matrix. Afterwards, a randomized Monte Carlo verification algorithm with one-sided error is introduced, whose superiority in designing inexpensive result verification algorithm for secure outsourcing is well demonstrated. In addition, it is analytically shown that the proposed protocol simultaneously fulfills the goals of correctness, security, robust cheating resistance, and high-efficiency. Extensive theoretical analysis and experimental evaluation also show its high-efficiency and immediate practicability. It is hoped that the proposed protocol can shed light in designing other novel secure outsourcing protocols, and inspire powerful companies and working groups to finish the programming of the demanded all-inclusive scientific computations outsourcing software system. It is believed that such software system can be profitable by means of providing large-scale scientific computation services for so many potential clients. Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LEs would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach&#x2014;iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design. Cloud computing is attracting increasing attention since it enables clients with limited computing resources to perform and complete large-scale computations. However, it also comes up with some security and privacy concerns and challenges, such as the input and output privacy of the client, and cheating behaviors of the cloud. Motivated by these issues and focused on engineering optimization tasks, we study secure outsourcing of large-scale nonlinear programming, which has not been investigated before. Specifically, a secure and efficient transformation scheme is employed to protect both input and output privacy of the client, and corresponding detailed proofs and analysis are also provided. We apply the reduced gradient method to solve the encrypted nonlinear programming problem in the cloud side. We conduct experiments to measure performance of the designed outsourcing protocol, and the results show the practicability of the proposed mechanism. The emerging ad hoc clouds form a new cloud computing paradigm by leveraging untapped local computation and storage resources. An important application of ad hoc clouds is to outsource computational intensive problems to nearby cloud agents. Specifically, for the problem of solving a linear algebraic equation (LAE), an outsourcing client assigns each cloud agent a subproblem, and then all involved agents apply a consensus-based algorithm to obtain the correct solution of the LAE in an iterative and distributed manner. However, such a distributed collaboration paradigm suffers from cyber security threats that undermine the confidentiality of the outsourced problem and the integrity of the returned results. In this paper, we identify a number of such security threats in this process, and propose a secure outsourcing scheme which not only preserves the privacy of the LAE parameters and the final solution from the participating agents, but also guarantees the correctness of the final solution. We prove that the proposed scheme has low computation complexity at each agent, and is robust against the identified security attacks. Numerical and simulation results are presented to demonstrate the effectiveness of the proposed method. We treat the problem of secure outsourcing of sequence comparisons by a client to remote servers, which given two strings λ and μ of respective lengths n and m, consists of finding a minimum-cost sequence of insertions, deletions, and substitutions (also called an edit script) that transform λ into μ. In our setting a client owns λ and μ and outsources the computation to two servers without revealing to them information about either the input strings or the output sequence. Our solution is non-interactive for the client (who only sends information about the inputs and receives the output) and the client’s work is linear in its input output. The servers’ performance is O(σmn) computation (which is optimal) and communication, where σ is the alphabet size, and the solution is designed to work when the servers have only O(σ(m + n)) memory. By utilizing garbled circuit evaluation in a novel way, we completely avoid public-key cryptography, which makes our solution particularly efficient. Private set intersection enables two parties -- a client and a server -- to compute the intersection of their respective sets without disclosing anything else. It is a fundamental operation -- equivalent to a secure, distributed database join -- and has many applications particularly in privacy-preserving law enforcement. In this paper we present a novel protocol that has linear complexity, is secure in the malicious model without random oracles, is client set size-independent and efficient. Furthermore, the computation of the intersection can be outsourced to an oblivious service provider, as in secure cloud computing. We leverage a completely novel construction for computing the intersection using Bloom filter and homomorphic encryption. For outsourcing we require and introduce a new homomorphic encryption scheme which may be of independent interest. Cloud computing enables resource-constrained clients to economically outsource their huge computation workloads to a cloud server with massive computational power. This promising computing paradigm inevitably brings in new security concerns and challenges, such as input output privacy and result verifiability. Since matrix inversion computation (MIC) is a quite common scientific and engineering computational task, we are motivated to design a protocol to enable secure, robust cheating resistant, and efficient outsourcing of MIC to a malicious cloud in this paper. The main idea to protect the privacy is employing some transformations on the original matrix to get a encrypted matrix which is sent to the cloud; and then transforming the result returned from the cloud to get the correct inversion of the original matrix. Next, a randomized Monte Carlo verification algorithm with one-sided error is employed to successfully handle result verification. In this paper, the superiority of this novel technique in designing inexpensive result verification algorithm for secure outsourcing is well demonstrated. We analytically show that the proposed protocol simultaneously fulfills the goals of correctness, security, robust cheating resistance, and high-efficiency. Extensive theoretical analysis and experimental evaluation also show its high-efficiency and immediate practicability. Searchable (symmetric) encryption allows encryption while still enabling search for keywords. Its immediate application is cloud storage where a client outsources its files while the (cloud) service provider should search and selectively retrieve those. Searchable encryption is an active area of research and a number of schemes with different efficiency and security characteristics have been proposed in the literature. Any scheme for practical adoption should be efficient -- i.e. have sub-linear search time --, dynamic -- i.e. allow updates -- and semantically secure to the most possible extent. Unfortunately, efficient, dynamic searchable encryption schemes suffer from various drawbacks. Either they deteriorate from semantic security to the security of deterministic encryption under updates, they require to store information on the client and for deleted files and keywords or they have very large index sizes. All of this is a problem, since we can expect the majority of data to be later added or changed. Since these schemes are also less efficient than deterministic encryption, they are currently an unfavorable choice for encryption in the cloud. In this paper we present the first searchable encryption scheme whose updates leak no more information than the access pattern, that still has asymptotically optimal search time, linear, very small and asymptotically optimal index size and can be implemented without storage on the client (except the key). Our construction is based on the novel idea of learning the index for efficient access from the access pattern itself. Furthermore, we implement our system and show that it is highly efficient for cloud storage. We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single-qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant. We also generalize our result to the setting of a purely classical client who communicates classically with two non-communicating entangled servers, in order to perform a blind quantum computation. By incorporating the authentication protocol, we show that any problem in BQP has an entangled two-prover interactive proof with a purely classical verifier. Our protocol is the first universal scheme which detects a cheating server, as well as the first protocol which does not require any quantum computation whatsoever on the client's side. The novelty of our approach is in using the unique features of measurement-based quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation. This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Off-the-shelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries. This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative, produces a sequence of matrices @math , and at each step mainly performs a soft-thresholding operation on the singular values of the matrix @math . There are two remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates @math is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal storage space and keep the computational cost of each iteration low. On the theoretical side, we provide a convergence analysis showing that the sequence of iterates converges. On the practical side, we provide numerical examples in which @math matrices are recovered in less than a minute on a modest desktop computer. We also demonstrate that our approach is amenable to very large scale problems by recovering matrices of rank about 10 with nearly a billion unknowns from just about 0.4 of their sampled entries. Our methods are connected with the recent literature on linearized Bregman iterations for @math minimization, and we develop a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms. We describe an algorithm for the direct solution of systems of linear algebraic equations associated with the discretization of boundary integral equations with non-oscillatory kernels in two dimensions. The algorithm is ''fast'' in the sense that its asymptotic complexity is O(n), where n is the number of nodes in the discretization. Unlike previous fast techniques based on iterative solvers, the present algorithm directly constructs a compressed factorization of the inverse of the matrix; thus it is suitable for problems involving relatively ill-conditioned matrices, and is particularly efficient in situations involving multiple right hand sides. The performance of the scheme is illustrated with several numerical examples. rformance of the scheme is illustrated with several numerical examples. ples. Oblivious RAM is a useful primitive that allows a client to hide its data access patterns from an untrusted server in storage outsourcing applications. Until recently, most prior works on Oblivious RAM aim to optimize its amortized cost, while suffering from linear or even higher worst-case cost. Such poor worst-case behavior renders these schemes impractical in realistic settings, since a data access request can occasionally be blocked waiting for an unreasonably large number of operations to complete. This paper proposes novel Oblivious RAM constructions that achieves poly-logarithmic worst-case cost, while consuming constant client-side storage. To achieve the desired worst-case asymptotic performance, we propose a novel technique in which we organize the O-RAM storage into a binary tree over data buckets, while moving data blocks obliviously along tree edges. Due to the increasing number of applications (and their data) being placed on mobile devices, access to dependable storage is becoming a key issue in mobile system design -- and cloud storage is becoming an attractive solution. However, this introduces a number of new issues related to unpredictable wireless network connectivity and data privacy over the network. In this article we present RFS, a wireless-friendly network file system for mobile devices and the cloud. RFS provides deviceaware cache management and client-driven data security and privacy protection. We implement the RFS client in the Linux kernel and the RFS server with Amazon S3 cloud storage, and we employ two new optimizations: server prepush (a server-side data pre-fetching mechanism) and client reintegration (synchronizing a mobile device's cache with the cloud). The empirical results over wired, WiFi and 3G networks show that RFS achieves good performance compared to Coda and FScache, and it reduces network activity visibly. Further, the privacy overhead is acceptable when RFS is run over wireless networks. We present a case study of booting Android over RFS, thereby demonstrating the ability for RFS to host a full mobile system. Overall, RFS can deliver a good user experience under undependable network conditions, allowing mobile users to seamlessly, and safely, use the cloud for data storage. Client-side apps (e.g., mobile or in-browser) need cloud data to be available in a local cache, for both reads and updates. For optimal user experience and developer support, the cache should be consistent and fault-tolerant. In order to scale to high numbers of unreliable and resource-poor clients, and large database, the system needs to use resources sparingly. The SwiftCloud distributed object database is the first to provide fast reads and writes via a causally-consistent client-side local cache backed by the cloud. It is thrifty in resources and scales well, thanks to consistent versioning provided by the cloud, using small and bounded metadata. It remains available during faults, switching to a different data centre when the current one is not responsive, while maintaining its consistency guarantees. This paper presents the SwiftCloud algorithms, design, and experimental evaluation. It shows that client-side apps enjoy the high performance and availability, under the same guarantees as a remote cloud data store, at a small cost. The emergence of cost-effective cloud services offers organizations great opportunity to reduce their cost and increase productivity. This development, however, is hampered by privacy concerns: a significant amount of organizational computing workload at least partially involves sensitive data and therefore cannot be directly outsourced to the public cloud. The scale of these computing tasks also renders existing secure outsourcing techniques less applicable. A natural solution is to split a task, keeping the computation on the private data within an organization's private cloud while moving the rest to the public commercial cloud. However, this hybrid cloud computing is not supported by today's data-intensive computing frameworks, MapReduce in particular, which forces the users to manually split their computing tasks. In this paper, we present a suite of new techniques that make such privacy-aware data-intensive computing possible. Our system, called Sedic, leverages the special features of MapReduce to automatically partition a computing job according to the security levels of the data it works on, and arrange the computation across a hybrid cloud. Specifically, we modified MapReduce's distributed file system to strategically replicate data, moving sanitized data blocks to the public cloud. Over this data placement, map tasks are carefully scheduled to outsource as much workload to the public cloud as possible, given sensitive data always stay on the private cloud. To minimize inter-cloud communication, our approach also automatically analyzes and transforms the reduction structure of a submitted job to aggregate the map outcomes within the public cloud before sending the result back to the private cloud for the final reduction. This also allows the users to interact with our system in the same way they work with MapReduce, and directly run their legacy code in our framework. We implemented Sedic on Hadoop and evaluated it using both real and synthesized computing jobs on a large-scale cloud test-bed. The study shows that our techniques effectively protect sensitive user data, offload a large amount of computation to the public cloud and also fully preserve the scalability of MapReduce. In cloud gaming the game is rendered on a distant cloud server and the resulting video stream is sent back to the user who controls the game via a thin client. The high resource usage of cloud gaming servers is a challenge. Expensive hardware including GPUs have to be efficiently shared among multiple simultaneous users. The cloud servers use virtualization techniques to isolate users and share resources among dedicated servers. The traditional virtualization techniques can however inflict notable performance overhead limiting the user count for a single server. Operating-system-level virtualization instances known as containers are an emerging trend in cloud computing. Containers don't need to virtualize the entire operating system still providing most of the benefits of virtualization. In this paper, we evaluate the container-based alternative to traditional virtualization in cloud gaming systems through extensive experiments. We also discuss the differences needed in system implementation using the container approach and identify the existing limitations. In a common use case for cloud computing, clients upload data and computation to servers that are managed by a third-party infrastructure provider. We describe MrCrypt, a system that provides data confidentiality in this setting by executing client computations on encrypted data. MrCrypt statically analyzes a program to identify the set of operations on each input data column, in order to select an appropriate homomorphic encryption scheme for that column, and then transforms the program to operate over encrypted data. The encrypted data and transformed program are uploaded to the server and executed as usual, and the result of the computation is decrypted on the client side. We have implemented MrCrypt for Java and illustrate its practicality on three standard benchmark suites for the Hadoop MapReduce framework. We have also formalized the approach and proven several soundness and security guarantees. We present PRISM, a privacy-preserving scheme for word search in cloud computing. In the face of a curious cloud provider, the main challenge is to design a scheme that achieves privacy while preserving the efficiency of cloud computing. Solutions from related research, like encrypted keyword search or Private Information Retrieval (PIR), fall short of meeting real-world cloud requirements and are impractical. PRISM 's idea is to transform the problem of word search into a set of parallel instances of PIR on small datasets. Each PIR instance on a small dataset is efficiently solved by a node in the cloud during the "Map" phase of MapReduce. Outcomes of map computations are then aggregated during the "Reduce" phase. Due to the linearity of PRISM, the simple aggregation of map results yields the final output of the word search operation. We have implemented PRISM on Hadoop MapReduce and evaluated its efficiency using real-world DNS logs. PRISM's overhead over non-private search is only 11 . Thus, PRISM offers privacy-preserving search that meets cloud computing efficiency requirements. Moreover, PRISM is compatible with standard MapReduce, not requiring any change to the interface or infrastructure.