Abstract
QR and LU factorizations are two basic mathematical methods for decomposition and dimensionality reduction of large-scale matrices. However, they are too complicated to be executed for a limited client because of big data. Outsourcing computation allows a client to delegate the tasks to a cloud server with powerful resources and therefore greatly reduces the client’s computation cost. However, the previous methods of QR and LU outsourcing factorizations need multiple interactions between the client and cloud server or have low accuracy and efficiency in large-scale matrix applications. In this paper, we propose a noninteractive and efficient outsourcing algorithm of large-scale QR and LU factorizations. The proposed scheme is based on the specific perturbation method including a series of consecutive and sparse matrices, which can be used to protect the original matrix and obtain the results of factorizations. The generation and inversion of sparse matrix has small workloads on the client’s side, and the communication cost is also small since the client does not need to interact with the cloud server in the outsourcing algorithms. Moreover, the client can verify the outsourcing result with a probability of approximated to 1. The experimental results manifest that as for the client, the proposed algorithms reduce the computational overhead of direct computation successfully, and it is most efficient compare with the previous ones.
Highlights
At the era of big data, the exponential growth of data volume has attracted more and more attention
It is necessary to protect the confidentiality of the input/output data simultaneously, we take an efficient encryption method on the original data, the client transforms the original matrix by multiplying a series of particular matrices, these appropriate matrices all are sparse enough to ensure efficiency, and ensure data security at the same time; in this way, the client only needs to turn to the cloud one time and receive results, and the interactions are no longer needed
We describe noninteractive and efficient outsourcing of large-scale QR and LU factorizations, including the following steps: the client generates a secret key Kwhich comprises stochastic parameters with input security parameter, the client employs some encryption steps to transform original matrix, the client sends the encrypted matrix which is exactly blind to the cloud server to the cloud, the complicated decomposing computation on the encrypted matrix will be completed by the cloud, and the client utilizes the key Kwhich is saved on his own to recover the results if the results after decomposing pass the verification
Summary
At the era of big data, the exponential growth of data volume has attracted more and more attention. Is presents an inevitable challenge, because the owners of data and analysts need to find a way to store and analyse enormous data properly and effectively. During the processing of large-scale data, the storage capacity and computing power are closely related to the computer system hardware and available memory. Due to the limitations of the local computation resources, the client can neither be able to employ large-scale data tasks nor meet the requirements for calculation time. Is promotes the motivation to develop outsourced computing server, known as cloud server. In an outsourcing computation scheme, the clients only need to upload data and computation tasks to the cloud server, and the server provides on-demand resources. Outsourcing computation allows source-constrained client to the abundant computing resources and save abundant local memory space or computation overhead
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