Outsourcing Large-scale Matrix Decomposition To A Public Cloud

Cloud computing provides convenient on-demand network access to a shared pool of config-urable computational resources. Computation outsourcing is one of the main services of the cloud paradigm, where the customer can outsource their intensive computational tasks to cloud with mas-sive computational resources. However, in order to utilize this computing paradigm, it presents various challenges that need to be addressed, especially the security. Matrix decomposition is one main class of scientific problem. It is also widely applied in engineering tasks. In this paper, we are motivated to design secure, correct, and efficient protocols for outsourcing eigen-decomposition, singular value decomposition and LU decomposition. We also introduce outsourcing protocols for principle component analysis and solving large-scale system of linear equations as the applications of outsourcing singular value decomposition and LU decomposition. In order to achieve the se-curity, outsourcing protocols employ efficient privacy-preserving transformations to protect both the input and output privacy. So as to check the correctness of the result returned from the cloud, an efficient verification algorithm is employed. Computational complexity analysis shows that our protocols are highly efficient.