摘要： Cloud computing enables customers with limited computational resources to outsource their huge computation workloads to the cloud with massive computational power. However, in order to utilize this computing paradigm, it presents various challenges that need to be addressed, especially security. As eigen-decomposition (ED) and singular value decomposition (SVD) of a matrix are widely applied in engineering tasks, we are motivated to design secure, correct, and efficient protocols for outsourcing the ED and SVD of a matrix to a malicious cloud in this paper. In order to achieve security, we employ efficient privacy-preserving transformations to protect both the input and output privacy. In order to check the correctness of the result returned from the cloud, an efficient verification algorithm is employed. A computational complexity analysis shows that our protocols are highly efficient. We also introduce an outsourcing principle component analysis as an application of our two proposed protocols.