Lightweight scheme of secure outsourcing SVD of a large matrix on cloud

This paper proposes a novel secure SVD computation on cloud, and the main idea is to locally encrypt a source matrix before sending it to a cloud. The cloud then computes the SVD in an encrypted matrix without requiring any special algorithm, and the outputs will be locally decrypted to obtain the final results. For the encryption, our approach adds a random matrix to the source matrix to ensure that no element including zeroes is exposed in a clear format on the cloud. Moreover, the encryption will preserve the equivalent SVD computation on cloud. The security analysis demonstrates that our proposed scheme gives secure and correct computation while all zeroes are kept hidden. In addition, our experimental results show that the entropy of our encrypted matrix is high; consequently, it would give high resistance to attacks. Furthermore, the performance analysis shows that the complexity of the local workload is O(n2) while the complexity of the cloud workload is O(n3).