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

For efficiency and economic reasons, a cloud system would be the most attractive choice for high computation tasks. But, computation on cloud is mostly done on clear text. As a result, the risk of data leak would be very high. The singular value decomposition (SVD) is widely used in several scientific computation areas including computer science, engineering, bioinformatics and physics, and the computation of the SVD consumes high computing power especially for large matrices. Hence, it would be efficient to outsource such computation to a cloud. In addition, many matrices are sparse containing lots of zeroes, and may have no meaning, whereas some applications contain sensitive bitmap images which the positions of zeroes are very significant. In other words, knowing the positions of zeroes would clearly expose the whole image. 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(n(2)) while the complexity of the cloud workload is O(n(3)). (c) 2018 Elsevier Ltd. All rights reserved.