Secure High-order Singular Value Decomposition In The Cloud

Tensor is a multilinear array that arises as a result of the growth of matrix theory, with good presentation skills for multidimensional data. Also, tensor is an emerging and useful tool that has been adopted in a wide range of big data applications. High-order Singular Value Decomposition(HOSVD) is one of the most widely used tensor decomposition algorithms for data analysis and processing. With the development of cloud computing technology, more and more users and corporations outsource data to the cloud platform for flexible management and processing. However, directly processing the plain data in cloud may arise serious security and privacy concerns, such as exposure of user privacy and business information. Therefore, it is necessary to study how to securely perform HOSVD on tensor composed by sensitive data without disclosuring privacy in cloud environment.This paper presents two HOSVD schemes in Cloud-Client model and Hybrid Cloud model respectively. The two schemes adopt homomorphic encryption to ensure the safety of private data, that is sensitive data need to be encrypted before being outsourced to cloud. In Cloud-Client model, three decomposition algorithms, namely the secure bidiagonalization algorithm, secure diagonalization algorithm, secure mode-n product algorithm, are proposed to achieve secure HOSVD. The experimental results provide evidence that this scheme is promising for secure HOSVD in cloud computing. In Hybrid Cloud model, we design a secure integer division protocol and a secure integer square root protocol over encrypted data, then, based on those sub protocols, secure matrix operations, secure SVD protocols and secure core tensor construction protocols are proposed to achieve secure HOSVD. Finally, experiments are conducted on synthetic and real datasets to verify the feasibility of the scheme.