SHOSVD: Secure Outsourcing of High-Order Singular Value Decomposition

Tensor decomposition is a popular tool for multi-dimensional data analysis. In particular, High-Order Singular Value Decomposition (HOSVD) is one of the most useful decomposition methods and has been adopted in many applications. Unfortunately, the computational cost of HOSVD is very high on large-scale tensor, and the desirable solution nowadays is to outsource the data to the clouds which perform the computation on behalf of the users. However, how to protect the data privacy against the possibly untrusted clouds is still a wide concern for users. In this paper, we design a new scheme called SHOSVD in the two-cloud model for secure outsourcing of tensor decomposition. At the core of our technique is the adoption of additive secret sharing. Our SHOSVD could guarantee the outsourced data privacy for users assuming no collusion between the two clouds. Moreover, it supports off-line users which means that no interaction between users and clouds is required during the computation process. We prove that our scheme is secure in the semi-honest model, and conduct the theoretical analyses regarding its computational and communicational overhead. The experiment results demonstrate that our scheme is of desirable accuracy.