Secure Tensor Decomposition Using Fully Homomorphic Encryption Scheme

As the rapidly growing volume of data are beyond the capabilities of many computing infrastructures, to securely process them on cloud has become a preferred solution which can both utilize the powerful capabilities provided by cloud and protect data privacy. This paper puts forward a new approach to securely decompose tensor, the mathematical model widely used in data-intensive applications, to a core tensor and some truncated orthogonal bases. The structured, semi-structured as well as unstructured data are all transformed to low-order sub-tensors which are then encrypted using the fully homomorphic encryption scheme. A unified high-order cipher tensor model is constructed by collecting all the cipher sub-tensors and embedding them to a base tensor space. The cipher tensor is decomposed through a proposed secure algorithm, in which the square root operations are eliminated during the Lanczos procedure. The paper makes an analysis of the secure algorithm in terms of time consumption, memory usage and decomposition accuracy. Experimental results reveals that this approach can securely decompose tensor models. With the advancement of fully homomorphic encryption scheme, the proposed secure tensor decomposition method is expected to be widely applied on cloud for privacy-preserving data processing.