Privacy-Preserving Tensor Decomposition Over Encrypted Data in a Federated Cloud Environment

Tensors are popular and versatile tools which model multidimensional data. Tensor decomposition has emerged as a powerful technique dealing with multidimensional data. With the booming development of cloud computing, a large number of users are inclined to outsource big data storage and computations to the cloud. However, because of the rise of various privacy concerns, sensitive data usually need to be encrypted prior to being outsourced to a cloud. Computations over encrypted data in the cloud without compromising the privacy of data is still a challenge. This paper presents a novel privacy-preserving tensor decomposition approach over semantically secure encrypted big data. The proposed approach leverages properties of homomorphic encryption and employs a federated cloud to securely decompose an encrypted tensor for multiple users, without the clouds learning any knowledge about users' data. This is, to our knowledge, the first attempt to solve privacy-preserving tensor decomposition without requiring interaction between users and cloud service providers. In addition, in our approach, we present the first secure integer division and integer square root schemes over encrypted data (the dividend, divisor and radicand are in encrypted format). Finally, we prove the security of our approach under semi-trusted model and empirically analyze its effectiveness, which demonstrates the utility of our proposed approach in cloud deployments.