A Secure High-Order Lanczos-Based Orthogonal Tensor SVD for Big Data Reduction in Cloud Environment

Singular value decomposition (SVD) has been applied to cyber security and cyber forensics since it can reduce data. However, SVD is hard to reduce high-order big data because it is designed for only matrix data initially. Reducing high-order big data is desired for cyber security applications, and is a very challenging issue. In this paper, we propose a novel orthogonal tensor SVD method using big data techniques for high-order big data (naturally represented as tensors) reduction, which can be extensively used in big data applications of cyber security and cyber forensics. More specifically, we first present a high-order lanczos-based orthogonal tensor SVD algorithm to reduce high-order data. Then, for utilizing the incomparable benefits of cloud, we develop a secure orthogonal tensor SVD method to outsource the computation task of the orthogonal tensor SVD algorithm to cloud. The secure orthogonal tensor SVD method can protect data security from untrusted cloud by applying garbled circuits to the orthogonal tensor SVD algorithm. This is, to our best knowledge, the first work to address high-order big data reduction by employing cloud computing. Finally, we analyze the security and efficiency of our proposed orthogonal tensor SVD on synthetic dataset and real network intrusion detection dataset, and the results demonstrate that our proposed method is very promising for big data reduction.