Privacy Preserving High-Order Bi-Lanczos in Cloud–Fog Computing for Industrial Applications

Industrial cyber–physical–social systems (CPSSs), a prominent data-driven paradigm, tightly couple and coordinate social space into cyber–physical systems (CPSs) within industrial environments. With the proliferation of cloud–fog computing, cloud–fog computing becomes the most prominent computing paradigm used to implement industrial data analysis. However, the open environment of cloud–fog computing and the limited control of industrial CPSSs users make industrial data analysis without compromising users’ privacy one great research challenge in practical cloud–fog-based industrial applications. High-order Bi-Lanczos (HOBI-Lanczos) approach has shown remarkable success in heterogeneous data analysis in industrial applications. In this article, a novel privacy preserving HOBI-Lanczos approach using tensor train in cloud–fog computing is proposed for industrial data applications. Specifically, a privacy preserving industrial data analysis model using cloud–fog computing and tensor train is firstly proposed. The proposed model enables fogs and clouds to securely carry out industrial data analysis for large-scale tensors given in a tensor train format. In addition, by using this model, a privacy preserving HOBI-Lanczos approach is provided. Last but not least, by using a brain-controlled robot system case study, the proposed approach is theoretically and empirically analyzed. Our proposed approach is proven to be secure. A series of experiments corroborate the superiority of the proposed approach in cloud–fog computing for industrial applications.