Tensors are popular and versatile tools which model multidimensional data. Tensor decomposition has emerged as a powerful recommendation 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 clouds. However, because of the rise of various privacy concerns, sensitive data usually need to be encrypted before being outsourced to a cloud. Computations over encrypted data on the clouds 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 best knowledge, the first work to address privacy-preserving tensor decomposition without requiring interaction between users and cloud service providers. More specifically, 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 demonstrate the utility of our proposed approach in cloud deployments.

Recurrent neural network (RNN), a branch of deep learning, is a powerful model for sequential data that has outstanding performance on a wide range of important Internet of Things (IoT) tasks. This unprecedented growth of RNN model has however encountered both heterogeneous IoT data and privacy issues. Existing RNN model can not deal with heterogeneous sequential data; often the larger datasets used in training of RNN model contain sensitive information. To tackle these challenges and for the first time, this research proposes a novel differentially private tensor-based RNN (DPTRNN) that can be applied in many challenging deep learning sequence tasks for IoT systems. Specifically, to process heterogeneous sequential data, we propose a tensor-based RNN model. To guarantee privacy, we develop a tensor-based back-propagation through time algorithm with perturbation to avoid exposing the sensitive information for training the tensor-based RNN model within the framework of differential privacy. Thorough security analysis shows that the differential private tensor-based RNN efficiently protects the confidentiality of sensitive user information for IoT. Our results from extensive experiments on two challenging large video datasets suggest that our proposed scheme is practical with guarantee of data privacy preservation and acceptable accuracy loss.

With an objective to provide the proactive and personalized services for human beings, Cyber-Physical-Social Systems (CPSS), which combine the cyber space, physical space, and social space together, need to process the large scale heterogenous data first. Tensor, as an appropriate data representation tool, has been widely used for representation of heterogeneous Cyber-Physical-Social big data. When computationally processing such tensor, many necessary constraints have to be taken into account, e.g., the execution time, energy consumption, economic cost, security as well as reliability. However, the systematic integration of these constraints and then the modelling of general optimization for tensor processing become more challenging. In this paper, with such constraints being considered together, a general model for tensor computation that optimizes the execution time, energy consumption, and economic cost with acceptable security and reliability is proposed. From diverse perspectives of user requirements, a case study for the tree-based distributed High-Order Singular Value Decomposition (HOSVD) is measured. With the focus on multi-objective combination, the experimental results validate the applicability and generality of the proposed model.

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.

Secure two-party neural network (2P-NN) inference allows the server with a neural network model and the client with inputs to perform neural network inference without revealing their private data to each other. However, the state-of-the-art 2P-NN inference still suffers from large computation and communication overhead especially when used in ImageNet-scale deep neural networks. In this work, we design and build Panther, a lightweight and efficient secure 2P-NN inference system, which has great efficiency in evaluating 2P-NN inference while safeguarding the privacy of the server and the client. At the core of Panther, we have new protocols for 2P-NN inference. Firstly, we propose a customized homomorphic encryption scheme to reduce burdensome polynomial multiplications in the homomorphic encryption arithmetic circuit of linear protocols. Secondly, we present a more efficient and communication concise design for the millionaires’ protocol, which enables non-linear protocols with less communication cost. Our evaluations over three sought-after varying-scale deep neural networks show that Panther outperforms the state-of-the-art 2P-NN inference systems in terms of end-to-end runtime and communication overhead. Panther achieves state-of-the-art performance with up to 24.95× speedup for linear protocols and 6.40× speedup for non-linear protocols in WAN when compared to prior arts.