Secure Tensor-based Big Data Analysis And Processing

With the increasing popularity of cloud computing or fog computing,the big data generated in cyber-physical-social systems are usually sent to clouds or fogs for analysis and processing.However,clouds or fogs are open and users have very limited control over their data on clouds or fogs,directly performing big data analysis and processing in clouds or fogs will arise serious security concerns,such as exposure of user privacy and business information.How to carry out big data analysis and processing in clouds without compromising users' privacy is still a challenge.Tensors have emerged as powerful tools for big data analysis and processing and it has been proved that better performance can be gotten by using tensor-based big data analysis and processing.This thesis focuses on secure tensor-based big data analysis and processing in cloud computing or fog computing.Our main goal is that clouds or fogs efficiently and effectively perform tensor-based big data analysis and processing without learning any knowledge about users' data.The main contributions of the thesis are summarized as follows.First of all,this thesis presents a novel privacy-preserving tensor decomposition approach over semantically secure encrypted big data on cloud.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 privacypreserving tensor decomposition without requiring interaction between users and cloud service providers.Furthermore,we present the first secure integer division and integer square root schemes over encrypted data required in our approach,where 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.Secondly,this thesis presents two novel secure principal eigentensor computation(SPEC)schemes in clouds.This is the first effort to address SPEC over encrypted big data in cloud without the interaction need between multiple users and a cloud.More specifically,we leverage cloud server and trusted hardware component to design a collaborative cloud model.Using the collaborative cloud model,we propose a basic SPEC scheme based on homomorphic cryptosystem,and an efficient SPEC scheme that combines the advantages of homomorphic cryptosystem and garbled circuits and exploits packing technology.We theoretically and empirically analyze the security and efficiency of our SPEC schemes and demonstrate that the proposed schemes provide a secure and efficient way of outsourcing computation.In addition,from the cloud user's perspective,our proposal is lightweight.Thirdly,this thesis presents secure high-order Lanczos schemes.The proposed schemes include secure high-order Lanczos-based orthogonal tensor SVD scheme in cloud,improved secure high-order Lanczos-based orthogonal tensor SVD scheme in cloud,secure high-order Bi-Lanczosscheme in fog-cloud computing.The high-order Lanczos algorithm,improved high-order Lanczos algorithm,and high-order Bi-Lanczos algorithm are introduced.The secure conversion approaches from encrypted tensor to garbled tensor in cloud,secure orthogonal tensor SVD over garbled tensor on cloud,and secure conversion approaches from garbled tensor to encrypted tensor in cloud are presented.A secure big data processing model using the synergy of fog and cloud are developed.The proposed model enables fog and cloud to cooperatively complete big data processing without compromising users' privacy.The secure high-order Bi-Lanczos scheme using the model are presented.Theoretical analyses and experiments are provided based on real-world datasets or case studies.The results support that our proposed schemes are feasible.Fourthly,the secure high-order Lanczos methods using tensor train networks are proposed.The proposed methods include secure high-order unsymmetric Lanczos method using tensor train networks in clouds and secure high-order Bi-Lanczos method using tensor train networks in fog-cloud computing.The secure big data processing model based on tensor train networks in cloud computing or fog-cloud computing is developed.The proposed model enables clouds or fogs and clouds to securely carry out big data processing for large-scale tensors given in a tensor train format.By making use of the model,the secure high-order unsymmetric Lanczos method in cloud computing and the secure high-order BiLanczos method in fog-cloud computing are proposed.Finally,we show that the proposed secure tensor-train-networks-based methods guarantee data privacy under the semi-honest model and evaluate them with case studies.Fifthly,this thesis proposes a tensor-based optimization model for the secure cyberphysical-social big data computations.The proposed model jointly optimizes the execution time,energy consumption,reliability,and quality of experience.Four optimization sub-models are developed to minimize execution time,minimize energy consumption,maximize reliability,and maximize QoE for the secure cyber-physical-social big data computations.The four optimization sub-models can take into account the factors such as step,task,time slot,type,node,core,cryptosystem,and security level.The case study and experiments are presented to illustrate the proposed tensor-based optimization model.