With the wide deployment of public clouds, owners of big graphs want to use the cloud to handle the scalability issues. However, the privacy and ownership of the graphs in the cloud has become a major concern. In this paper, we study privacy-preserving algorithms for graph spectral analysis of outsourced encrypted graph in the cloud. We consider a cloud-centric framework with three collaborative parties: data contributors, data owner, and a honest-but-curious cloud provider. For a $N\times N$ graph matrix, our algorithms achieve a practical work allocation with preserved privacy: the cloud handles expensive storage and computation in $O(N^2)$ complexity, and data owner and data contributors' algorithms cost only $O(N)$. We have developed the privacy-preserving versions of the two approximate eigendecomposition algorithms: the Lanczos algorithm and the Nyström algorithm, based on different encryption methods: additive homomorphic encryption (AHE) methods and somewhat homomorphic encryption (SHE) methods. Both dense and sparse matrices are studied, while sparse matrices also involve a differentially private data submission protocol to allow the trade-off between data sparsity and privacy. Experimental results show that the Nyströ algorithm with sparse encoding can dramatically reduce data owners' costs; SHE-based methods have lower computational time while AHE-based methods have lower communication costs.

With the ever-growing data and the need for developing powerful machine learning models, data owners increasingly depend on various untrusted platforms (e.g., public clouds, edges, and machine learning service providers) for scalable processing or collaborative learning. Thus, sensitive data and models are in danger of unauthorized access, misuse, and privacy compromises. A relatively new body of research confidentially trains machine learning models on protected data to address these concerns. In this survey, we summarize notable studies in this emerging area of research. With a unified framework, we highlight the critical challenges and innovations in outsourcing machine learning confidentially. We focus on the cryptographic approaches for confidential machine learning (CML), primarily on model training, while also covering other directions such as perturbation-based approaches and CML in the hardware-assisted computing environment. The discussion will take a holistic way to consider a rich context of the related threat models, security assumptions, design principles, and associated trade-offs amongst data utility, cost, and confidentiality.