  With ever-growing data and the need for developing powerful machine learning
models, data owners increasingly depend on untrusted platforms (e.g., public
clouds, edges, and machine learning service providers). However, sensitive data
and models become susceptible to unauthorized access, misuse, and privacy
compromises. Recently, a body of research has been developed to train machine
learning models on encrypted outsourced data with untrusted platforms. In this
survey, we summarize the studies in this emerging area with a unified framework
to highlight the major challenges and approaches. We will focus on the
cryptographic approaches for confidential machine learning (CML), while also
covering other directions such as perturbation-based approaches and CML in the
hardware-assisted confidential computing environment. The discussion will take
a holistic way to consider a rich context of the related threat models,
security assumptions, attacks, design philosophies, and associated trade-offs
amongst data utility, cost, and confidentiality.
