Machine learning over encrypted data: a survey of fully homomorphic encryption for AI systems

The increasing use of machine learning (ML) in privacy-sensitive domains such as healthcare, finance, and user-facing services has intensified the need for techniques that enable data-driven intelligence without exposing sensitive information. Fully Homomorphic Encryption (FHE) offers a cryptographically rigorous approach to privacy-preserving machine learning by allowing computations to be performed directly on encrypted data. While appealing in principle, the integration of FHE into modern ML pipelines introduces substantial challenges that fundamentally affect model design, algorithm selection, and system performance. This survey provides a comprehensive and structured review of machine learning over encrypted data using non-interactive FHE-based approaches. We examine how a wide range of machine learning models, including traditional ML algorithms, deep neural networks, and emerging transformer architectures, are adapted to operate under the arithmetic, precision, and efficiency constraints imposed by FHE. To organize a rapidly growing body of work, we introduce a unifying taxonomy that captures key design dimensions such as encryption schemes, nonlinearity handling strategies, model families, system-level optimizations, and privacy objectives. Using this framework, we synthesize existing approaches, analyze trade-offs between accuracy, efficiency, and security, and highlight recurring design patterns across the literature. Beyond summarizing existing techniques, this survey discusses practical limitations, deployment considerations, and open research challenges that shape the future of privacy-preserving machine learning under encryption. By bridging cryptographic techniques and modern AI system design, this work aims to serve as a reference for researchers and practitioners seeking to develop secure, scalable, and trustworthy machine learning systems.