# A Survey on Homomorphic Encryption Schemes: Theory and Implementation

arXiv: https://arxiv.org/abs/1704.03578 · HTML: https://mlsanity.com/paper/1704.03578/

## Key facts

- Cited by 156 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2017.

## Built on by (most cited first, 30 of 156)

- [Personal LLM Agents: Insights and Survey about the Capability, Efficiency and Security](https://mlsanity.com/paper/2401.05459/) (2024)
- [Trustworthy AI: A Computational Perspective](https://mlsanity.com/paper/2107.06641/) (2021)
- [TRiSM for Agentic AI: A Review of Trust, Risk, and Security Management in LLM-based Agentic Multi-Agent Systems](https://mlsanity.com/paper/2506.04133/) (2025)
- [Privacy-Preserving Machine Learning: Methods, Challenges and Directions](https://mlsanity.com/paper/2108.04417/) (2021)
- [Survey: Leakage and Privacy at Inference Time](https://mlsanity.com/paper/2107.01614/) (2021)
- [A Survey on Heterogeneous Federated Learning](https://mlsanity.com/paper/2210.04505/) (2022)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [Federated Unlearning: A Survey on Methods, Design Guidelines, and Evaluation Metrics](https://mlsanity.com/paper/2401.05146/) (2024)
- [Security of AI Agents](https://mlsanity.com/paper/2406.08689/) (2024)
- [Overview of AI and Communication for 6G Network: Fundamentals, Challenges, and Future Research Opportunities](https://mlsanity.com/paper/2412.14538/) (2024)
- [A Survey on Federated Recommendation Systems](https://mlsanity.com/paper/2301.00767/) (2022)
- [A Vertical Federated Learning Framework for Graph Convolutional Network](https://mlsanity.com/paper/2106.11593/) (2021)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [A Survey on Privacy Risks and Protection in Large Language Models](https://mlsanity.com/paper/2505.01976/) (2025)
- [Shadow in the Cache: Unveiling and Mitigating Privacy Risks of KV-cache in LLM Inference](https://mlsanity.com/paper/2508.09442/) (2025)
- [PointNCBW: Towards Dataset Ownership Verification for Point Clouds via Negative Clean-label Backdoor Watermark](https://mlsanity.com/paper/2408.05500/) (2024)
- [Secure On-Device Video OOD Detection Without Backpropagation](https://mlsanity.com/paper/2503.06166/) (2025)
- [Secure Neuroimaging Analysis using Federated Learning with Homomorphic Encryption](https://mlsanity.com/paper/2108.03437/) (2021)
- [Zero-Knowledge Proof-based Verifiable Decentralized Machine Learning in Communication Network: A Comprehensive Survey](https://mlsanity.com/paper/2310.14848/) (2023)
- [Intelligent AI Delegation](https://mlsanity.com/paper/2602.11865/) (2026)
- [Applications of Federated Learning in Smart Cities: Recent Advances, Taxonomy, and Open Challenges](https://mlsanity.com/paper/2102.01375/) (2021)
- [Efficient and Secure Federated Learning for Financial Applications](https://mlsanity.com/paper/2303.08355/) (2023)
- [Batch Label Inference and Replacement Attacks in Black-Boxed Vertical Federated Learning](https://mlsanity.com/paper/2112.05409/) (2021)
- [How to keep text private? A systematic review of deep learning methods for privacy-preserving natural language processing](https://mlsanity.com/paper/2205.10095/) (2022)
- [THC: Accelerating Distributed Deep Learning Using Tensor Homomorphic Compression](https://mlsanity.com/paper/2302.08545/) (2023)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [Combined Federated and Split Learning in Edge Computing for Ubiquitous Intelligence in Internet of Things: State of the Art and Future Directions](https://mlsanity.com/paper/2207.09611/) (2022)
- [Federated Graph Machine Learning: A Survey of Concepts, Techniques, and Applications](https://mlsanity.com/paper/2207.11812/) (2022)
- [Towards Efficient Communication and Secure Federated Recommendation System via Low-rank Training](https://mlsanity.com/paper/2401.03748/) (2024)
- [SLIP: Securing LLMs IP Using Weights Decomposition](https://mlsanity.com/paper/2407.10886/) (2024)

## Abstract (arXiv)

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.