A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Open accessAbstract
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. The users or service providers with the key have exclusive rights on the data. Especially with popular cloud services, 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. Therefore, this survey focuses on HE and FHE schemes. 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 for 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, and extending the state-of-the-art HE, PHE, SWHE, and FHE systems.
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High computational costs and complexity associated with HE still persist when integrating in PPML.
“Despite various advances, high computational costs and complexity associated with HE still persist when integrating in PPML [2].”
From Privacy-preserving Machine Learning in Internet of Vehicle Applications: Fundamentals, Recent Advances, and Future Direction (2025) · cites this paper as [2]
The Introduction describes FHE bootstrapping as too computationally costly, and §4.0.4 says HElib is difficult to use because its low-level implementation and parameter selection require sophistication. These passages support persistent cost and complexity challenges for HE, but they do not establish those challenges specifically when integrating HE into privacy-preserving machine learning (PPML). (LLM, conf=0.85)
Experimental — accuracy not yet measuredHE can be broadly categorized into three types: partially homomorphic, somewhat homomorphic, and FHE.
“HE can be broadly categorized into three types: partially homomorphic, somewhat (or strong) homomorphic, and FHE [2].”
From Privacy-preserving Machine Learning in Internet of Vehicle Applications: Fundamentals, Recent Advances, and Future Direction (2025) · cites this paper as [2]
The Introduction (page unavailable) names partially, somewhat, and fully homomorphic encryption schemes, and Section 3 (page unavailable) likewise presents PHE, SWHE, and FHE. These passages support the three-category claim, but our copy does not identify “strong” as another name for somewhat homomorphic encryption. (LLM, conf=0.84)
Experimental — accuracy not yet measuredHE introduces prohibitive latency in large-scale traffic simulations due to polynomial-degree ciphertext operations, conflicting with sub-second response requirements for dynamic traffic management.
“HE, though theoretically robust, introduces prohibitive latency in large-scale traffic simulations due to polynomial-degree ciphertext operations, conflicting with sub-second response requirements for dynamic traffic management [2, 109, 132].”
From Privacy-preserving Machine Learning in Internet of Vehicle Applications: Fundamentals, Recent Advances, and Future Direction (2025) · cites this paper as [2]
The Conclusion’s Table 5 (page not available in our copy) reports substantial evaluation times for several FHE implementations, supporting a general concern about latency. It does not assess large-scale traffic simulations, attribute their latency to polynomial-degree ciphertext operations, or establish sub-second requirements for dynamic traffic management. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe first FHE scheme was proposed using lattice-based cryptography, which introduced the concept of bootstrapping to refresh ciphertexts and manage noise accumulation during computations.
“The first FHE scheme was proposed using lattice-based cryptography, which introduced the concept of bootstrapping to refresh ciphertexts and manage noise accumulation during computations [2].”
From Privacy-preserving Machine Learning in Internet of Vehicle Applications: Fundamentals, Recent Advances, and Future Direction (2025) · cites this paper as [2]
Several implementations of homomorphic encryption algorithms with varying levels of efficiency exist, and the application of homomorphic encryption represents an efficiency-security trade-off, with computational performance currently the most notable issue.
“Several implementations of HE algorithms 69 with varying levels of efficiency exist, and the application of HE represents an efficiencysecurity trade-off, with computational performance currently the most notable issue.”
From Secure, privacy-preserving and federated machine learning in medical imaging (2020) · cites this paper as [69]
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- Authors
- Acar, A., Aksu, H., Uluagac, A. S., & Conti, M.
- Affiliations
- Florida International University (US)
- University of Padua (IT)
- Venue
- ACM Computing Surveys
- Published
- 2018-07-25
- Volume
- 51
- Issue
- 4
- Pages
- 1-35
- ISSN
- 0360-0300 (ISSN-L)
- 1557-7341
- OpenAlex
- W2606882085
- Semantic Scholar
- a53de06437f166b89f952211e7e882d7dbec4e58
- Cited by
- 1,397
- References
- 180
- Citations by year
- 2026: 190 · 2025: 307 · 2024: 250 · 2023: 177 · 2022: 150 · 2021: 146 · 2020: 106 · 2019: 60 · 2018: 8 · 2017: 3
- FWCI
- 45.03
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Computing Surveys (publishedVersion)
- Padua Research Archive (University of Padova) (submittedVersion)
- Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, other-oa)
- Funders
- National Science Foundation (1718116)
- European Commission (PCIG11-GA-2012-321980)
- NSF-CNS (1718116)
- EU TagItSmart! Project (H2020-ICT30-2015-688061)
- EU-India REACH Project (ICI+/2014/342-896)
- Cisco University Research Program Fund and Silicon Valley Community Foundation (2017-166478 (3696))
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptography and Data Security
- Physical Sciences › Computer Science › Information Systems › Cloud Data Security Solutions
- Physical Sciences › Computer Science › Artificial Intelligence › Internet Traffic Analysis and Secure E-voting
- Keywords
- homomorphic encryption, fully homomorphic encryption, partially homomorphic encryption, somewhat homomorphic encryption, privacy-preserving computation, cloud data privacy, untrusted server
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