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A survey on implementations of homomorphic encryption schemes

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Abstract

With the increased need for data confidentiality in various applications of our daily life, homomorphic encryption (HE) has emerged as a promising cryptographic topic. HE enables to perform computations directly on encrypted data (ciphertexts) without decryption in advance. Since the results of calculations remain encrypted and can only be decrypted by the data owner, confidentiality is guaranteed and any third party can operate on ciphertexts without access to decrypted data (plaintexts). Applying a homomorphic cryptosystem in a real-world application depends on its resource efficiency. Several works compared different HE schemes and gave the stakes of this research field. However, the existing works either do not deal with recently proposed HE schemes (such as CKKS) or focus only on one type of HE. In this paper, we conduct an extensive comparison and evaluation of homomorphic cryptosystems’ performance based on their experimental results. The study covers all three families of HE, including several notable schemes such as BFV, BGV, FHEW, TFHE, CKKS, RSA, El-Gamal, and Paillier, as well as their implementation specification in widely used HE libraries, namely Microsoft SEAL, PALISADE, and HElib. In addition, we also discuss the resilience of HE schemes to different kind of attacks such as indistinguishability under chosen plaintext attack and integer factorization attacks on classical and quantum computers.

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Funding

The research depicted in this paper is funded by the French National Research Agency (ANR), project ANR-19-CE23-0005 BI4people (Business Intelligence for the people).

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Authors and Affiliations

  1. Université Catholique de Louvain, Ottignies-Louvain-la-Neuve, Belgium

    Thi Van Thao Doan

  2. Univ Lyon, Univ Lyon 2, UR ERIC, Lyon, France

    Mohamed-Lamine Messai & Jérôme Darmont

  3. Univ Lyon, Univ Lyon 1, UR ERIC, Lyon, France

    Gérald Gavin

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  1. Thi Van Thao Doan
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  2. Mohamed-Lamine Messai
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  3. Gérald Gavin
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  4. Jérôme Darmont
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Contributions

T.V.T. Doan did the experimentation, wrote the code, and the main manuscript text. M.-L. Messai wrote parts of the manuscript and reviewed it. G. Gavin and J. Darmont reviewed the manuscript.

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Correspondence to Thi Van Thao Doan.

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Doan, T.V.T., Messai, ML., Gavin, G. et al. A survey on implementations of homomorphic encryption schemes. J Supercomput 79, 15098–15139 (2023). https://doi.org/10.1007/s11227-023-05233-z

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