Paper 2024/181

Functional Bootstrapping for FV-style Cryptosystems

Dongwon Lee, Seoul National University
Seonhong Min, Seoul National University
Yongsoo Song, Seoul National University

Fully Homomorphic Encryption (FHE) enables the computation of an arbitrary function over encrypted data without decrypting them. In particular, bootstrapping is a core building block of FHE which reduces the noise of a ciphertext thereby recovering the computational capability. This paper introduces a new bootstrapping framework for the Fan-Vercauteren (FV) scheme, called the functional bootstrapping, providing more generic and advanced functionality than the ordinary bootstrapping method. More specifically, the functional bootstrapping allows us to evaluate an arbitrary function while removing the error of an input ciphertext. Therefore, we achieve better depth consumption and computational complexity as the evaluation of a circuit can be integrated as part of the functional bootstrapping procedure. In particular, our approach extends the functionality of FV since it is even applicable to functions between different plaintext spaces. At the heart of our functional bootstrapping framework is a homomorphic Look-Up Table (LUT) evaluation method where we represent any LUT using only the operations supported by the FV scheme. Finally, we provide a proof-of-concept implementation and present benchmarks of the functional bootstrapping. In concrete examples, such as delta and sign functions, our functional bootstrapping takes about 46.5s or 171.4s for 9-bit or 13-bit plaintext modulus, respectively.

Available format(s)
Public-key cryptography
Publication info
Homomorphic EncryptionBFVBootstrapping
Contact author(s)
dongwonlee95 @ snu ac kr
minsh @ snu ac kr
y song @ snu ac kr
2024-03-22: revised
2024-02-07: received
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Creative Commons Attribution


      author = {Dongwon Lee and Seonhong Min and Yongsoo Song},
      title = {Functional Bootstrapping for FV-style Cryptosystems},
      howpublished = {Cryptology ePrint Archive, Paper 2024/181},
      year = {2024},
      note = {\url{}},
      url = {}
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