Paper 2018/1043

Improved Bootstrapping for Approximate Homomorphic Encryption

Hao Chen, Ilaria Chillotti, and Yongsoo Song


Since Cheon et al. introduced a homomorphic encryption scheme for approximate arithmetic (Asiacrypt ’17), it has been recognized as suitable for important real-life usecases of homomorphic encryption, including training of machine learning models over encrypted data. A follow up work by Cheon et al. (Eurocrypt ’18) described an approximate bootstrapping procedure for the scheme. In this work, we improve upon the previous bootstrapping result. We improve the amortized bootstrapping time per plaintext slot by two orders of magnitude, from ∼ 1 second to ∼ 0.01 second. To achieve this result, we adopt a smart level-collapsing technique for evaluating DFT-like linear transforms on a ciphertext. Also, we replace the Taylor approximation of the sine function with a more accurate and numerically stable Chebyshev approximation, and design a modified version of the Paterson-Stockmeyer algorithm for fast evaluation of Chebyshev polynomials over encrypted data.

Available format(s)
Publication info
Preprint. MINOR revision.
Fully Homomorphic EncryptionBootstrapping
Contact author(s)
haoche @ microsoft com
2018-11-02: received
Short URL
Creative Commons Attribution


      author = {Hao Chen and Ilaria Chillotti and Yongsoo Song},
      title = {Improved Bootstrapping for Approximate Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2018/1043},
      year = {2018},
      note = {\url{}},
      url = {}
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