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Paper: Improved Bootstrapping for Approximate Homomorphic Encryption

Authors:
Hao Chen
Ilaria Chillotti
Yongsoo Song
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DOI: 10.1007/978-3-030-17656-3_2
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Abstract: 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 $$\sim $$∼1 s to $$\sim $$∼0.01 s. 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.
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BibTeX
@article{eurocrypt-2019-29354,
  title={Improved Bootstrapping for Approximate Homomorphic Encryption},
  booktitle={Advances in Cryptology – EUROCRYPT 2019},
  series={Advances in Cryptology – EUROCRYPT 2019},
  publisher={Springer},
  volume={11477},
  pages={34-54},
  doi={10.1007/978-3-030-17656-3_2},
  author={Hao Chen and Ilaria Chillotti and Yongsoo Song},
  year=2019
}