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Improved Bootstrapping for Approximate Homomorphic Encryption

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11477))

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.

Most of this work was done while the second author was an intern in the Cryptography Research group at Microsoft Research (Redmond, USA).

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Notes

  1. 1.

    The subsum algorithm can be understood as the evaluation of trace with respect to the field extension \({\mathbb Q}[X]/(X^N+1)\ge {\mathbb Q}[Y]/(Y^{2\ell }+1)\). It does nothing when \(\ell =N/2\).

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Author information

Authors and Affiliations

  1. Microsoft Research, Redmond, USA

    Hao Chen & Yongsoo Song

  2. imec-COSIC, KU Leuven, Leuven, Belgium

    Ilaria Chillotti

Authors
  1. Hao Chen
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  2. Ilaria Chillotti
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  3. Yongsoo Song
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Corresponding author

Correspondence to Hao Chen .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Chen, H., Chillotti, I., Song, Y. (2019). Improved Bootstrapping for Approximate Homomorphic Encryption. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11477. Springer, Cham. https://doi.org/10.1007/978-3-030-17656-3_2

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  • DOI: https://doi.org/10.1007/978-3-030-17656-3_2

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  • Online ISBN: 978-3-030-17656-3

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