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Australasian Conference on Information Security and Privacy

ACISP 2021: Information Security and Privacy pp 590–609Cite as

Optimizing Bootstrapping and Evaluating Large FHE Gates in the LWE-Based GSW-FHE

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13083))

Abstract

Fully homomorphic encryption (FHE) allows us to perform computations directly over encrypted data and can be widely used in some highly regulated industries. Gentry’s bootstrapping procedure is used to refresh noisy ciphertexts and is the only way to achieve the goal of FHE up to now. In this paper, we optimize the LWE-based GSW-type bootstrapping procedure. Our optimization decreases the lattice approximation factor for the underlying worst-case lattice assumption from \(\tilde{O}(N^{2.5})\) to \(\tilde{O}(N^{2})\), and is time-efficient by a \(O(\lambda )\) factor. Our scheme can also achieve the best factor in prior works on bootstrapping of standard lattice-based FHE by taking a larger lattice dimension, which makes our scheme as secure as the standard lattice-based PKE. Furthermore, in this work we present a technique to perform more operations per bootstrapping in the LWE-based FHE scheme. Although there have been studies to evaluate large FHE gates using schemes over ideal lattices, (i.e. using FHEW or TFHE), we are the first to study how to perform complex functions homomorphically over standard lattices.

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Notes

  1. 1.

    The correctness can be verified at https://github.com/LiuChaoCrypto/MatGSWscheme. This implementation can perform decryption and some Boolean gates homomorphically. Because of the huge storage and time consumption of the LWE-based FHE, we use a very small parameter to verify the correctness, and it is only for the correctness verification, but not for the performance testing.

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Acknowledgments

This paper is supported by National Key Research and Development Program of China (Grant No. 2020YFA0309705, 2018YFA0704701), Major Program of Guangdong Basic and Applied Research (No. 2019B030302008), Major Scientific and Techological Innovation Project of Shandong Province (No. 2019JZZY010133), and Shandong Key Research and Development Program (No. 2020ZLYS09). Authors thank the anonymous ACISP’21 reviewers for helpful comments.

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Authors and Affiliations

  1. School of Cyber Science and Technology, Shandong University, Qingdao, People’s Republic of China

    Chao Liu

  2. Institute for Advanced Study/BNRist, Tsinghua University, Beijing, People’s Republic of China

    Anyu Wang & Zhongxiang Zheng

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  1. Chao Liu
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  2. Anyu Wang
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  3. Zhongxiang Zheng
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Correspondence to Anyu Wang .

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Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Joonsang Baek

  2. Data61, CSIRO, Marsfield, NSW, Australia

    Sushmita Ruj

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Liu, C., Wang, A., Zheng, Z. (2021). Optimizing Bootstrapping and Evaluating Large FHE Gates in the LWE-Based GSW-FHE. In: Baek, J., Ruj, S. (eds) Information Security and Privacy. ACISP 2021. Lecture Notes in Computer Science(), vol 13083. Springer, Cham. https://doi.org/10.1007/978-3-030-90567-5_30

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  • DOI: https://doi.org/10.1007/978-3-030-90567-5_30

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