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Circuit Bootstrapping: Faster and Smaller

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Advances in Cryptology – EUROCRYPT 2024 (EUROCRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14652))

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Abstract

We present a novel circuit bootstrapping algorithm that outperforms the state-of-the-art TFHE method with 9.9\(\times \) speedup and 15.6\(\times \) key size reduction. These improvements can be attributed to two technical contributions. Firstly, we redesigned the circuit bootstrapping workflow to operate exclusively under the ring ciphertext type, which eliminates the need for conversion between LWE and RLWE ciphertexts. Secondly, we improve the LMKC+ blind rotation algorithm by reducing the number of automorphisms, then propose the first automorphism type multi-value functional bootstrapping. These automorphism-based techniques lead to further key size optimization, and are of independent interest besides circuit bootstrapping. Based on our new circuit bootstrapping we can evaluate AES-128 in 26.2 s (single thread), achieving 10.3\(\times \) speedup compared with the state-of-the-art TFHE-based approach.

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Notes

  1. 1.

    Sample extraction is to extract LWE sample from RLWE, which is detailed in Sect. 2.4.

  2. 2.

    This results in a slight increase in circuit computation latency as we discussed in the full version of this paper [35], but allows for greater circuit depth and the batch processing of more ciphertexts at once (see TFHE horizontal/ vertical/mixed packing technology [11]).

  3. 3.

    They also propose a 4-minute variant without bootstrapping. However, it can not be used for transciphering since the ciphertext is too noisy to do further evaluation.

  4. 4.

    The parameters chosen for the TFHE circuit bootstrapping are listed in Table 6. Our new framework utilizes the parameter set \(\textsf{CMUX}_1\) recommended in Table 5.

  5. 5.

    LMKC+ has proposed an optimization to reduce the number of automorphisms by using additional storage. More details can be found in Sect. 4.2.

  6. 6.

    https://github.com/malb/lattice-estimator.

  7. 7.

    https://github.com/tfhe/experimental-tfhe.

  8. 8.

    We detailed this application scenario in the full version of this paper [35].

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Acknowledgments

We are grateful for the helpful comments from the anonymous reviewers. This work was supported by the Huawei Technologies Co., Ltd and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-035).

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Authors and Affiliations

  1. Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Ruida Wang, Zhihao Li, Xianhui Lu, Benqiang Wei, Kun Liu & Kunpeng Wang

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Ruida Wang, Zhihao Li, Xianhui Lu, Benqiang Wei, Kun Liu & Kunpeng Wang

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Yundi Wen

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Correspondence to Xianhui Lu .

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  1. Zama, Paris, France

    Marc Joye

  2. Ruhr University Bochum, Bochum, Germany

    Gregor Leander

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Wang, R. et al. (2024). Circuit Bootstrapping: Faster and Smaller. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14652. Springer, Cham. https://doi.org/10.1007/978-3-031-58723-8_12

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