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International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2021: Advances in Cryptology – ASIACRYPT 2021 pp 640–669Cite as

Transciphering Framework for Approximate Homomorphic Encryption

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13092))

Abstract

Homomorphic encryption (HE) is a promising cryptographic primitive that enables computation over encrypted data, with a variety of applications including medical, genomic, and financial tasks. In Asiacrypt 2017, Cheon et al. proposed the \(\mathsf {CKKS}\) scheme to efficiently support approximate computation over encrypted data of real numbers. HE schemes including \(\mathsf {CKKS}\), nevertheless, still suffer from slow encryption speed and large ciphertext expansion compared to symmetric cryptography.

In this paper, we propose a novel hybrid framework, dubbed \(\mathsf {RtF}\) (Real-to-Finite-field) framework, that supports \(\mathsf {CKKS}\). The main idea behind this construction is to combine the \(\mathsf {CKKS}\) and the \(\mathsf {FV}\) homomorphic encryption schemes, and use a stream cipher using modular arithmetic in between. As a result, real numbers can be encrypted without significant ciphertext expansion or computational overload on the client side.

As an instantiation of the stream cipher in our framework, we propose a new HE-friendly cipher, dubbed \(\mathsf {HERA}\), and extensively analyze its security and efficiency. The main feature of \(\mathsf {HERA}\) is that it uses a simple randomized key schedule. Compared to recent HE-friendly ciphers such as \(\mathsf {FLIP}\) and \(\mathsf {Rasta}\) using randomized linear layers, \(\mathsf {HERA}\) requires a smaller number of random bits. For this reason, \(\mathsf {HERA}\) significantly outperforms existing HE-friendly ciphers on both the client and the server sides.

With the \(\mathsf {RtF}\) transciphering framework combined with \(\mathsf {HERA}\) at the 128-bit security level, we achieve small ciphertext expansion ratio with a range of 1.23 to 1.54, which is at least 23 times smaller than using (symmetric) \(\mathsf {CKKS}\)-only, assuming the same precision bits and the same level of ciphertexts at the end of the framework. We also achieve 1.6 \(\upmu \)s and 21.7 MB/s for latency and throughput on the client side, which are 9085 times and 17.8 times faster than the \(\mathsf {CKKS}\)-only environment, respectively.

Jooyoung Lee—This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1047146).

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Notes

  1. 1.

    https://github.com/KAIST-CryptLab/RtF-Transciphering.

  2. 2.

    https://github.com/LowMC/lowmc/blob/master/determine_rounds.py.

  3. 3.

    A primitive root of unity \(\xi \) exists if the characteristic t of the message space is an odd prime such that \(t\equiv 1 \pmod {M}\).

  4. 4.

    We note that \(\mathbf {c}_\mathsf {ctr}\)’s are in coefficients, not in slots.

  5. 5.

    https://github.com/Alibaba-Gemini-Lab/OpenPEGASUS.

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Authors and Affiliations

  1. Samsung SDS, Seoul, Korea

    Jihoon Cho, Joohee Lee, Dukjae Moon & Hyojin Yoon

  2. KAIST, Daejeon, Korea

    Jincheol Ha, Seongkwang Kim, Byeonghak Lee & Jooyoung Lee

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  1. Jihoon Cho
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  2. Jincheol Ha
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  3. Seongkwang Kim
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  4. Byeonghak Lee
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  5. Joohee Lee
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Correspondence to Jihoon Cho , Seongkwang Kim or Jooyoung Lee .

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Editors and Affiliations

  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Cho, J. et al. (2021). Transciphering Framework for Approximate Homomorphic Encryption. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13092. Springer, Cham. https://doi.org/10.1007/978-3-030-92078-4_22

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