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Batched Fully Dynamic Multi-key FHE from FHEW-Like Cryptosystems

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Provable and Practical Security (ProvSec 2022)

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Abstract

Multi-key fully homomorphic encryption (MKFHE) schemes support arbitrary computations on data encrypted by different keys. Especially, in the fully dynamic setting, any ciphertexts can be computed at any time while maintaining the compactness. In this case, no information about the parties and the computation function need be known before the evaluation. However, all existing constructions are based on the learning with errors (LWE) problem or learning with rounding (LWR) problem, and thus only allow to encrypt a single bit. On the other hand, FHEW-like cryptosystems are computation-efficient in the sense that they can evaluate arbitrary Boolean circuits on encrypted data followed by the boostrapping procedure. To this end, in this paper, we propose a batched fully dynamic multi-key FHE scheme based on FHEW-like cryptosystems. Specifically, instead of a single bit, our construction encrypts a ring element, and thus has low amortized cost. In addition, as a core building block of construction, we put forward a new multi-key ring-LWE accumulator with homomorphic discrete Fourier transform (DFT) for the boostrapping procedure, which might be of independent interest. The theoretical analysis indicates that the amortized computation cost of generating evaluation key and storage cost achieve optimal.

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Notes

  1. 1.

    The Homomorphic Encryption standardization document [7] supports the use of Gaussian and ternary secrets.

  2. 2.

    k denots the number of the parties involved in the evaluation.

  3. 3.

    k is always larger than \(k'\).

  4. 4.

    T represents a transposition.

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Acknowledgement

This work was supported by the National Nature Science Foundation of China under Grant 62172434.

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks (ISN), Xidian University, Xi’an, 710071, China

    Yuting Jiang

  2. State Key Laboratory of Mathematical Engineering and Advanced Computing, PLA Strategic Support Force Information Engineering University, Zhengzhou, 450001, China

    Jianghong Wei

  3. Guangzhou Institute of Technology, Xidian University, Guanzhou, 510555, China

    Jing Pan

Authors
  1. Yuting Jiang
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Correspondence to Yuting Jiang .

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Editors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Chunpeng Ge

  2. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

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Jiang, Y., Wei, J., Pan, J. (2022). Batched Fully Dynamic Multi-key FHE from FHEW-Like Cryptosystems. In: Ge, C., Guo, F. (eds) Provable and Practical Security. ProvSec 2022. Lecture Notes in Computer Science, vol 13600. Springer, Cham. https://doi.org/10.1007/978-3-031-20917-8_8

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