International Association for Cryptologic Research

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Paper: MHz2k: MPC from HE over $\mathbb{Z}_{2^k}$ with New Packing, Simpler Reshare, and Better ZKP

Authors:
Jung Hee Cheon , Seoul National University
Dongwoo Kim , Western Digital Research
Keewoo Lee , Seoul National University
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Presentation: Slides
Conference: CRYPTO 2021
Abstract: We propose a multi-party computation (MPC) protocol over $\mathbb{Z}_{2^k}$ secure against actively corrupted majority from somewhat homomorphic encryption. The main technical contributions are: (i) a new efficient packing method for $\mathbb{Z}_{2^k}$-messages in lattice-based somewhat homomorphic encryption schemes, (ii) a simpler reshare protocol for level-dependent packings, (iii) a more efficient zero-knowledge proof of plaintext knowledge on cyclotomic rings $\Z[X]/\Phi_M(X)$ with $M$ being a prime. Integrating them, our protocol shows from 2.2x upto 4.8x improvements in amortized communication costs compared to the previous best results. Our techniques not only improve the efficiency of MPC over $\mathbb{Z}_{2^k}$ considerably, but also provide a toolkit that can be leveraged when designing other cryptographic primitives over $\mathbb{Z}_{2^k}$.
Video from CRYPTO 2021
BibTeX
@inproceedings{crypto-2021-31178,
  title={MHz2k: MPC from HE over $\mathbb{Z}_{2^k}$ with New Packing, Simpler Reshare, and Better ZKP},
  publisher={Springer-Verlag},
  author={Jung Hee Cheon and Dongwoo Kim and Keewoo Lee},
  year=2021
}