[Resource Topic] 2021/1383: MHz2k: MPC from HE over $\mathbb{Z}_{2^k}$ with New Packing, Simpler Reshare, and Better ZKP

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

Authors: Jung Hee Cheon, Dongwoo Kim, Keewoo Lee


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 \mathbb{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}.

ePrint: https://eprint.iacr.org/2021/1383

Talk: https://www.youtube.com/watch?v=Hi6pU7eT0k4

Slides: https://iacr.org/submit/files/slides/2021/crypto/crypto2021/378/slides.pdf

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