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Paper: Homomorphic Secret Sharing for Multipartite and General Adversary Structures Supporting Parallel Evaluation of Low-Degree Polynomials

Authors:
Reo Eriguchi , The University of Tokyo / AIST
Koji Nuida , Kyushu University / AIST
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Conference: ASIACRYPT 2021
Abstract: Homomorphic secret sharing (HSS) for a function $f$ allows input parties to distribute shares for their private inputs and then locally compute output shares from which the value of $f$ is recovered. HSS can be directly used to obtain a two-round multiparty computation (MPC) protocol for possibly non-threshold adversary structures whose communication complexity is independent of the size of $f$. In this paper, we propose two constructions of HSS schemes supporting parallel evaluation of a single low-degree polynomial and tolerating multipartite and general adversary structures. Our multipartite scheme tolerates a wider class of adversary structures than the previous multipartite one in the particular case of a single evaluation and has exponentially smaller share size than the general construction. While restricting the range of tolerable adversary structures (but still applicable to non-threshold ones), our schemes perform $\ell$ parallel evaluations with communication complexity approximately $\ell/\log\ell$ times smaller than simply using $\ell$ independent instances. We also formalize two classes of adversary structures taking into account real-world situations to which the previous threshold schemes are inapplicable. Our schemes then perform $O(m)$ parallel evaluations with almost the same communication cost as a single evaluation, where $m$ is the number of parties.
BibTeX
@inproceedings{asiacrypt-2021-31359,
  title={Homomorphic Secret Sharing for Multipartite and General Adversary Structures Supporting Parallel Evaluation of Low-Degree Polynomials},
  publisher={Springer-Verlag},
  author={Reo Eriguchi and Koji Nuida},
  year=2021
}