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Succinct Homomorphic Secret Sharing
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| Conference: | EUROCRYPT 2024 |
| Abstract: | This work introduces homomorphic secret sharing (HSS) with succinct share size. In HSS, private inputs are shared between parties, who can then homomorphically evaluate a function on their shares, obtaining a share of the function output. In succinct HSS, a portion of the inputs can be distributed using shares whose size is sublinear in the number of such inputs. The parties can then locally evaluate a function f on the shares, with the restriction that f must be linear in the succinctly shared inputs. We construct succinct, two-party HSS for branching programs, based on either the decisional composite residuosity assumption, a DDH-like assumption in class groups, or learning with errors with a superpolynomial modulus-to-noise ratio. We then give several applications of succinct HSS, which were only previously known using fully homomorphic encryption, or stronger tools: 1. Succinct vector oblivious linear evaluation (VOLE): Two parties can obtain secret shares of a long, arbitrary vector x, multiplied by a scalar ∆, with communication sublinear in the size of the vector. 2. Batch, multi-party distributed point functions: A protocol for distributing a batch of secret, random point functions among N parties, for any polynomial N, with communication sublinear in the number of DPFs. 3. Sublinear MPC for any number of parties: Two new constructions of MPC with sublinear communication complexity, with N parties for any polynomial N: (1) For general layered Boolean circuits of size s, with communication O(N s/log log s), and (2) For layered, sufficiently wide Boolean circuits, with communication O(N s/log s). |
BibTeX
@inproceedings{eurocrypt-2024-33969,
title={Succinct Homomorphic Secret Sharing},
publisher={Springer-Verlag},
author={Damiano Abram and Lawrence Roy and Peter Scholl},
year=2024
}