Paper 2025/966

Multiparty Homomorphic Secret Sharing and More from LPN and MQ

Abstract

We give the first constructions of multiparty pseudorandom correlation generators, distributed point functions, and (negligible-error) homomorphic secret sharing for constant-degree polynomials for any number of parties without using LWE or iO. Our constructions are proven secure under the combination of LPN with dimension $n$, $2n$ samples, and noise rate $n^{\varepsilon-1}$ for a small constant $\varepsilon$, and MQ with $n$ variables and $n^{1+\delta}$ equations. As applications of our results, we obtain from the same assumptions secure multiparty computation protocols with sublinear communication and silent preprocessing, as well as private information retrieval for $M$ servers and size-$\lambda^d$ databases with optimal download rate and client-to-server communication $M^d\cdot \lambda^3$.