Multi-key Homomorphic Secret Sharing from LWE Without Multi-key HE.

Homomorphic secret sharing (HSS) allows participants to share their private data between computing servers for the joint computation of a public function without fully homomorphic encryption. It serves as a competitive alternative to somewhat/fully homomorphic encryption (S/FHE) in some scenarios. However, the existing HSS schemes capable of computing on multi-source data either only support evaluating polynomials whose degrees are limited by the number of participants, or involve relatively complex multi-key HE in their constructions. In this paper, we introduce the formal notion of multi-key HSS, and propose a multi-key two-server HSS scheme from LWE without multi-key HE, by leveraging the technique of homomorphic linear combination that was previously used to construct multi-key FHE from GSW-FHE in [ 18 ]. As a result, our scheme supports server-aided secure computation of restricted multiplication straight-line (RMS) programs over private data from multiple independent sources, and the number of input clients and the degree of evaluated polynomials can be as high as a polynomial in the security parameter. Finally, we prove the security of the multi-key HSS scheme, and demonstrate its implementation performance.