Paper 2026/2308

Multiparty Homomorphic Secret Sharing From Distributed Discrete Logarithm

Abstract

Homomorphic secret sharing (HSS) enables non-interactive distributed evaluation of functions on secret-shared inputs. While two-party HSS is well understood, multiparty constructions remain limited in expressiveness and efficiency. We present a general framework for constructing multiparty HSS from two-party semi-private HSS (which in turn can be instantiated using distributed discrete logarithms) via a new party virtualization paradigm. In a semi-private HSS, some designated inputs may be fully known to specific servers, while the remaining inputs remain hidden. Starting from two-party semi-private schemes, we obtain $N$-party semi-private HSS supporting compositions of polynomial computations and restricted multiplication straight-line programs, for $N = O(\log \lambda / \log \log \lambda)$. We further upgrade semi-private HSS to fully private HSS for functions of polynomial degree and polynomially bounded Waring rank. As a consequence, we obtain multiparty distributed point functions with key size polynomial in $\lambda$ and $\log |D|$, for a domain $D$ of superpolynomial size. When the underlying two-party scheme supports offline/online sharing, the resulting multiparty DPFs are programmable. Our framework admits instantiations under standard assumptions including DCR and class-group assumptions.