We present z-MPC, a novel one-round multi-party computation (MPC) protocol based on Laurent Series Secret Sharing (LSSS). Traditional MPC protocols suffer from quadratic computational complexity in secret reconstruction due to their reliance on Lagrange interpolation. Our protocol fundamentally reimagines secret sharing by encoding secrets as residues in Laurent series rather than polynomial coefficients, enabling direct linear composition for secret reconstruction. This innovation reduces computational complexity from O(t2) to O(t) while maintaining perfect information-theoretic security. z-MPC achieves efficient key refresh mechanisms, scalable multi-party computation, and dealerless distributed key generation, representing a paradigm shift in MPC efficiency particularly beneficial for threshold cryptography applications where traditional methods face significant scalability limitations.
Shim et al. (Fri,) studied this question.