Hybrid Multiplicative Secret Sharing

Abstract

A secret-sharing scheme is d-multiplicative if it allows the players to multiply d (rather than two) shared secrets (without recovering them) by locally converting their shares into an additive sharing of the product. In this work, the d-multiplicative secret-sharing (MSS) is extended to a hybrid MSS (HMSS), which is mainly designed for sharing d secrets against different access structures. A necessary and sufficient condition for n-player d-HMSS schemes to exist is presented. The condition is necessary for arbitrary (possibly inefficient or even nonlinear) secret-sharing schemes.