On the Context-Hiding Property of Shamir-Based Homomorphic Secret Sharing

Homomorphic secret sharing (HSS) allows multiple input clients to secretly share their private inputs to a function among several servers such that each server can homomorphically compute the function over its share to produce a share of the function's output. In HSS-enabled applications such as secure multi-party computation (MPC), security requires that the output shares leak no more information about the inputs than the function output. Such security is ensured by the context-hiding property of HSS. The typical rerandomization technique achieves context hiding but increases the share size. To address this, we formalize the context-hiding property of HSS for individual functions, examine the context-hiding property of Shamir-based HSS for monomials, and extend the study to polynomials.