How to Share an NP Statement or Combiners for Zero-Knowledge Proofs

Benny Applebaum, Eliran Kachlon

Abstract: In Crypto’19, Goyal, Jain, and Sahai (GJS) introduced the elegant notion of secret-sharing of an \(\textbf{NP}\) statement (NPSS). Roughly speaking, a \(t\)-out-of-\(n\) secret sharing of an \(\textbf{NP}\) statement is a reduction that maps an instance-witness pair to \(n\) instance-witness pairs such that any subset of \((t-1)\) reveals no information about the original witness, while any subset of \(t\) allows full recovery of the original witness. Although the notion was formulated for general \(t \le n\), the only existing construction (due to GJS) applies solely to the case where \(t = n\) and provides only computational privacy. In this paper, we further explore NPSS and present the following contributions.

External IDs:dblp:conf/crypto/ApplebaumK25a