Brief Announcement: Distributed Statistical Zero-Knowledge Proofs via Sumcheck

Abstract

We study distributed zero-knowledge proofs, introduced by Bick, Kol, and Oshman (SODA 2022). While distributed interactive proofs have advanced rapidly in recent years, general-purpose techniques for distributed zero-knowledge remain scarce and mostly problem-specific. We address this gap by introducing distributed statistical zero-knowledge, requiring that each node's view be simulatable up to negligible statistical distance, and by lifting the robust Sumcheck protocol (Lund, Fortnow, Karloff, and Nisan; FOCS 1990) into a modular primitive for distributed zero-knowledge proofs.