Paper 2023/1737

On the Security of Succinct Interactive Arguments from Vector Commitments

Abstract

We study the security of a fundamental family of succinct interactive arguments in the standard model, stemming from the works of Kilian (1992) and Ben-Sasson, Chiesa, and Spooner (``BCS'', 2016). These constructions achieve succinctness by combining probabilistic proofs and vector commitments. Our first result concerns the succinct interactive argument of Kilian, realized with any probabilistically-checkable proof (PCP) and any vector commitment. We establish the tightest known bounds on the security of this protocol. Prior analyses incur large overheads, or assume restrictive properties of the underlying PCP. Our second result concerns an interactive variant of the BCS succinct non-interactive argument, which here we call IBCS, realized with any public-coin interactive oracle proof (IOP) and any vector commitment. We establish the first security bounds for the IBCS protocol. Prior works rely upon this protocol without proving its security; our result closes this gap. Finally, we study the capabilities and limitations of succinct arguments based on vector commitments. We show that a generalization of the IBCS protocol, which we call the \emph{Finale protocol}, is secure when realized with any \emph{public-query} IOP (a notion that we introduce) that satisfies a natural ``random continuation sampling'' (RCS) property. We also show a partial converse: if the Finale protocol satisfies the RCS property (which in particular implies its security), then so does the underlying public-query IOP.