New Perspectives on Multi-Prover Interactive Proofs

In this work, we introduce the locality hierarchy for multiparty (multi-round) interaction, and for the first time a complete definition of multi-round multiparty no-signalling distributions and strategies. Within this framework, we define the locality of a protocol which involves the provers, verifiers, simulators and distinguishers. We show that the existing protocol [BFL90] for {NEXP} and a new zero-knowledge variant are sound in a local sense, and are zero-knowledge in a sense that is even stronger than usually understood. Finally, we present similar constructions for entangled and no-signalling prover sets for {NEXP} and {EXP} based on [IV12] and [KRR14] using new multi-prover commitment schemes.