Interactive Distributed Proofs

18^th March 2021, 11:00 Microsoft Teams
Dr. Rotem Oshman
Department of Computer Science, Tel-Aviv University

Abstract

Interactive proof systems allow a resource-bounded verifier to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee that the prover can only convince the verifier of true statements. In the context of centralized computation, a celebrated result shows that interactive proofs are extremely powerful, allowing polynomial-time verifiers to decide any language in PSPACE. In this work we initiate the study of distributed interactive proofs: a network of nodes interacts with a single untrusted prover, who sees the entire network graph, to decide whether the graph satisfies some property. We focus on the communication cost of the protocol — the number of bits the nodes must exchange with the prover and each other. Our model can also be viewed as a generalization of the various models of “distributed NP” (proof labeling schemes, etc.) which received significant attention recently: while these models only allow the prover to present each network node with a string of advice, our model allows for back-and-forth interaction.
We show that for some problems, interaction can exponentially decrease the communication cost compared to a non-interactive prover, but on the other hand, some problems retain non-trivial cost even with interaction. Time permitting, we will also touch on recent work on zero-knowledge in distributed interactive proofs.