Paper 2024/1385

Locally Verifiable Distributed SNARGs

Abstract

The field of distributed certification is concerned with certifying properties of distributed networks, where the communication topology of the network is represented as an arbitrary graph; each node of the graph is a separate processor, with its own internal state. To certify that the network satisfies a given property, a prover assigns each node of the network a certificate, and the nodes then communicate with one another and decide whether to accept or reject. We require soundness and completeness: the property holds if and only if there exists an assignment of certificates to the nodes that causes all nodes to accept. Our goal is to minimize the length of the certificates, as well as the communication between the nodes of the network. Distributed certification has been extensively studied in the distributed computing community, but it has so far only been studied in the information- theoretic setting, where the prover and the network nodes are computationally unbounded. In this work we introduce and study computationally bounded distributed certification: we define locally verifiable distributed $\mathsf{SNARG}$s ($\mathsf{LVD}$-$\mathsf{SNARG}$s), which are an analog of SNARGs for distributed networks, and are able to circumvent known hardness results for information-theoretic distributed certification by requiring both the prover and the verifier to be computationally efficient (namely, PPT algorithms). We give two $\mathsf{LVD}$-$\mathsf{SNARG}$ constructions: the first allows us to succinctly certify any network property in $\mathsf{P}$, using a global prover that can see the entire network; the second construction gives an efficient distributed prover, which succinctly certifies the execution of any efficient distributed algorithm. Our constructions rely on non-interactive batch arguments for $\mathsf{NP}$ ($\mathsf{BARG}$s) and on $\mathsf{RAM}$ $\mathsf{SNARG}$s, which have recently been shown to be constructible from standard cryptographic assumptions.