Paper 2024/1664

Consensus on SNARK pre-processed circuit polynomials

Abstract

This paper addresses verifiable consensus of pre-processed circuit polynomials for succinct non-interactive argument of knowledge (SNARK). More specifically, we focus on parts of circuits, referred to as wire maps, which may change based on program inputs or statements being argued. Preparing commitments to wire maps in advance is essential for certain SNARK protocols to maintain their succinctness, but it can be costly. SNARK verifiers can alternatively consider receiving wire maps from an untrusted parties. We propose a consensus protocol that reaches consensus on wire maps using a majority rule. The protocol can operate on a distributed, irreversible, and transparent server, such as a blockchain. Our analysis shows that while the protocol requires over 50\% honest participants to remain robust against collusive attacks, it enables consensus on wire maps with a low and fixed verification complexity per communication, even in adversarial settings. The protocol guarantees consensus completion within a time frame ranging from a few hours to several days, depending on the wire map degree and the honest participant proportion. Technically, our protocol leverages a directed acyclic graph (DAG) structure to represent conflicting wire maps among the untrusted deliverers. Wire maps are decomposed into low-degree polynomials, forming vertices and edges of this DAG. The consensus participants, or deliverers, collaboratively manage this DAG by submitting edges to branches they support. The protocol then returns a commitment to the wire map that is written in the first fully grown branch. The protocol's computational efficiency is derived from an interactive commit-prove-verify scheme that enables efficient validation of submitted edges. Our analysis implies that the practical provides a practical solution for achieving secure consensus on SNARK wire maps in environments with dynamic proportion of honest participants. Additionally, we introduce a tunable parameter $N$ that allows the protocol to minimize cost and time to consensus while maintaining a desired level of security.