Paper 2025/1349 Original: eprint.iacr.org/2025/1349 ↗

$\mathsf{HyperFond}$: A Transparent and Post-Quantum Distributed SNARK with Polylogarithmic Communication

Abstract

Recent years have witnessed the surge of academic researches and industrial implementations of succinct non-interactive arguments of knowledge (SNARKs). However, proving time remains a bottleneck for applying SNARKs to large-scale circuits. To accelerate the proof generation process, a promising way is to distribute the workload to several machines running in parallel, the SNARKs with which feature are called \textit{distributed SNARKs}. Nevertheless, most existing works either require a trusted setup, or rely on quantum-insecure assumptions, or suffer from linear communication costs. In this paper, we introduce $\mathsf{HyperFond}$, the first distributed SNARK that enjoys a transparent setup, post-quantum security and polylogarithmic communication cost, as well as field-agnosticity (no reliance on specific choices of fields). To this end, we first propose a distributed proof system based on HyperPlonk (by Chen et al. in EUROCRYPT 2023). To instantiate the system, we then put forward a novel approach to distribute the multilinear polynomial commitment scheme in BaseFold (by Zeilberger et al. in CRYPTO 2024), and present a trade-off between communication cost and proof size. In $\mathsf{HyperFond}$, after committing to polynomial coefficients with quasilinear complexity, each sub-prover generates proofs with time linear in subcircuit size. We implement $\mathsf{HyperFond}$ using up to 16 machines. Experimental results demonstrate that the proving time of $\mathsf{HyperFond}$ is 15.6 $\times$ faster than HyperPlonk instantiated with BaseFold. We also compare to deVirgo (by Xie et al. in CCS 2022), so far the only post-quantum distributed SNARK, and achieve a 1.45 $\times$ speedup.