Paper 2026/258

Lightning, Field-Agnostic Super-Efficient Polynomial Commitment Scheme

Abstract

Polynomial commitment schemes (PCS) are a fundamental building block of modern zkSNARKs. In this paper, we propose \emph{Lightning}, a new coding-based PCS that achieves state-of-the-art prover efficiency. Our main technical contribution is a systematic code family, the \emph{Lightning code}, which can be instantiated from any base code with constant relative distance. Compared with the base code, the Lightning code significantly reduces encoding cost by trading off relative distance. At a comparably small relative distance, Lightning's $\delta=0.005$ configuration has an equivalent encoding cost $2.8\times$ lower than Brakedown-fastest at $\delta=0.0043$; at the common relative distance $\delta=0.020$, its equivalent encoding cost is $1.53\times$ lower than that of the Brakedown code. We integrate the Lightning code into the standard coding-based PCS framework of Ligero and Brakedown. When committing to $2^{28}$ coefficients at matched proof sizes, Lightning reduces commitment time from about $349$s to $256$s ($1.36\times$ faster) for $80$MB proofs, compared with Brakedown.