Paper 2026/258

Lightning, Field-Agnostic Super-Efficient Polynomial Commitment Scheme

Yanpei Guo, National University of Singapore

Jiaheng Zhang, National University of Singapore

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 new linear code family, the \emph{Lightning code}, which can be instantiated from any base code with constant relative distance. Compared to the base code, Lightning code significantly reduces encoding cost by trading off relative distance. We integrate Lightning code into the standard coding-based PCS framework of Ligero and Brakedown. Experimental results show that Lightning PCS reduces prover commitment time by up to $2.3\times$ compared to the fastest prover configuration of Brakedown, at the cost of a $2.1\times$ increase in proof size. Overall, Lightning provides a practical mechanism for trading proof size for prover efficiency in coding-based PCS constructions.

@misc{cryptoeprint:2026/258,
      author = {Wenjie Qu and Yanpei Guo and Jiaheng Zhang},
      title = {Lightning, Field-Agnostic Super-Efficient Polynomial Commitment Scheme},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/258},
      year = {2026},
      url = {https://eprint.iacr.org/2026/258}
}