(2026-02) Lightning, Field-Agnostic Super-Efficient Polynomial Commitment Scheme
2026-02-14
Polynomial commitment schemes (PCS) are a fundamental building block of modern zkSNARKs. In this paper, we propose 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 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 compared to the fastest prover configuration of Brakedown, at the cost of a increase in proof size. Overall, Lightning provides a practical mechanism for trading proof size for prover efficiency in coding-based PCS constructions.