Lightning, Field-Agnostic Super-Efficient Polynomial Commitment Scheme

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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. A