Efficient Transparent Polynomial Commitments for zk-SNARKs

Abstract

This paper proposes a new efficient transparent polynomial commitment scheme. In a polynomial commitment scheme, a prover commits a polynomial and a verifier sends a random point to the prover. The prover then evaluates the polynomial on the given point with generating a proof that the evaluated value is correctly computed according to the committed function. Our construction is based on the polynomial commitment scheme (the DARK compiler) proposed by Bünz, Fisch, and Szepieniec in EUROCRYPT 2020. The approach of DARK is that a prover recursively generates 2 group elements as the proof for a polynomial with a halved degree and a verifier indirectly verifies them at each recursion. In our construction, a prover commits all the reduced polynomials across recursions at once, and then generates a single aggregated proof for them. By aggregating commitments from recursive steps in DARK, the proposed scheme reduces the proof size by half, and provides better performance in the proof generation and the proof verification compared to DARK. By adopting the proposed scheme, the efficiency of transparent SNARKs from polynomial IOPs can be significantly improved.