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Title:
Behemoth: transparent polynomial commitment scheme with constant opening proof size and verifier time
Authors: István András Seres, Péter Burcsi
Abstract:Polynomial commitment schemes are fundamental building blocks in numerous cryptographic protocols such as verifiable secret sharing, zero-knowledge succinct non-interactive arguments, and many more. The most efficient polynomial commitment schemes rely on a trusted setup which is undesirable in trust-minimized applications, e.g., cryptocurrencies. However, transparent polynomial commitment schemes are inefficient (polylogarithmic opening proofs and/or verification time) compared to their trusted counterparts. It has been an open problem to devise a transparent, succinct polynomial commitment scheme or prove an impossibility result in the transparent setting. In this work, for the first time, we create a transparent, constant-size polynomial commitment scheme called Behemoth with constant-size opening proofs and a constant verifier. The downside of Behemoth is that it employs a quadratic prover in the degree of the committed polynomial. We prove the security of our scheme in the generic group model and discuss parameter settings in which Behemoth remains practical even for the prover.
ePrint: https://eprint.iacr.org/2023/670
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