Welcome to the resource topic for 2025/1354
Title:
Shred-to-Shine Metamorphosis in Polynomial Commitment Evolution
Authors: Weihan Li, Zongyang Zhang, Sherman S. M. Chow, Yanpei Guo, Boyuan Gao, Xuyang Song, Yi Deng, Jianwei Liu
Abstract:Polynomial commitment schemes (PCSs) enable verifying evaluations of committed polynomials. Multilinear (ML) PCSs from linear codes are favored for their prover time. Distributed MLPCSs further reduce it by enabling multiple provers to distribute both commitment and proof generation.
We propose \mathsf{PIP}_\mathsf{FRI}, an FRI-based MLPCS that unites the linear prover time of PCSs from encodable codes with the compact proofs and fast verification of Reed–Solomon (RS) PCSs. By cutting FFT and hash overhead for both committing and opening, \mathsf{PIP}_\mathsf{FRI} runs 10\times faster in prover than the RS-based DeepFold (Usenix Security’25) while retaining competitive proof size and verifier time, and beats Orion (Crypto’22) from linear codes by 3.5-fold in prover speed while reducing proof size and verification time by 15-fold.
Its distributed version \mathsf{DePIP}_\mathsf{FRI} delivers the first code-based distributed SNARK for arbitrary circuits over a single polynomial, and further achieves accountability. \mathsf{DePIP}_\mathsf{FRI} outperforms DeVirgo (CCS’22)—the only prior code-based distributed MLPCS, limited to data-parallel circuits and lacking accountability—by 25\times in prover time and 7\times in communication, with the same number of provers.
A central insight in both constructions is the shred-to-shine technique. It further yields a group-based MLPCS of independent interest, with 16\times shorter structured reference string and 10\times faster opening time than multilinear KZG (TCC’13).
ePrint: https://eprint.iacr.org/2025/1354
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