Paper 2025/2327 Original: eprint.iacr.org/2025/2327 ↗

Code-based Distributed Polynomial Commitment Scheme with Linear Prover Time and Polylogarithmic Communication

Abstract

We present the first fully distributed, code-based polynomial commitment scheme (PCS) that achieves linear prover time and polylogarithmic communication for multilinear polynomials. Our construction builds on Brakedown with proof composition. We design a distributed proof of correct linear encoding. Codeword validity is reduced to a sumcheck relation over the sparse parity-check matrix, whereas systematic consistency is verified through multilinear evaluation checks. These techniques preserve linear prover complexity while reducing the communication size between sub-provers to polylogarithmic scale. We implement our construction and evaluate it on multilinear polynomials ranging in size from $2^{22}$ to $2^{28}$. The prover exhibits near-linear parallel scalability. Compared with existing evaluated distributed PCS implementations with 8 parties, it reduces communication by at least $13\times$ at every tested polynomial size, while its prover time remains within $1.31\times$ of the fastest implementation. These results demonstrate that our asymptotic communication improvements translate into substantial concrete savings while retaining efficient proving.