International Association
for Cryptologic Research

We construct the first polynomial commitment scheme (PCS) that has a transparent setup, quasi-linear prover time, $\log N$ verifier time, and $\log \log N$ proof size, for multilinear polynomials of size $N$. Concretely, we have the smallest proof size amongst transparent PCS, with proof size less than $4.5$KB for $N\leq 2^{30}$. We prove that our scheme is secure entirely under falsifiable assumptions about groups of unknown order. The scheme significantly improves on the prior work of Dew (PKC 2023), which has super-cubic prover time and relies on the Generic Group Model (a non-falsifiable assumption). Along the way, we make several contributions that are of independent interest: $\PoKEMath$, a protocol for efficiently proving that an arbitrary predicate over committed integer vectors holds; $\SIPA$, a bulletproofs-style inner product argument in groups of unknown order; we also distill out what prior work required from the Generic Group Model and frame this as a falsifiable assumption.