Paper 2026/2067

Maltese: Succinct Polynomial Commitment from Lattices

Abstract

Succinct polynomial commitment schemes are a key building block in succinct non-interactive arguments of knowledge (SNARKs). Existing succinct lattice-based polynomial commitment schemes take a "split-and-fold" strategy making use of homomorphism to compress proof size to $O(\text{polylog} N)$ for polynomials of size $N$. Prior works either (1) incur superlogarithmic verifier work (e.g., $O(\sqrt{N})$), (2) incur concretely large proof sizes and verifier work (e.g., hundreds of MB), or (3) rely on non-standard lattice assumptions. We proprose a new succinct polynomial commitment scheme Maltese that operates over a Merkle tree commitment of the lattice-based Ajtai hash function. We employ a folding strategy and propose new sum-check-based reductions for managing norm growth of the tree commitment over folding rounds. Maltese is secure under the standard Module-SIS assumption and produces opening proofs of $335$KB for multilinear polynomials of size $N=2^{30}$; proofs are around $300\times$ smaller than prior work with polylogarithmic verifier complexity but between $2$-$6\times$ larger than prior work with larger verifier complexity or stronger structured assumptions.