Grand Danois: Succinct Multilinear Polynomial Commitments over Lattices

We present Grand Danois, a new post-quantum multilinear polynomial commitment scheme from lattices for polynomials over $\mathbb{F}_q$ that achieves polylogarithmic $O(\lambda \ell)$ verification complexity and proof sizes. We build on the general approach introduced in Hachi (ePrint 2026/156) with two key changes. First, we switch to the vanishing Short Integer Solution (vSIS) assumption to obtain structured public parameters for our commitment scheme and utilize this structure to design an ada