Greyhound: Fast Polynomial Commitments from Lattices

In this paper, we propose Greyhound, the first concretely efficient polynomial commitment scheme from standard lattice assumptions. At the core of our construction lies a simple three-round protocol for proving evaluations for polynomials of bounded degree $N$ with verifier time complexity $O(\sqrt{N})$. By composing it with the LaBRADOR proof system (CRYPTO 2023), we obtain a succinct proof of polynomial evaluation (i.e. polylogarithmic in $N$) that admits a sublinear verifier runtime.

To highlight practicality of Greyhound, we provide implementation details including concrete sizes and runtimes. Notably, for large polynomials of degree at most $N=2^{30}$, the scheme produces evaluation proofs of size $53$KB, which is more than $10^4$ times smaller than the recent lattice-based framework, called SLAP (EUROCRYPT 2024), and around three orders of magnitude smaller than Ligero (CCS 2017) and Brakedown (CRYPTO 2023).