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 53KB, 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).