Paper 2025/1187

Ligerito: A Small and Concretely Fast Polynomial Commitment Scheme

Abstract

In this note we present Ligerito, a small and practically fast polynomial commitment and inner product scheme. For the case of univariate and multilinear polynomial evaluations, the scheme has a proof size of $\sim \log(N)^2/\log\log(N)$ up to constants and for a large enough field, where $N$ is the size of the input. Ligerito is also fast on consumer hardware: when run on an M1 MacBook Pro for a polynomial with $2^{24}$ coefficients over a 32-bit binary field, our Julia prover implementation has a proving time of 1.3 seconds and a proof size of 255 KiB. Ligerito is also relatively flexible: any linear code for which the rows of the generator matrix can be efficiently evaluated can be used. Such codes include Reed–Solomon codes, Reed–Muller codes, among others. This, in turn, allows for a high degree of flexibility on the choice of field and can likely give further efficiency gains in specific applications.