Paper 2024/1606

NeutronNova: Folding everything that reduces to zero-check

Abstract

We introduce NeutronNova, a new folding scheme for the zero-check relation: an instance-witness pair is in the zero-check relation if a corresponding multivariate polynomial evaluates to zero for all inputs over a suitable Boolean hypercube. The folding scheme is a two-round protocol, and it internally invokes a \emph{single} round of the sum-check protocol. The folding scheme is more efficient than prior state-of-the-art schemes and directly benefits from recent improvements to the sum-check prover. The prover’s work is the cost to commit to a witness and field operations in a single round of the sum-check protocol. So, if the witness contains "small" field elements, the prover only commits to "small" field elements. The verifier’s work is a constant number of group scalar multiplications, field operations, and hash computations. Moreover, the folding scheme generalizes to fold multiple instances at once and requires only $\log{n}$ rounds of the sum-check protocol, where $n$ is the number of instances folded. As a corollary, we provide a folding scheme for any relation R for which there is a reduction of knowledge (RoK) from $\mathcal{R}$ to one or more instance-witness pairs in the zero-check relation. Such RoKs appear implicitly in prior lookup arguments (e.g., Lasso) and high-performance zkVMs for RISC-V (e.g., Jolt). We formalize these RoKs for several relations including indexed lookups, grand products, and CCS (which generalizes Plonkish, AIR, and R1CS). These are simple and constant round RoKs that leverage interaction to perform randomized checks on committed witness elements. Instead of proving these resulting zero-check instances as is done in prior proof systems such as Jolt, NeutronNova provides the more efficient option of continual folding of zero-check instances into a single running instance.