NeutronNova: Group-Based Folding Done Right

A folding scheme reduces the task of checking multiple NP instances into checking a single instance, providing an efficient route to incrementally verifiable computation (IVC). We identify five desirable properties of a practical folding scheme: constant recursion overheads, multi-folding, linear scaling with the number of instances, no extraneous commitments, and modularity. No existing scheme achieves all five simultaneously.

We introduce NeutronNova, the first folding scheme to achieve all five. The prover’s work is dominated by the cost to commit to its witness—with no extraneous commitments—and the recursive verifier performs only three group scalar multiplications and a constant number of hash computations. We construct NeutronNova modularly using the reductions of knowledge (RoK) framework around a core relation called zero-check, and build folding schemes for circuit satisfiability (CCS), grand products, and lookups by reducing each to zero-check. In experiments, NeutronNova folds a SHA-256 circuit with  constraints in 91 ms, a  improvement over Nova. Several subsequent works have used NeutronNova to achieve new results, including space-efficient SNARKs with optimal prover time, packed sum-check protocols over small fields, and client-side zero-knowledge proofs with low end-to-end latency.