Glossary
Sumcheck Protocol
An interactive proof for the sum of a multivariate polynomial's values over a boolean hypercube — the heart of many modern SNARKs and STARKs.
The sumcheck protocol, due to Lund, Fortnow, Karloff, and Nisan (1990), is an interactive proof that reduces a claim about a sum of a multivariate polynomial's evaluations over the boolean hypercube to a claim about a single evaluation at a random point. Each round, the prover sends a univariate polynomial; the verifier sends a random challenge.
Sumcheck is the engine inside many production proving systems: Halo2, HyperPLONK, Spartan, Nova, and GKR-style circuits all use sumcheck as a core building block. Its near-linear prover cost is what makes large ZK proofs practical.