Introduction to Interactive Proofs & The Sumcheck Protocol

Traditional mathematical proofs are static objects: a prover P writes down a sequence of mathematical statements, and then at some later time a verifier V checks that these statements are consistent and correct. Over the years, computer science has changed the notion of a mathematical proof. The first such change was the observation that for all practical purposes, the verification procedure should be efficient; V should not have to expend large amounts of effort to verify the proof of a claim (at least much less than P expended to find the proof). This notion of “efficient verification” corresponds to the complexity class NP: