Folding Custom Gates with Verifier Input

In the context of interactive proofs, a "folding scheme" (popularized by Nova) is a way to combine multiple instances of a constraint system into a single instance, so the validity of the multiple instances can statistically be reduced to the validity of a single one. We show how Nova folding can be generalized to “custom” gates and extra rounds of verifier randomness. As an application of this extension, we present Origami, the first (to our knowledge) known example of a folding scheme for lookups.