Incrementally Verifiable Computation via Rate-1 Batch Arguments

Abstract

Non-interactive delegation schemes enable producing succinct proofs (that can be efficiently verified) that a machine M transitions from c1 to c2 in a certain number of deterministic steps. We here consider the problem of efficiently merging such proofs: given a proof Π1 that M transitions from c1 to c2, and a proof Π2 that M transitions from c2 to c3, can these proofs be efficiently merged into a single short proof (of roughly the same size as the original proofs) that M transitions from c1 to c3? To date, the only known constructions of such a mergeable delegation scheme rely on strong non-falsifiable “knowledge extraction” assumptions. In this work, we present a provably secure construction based on the standard LWE assumption. As an application of mergeable delegation, we obtain a construction of incrementally verifiable computation (IVC) (with polylogarithmic length proofs) for any (unbounded) polynomial number of steps based on LWE; as far as we know, this is the first such construction based on any falsifiable (as opposed to knowledge-extraction) assumption. The central building block that we rely on, and construct based on LWE, is a rate-l batch argument (BARG): this is a non-interactive argument for NP that enables proving k NP statements $x_{1},\ldots, x_{k}$ with communication/verifier complexity m + o(m), where m is the length of one witness. rate-1 BARGs are particularly useful as they can be recursively composed a super-constant number of times.