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**2023/1394**

**Title:**

Incrementally Verifiable Computation via Rate-1 Batch Arguments

**Authors:**
Omer Paneth, Rafael Pass

**Abstract:**

Non-interactive delegation schemes enable producing succinct proofs (that can be efficiently verified) that a machine M transitions from c_1 to c_2 in a certain number of deterministic steps. We here consider the problem of efficiently \emph{merging} such proofs: given a proof \Pi_1 that M transitions from c_1 to c_2, and a proof \Pi_2 that M transitions from c_2 to c_3, can these proofs be efficiently merged into a single short proof (of roughly the same size as the original proofs) that M transitions from c_1 to c_3? 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-1 batch argument (BARG): this is a non-interactive argument for NP that enables proving k NP statements x_1,..., 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.

**ePrint:**
https://eprint.iacr.org/2023/1394

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