## IACR News item: 18 September 2023

###### Omer Paneth, Rafael Pass

ePrint Report
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.

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.

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