Vector Commitments with Efficient Updates

TL;DR

This paper introduces a novel vector commitment scheme that achieves sublinear update information size and runtime, optimizing dynamic proof updates for applications like verifiable databases and blockchain clients.

Contribution

It presents a new vector commitment scheme with asymptotically optimal trade-offs between update size and runtime, outperforming existing schemes like Verkle commitments.

Findings

Achieves sublinear update information size and runtime in the number of updated elements.

Proves an information-theoretic lower bound showing optimality of the scheme.

Outperforms Verkle commitments by about a factor of 2 in key metrics.

Abstract

Dynamic vector commitments that enable local updates of opening proofs have applications ranging from verifiable databases with membership changes to stateless clients on blockchains. In these applications, each user maintains a relevant subset of the committed messages and the corresponding opening proofs with the goal of ensuring a succinct global state. When the messages are updated, users are given some global update information and update their opening proofs to match the new vector commitment. We investigate the relation between the size of the update information and the runtime complexity needed to update an individual opening proof. Existing vector commitment schemes require that either the information size or the runtime scale linearly in the number $k$ of updated state elements. We construct a vector commitment scheme that asymptotically achieves both length and runtime that is sublinear in $k$, namely $k^\nu$ and $k^{1-\nu}$ for any $\nu \in (0,1)$. We prove an information-theoretic lower bound on the relation between the update information size and runtime complexity that shows the asymptotic optimality of our scheme. For $\nu = 1/2$, our constructions outperform Verkle commitments by about a factor of $2$ in terms of both the update information size and runtime, but makes use of larger public parameters.