Vector Commitments with Efficient Updates
Ertem Nusret Tas, Dan Boneh
TL;DR
This work addresses dynamic vector commitments that support local updates of opening proofs by introducing sublinear-update VCs parameterized by ν ∈ (0,1). The authors construct two families—homomorphic trees and homomorphic Merkle trees—that achieve update-information size |U| = Θ(k^ν λ) and proof-update time Θ(k^{1−ν}) for updating k elements, and prove an information-theoretic lower bound showing asymptotic optimality. They provide concrete evaluations demonstrating practical improvements (e.g., ν = 1/2 yields roughly half the update size and faster updates compared to Verkle, albeit with trade-offs in public parameters and quantum security considerations) and extend the framework to post-quantum secure constructions without trusted setups. Applications include stateless Ethereum clients and databases with frequent membership changes, where sublinear-update VCs reduce communication overhead while maintaining succinct proofs. The work thus advances the design space for dynamic VCs by balancing global update information and per-user computation, with implications for scalable, verifiable data systems under both classical and post-quantum threat models.
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 $k^ν$ and $k^{1-ν}$ for any $ν\in (0,1)$. 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 $ν= 1/2$, 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.