具有高效更新能力的向量承诺
Vector Commitments with Efficient Updates
AI总结：
本文研究动态向量承诺中更新信息大小与单证明更新复杂度的权衡，提出一种在渐近意义上二者均次线性于更新元素数$k$的方案，并证明其信息论最优性，在$ν=1/2$时较Verkle承诺提升约2倍。
摘要：
支持打开证明本地更新的动态向量承诺，其应用范围涵盖从具有成员关系变化的可验证数据库到区块链上的无状态客户端。在这些应用中，每个用户维护已承诺消息的一个相关子集以及相应的打开证明，目标是确保简洁的全局状态。当消息被更新时，用户会获得一些全局更新信息，并更新其打开证明以匹配新的向量承诺。我们研究了更新信息的大小与更新单个打开证明所需的运行时复杂度之间的关系。现有的向量承诺方案要求信息大小或运行时随已更新状态元素的数量$k$线性增长。我们构造了一种向量承诺方案，该方案在渐近意义上同时实现了长度和运行时对$k$的次线性，即对于任意$ν\in (0,1)$，分别为$k^ν$和$k^{1-ν}$。我们证明了关于更新信息大小与运行时复杂度之间关系的信息论下界，表明我们的方案具有渐近最优性。对于$ν= 1/2$，我们的构造在更新信息大小和运行时两方面均比Verkle承诺高出约$2$倍，但使用了更大的公共参数。
英文摘要：
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.
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