With the goal of building a decentralized and fully parallel payment system, we address the Fractional Spending Problem using (k1, k2)-quorum systems - both introduced by Bazzi and Tucci-Piergiovanni (PODC 2024). Fractional spending enables payments without immediate validation of an entire quorum, as necessary in classical approaches. Multiple spending from a same fund can occur concurrently, with final settlement involving previously contacted quorums. To tolerate a rushing-adaptive adversary, the composition of these quorums must stay hidden until settlement succeeds. We propose a new abstraction called secret quorums - of independent interest - that fulfill this property and implement it through ring verifiable random functions. We then propose a new protocol called StealthDust, where secret quorums allow to reduce payment latency from five to three communications steps and improve settlment message complexity from O(n^3) to O(n^2) compared to the original protocol.

翻译：为构建一个去中心化且完全并行的支付系统，我们利用 (k1, k2)-仲裁系统来解决部分支付问题——这两个概念均由 Bazzi 和 Tucci-Piergiovanni 在 PODC 2024 上提出。部分支付使得支付无需像经典方法那样立即验证整个仲裁。来自同一资金的多次支付可以并发进行，最终结算将涉及之前联系过的仲裁。为了抵御快速自适应攻击者，这些仲裁的组成必须在结算成功前保持隐藏。我们提出了一种称为秘密仲裁的新抽象概念——其本身具有独立研究价值——该概念满足此属性，并通过环可验证随机函数实现。随后，我们提出了一种名为 StealthDust 的新协议，其中秘密仲裁使得支付延迟从五个通信步骤减少到三个，并且与原协议相比，将结算消息复杂度从 O(n^3) 降低到 O(n^2)。