Optimistic Asynchronous Dynamic-Committee Proactive Secret Sharing

Dynamic-committee Proactive Secret Sharing (DPSS) has gained increased attention for its ability to dynamically update the shareholder committees and refresh secret shares, even against adversaries that gradually corrupt all nodes. However, existing state-of-the-art asynchronous DPSS protocols suffer from significant $\mathcal{O}\left(n^{3}\right)$ message complexity and $\mathcal{O}\left(\lambda n^{3}\right)$ communication complexity, where $\lambda$ denotes the security parameter and n is the committee size. In this paper, we distinguish optimistic-case and worstcase scenarios based on node behaviors and network conditions, thus reducing the redundant communication overhead of asynchronous DPSS. Under the trusted setup assumption, we achieved an $\mathcal{O}\left(n^{2}\right)$ message complexity in all scenarios. Additionally, our protocol has an $\mathcal{O}\left(\lambda n^{2}\right)$ communication complexity in the optimistic case, where all nodes are honest and the network is synchronous, and $\mathcal{O}\left(\lambda n^{3}\right)$ communication complexity in the worst case. We also propose two strategies to eliminate the strong trusted setup assumptions, and the asymptotic performance still surpasses the state-of-the-art protocols. For committee sizes of 4 to 400, the estimated concrete communication cost of our DPSS is 19-100x (resp., 8-14x) smaller in the optimistic case (resp., worst case) compared to LongLive (USENIX Security '23). Experiments in AWS show that our DPSS achieves a latency of $\mathbf{1. 9 - 8}$ seconds for committee sizes from 4 to 64. Single-machine benchmarks reveal a (computational) runtime reduction of up to 44 %.