GoSSamer: Lightweight and Linear-Communication Asynchronous (Dynamic Proactive) Secret Sharing and the Applications

Asynchronous complete secret sharing (ACSS) and asynchronous dynamic proactive secret sharing (ADPSS) are fundamental primitives for secret sharing and resharing in modern threshold systems, such as multi-party computation, distributed key management, and blockchain. However, existing ACSS constructions that employ homomorphic commitments incur notable computational overhead, while the lightweightcomputation constructions require quadratic per-secret communication, limiting scalability as the number of parties grows. ADPSS constructions inevitably inherit these inefficiencies due to their tight coupling to the commitment-based ACSS and requiring at least quadratic cross-committee communication. To break these bottlenecks, we design GoSSamer, a concretely and asymptotically efficient protocol suite, where both our ACSS and ADPSS achieve (1) lightweight computation with only hash function and symmetric encryption; (2) asymptotically optimal, linear per-secret communication; (3) optimal resilience in asynchronous networks; and (4) postquantum security. In GoSSamer-ACSS, we propose an originalevaluation propagation paradigm for linear communication without commitment-requiring interpolation, which further unlocks our lightweight bivariate-polynomial-based degree checking for share verification. Building on this foundation, GoSSamer-ADPSS contributes two further techniques: a consistency verification technique that decouples the ADPSS framework from the commitment-based ACSS, and a dualcommittee reconstruction technique that yields linear per-secret communication. When deployed in distributed AWS instances, GoSSamer-ACSS reduces the runtime by 95.6 % compared to the linear-communication scheme hbACSS (NDSS'22) and $\mathbf{4 5. 8} \boldsymbol{\%}$ compared to lightweight SS24 (JoC'24). GoSSamerADPSS reduces the runtime by at least 67.7 % compared to LongLive (Usenix Security'23). Moreover, when applied to practical distributed key management systems, the GoSSamer-ACSS-based distributed key generation is $\mathbf{7}-\mathbf{1 1} \times$ faster than DXK+23 (Usenix Security'23), and GoSSamer-ADPSS-based key resharing reaches a throughput of $1994 \text{keys} / \mathrm{s}$ across 10 -node committees, compared to $85 \text{keys} / \mathrm{s}$ in LongLive.