hbACSS: How to Robustly Share Many Secrets

—Despite significant recent progress toward making multi-party computation (MPC) practical, no existing MPC library offers complete robustness—meaning guaranteed output delivery, including in the offline phase—in a network that even has intermittent delays. Importantly, several theoretical MPC constructions already ensure robustness in this setting. We observe that the key reason for this gap between theory and practice is the absence of efficient verifiable/complete secret sharing (VSS/CSS) constructions; existing CSS protocols either require a) challenging broadcast channels in practice or b) introducing computation and communication overhead that is at least quadratic in the number of players. This work presents hbACSS, a suite of optimal-resilience asynchronous complete secret sharing protocols that are (quasi)linear in both computation and communication overhead. Towards developing hbACSS, we develop hbPolyCommit, an efficient polynomial commitment scheme that is (quasi)linear (in the polynomial degree) in terms of computation and communication overhead without requiring a trusted setup. We implement our hbACSS protocols, extensively analyze their practicality, and observe that our protocols scale well with an increasing number of parties. In particular, we use hbACSS to generate MPC input masks: a useful primitive which had previously only been calculated nonrobustly in practice.