Asynchronous Complete Secret Sharing with Linear Communication Cost

Asynchronous Complete Secret Sharing (ACSS) in Byzantine fault-tolerant systems has become one of the essential building blocks in multiple threshold cryptosystems. However, current ACSS schemes scale poorly due to high communication costs, which are quadratic in the number of participants n. In this paper, we propose a new scheme ALCES to reduce such communication costs from O(n²) to O(cn) with a negligible probability of failure ${e^{ - \frac{c}{{18}}}}$, while guaranteeing completeness and agreement properties. The key point of ALCES is to sample c parties to construct a committee, which then verifies and distributes the encrypted shares to other parties. Additionally, we introduce a new mechanism, referred to as secret labels in ALCES, by encoding the information of labels in polynomial coefficients. This mechanism allows an arbitrary string to act as the label, binding it to a specific secret while efficiently ensuring security and privacy with minimal communication cost. Experimental results show that our technique reduces the overall communication cost in a single sharing process by 66% and 83% for very large quantities, such as 4096 and 8192 parties, respectively, when compared with prior work.