High-Threshold AVSS with Optimal Communication Complexity

Abstract

Asynchronous verifiable secret sharing (AVSS) protocols protect a secret that is distributed among n parties. Dual-threshold AVSS protocols guarantee consensus in the presence of t Byzantine failures and privacy if fewer than p parties attempt to reconstruct the secret. In this work, we construct a dual-threshold AVSS protocol called Haven that is optimal along several dimensions. First, it is a high-threshold AVSS scheme, meaning that it is a dual-threshold AVSS with optimal parameters $t < n/3$ and $p < n - t$. Second, it has $O(n^2)$ message complexity, and for large secrets it achieves the optimal O(n) communication overhead, without the need for a public key infrastructure or trusted setup. While these properties have been achieved individually before, to our knowledge this is the first protocol that achieves all of the above simultaneously. The core component of Haven is a high-threshold AVSS scheme for small secrets based on polynomial commitments that achieves $O(n^2 \log (n))$ communication overhead, as compared to prior schemes that require $O(n^3)$ overhead with $t < n/4$ Byzantine failures or $O(n^4)$ overhead for the recent high-threshold protocol of Kokoris-Kogias et al. (CCS 2020). Using standard amortization methods based on erasure coding, we can reduce the communication complexity to $O(n \vert s \vert )$ for a large secret $s$.