Verifiable Secret Sharing Simplified

Verifiable Secret Sharing (VSS) is a fundamental building block in cryptography. Despite its importance and extensive studies, existing VSS protocols are often complex and inefficient. Many of them do not support dual thresholds, are not publicly verifiable, or do not properly terminate in asynchronous networks. This paper presents a new and simple approach for designing VSS protocols in synchronous and asynchronous networks. Our VSS protocols are optimally fault-tolerant, i.e., they tolerate a 1/2 and a 1/3 fraction of malicious nodes in synchronous and asynchronous networks, respectively. They only require a public key infrastructure and the hardness of discrete logarithms. Our protocols support dual thresholds, and their transcripts are publicly verifiable. We implement our VSS protocols and evaluate them in a geo-distributed setting with up to 256 nodes. The evaluation demonstrates that our protocols offer asynchronous termination and public verifiability with performance that is comparable to that of existing schemes that lack these features. Compared to the existing schemes with similar guarantees, our approach lowers the bandwidth usage and latency by up to 90%.