Paper 2023/992

VSS from Distributed ZK Proofs and Applications

Abstract

Non-Interactive Verifiable Secret Sharing (NI-VSS) is a technique for distributing a secret among a group of individuals in a verifiable manner, such that shareholders can verify the validity of their received share and only a specific number of them can access the secret. VSS is a fundamental tool in cryptography and distributed computing. In this paper, we present an efficient NI-VSS scheme using Zero-Knowledge (ZK) proofs on secret shared data. While prior VSS schemes have implicitly used ZK proofs on secret shared data, we specifically use their formal definition recently provided by Boneh et al. in CRYPTO 2019. Our proposed NI-VSS scheme uses a quantum random oracle and a quantum computationally hiding commitment scheme in a black-box manner, which ensures its ease of use, especially in post-quantum threshold protocols. The practicality of the proposed NI-VSS is confirmed by our implementation results, establishing it as a viable choice for large-scale threshold protocols. Using the proposed NI-VSS scheme, a dealer can share a secret with 4096 parties in less than 2 seconds, and the shareholders can verify the validity of their shares in less than 2 milliseconds. We demonstrate the potential of new NI-VSS scheme by revisiting several threshold protocols and improving their efficiency. Specifically, we present two DKG protocols for CSIDH-based primitives, that outperform the current state of the art. Furthermore, we show similar improvements in some threshold signatures built based on Schnorr and CSI-FiSh signature schemes. We think, due to its remarkable efficiency and ease of use, the new NI-VSS scheme can be a valuable tool for a wide range of threshold protocols.