International Association
for Cryptologic Research

Generalized secret sharing (GSS), which accommodates monotone access structures, has been under-explored in distributed computing over the past decades. In this paper, we propose the publicly verifiable generalized secret sharing (PVGSS) scheme, enhancing the applicability of GSS in transparent systems. PVGSS not only enables a dealer to share a secret with fine-grained access structures, but also allows anyone to verify whether the dealer and shareholders are acting honestly or not. We begin by introducing two approaches to implement GSS schemes: one based on recursive Shamir secret sharing and another utilizing linear secret sharing scheme (LSSS). Then, we present PVGSS constructions by integrating non-interactive zero-knowledge proofs into the GSS schemes. Further, we prove that the proposed PVGSS schemes achieve IND1-secrecy under DDH assumption. To showcase the practical applicability of PVGSS schemes, we implement a decentralized exchange (DEX) protocol that enables fair atomic swaps of ERC-20 tokens. A sophisticated access structure is devised to: (1) enable fair atomic swaps during normal protocol execution, and (2) incorporate fault-tolerant passive watchers to provide accountable arbitration when disputes occur. Our benchmarks on the BN128 curve demonstrate the computational efficiency of PVGSS schemes, while Ethereum gas cost analysis confirms the viability of the DEX implementation.