Paper 2025/664

Publicly Verifiable Generalized Secret Sharing Schemes and Their Applications

Abstract

Generalized secret sharing (GSS) enables flexible access control in distributed systems by allowing secrets to be shared across arbitrary monotone access structures. However, its adoption in transparent and trustless environments is hindered due to the reliance on trusted participants and secure communication channels. This reliance restricts GSS's ability to provide flexible control in the presence of adversaries. In this paper, we propose publicly verifiable generalized secret sharing (PVGSS), a scheme that allows to distribute a secret using generalized access structures while enabling non-interactive public verifiability of participant honesty. PVGSS scheme offers significant potential to advance the fields of blockchain and applied cryptography, such as attribute-based cryptosystem, fine-grained MPC and on-chain secret escrow. Intuitively, we first build two GSS schemes by leveraging recursive Shamir secret sharing and linear secret sharing scheme. Then, we encrypt GSS shares and generate the corresponding non-interactive zero-knowledge proofs. Further, we innovatively adopt the GSS reconstruction algorithm to prove that all the encrypted shares are bound to the dealer's secret with only $$ verification complexity. To exemplify the practical applicability, we implement a decentralized exchange (DEX) protocol, where fairness and accountable arbitration are considered. 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.