摘要：

为解决秘密共享中因未充分考虑参与方自利行为而引发的诚实参与方无法重构共享秘密、非诚实参与方可重构共享秘密等不公平问题，将秘密共享与区块链相结合，基于智能合约提出一种兼具公平性和可验证性的秘密共享方案(FVSS)。首先，构建一种秘密份额混淆机制，通过绑定用户口令与秘密值，向参与方分发虚假影子秘密份额，以保护真实份额的共享免受猜测攻击；然后，基于多项式承诺设计影子秘密份额完整性验证方法，在参与方之间实现影子秘密份额的双向可验证，确保参与方互相监督的有效性；随后，为实现秘密共享的针对性公平保障，基于智能合约构建一种公平性奖惩策略，激励参与方高效地实现秘密重构，并实现对第三方恶意分发行为的有效监控；最后，对方案的可验证性、公平性、安全性、资源开销等方面进行理论分析和实验验证。分析和实验结果表明，该方案能有效约束恶意参与方在秘密共享中的自利行为，可以抵抗已知攻击，且通过支持用户口令和承诺值来提供更高的安全性，同时该方案的平均时间开销在毫秒级，具备较好的实用性和可扩展性。

关键词: 秘密共享, 智能合约, 多项式承诺, 公平性, 可验证性

Abstract:

Unfair issues arise in secret sharing owing to the insufficient consideration given to participants′self-interested behaviors, such as honest participants being unable to reconstruct the shared secret while dishonest participants are able to. To address this issue, this study proposes a secret sharing scheme called FVSS by integrating secret sharing with blockchain technology and leveraging smart contracts. First, the study constructs a secret share obfuscation mechanism that binds user passwords with secret values to distribute false shadow secret shares to participants, thereby protecting the sharing of real shares from guessing attacks. Second, it designs a method for verifying the integrity of shadow secret shares based on polynomial commitments, enabling the bidirectional verifiability of shadow secret shares among participants and ensuring the effectiveness of mutual supervision. Subsequently, to achieve targeted fairness guarantees in secret sharing, the study establishes a fairness incentive-penalty strategy based on smart contracts to motivate participants to reconstruct secrets efficiently and monitor malicious third-party distribution behaviors effectively. Finally, the study conducts theoretical analyses and experimental validation of the verifiability, fairness, security, and resource overhead of the proposed scheme. Analysis and experimental results demonstrate that the scheme can effectively constrain the self-interested behaviors of malicious participants in secret sharing, resist known attacks, and provide greater security by supporting user passwords and commitment values. Moreover, the scheme′s average time overhead is at the millisecond level, indicating good practicality and scalability.

Key words: secret sharing, smart contracts, polynomial commitment, fairness, verifiability