Abstract: The existing verifiable secret sharing schemes with self-selecting sub-secret can not make sub-secret renewable and publicly verifiable simultaneously. Based on bilinear pairings, a publicly verifiable and renewable multi-secret sharing scheme is proposed. Each participant selects sub-secret, the shadow secrets are used in the reconstruction and the true secret shares can not be exposed. The one-way hash chain is used to make the shadow secrets renewable. Anyone can verify the correctness of the shadow secrets and the effectiveness of the public information. Finally, the analysis of the correctness about the scheme is given, the performance is compared with the existing schemes and the security of the scheme is proven in the random oracle model. Under the assumptions of Discrete Logarithm Problem and computational Diffie-Hellman Problem, the analysis indicates that the mentioned scheme is safe and effective.

Key words: self-selecting sub-secret, publicly verifiable, bilinear pairings, one-way hash chain, random oracle model, computational Diffie-Hellman problem

摘要： 现有自选子秘密的可验证秘密共享方案，不能同时实现对子秘密的更新和公开验证。为此，基于双线性对提出一种可公开验证可更新多秘密共享方案。参与者选取子秘密，影子秘密参与重构，不会泄漏真实的秘密份额;利用单向散列链，实现对影子秘密的更新;任何人均可对影子秘密的正确性和公开信息的有效性进行公开验证;分析方案的正确性，并与现有方案进行性能比较，而且在随机预言模型下证明方案的安全性。分析表明，在离散对数问题和计算Diffie-Hellman问题假设下，所提方案是安全有效的。

关键词: 自选子秘密, 可公开验证, 双线性对, 单向散列链, 随机预言模型, 计算Diffie-Hellman问题