Abstract: A publicly verifiable and periodically renewable multi-secret sharing scheme is proposed, which is based on the YCH scheme and the properties of bilinear pairings. The secret shares can be verified publicly and updated periodically with keeping the advantages of YCH scheme. The secrets can be reconstructed while one participant only needs holding one secret share. The features of the one-way hash chain are used to make secret shares publicly verifiable and regularly renewable. Anyone can verify the effectiveness of the public information and the correctness of the secret shares. The cheating of the distributor and participants can be prevented effectively. Finally, analyses of the correctness and performance of the scheme ae given in detail and the security of the scheme is proved in the random oracle model. Under assumptions of the discrete logarithm problem of the elliptic curve, bilinear Diffie-Hellman problem and computer Diffie-Hellman problem, the analysis indicates that the mentioned scheme is safe and effective.

Key words: bilinear pairing, publicly verifiable, one-way hash chain, bilinear Diffie-Hellman problem, computer Diffie-Hellman problem, random oracle model

摘要： 基于YCH方案和双线性对的性质，提出了一个可公开验证可定期更新的多秘密共享方案。该方案在保留YCH方案原有优点的同时实现了对秘密份额的公开验证和定期更新。每个参与者只需持有一个秘密份额即可实现对多个秘密的重构，利用单向散列链的性质，实现对秘密份额的定期更新，任何人都可以对公开信息的有效性和秘密份额的正确性进行公开验证，有效防止分发者和参与者的欺诈。最后详细分析了方案的正确性和性能，并在随机预言模型中证明方案的安全性。分析表明，在椭圆曲线上的离散对数问题、双线性Diffie-Hellman问题和计算Diffie-Hellman问题假设下，所提出的方案是安全有效的。

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