中文摘要：

提出了一种可认证的门限多秘密共享的新方案，通过成员提供的子密钥的一个影子来恢复秘密，由影子难以得到子密钥本身，因此可以复用，也即通过同一组子密钥共享多个秘密．该方案可以对分发者发布的信息和参与者提供的子密钥影子进行认证，从而可以抵御分发者欺骗和参与者欺骗．方案的安全性基于RSA密码系统和Shamir的（k，n）门限秘密共享方案。另外，本文还提出两种对这类门限多秘密共享方案的欺骗方法，能不同程度的破坏几个已有方案的安全性，但本文所提出的方案对这些欺骗有免疫能力，该方案是计算安全的，并且性能较现有诸方案更好。

英文摘要：

A verifiable threshold multi-secret sharing scheme is proposed in this paper. As the secret can be recovered with the shadows provided by participants and it is computationally difficult to get the sub-keys from the shadows, the sub-keys can be reused to share the multi-secret in this ,scheme. By verifying the information published by the dealer as well as the shadows of subkeys provided by participants, this scheme can prevent both dealer and participant from cheating. The security of this scheme is the same as that of RSA cryptosystem and Shamir＇ s （ k, n）-threshold scheme. Two kinds of cheating methods against threshold multisecret sharing scheme are also proposed, which can threaten the .security of previous schemes more or less, But the scheme proposed in this paper provides efficient solutions against these cheatings and achieves the same computational ,security with a better performance compared with the previous ,schemes.