一种安全的公开可验证门限多秘密共享方案

基于大整数分解以及离散对数问题的难解性，使用非交互的零知识证明协议，以Shamir共享体制为基础提出一种公开可验证的门限多秘密共享方案。分发者给每个参与者分发子秘密的有效性可以被任何人验证。在恢复秘密的时候，参与者只需要提供子秘密的一个影子来恢复秘密，由于影子难以得到子秘密，因此可以通过一组子秘密共享多个秘密。子秘密的影子的有效性也可以被其他参与者验证。该方案不但安全、高效，而且可以有效地防止分发者欺骗和参与者欺骗。

Secure Publicly Verifiable Threshold Multi-secret Sharing Scheme

A publicly verifiable multi-secret sharing scheme is proposed, using non-interactive zero-knowledge proof protocol and Shamir’s sharing system. The security of the scheme is based on the intractability of integer factorization problem and discrete logarithm problem. The validity of the sharing distributed by the dealer can be verified by anyone. Recovering the secret, participants only need to provide a shadow of the sharing. It is difficult to get the sharing from the shadow. So the sharing can be reused to share the multi-secret. Moreover, the validity of the shadow can also be verified by anyone. So the scheme is secure, efficient, and can prevent both dealer and participant from cheating.