Abstract: A threshold verifiable multi-secret sharing scheme is proposed, which is based on Shamir [(t,n)]-threshold scheme, modular arithmetic over finite field and the Lagrange interpolation polynomial. The minimum access structure of each secret is a threshold access structure. This access structure realizes that a part of secrets is recovered in the reconstruction phase, and the more participants there are, the more secrets can be recovered. Compared with the previous verifiable[(t,n)]-threshold multi-secret sharing scheme, this scheme is more practical.

Key words: multi-secret sharing, Shamir[(t,n)]-threshold secret sharing scheme, two-variable one-way function, discrete logarithm problem

摘要： 利用Shamir[(t,n)]门限方案、有限域上的模运算和Lagrange插值多项式提出了一个可验证的多秘密共享门限方案。该方案中，每一个密钥对应的极小访问结构是一个门限访问结构，这样的访问结构实现了在重构阶段可重构部分密钥，而且重构的参与者越多可重构的密钥就越多；与以前的可验证的[(t,n)]门限多秘密共享方案相比，该方案更具有实用性。

关键词: 多秘密共享, Shamir[(t, n)]门限方案, 双变量单向函数, 离散对数