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

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