中文摘要：

(t→t′,n)门限可变方案研究如何将门限t改变为t′(>t)以增加攻击者攻击方案的难度。基于拉格朗日插值多项式提出两类完美的门限可变多秘密共享方案：(t→t+1,n)门限可变方案Π,Π′、(t→t+v-1,n)门限可变方案Π,Π″，并证明Π′是(t-1,t+1,n)ramp秘密共享方案，Π″是最优(t-1,t+v-1,n)ramp秘密共享方案，Π,Π″是最优(t→t+v-1,n)门限可变方案。

英文摘要：

The threshold t can be changed into t ′(> t) in (t→t ′,n) threshold changeable schemes, which can increase the difficulty for attackers to attack the schemes. Based on Lagrange interpolation polynomial, two perfect threshold changeable multi- secret sharing schemes: (t→t + 1,n) threshold changeable scheme Π,Π′ and (t→t + v - 1,n)threshold changeable scheme Π,Π″ are proposed. It is shown that Π′ is a (t - 1,t + 1,n) ramp secret sharing scheme,Π″ is an optimal (t - 1,t + v - 1,n) ramp secret sharing scheme and Π,Π″ is an optimal (t→t + v - 1,n) threshold changeable scheme.