Abstract: 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.

Key words: Lagrange interpolation polynomial, multi-secret sharing, ramp secret sharing, threshold changeable secret sharing

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。

关键词: 拉格朗日插值多项式, 多秘密共享, ramp秘密共享, 门限可变秘密共享