中文摘要：

在复杂的现实环境中,带权重的(t,n)秘密共享方案中的参与者具有不同的权重,任意权重之和大于等于t的参与者集合可以重构出秘密,权重和小于t的参与者集合无法获得关于秘密的任何信息,有效地满足了应用中不同权限参与者的实际需求.然而,如何平衡增强方案安全性与减少计算开销之间的矛盾,提高已有方案的灵活性一直需要解决的关键问题之一.为了提高已有方案的安全性、降低计算开销和增加方案实用性和灵活性,本文提出了一种带权重动态可验证多秘密共享方案.本文所设计的方案基于中国剩余定理实现了参与者有权重的秘密共享;方案利用单向哈希函数简单、易构造的性质,在秘密重构的过程中对秘密份额的有效性进行了验证,使得方案具有较高的执行效率;方案将要共享的秘密转化为多项式的线性组合,可以同时共享多个秘密且易于动态添加或更新秘密,使得方案具有较好的灵活性;同时,本文所设计的方案可以动态添加或删除参与者,使得方案易于控制并具有较好的实用性.

英文摘要：

In complicated network environments, a weighted (t,n) secret sharing scheme allows each participant to own a different weight that describes the importance of the participant and the secret can be recovered by any subsets of participants when the sum of weights of the subsets is no less than a weighted threshold value, but the secret cannot be recovered if the sum of weights is smaller than the threshold value. However, there are some crucial problems to be solved, for example, how to balance the security and the computational overhead, how to improve the flexibility of the secret sharing schemes, and so on. To improve the schemes’ security, efficiency and practicality and thus reduce the computational overhead, this paper proposes a weighted dynamic and verifiable multi-secret sharing scheme based on the Chinese Remainder Theorem (CRT). In the secret reconstruction phase, the validity of the shadows are verified, and by the nature of the one-way function, which provides the simplicity and easy construction, it can achiece an improved efficiency of the scheme. The proposed scheme, which uses a technique to transform the secrets into a linear combination of polynomials, can share multiple secrets dynamically, and can add new secrets or delete existing secrets. The scheme has preferable practicality, and the participants can be removed or added freely.