中文摘要：

提出了一种基于模运算的加权的门限秘密共享方案,当参与者的权重之和大于等于门限值时可以恢复秘密,而小于门限值时则不能.目前仅有的关于加权秘密共享方案都是基于分解结构的,其缺点是参与者需要掌握多个子秘密,并且各个子秘密使用场合不相同,管理和使用不太方便.方案中每个参与者只需要保存一个子秘密,简化了密钥管理与使用.该方案适用于强调管理方便性的环境.在某些情况下,还可以调整权重和门限参数来减小问题的规模,但达到的效果跟原来的系统一致,为此,提出了控制结构的等价性的概念,并提出了一种基于整数规划的参数调整算法.

英文摘要：

A weighted threshold secret sharing scheme based on modular computation is proposed in this paper. Weights are used to give differential influence to participants. When the sum of weights of the participants is as big as or bigger than the threshold value, they can recover the secret, otherwise they can not. The participants of the previous weighted secret sharing schemes based on decomposition structure have to hold several sub-secrets which have different application circumstances and are very difficult to manage. But the proposed scheme only requires each participant to hold one single sub-secret, which simplifies the management and usage of the sub-secrets, and enables this scheme applicable for the cases where the management convenience is more important. In some cases, the weights and the threshold value could be adjusted to reduce the size of the scheme but still with the same effect compared with the original one. For this purpose, the concept of the equivalence of access structures is suggested, and an algorithm for parameter adjustment based on integer programming is proposed to minimize the threshold.