Weighted Threshold Secret Sharing

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.