Weighted Threshold Secret Sharing Based on the Chinese Remainder Theorem

A secret sharing scheme derives from a given secret certain shares (or shadows) which are distributed to users. The secret can be recovered only by certain predetermined groups. In the first secret sharing schemes only the number of the participants in the reconstruction phase was important for recovering the secret. Such schemes have been referred to as threshold secret sharing schemes. In the weighted threshold secret sharing schemes, the users do not have the same status. More exactly, a positive weight is associated to each user and the secret can be reconstructed if and only if the sum of the weights of all participants is greater than or equal to a fixed threshold. In this paper we extend the threshold secret sharing schemes based on the Chinese remainder theorem in order to realize weighted threshold secret sharing.