An improved threshold multistage secret sharing scheme with cheater identificaion

He and Dawson first proposed a threshold Multistage Secret Sharing scheme to share multiple secrets based on one-way function. In this scheme, multiple secrets are reconstructed stage by stage in the dealer's predetermined order, and only one secret shadow is kept by every participant. Later Harn improved the He and Dawson's scheme to reduce the total number of public values. But Chang et al. showed that both He and Dawson's scheme and Harn's scheme are not multi use schemes and secrets are not infact reconstructed stage by stage and proposed a new scheme to deal with these problems. Then Li et al. improved Chang et al.'s scheme to reduce the total number of public values. In all of the above schemes the number of public values will be increased greatly with the number of secrets. In addition, in order to reconstruct k secrets, you have to use k Lagrange interpolation polynomials. To deal with these problems, in this paper, we propose a multi-stage secret sharing scheme based on Chinese Remainder Theorem which needs only n-t+k+2 public values. Moreover, only one Lagrange interpolation polynomial is used to reconstruct all secrets. In addition, all other participants together can verify whether the share submitted by a participant is correct or not.