Dynamic threshold secret reconstruction and its application to the threshold cryptography

• An efficient (t,n)(t,n) SS is proposed in which shares can reconstruct the secret, have a dynamic threshold and protect exchange information.
• Our proposed SSs can be extended to develop efficient threshold cryptographic algorithms (threshold signature/encryption).

Shamir's (t,nt,n) secret sharing scheme (SS) is based on a univariate polynomial and is the most cited SS in the literature. The secret in a (t,nt,n) SS can be recovered either by exactly t or more than t shareholders. Most SSs only consider when there are exactly t shareholders participated in the secret reconstruction. In this paper, we examine security issues related to the secret reconstruction if there are more than t shareholders participated in the secret reconstruction. We propose a dynamic threshold SS based on a bivariate polynomial in which shares generated by the dealer can be used to reconstruct the secret but having a larger threshold which is equivalent to the exact number of participated shareholders in the process. In addition, we extend the proposed scheme to enable shares which can also be used to establish pairwise keys to protect the reconstructed secret from non-shareholders. Shamir's SS has been used in conjunction with other public-key algorithms in most existing threshold algorithms. Our proposed SS can also be applied to the threshold cryptography to develop efficient threshold algorithms.