A secret sharing scheme with a short share realizing the (t, n) threshold and the adversary structure

摘要

On the basis of the properties of the Jordan matrix, we proposed a secret sharing scheme which can realize both the (t, n) threshold and the adversary structure and share a large secret while each participant has a short share. At the same time, the scheme can prevent the participants from cheating. The shares can be kept secret in the process of reconstruction and do not need to be renewed when the shared secret is changed. If n participants want to share a large secret using a short share such that t or more participants can reconstruct the shared secret and there are some subsets that each contain at least t participants that cannot reconstruct the shared secret, our scheme will be effective.