A New Verifiable Multi-secret Sharing Scheme Realizing Adversary Structure

In some practical applications of secret sharing schemes, such as Byzantine Quorum systems and secure multi-party protocols, the adversary can corrupt subsets of participants at the same time and exploits their shares to recover the secret. In these applications, the system can be described directly by corruptible subsets of participants (so-called adversary structure). A secret sharing scheme realizing adversary structure is a tool for these applications. It is a method of sharing a secret among a finite set of participants in such a way that only certain pre-specified subsets of participants cannot recover the secret. In this paper, we propose a verifiable multi-secret sharing scheme based on one-way hash function that realizes adversary structure, in which each participant has only one reusable shadow. In this scheme, the participant set and the adversary structure can be changed without refreshing any participant's secret shadow and new secrets can be shared. The security of the proposed scheme is based on the properties of the one-way hash function. Our scheme has the advantages of better verifiability and fewer shadows preserves by every participant respect to other schemes realizing adversary structures.