Secret sharing with access structures in a hierarchy has two properties. First, each group wants to communicate with the others, the participants in the group need to share their secrets based upon access structures. Second, groups are divided into several levels, and each level has its own ancestors and descendants. Based upon the properties of hierarchical key management, only the ancestor groups can hold the descendant groups’ secret keys. In this paper, we suggest two approaches to solve the problem of secret sharing with access structures in a hierarchy. In the first approach, we use the concept of discrete logarithm to reuse shadows, and we adopt Cho’s mechanism to achieve the properties of hierarchical key management. The drawback of the first approach is to spend a lot of time on computation. In the second approach, we use one way hash function to allow the shadows to be reused, and we use the symmetric key cryptography to achieve the properties of hierarchical key management. The second approach is more efficient than the first one. The presented schemes are based upon general hierarchies. They are suitable for many real applications. For example, a business with hierarchical organization can use the proposed schemes to transmit documents and data, and military departments can exchange their reports by the proposed schemes to achieve the properties of hierarchical access control and secret sharing.
