Membership authentication for hierarchical multigroups using the extended fiat-shamir scheme

Abstract

We propose two membership authentication schemes that allow an authorized user to construct one master secret key for accessing the set of hierarchically ordered groups denned by the user, without releasing any private user information. The key allows the user to prove his membership of his true groups and all lower groups, without revealing his name or true groups. The user can calculate the secret member information needed to access a group from his master secret key, and can convince a verifier using the extended Fiat-Shamir scheme. Each of two proposed schemes can generate the master secret key. To ensure the user’s privacy, one uses the blind signature and pseudonym encryption techniques, and the other uses Euclid’s algorithm. Because each user stores only one master secret key, memory usage is very efficient. Moreover, verifiers can check membership validity using public information independent of the number of users in an off-line environment. Therefore, our schemes are suitable for smart card applications.