Research On ID-Based Group Signature Scheme From Lattice Assumptions

Group signature, as a special kind of digital signature, can allow any member of the group to sign on behalf of the group, and the signature is anonymous. Once a controversy happens, the group manager can trace the signer by the opening algorithm. Group signature has abroad application foreground because of its anonymity and traceability, such as the management of public resources, issuing orders, the elections, the news release, e-commerce. The cryptosystem relying on lattice-based assumptions is currently recognized to be immune to quantum attacks. Besides it offers several concrete advantages as well:The structure of the algorithm is simple. The basic lattice operations manipulate relatively small numbers. And lattice problems under worst-case and average-case are equivalent. Therefore, constructing group signature based on lattice is a hot issue of group signature research.This paper studies the construction of a group signature scheme from lattice assumptions, and proposes an ID-based group signature scheme from lattice assumptions. Comparing with the existing group signature scheme, we have achieved the following results.Our construction is the first ID-based group signature scheme. In the construction of the scheme, users’secret keys are generated by the key generator center (KGC), a user can use one secret key for both an ordinary signature and a group signature if he has joined into a certain group. Furthermore, the group manager has no longer the permission to generate the group members’secret keys, and even doesn’t know a member’s secret key, what the manager can do is to issue a certificate to a user once validated, so that the scheme can effectively prevent the group manager forging a group signature as a group member, and improve security when a user ask for joining into a group at the same time.