Group Signatures: Provable Security, Efficient Constructions and Anonymity from Trapdoor-Holders

To date, a group signature construction which is efficient, scalable, allows dynamic adversarial joins, and proven secure in a formal model has not been suggested. In this work we give the first such construction in the random oracle model. The demonstration of an efficient construction proven secure in a formal model that captures all intuitive security properties of a certain primitive is a basic goal in cryptographic design. To this end we adapt a formal model for group signatures capturing all the basic requirements that have been identified as desirable in the area and we construct an efficient scheme and prove its security. Our construction is based on the Strong-RSA assumption (as in the work of Ateniese et al.). In our system, due to the requirements of provable security in a formal model, we give novel constructions as well as innovative extensions of the underlying mathematical requirements and properties. Our task, in fact, requires the investigation of some basic number-theoretic techniques for arguing security over the group of quadratic residues modulo a composite when its factorization is known. Along the way we discover that in the basic construction, anonymity does not depend on factoring-based assumptions, which, in turn, allows the natural separation of user join management and anonymity revocation authorities. Anonymity can, in turn, be shown even against an adversary controlling the join manager.