Group signature schemes are fundamental cryptographic tools that enable unlinkably anonymous authentication, in the same fashion that digital signatures provide the basis for strong authentication protocols. In this paper we present the first group signature scheme with constantsize parameters that does not employ any trapdoor function. This novel type of group signature scheme allows public parameters to be shared among organizations. Such sharing represents a highly desirable simpli cation over existing schemes, which require each organization to maintain a separate cryptographic domain.

We study the benefits of revocable items (like electronic payments which can be undone by the bank) for the design of efficient fair exchange protocols. We exploit revocability to construct a new optimistic fair exchange protocol that even works with asynchronous communication channels. All previous protocols with comparable properties follow the idea of Asokan's exchange protocol for two generatable items [Aso98, ASW98]. But compared to that, our protocol is more efficient: We need less messages in the faultless case and our conflict resolution is less complicated. Furthermore, we show that the generatability, which is required by [Aso98, ASW98], is difficult to implement in the context of some electronic payments. Instead, revocability of payments may be much easier to realize. Thus, our new protocol is very well suited for the fair exchange of revocable payments for digital goods.