Group-oriented fair exchange of signatures

In an Optimistic Fair Exchange (OFE) for digital signatures, two parties exchange their signa-tures fairly without requiring any online trusted third party. The third party is only involved whena dispute occurs. In all the previous work, OFE has been considered only in a setting where both ofthe communicating parties are individuals. There is little work discussing about the fair exchangebetween two groups of users, though we can see that this is actually a common scenario in actualOFE applications. In this paper, we introduce a new variant of OFE, called Group-Oriented Op-timistic Fair Exchange (GOFE). A GOFE allows two users from two different groups to exchangesignatures on behalf of their groups in a fair and anonymous manner. Although GOFE may beconsidered as a fair exchange for group signatures, it might be inefficient if it is constructed gener-ically from a group signature scheme. Instead, we show that GOFE is backward compatible to theAmbiguous OFE (AOFE). Also, we propose an efficient and concrete construction of GOFE, andprove its security under the security models we propose in this model. The security of the schemerelies on the decision linear assumption and strong Diffie-Hellman assumption under the randomoracle model.