Group-oriented fair exchange of signatures

Optimistic Fair Exchange (OFE) of digital signatures allows two parties to exchange their signatures in a fair manner so that a third party, called the arbitrator, gets involved only when there is a dispute. Previous work on OFE considers the two parties as individuals and there is no formal study on the scenario where the two parties are two groups of users. In this paper, we formalize this new variant and call it a Group-oriented Optimistic Fair Exchange (GOFE). GOFE allows two users from two different groups to exchange signatures on behalf of their groups in a fair and anonymous manner. We formalize the notion by providing the first set of security models for GOFE, and show that it is closely related to Ambiguous OFE (AOFE) proposed by Huang et al. in Asiacrypt 2008. In particular, we propose a generic transformation which converts a GOFE to an AOFE. We also give an efficient and concrete GOFE construction and prove its security under the security models we defined. The security of the scheme relies on the decision linear assumption and strong Diffie–Hellman assumption in the random oracle model.