Paper 2009/324

Group-Oriented Fair Exchange of Signatures

Qiong Huang, Duncan S. Wong, and Willy Susilo

Abstract

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

Note: The definition of GOFE and the scheme were revised to include the Trace algorithm for opening a signature.