On the Impossibility of Fair Exchange without a Trusted Third Party

We attempt to formally deene the strong fair exchange problem and present a proof that it is impossible to solve strong fair exchange without a trusted third party. The proof is established by relating strong fair exchange to the problem of consensus and adapting the impossibility result of Fischer, Lynch and Paterson. We show that strong fair exchange is at least as hard as consensus and explore a few requirements for trusted third parties in order to be of use in fair exchange. Impossibility of Fair Exchange 1 1. INTRODUCTION There are numerous notions of fairness in distributed systems, most of which are related to the scheduling of concurrent actions Francez 1986]. Lately, there has been an interesting adaption of the term to protocols used in the eld of electronic commerce Asokan 1998]. There, fairness refers to the equal treatment of parties (or agents) which are involved in some form of electronic business transaction. The basic operation necessary in the usual form of commercial interaction is the exchange of one item for another. This can be a purchase of some item in exchange for payment, or the signing of a contract, where signed terms of agreement are exchanged. In his recent thesis, Asokan 1998] deenes fairness as a security requirement on exchanges: An exchange is fair if at the end of the exchange, either each player receives the item it expects or neither player receives any additional information about the other's item. Asokan 1998, p. 8] While there are some weaknesses in this deenition (see for example the discussion in Pagnia and Vogt 1999]), this notion of fairness can be used to deene a new problem in distributed systems: the problem of fair exchange between two parties. There exist a variety of fair exchange protocols in the literature, all with their own speciications and system models Camp et al.