Optimal Efficiency of Optimistic Contract Signing

A contract is a non-repudiable agreement on a given contract text, i.e., a contract can be used to prove agreement between its signatories to any verifier. A contract signing scheme is used to fairly compute a contract so that, even if one of the signatories misbehaves, either both or none of the signatories obtain a contract. Optimistic contract signing protocols use a third party to ensure fairness, but in such a way that the third party is not actively involved in the fault-less case. As no satisfactory protocols without any third party exist, this seems to be the best one can hope for. We prove tight lower bounds on the message and round complexity of optimistic contract signing on synchronous and asynchronous networks, and present new and efficient protocols based on digital signatures which achieve provably optimal efficiency. Furthermore, we investigate what can be gained if the third party
participates in the contract verification.