A fair contract signing protocol is used to enable two mistrusted parties to exchange two signatures on a given contract, in such a way that either both of them get the other party’s signature, or none of them gets anything. A new signature scheme is presented, which is a variant of Boneh and Boyen’s scheme, and building on it, we propose a new signature fair exchange protocol for which all the properties of being optimistic, setup-free and abuse-free can be proved without random oracles, and it is more efficient than the known schemes with comparable properties.