A fair contract signing protocol allows two potentially mistrusted parities to exchange their commitments (i.e., digital signatures) to an agreed contract over the Internet in a fair way, so that either each of them obtains the other’s signature, or neither party does. Based on the RSA signature scheme, a new digital contract signing protocol is proposed in this paper. Like the existing RSA-based solutions for the same problem, our protocol is not only fair, but also optimistic, since the third trusted party is involved only in the situations where one party is cheating or the communication channel is interrupted. Furthermore, the proposed protocol satisfies a new property, i.e., it is abuse-free. That is, if the protocol is executed unsuccessfully, none of the two parties can show the validity of intermediate results to others. Technical details are provided to analyze the security and performance of the proposed protocol. In summary, we present the first abuse-free fair contract...