With the economy developing and popular Internet, the general concept of contract signing has changed. In the past, people usually sign a contract at the same time and same place face to face, but actually each party involved in contract may live in different part of earth, they want to sign something for business or some other things in economic, efficient, secure and fairway. A fair contract signing protocol allows two potentially mis-trusted 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 LUCAS signature scheme, a new digital anonymous contract signing protocol is proposed in this paper. Like the existing LUCAS-based solutions for the same problem, our protocol is fair, anonymous and optimistic. Furthermore, the proposed protocol satisfied a new property, i.e., it is abuse-free. That is, if the protocol is executed unsuccessfully, either of the two parties can not show the validity of intermediate results to others.
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