Contract signing protocols have been proposed and analyzed for more than three decades now. One of the main problems that appeared while studying such schemes is the impossibility of achieving both fairness and guaranteed output delivery. As workarounds, cryptographers have put forth three main categories of contract signing schemes: gradual release, optimistic and concurrent or legally fair schemes. Concurrent signature schemes or legally fair protocols do not rely on trusted arbitrators and, thus, may seem more attractive for users. Boosting user trust in such manner, an attacker may cleverly come up with specific applications. Thus, our work focuses on embedding trapdoors into contract signing protocols. In particular, we describe and analyze various SETUP (Secretly Embedded Trapdoor with Universal Protection) mechanisms which can be injected in concurrent signature schemes and legally fair protocols without keystones.
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