One-Time Trapdoor One-Way Functions

Trapdoors are widely used in cryptography, in particular for digital signatures and public key encryption. In these classical applications, it is highly desirable that trapdoors remain secret even after their use. In this paper, we consider positive applications of trapdoors that do not remain secret when they are used. We introduce and formally define one-time trapdoor one-way functions (OTTOWF), a primitive similar in spirit to classical trapdoor one-way functions, with the additional property that its trapdoor always becomes public after use. We provide three constructions of OTTOWF. Two of them are based on factoring assumptions and the third one on generic one-way functions. We then consider potential applications of our primitive, and in particular the fair exchange problem. We provide two fair exchange protocols using OTTOWF, where the trapdoor is used to provide some advantage to one of the parties, whereas any (abusive) use of this trapdoor will make the advantage available to the other party as well. We compare our protocols with well-established solutions for fair exchange and describe some scenarios where they have advantageous characteristics. These results demonstrate the interest of one-time trapdoor one-way functions, and suggest looking for further applications of them.