How to protect privacy in Optimistic Fair Exchange of digital signatures

In this work, we introduce a new notion called Privacy-Preserving Optimistic Fair Exchange (P2OFE) for protecting the privacy of users, in which other than Alice and Bob, no one else including the arbitrator, can collect any evidence about an exchange between them even after the resolution of a dispute. We formally define P2OFE and present the corresponding security models and propose a concrete and efficient construction of P2OFE. We also discuss about several extensions about implementation. Our scheme is proved to be secure under the given security models based on the Strong Diffie-Helllman and Decision Linear assumptions without relying on the random oracle heuristic.