Optimistic fair exchange is a kind of protocols to solve the problem of fair exchange between two parties. Almost all the previous work on this topic are provably secure only in the random oracle model. In PKC 2007, Dodis et al. considered optimistic fair exchange in a multi-user setting, and showed that the security of an optimistic fair exchange in a single-user setting may no longer be secure in a multi-user setting. Besides, they also proposed one and reviewed several previous construction paradigms and showed that they are secure in the multi-user setting. However, their proofs are either in the random oracle model, or involving a complex and very inefficient NP-reduction. Furthermore, they only considered schemes in the certified-key model in which each user has to show his knowledge of the private key corresponding to his public key. In this paper, we make the following contributions. First, we consider a relaxed model called chosen-key model in the context of optimistic fair exchange, in which the adversary can arbitrarily choose public keys without showing the knowledge of the private keys. We separate the security of optimistic fair exchange in the chosen-key model from the certifiedkey