Huang, Qiong; Yang, Guomin; Wong, Duncan S.; and Susilo, Willy, 2008, Efficient optimistic fair exchange secure in the multi-user setting and chosen-key model without random oracles, in T. Malkin (Ed.), RSA Conference 2008, Cryptographers Track (CT-RSA 2008), 4964, 106-120.
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 multiuser 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 certified-key model by giving a concrete counterexample. Second, we strengthen the previous static security model in the multi-user setting to a more practical one which allows an adversary to choose a key adaptively. Third, we propose an efficient and generic optimistic fair exchange scheme in the multi-user setting and chosen-key model. The security of our construction is proven without random oracles. We also propose some efficient instantiations.