Concurrent signature without random oracles

A concurrent signature provides an efficient way to exchange digital signatures between parties in a fair manner. Since its introduction in Eurocrypt 2004, removing the random oracle heuristic in the security analysis of a concurrent signature scheme has become an open problem, and the security of all the existing provably secure schemes could have only been done in the random oracle model, while it has been known that the security in the random oracle model may not be guaranteed when the underlying random oracles are replaced by real-life hash functions. In this paper, we solve this open problem by proposing a new concurrent signature scheme, which allows us to prove its security without random oracles. The security model we consider in this paper also slightly differs from previous works. Signatures before revealing the keystone are strongly ambiguous (or anonymous) in the sense that everyone is able to produce signatures that are indistinguishable from those generated honestly by the parties involved in the exchange, while signatures after revealing the keystone remain unforgeable without sacrificing the fairness property. In the multi-user setting and without random oracles, we prove the security of our scheme based on the intractability of Computational Diffie-Hellman (CDH) problem and collision resistance of hash functions.