Tonien, Dongvu; Susilo, Willy; and Safavi-Naini, Reihaneh, 2006, Multi-party concurrent signatures, Information Security, Lecure Notes in Computer Science, 4176, 131-145.
The concept of concurrent signatures was introduced by Chen, Kudla and Paterson at Eurocrypt 2004. In a concurrent signature scheme, users sign their messages in an ambiguous way so that the signatures are only verifiable by the users themselves but not by any other outsiders. At a later stage, one of the users releases an extra bit of information called the keystone, then all the signatures become binding to their signers concurrently. At this stage, any outsider can verify the signatures. Chen, Kudla and Paterson proposed a concurrent signature scheme for two users. Recently, Susilo and Mu constructed a scheme for three users. It is an open problem to construct concurrent signature schemes for multi users. In this paper, we answer this open problem affirmatively. Using techniques of ring signatures and bilinear pairings, for the first time we construct a concurrent signature scheme for multi-users.