Multi-party concurrent signatures based on short ring signatures

In order to resolve the multi-party fair-exchange problem of the e-commerce, a new model of multi-party concurrent signatures based on short ring signatures was proposed. Using the technique of bilinear pairings, a concurrent signature scheme for multi-users which we prove secure in the random oracle model was constructed. Since the short ring signature is constructed based on dynamic accumulators, it has the advantage of constant-size signatures and simple public keys. Compared with the scheme proposed by Tonien, the signature size of our scheme has been shortened to 0(n). So the open problem questioned by Tonien is solved.