Transferable conditional e-cash with optimal Anonymity in the standard model

Transferable conditional electronic-cash (e-cash) allows the recipient of a coin in a transaction to transfer it in a later payment transaction to the third person based on the outcome not known in advance. Anonymity is a very important property for a transferable conditional e-cash. However, none of the existed transferable conditional e-cash achieve the optimal anonymity because of its special structure, that is, introducing transferability in the conditional e-cash. In this study, they novelly present a transferable conditional e-cash scheme using a totally different structure, that is, adding condition into the transferable ecash. Thanks to employing Groth-Sahai proofs systems and commuting signatures, the new transferable conditional e-cash satisfies optimal anonymity. Accordingly, they present an extended security model by introducing a publisher who is responsible for publishing two outcomes of a condition. Then, they prove the new scheme's security in the standard model. Compared with the existing transferable conditional e-cash, the efficiency of the new scheme is also improved since the size of the computation and communication is constant.