Efficient divisible E-cash system based on reverse binary tree

There exist some defects such as low efficiency in the spending protocol and deposit protocol of the proposed by Izabachene et al. (2012) divisible E-cash system based on the standard model. Using the Groth-Sahai (GS) proof system and accumulator, this paper proposes a reverse binary tree algorithm and designs an efficient divisible E-cash system under the standard model. The new system can calculate simultaneously the series number of the leaf nodes of the binary tree in the process of the binary tree construction. A user can prove the correctness of spending path directly, thus the computation load of user is constant in the spending protocol. The new system achieves both the weak exculpability and the strong exculpability. Finally, the security proof of the system is given in the standard model which includes unforgeability, anonymity, identification of double spender and exculpability.