An efficiency improvement on an unlinkable divisible electronic cash system

We present an efficiency improvement on an existing unlinkable divisible e-cash system. In the based e-cash system, an e-coin can be divided to spent, and thus the exact payments are available. Furthermore, to protect customer's privacy, the system also satisfies the unlinkability in all the payments, which is not satisfied in other existing divisible e-cash systems. The unlinkability means the infeasibility of determining whether two payments are made by the same customer. However, in the unlinkable divisible e-cash system, the payment protocol needs O(N) computations, and thus inefficient, where N indicates the divisibility precision. For example, in case of N = 100,000, about 200,000 exponentiations are needed for the worst. We improve the payment protocol using the tree approach. In case of N = 100,000, the protocol with our improvement needs only about 600 exponentiations for the worst. This good result can be obtained for other N which is more than about 100.