Design and implementation of an efficient fair off-line e-cash system based on elliptic curve discrete logarithm problem

In this paper, we design and implement an efficient fair off-line electronic cash system based on Elliptic Curve Discrete Logarithm Problem (ECDLP), in which the anonymity of coins is revocable by a trustee in case of dispute. To achieve this, we employ the Petersen and Poupard´s electronic cash system [1] and extend it by using an elliptic curve over the finite field GF(2ⁿ). This naturally reduces message size by 85% compared with the original scheme and makes a smart card to store coins easily. Furthermore, we use the Baek et al.´s provably secure public key encryption scheme [2] to improve the security of electronic cash system. As an extension, we propose a method to add atomicity into new electronic cash system. To the best of our knowledge, this is the first result to implement a fair off-line electronic cash system based on ECDLP with provable security.