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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  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  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.