A fair electronic cash system is a system that allows customers to make payments anonymously. Moreover, under certain circumstances, a trusted authority can revoke the anonymity of suspicious transactions. Various fair e-cash systems using group signature schemes have been proposed [4,15,16,18]. Unfortunately, they do not realize coin tracing [4,15,18] (the possibility to trace the coins withdrawn by a customer). In this paper, we describe several failures in the solution of [16] and we present a secure and efficient fair e-cash system based on a group signature scheme. Our system ensures traceability of double-spenders, supports coin tracing and provides coins that are unforgeable and anonymous under standard assumptions. A fair electronic cash system is a system that allows customers to make payments anonymously. Moreover, under certain circumstances, a trusted authority can revoke the anonymity of suspicious transactions. Various fair e-cash systems using group signature schemes have been proposed [4,15,16,18]. Unfortunately, they do not realize coin tracing [4,15,18] (the possibility to trace the coins withdrawn by a customer). In this paper, we describe several failures in the solution of [16] and we present a secure and efficient fair e-cash system based on a group signature scheme. Our system ensures traceability of double-spenders, supports coin tracing and provides coins that are unforgeable and anonymous under standard assumptions. A fair electronic cash system is a system that allows customers to make payments anonymously. Moreover, under certain circumstances, a trusted authority can revoke the anonymity of suspicious transactions. Various fair e-cash systems using group signature schemes have been proposed [4,15,16,18]. Unfortunately, they do not realize coin tracing [4,15,18] (the possibility to trace the coins withdrawn by a customer). In this paper, we describe several failures in the solution of [16] and we present a secure and efficient fair e-cash system based on a group signature scheme. Our system ensures traceability of double-spenders, supports coin tracing and provides coins that are unforgeable and anonymous under standard assumptions.