An off-line electronic cash system having an electronic coin, a bank B, a payee S, and a user U with an account at the bank B as well as a user password z.sub.u,i, has a method for performing an electronic cash transfer. An electronic coin is withdrawn from the bank B by the user U and an electronic record of the electronic coin is stored by the bank B. The coin is paid to the payee S by the user U. The payee S deposits the coin with the bank B. A determination is made that the coin is spent and the record of the coin is deleted by the bank B. A further deposit of the same coin after the record is deleted is determined. Additionally, a determination is made which user U originally withdrew the coin after deleting the record. To perform these operations a key pair is generated by the user, including public and secret signature keys. The public signature key along with a user password z.sub.u,i and a withdrawal amount are sent to the bank B by the user U. In response, the bank B sends a coin to the user U signed by the secret key of the bankindicating the value of the coin and the public key of the user U. The payee S transmits a challenge counter to the user U prior to receiving the coin.