In an authentication-data issuing system based on unique time, a master computer (1) creates authentication data on the basis of an elapsed time measurement indicated by an unique time generating device (6) and transmits the created authentication data to a lower-level computer (2A), which further delivers the authenticating data to a still-lower-level computer (3A). The lower-level computer and still-lower-level computer sequentially impart respective unique additional data to the authentication data and then transmits the resultant additional-data-imparted data to a lowest-level vending machine (5). The lowest-level vending machine (5) also imparts its unique additional data to the authentication data, received from the still-lower-level computer, to create unique authentication data and records the thus-created unique authentication data on a prepaid card (20) to be issued thereby. Simultaneously, the ultimately-created unique authentication data is sent from the vending machine, through the still-lower-level computer and lower-level computer, back to the master computer (1) for registration therein. When the thus-issued prepaid card (20) is used on a pachinko machine in a pachinko house under the control of the master computer (1), the pachinko machine reads the unique authentication data recorded on the card, and the thus-read data is collated with the data registered in the master computer (1) to ascertain the authenticity of the card.