An electronic ticket is a contract, in digital format, between the user and the service provider, and reduces both economic costs and time in many services such as air travel industries or public transport. However, the electronic ticket security has to be strongly guaranteed, as well as the privacy of their users. We present an electronic ticketing system that considers these security requirements and includes the exculpability as a security requirement for these systems, i.e users and the service provider can not falsely accuse each other of misbehaviour. The system ensures that either both parties receive their desired data from other or neither does (fair exchange). Furthermore, this scheme takes special care of the computational requirements on the users' side, as we consider the use of mobile devices with light-weight cryptography, because they are the best positioned in order to manage the electronic tickets in the near future.