A computer, such as a Windows-based PC 23, has associated with it a Subscriber Identity Module (SIM) 15, such as of the type used in a GSM or UMTS cellular or mobile telecommunications network. The SIM 15 can be authenticated with the network 3 in the same way as for authenticating SIMs of mobile telephone handsets used in the network, and can in this way authenticate the user of the PC 23 or the PC 23 itself. Such authentication can, for example, permit use of the PC 23 in relation to a particular application running on the PC 23. Challenge and response messages are transmitted between the network 3 and the SIM 15 via an authenticator module 30 implemented on the PC 23. These authentication messages have the predetermined format of an Over The Air (OTA) message, which is also used in GSM or UMTS telecommunications networks to transmit non-authentication messages—for example, SMS messages. The authentication data is encapsulated within OTA messages. The OTA messages are not necessarily transmitted wirelessly (that is, over the air). They may be transmitted via a fixed network; however, they have the predetermined format of OTA messages.