Abstract: A security system with cross-checking for authenticating users on data communications networks comprises means for receiving from a service provider identification data of a user and of a point of access to a service; means for identifying the geographic location of the access point and a of mobile telephone number associated with the user; means for sending the mobile telephone number to a mobile telephone carrier; means for receiving from the telephone carrier data that identify the geographic location of a mobile telephone that corresponds to the sent mobile telephone number; computing means for generating a result of a comparison between the geographic location of the service access point and the geographic location of the mobile telephone and means for sending the result or data as a function of the result to the service provider or to the mobile telephone number.