A method for authenticating a mobile telecommunication terminal on a service computer system via a public network, the mobile telecommunication terminal comprising a secure memory area in which a first authentication code is stored, and a second authentication code being stored in the service computer system, the second authentication code being assigned to a user identifier, comprising the following steps: - establishing a network connection between a user computer system and a service computer system via the public network; - authenticating a user with respect to the service computer system via the user computer system and the network connection using a 2-factor authentication, a user identifier being sent from the user computer system to the service computer system via the network connection; - sending the second authentication code assigned to the user identifier to the user computer system via the network connection after the user has been authenticated with respect to the service computer system; - displaying the second authentication code to a display device of the user computer system; - authenticating the user with respect to the mobile telecommunication terminal by detecting user-specific information; - optically detecting the second authentication code by the mobile telecommunication terminal from the user computer system; - generating an authentication key from the first and second authentication codes (124, 128) by the mobile telecommunication terminal; - establishing a mobile communication connection between the mobile telecommunication terminal and the client computer system via the public network; and - authenticating the mobile telecommunication terminal with respect to the service computer system by way of the authentication key via the mobile communication connection. - establishing a network connection between a user computer system and a service computer system via the public network; - authenticating a user with respect to the service computer system via the user computer system and the network connection using a 2-factor authentication, a user identifier being sent from the user computer system to the service computer system via the network connection; - sending the second authentication code assigned to the user identifier to the user computer system via the network connection after the user has been authenticated with respect to the service computer system; - displaying the second authentication code to a display device of the user computer system; - authenticating the user with respect to the mobile telecommunication terminal by detecting user-specific information; - optically detecting the second authentication code by the mobile telecommunication terminal from the user computer system; - generating an authentication key from the first and second authentication codes (124, 128) by the mobile telecommunication terminal; - establishing a mobile communication connection between the mobile telecommunication terminal and the client computer system via the public network; and - authenticating the mobile telecommunication terminal with respect to the service computer system by way of the authentication key via the mobile communication connection.