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, said method 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; - 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 the second authentication codes (124, 128) by the mobile telecommunication terminal; - establishing a mobile communications connection between the mobile telecommunication terminal and the service computer system via the public network; and - authenticating the mobile telecommunication terminal with respect to the service computer system by means of the authentication key via the mobile communications connection, wherein the second authentication code is the authentication key encrypted with the first authentication code, and the generation of the authentication key comprises the decryption of the second authentication code with the first authentication code. - 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; - 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 the second authentication codes (124, 128) by the mobile telecommunication terminal; - establishing a mobile communications connection between the mobile telecommunication terminal and the service computer system via the public network; and - authenticating the mobile telecommunication terminal with respect to the service computer system by means of the authentication key via the mobile communications connection,