An authentication method for trusted communication between a first party and a second party by combining password-based authentication and certificate-based authentication in such a manner that, for the certificate-based authentication, the first party has a static key pair consisting of a private static key and a public static key and a certificate for the public static key issued by a certification authority, and the certification authority is assigned a public key which is known by the second party in such a manner • that password-based authentication is first of all carried out with the following steps: the first party and the second party a) each generate an ephemeral key pair consisting of a private ephemeral key and a public ephemeral key, b) each interchange the public ephemeral key and validate the latter using a common password, c) generate and then validate a session key, on the basis of which a secure communication channel is established, • that certificate-based authentication is then carried out with the following steps: d) the first party calculates a transformation between its own ephemeral key pair from the password-based authentication and its own static key pair from the certificate-based authentication so as to obtain a parameter of the transformation, e) the first party transmits the parameter of the transformation, together with the certificate issued by the certification authority, to the second party via the secure communication channel, f) the second party applies the received parameter of the transformation to the public ephemeral key and/or the public static key of the first party and in the process obtains at least one transformed public key, the correctness of which is checked, and g) the second party validates the certificate received from the first party using the public key of the certification authority, and • that, in step d), the private static key is mapped to the private ephemeral key in order to calculate the parameter of the transformation. • that password-based authentication is first of all carried out with the following steps: the first party and the second party a) each generate an ephemeral key pair consisting of a private ephemeral key and a public ephemeral key, b) each interchange the public ephemeral key and validate the latter using a common password, c) generate and then validate a session key, on the basis of which a secure communication channel is established, a) each generate an ephemeral key pair consisting of a private ephemeral key and a public ephemeral key, b) each interchange the public ephemeral key and validate the latter using a common password, c) generate and then validate a session key, on the basis of which a secure communication channel is established, • that certificate-based authentication is then carried out with the following steps: d) the first party calculates a transformation between its own ephemeral key pair from the password-based authentication and its own static key pair from the certificate-based authentication so as to obtain a parameter of the transformation, e) the first party transmits the parameter of the transformation, together with the certificate issued by the certification authority, to the second party via the secure communication channel, f) the second party applies the received parameter of the transformation to the public ephemeral key and/or the public static key of the first party and in the process obtains at least one transformed public key, the correctness of which is checked, and g) the second party validates the certificate received from the first party using the public key of the certification authority, and d) the first party calculates a transformation between its own ephemeral key pair from the password-based authentication and its own static key pair from the certificate-based authentication so as to obtain a parameter of the transformation, e) the first party transmits the parameter of the transformation, together with the certificate issued by the certification authority, to the second party via the secure communication channel, f) the second party applies the received parameter of the transformation to the public ephemeral key and/or the public static key of the first party and in the process obtains at least one transformed public key, the correctness of which is checked, and g) the second party validates the certificate received from the first party using the public key of the certification authority, and • that, in step d), the private static key is mapped to the private ephemeral key in order to calculate the parameter of the transformation.