In a cryptographic method between a portable data carrier and a terminal device there are employed a public data-carrier key and a secret data-carrier key of the data carrier as well as a public terminal key and a secret terminal key of the terminal device. The data carrier employs as a public data-carrier key a static public key. As a secret data-carrier key the data carrier employs a secret key that is derived from a secret basic key associated with the public data-carrier key. Within the framework of the method, the terminal device checks an authentication parameter associated with the data carrier and different from the data-carrier keys.