Abstract: A process of authentication, by an outside medium, of a portable object connected to that medium via a transmission line and a system for carrying out the process. To authenticate a portable object (7) connected to a terminal linked to the outside medium by a transmission line, the outside medium (1) manages a control table (11) containing a non-secret piece of data (N.sub.7) specific to each object that can be identified, as well as a parameter (E.sub.a ) and a result (R.sub.a) entered in the control table during the preceding authentication of the object. A new parameter (E.sub.b), produced by the medium during authentication, is used to calculate a new result (R.sub.b) in the object. The old result is recalculated. If it matches the one in the table (11), the object is authenticated, and the new parameter (E.sub.b) and result (R.sub.b) are entered in the control table in place of the preceding ones. The process is well suited for use in protecting computer networks.