With the interaction of a medical measuring system (3) with a ventilator or anesthesia device (5) via a data network (60), data transmission security and mutual authentication between the medical measuring system (3) and the ventilator or anesthesia device (5) is improved in a medical system (1) by the use of asymmetric encryption pairs. A classification of the measuring systems (3) is possible on the basis of an identification/authentication provided by the asymmetric encryption pairs. The classification may be used to adapt a ventilation by the ventilator or anesthesia device (5) in respect to different defined measuring systems (3), for example, measuring systems (3) for detecting an oxygen saturation (SpO2).