Age of information is not just a number: Status updates against an eavesdropping node

We consider status updates exchanged between a transmitter and a legitimate receiver, also including an eavesdropper that captures pieces of information. In the absence of such a threat, the connection between the transmitter and the receiver is controlled by the transmitter with the aim of delivering fresh information at the receiver's side quantified through the age of information. Due to the presence of the eavesdropper, the transmitter may further tune the generation rate of status updates to trade off the ages of information acquired by the eavesdropper and the receiver, respectively. We combine both objectives according to a Bergson social welfare framework and we solve the problem of finding the optimal generation rate as a function of the probability of data capture by the eavesdropper. We consider the age of information minimization task in the context of queuing systems, at first assuming equal service rates at the legitimate receiver and the eavesdropper, then analyzing scenarios where the eavesdropper's service rate is different. This enables us to derive notable and sometimes counter-intuitive conclusions, and possibly establish an extension of the age of information framework to security aspects from a performance evaluation perspective.