We consider the scenario in which the source sends status updates, or packets, to the receiver through an infinite capacity transmitter, where the transmitted packets are subject to potential illegal eavesdropping. Time is discretized into identical time slots. In recent years, the age of information (AoI) metric, which was defined as the time has elapsed since the generation instant of the latest received packet, has been widely applied to characterize the freshness of obtained packets. Due to the presence of eavesdroppers, some packets may be eavesdropped during their transmissions, causing information leakages. To assess an infinite-capacity system’s performance of securely transmitting status updates, in this paper, we define an AoI-related metric called the freshness advantage of the legitimate receiver, F, to be average instantaneous gap between eavesdropper’s and legitimate receiver’s AoI. For arbitrarily distributed packet interarrival times, and assuming that in each time slot with probabilities ${\gamma }_d$, ${\gamma }_E$, the transmitted packet is received by the legitimate receiver and the eavesdropper, we derive the explicit formula of F. The concise expression shows that F is fully determined by the average interarrival time and the ratio of ${\gamma }_d$ to ${\gamma }_E$. For special cases where the interarrival time follows geometric distributions, we first determine the explicit distribution of instantaneous AoI gap. Then, given ${\gamma }_d$ and ${\gamma }_E$, we derive the optimal packet generation rate $p^{\ast }$ that minimizes the combined performance Q, which is constructed as the average AoI minus the freshness advantage F. When imposing timeliness and security constraints at the same time, the feasible regions of p and ${\gamma }_d$ such that both two required performances can be satisfied are depicted and discussed. Finally, we investigate the impacts of different parameters on F and show the tradeoffs between timeliness performance and security performance through numerical simulations.

We consider that the source sends packets to the receiver through a Ber/Geo/1/2 queue modeled status updating system, where the transmitted packets are subject to potential eavesdropping. Time is discretized into identical time slots. This paper studies the tradeoffs between the information freshness and transmission security of a system, where freshness is characterized by the age of information (AoI) metric and transmission security is represented by the proportion of obtained insecure packets over a long period of time. We assume that in a time slot, the source generates a new packet with probability p, and a packet arrives at the receiver with probability ${\gamma }_d$. With probability ${\gamma }_E$, a transmitted packet is eavesdropped. At the receiver, AoI is defined as the elapsed time since the generation instant of the latest obtained packet. A packet is defined to be insecure if it is obtained by the eavesdropper earlier than the receiver. To control the proportion of insecure packets obtained in the receiver, we propose using the probabilistic deletion/retaining scheme. More specifically, when a packet is eavesdropped before arriving at the receiver, this packet is deleted with probability $\delta$ or retained with probability $1-\delta$. Under this transmission policy, we derive the system’s average AoI which we call the average $\delta -$secure AoI, and investigate its relations with the insecure packet proportion, which is denoted as $\eta \left(\delta \right)$. The obtained formulas are then calculated in three special cases, including ${\gamma }_E=0$, ${\gamma }_E=1$, and $\delta =1$. We explain that these cases correspond to the average AoI of a basic status updating system with Ber/Geo/1/2 queue, packet with random geometric deadline in service process, and average age of secure information (AoSI), respectively. Numerical simulations of obtained results are provided. In particular, the tradeoffs between average $\delta -$secure AoI and $\eta \left(\delta \right)$ are analyzed in detail. We demonstrate that depending on the value of the eavesdropping probability ${\gamma }_E$, average $\delta -$secure AoI varies in different trends with $\eta \left(\delta \right)$, and in most cases the average $\delta -$secure AoI and $\eta \left(\delta \right)$ can be minimized simultaneously.