## 5 Application to Platoon Protection
### Effect of Whisper Check With Platoons  
We first measure the time it takes for the last vehicle \(Z\) of the entire vehicle groups to pass through the endpoint of the 10 km stretch, while varying \(\alpha\), \(\beta\) and \(\gamma\) (\(5\leq\alpha\leq 10,1\leq\beta,\gamma\leq 10\)). It will reveal any accumulated delay effect if the vehicles in front are affected by the forged message attacks. Specifically, without the whisper check, each vehicle with a block front view will believe that \(G\) is actually present at the forged coordinate. If the vehicle determines that there is a risk of colliding with \(G\), it will activate its brake. For this, we assume that each vehicle brakes at 30% of the maximum deceleration when the time to collision (TTC) with the preceding vehicle is 2.6 s, and at the maximum deceleration when the TTC is 1 s to prevent collision [PERSON] _et al._ (2018). Each vehicle activates the brake until its LoS sensors finally perceive that \(G\) is not actually present. When the whisper check is not employed, Figure 11 shows the velocity changes of some of the non-platoon vehicles in the first vehicle group under the forged message attack that a ghost vehicle is at \(G\). We assume \(\alpha=\beta=10\) in this example. Since \(N_{1}^{1}\) has the LoS for the ghost vehicle \(G\), it can use its sensors to perceive that \(K\)'s messages are forged and keeps going at the same velocity as before without braking. But as for the other vehicles in the group, they brake to slow down due to the absence of LoS to \(G\). So, \(N_{1}^{2}\) begins to brake at 30% of the maximum braking when its TTC to \(G\) reaches 2.6 s. But as soon as \(N_{1}^{1}\) passes the forged position, the LoS to the forged coordinate is clear for \(N_{1}^{2}\). Its sensors detect that \(G\) does not exist, so accelerates again to reach the target safe distance with \(N_{1}^{1}\) (at around \(t=90\) s in Figure 11). Notice that the velocity of the following vehicles more severely decreases towards the end of the non-platoon vehicle column. Due to the slowed vehicles in front, the latter vehicles spend more time until they reach \(G\), when their sensors find the absence of the ghost vehicle. Some middle vehicles are not shown for readability, but this accumulated slowdown effect is amplified to a very large and elongated velocity instability as it propagates to the last non-platoon vehicle \(N_{1}^{10}\). From the velocity changes of \(N_{1}^{10}\), we observe in the simulation data that its acceleration and deceleration occurs as many as 60 times, potentially causing discomfort to the passengers. The velocity fluctuation in the non-platoon vehicles directly affects the immediately following platoon vehicles. The leader of the platoon \(P^{1}\) that immediately follows \(N_{1}^{10}\) has to slow down due to the attack and then increases its speed to the original speed only after its other sensors check the absence of \(G\). However, unlike the non-platoon vehicles, the platoon members of \(P^{1}\) are controlled by the leader, so at the command of the leader, they move at the same speed. Recollect that the platoon members are prohibited from accelerating to more than 80 km/h. The other platoons \(P^{2},\ldots,P^{10}\) experience similar dynamics. Furthermore, the speed of \(P^{i}\) decreases more than that of \(P^{i-1}\) as the effect accumulates. Figure 12 shows the velocity changes of some of the platoons. In general, \(P^{i}\) suffers \(i\) episodes of significant velocity fluctuation due to the remote attack. We observe that the latter platoons, most notably \(P^{10}\), suffer from elongated and repeated instability. Using the whisper check can drastically reduce the undesirable impacts of the remote forged position attack such as exposed by Figures 11 and 12. Figure 13 sheds light on these impacts of whisper checks from yet another angle, the distance loss.