# CAVVPM: Challenge-Based Authentication and Verification of Vehicle Platooning at Motorway
## 3 The _CAVVPM_ Pof Protocol
### Parameter Selection  
Checkpoint selection. The verifier calculates a discrete range S around the nominal following distance dref to choose each checkpoint \(d_{i}\). Assuming UV is the verifier's velocity,  
Figure 4: The CAVVPM protocol. we may write \(gap\ d_{ref}/U_{V}\) in the usual time gap notation to represent following distances of \(d_{ref}\). We let gmin be the minimum and maximum safety time gaps between any two vehicles. With this, the verifier determines an unbroken range \([g_{min}\cdot U_{V},g_{max}\cdot U_{V}]\) for choosing milestone. A discrete range of M checkpoints \(S=\{\ s_{1},s_{2},\ldots,\ s_{M}\}\) is calculated by dividing this range into equal pieces with a length of \(2p\) (twice as high as the radar resolution \(\rho\)). \[M=\frac{(g_{max}-g_{min})\cdot U_{V}}{2\rho}+1\]  
From \(S\)., a random checkpoint is picked for each task. We consider a verifier moving at \(U_{V}=30\) m/s to illustrate the checkpoint selection procedure, as shown in Figure 5 and the simulation setting shown in Figure 6. We let \(g_{min}=1\) s, \(g_{max}=2\) s with a resolution of radar \(\rho=0.3\) m. Calculations are carried out by the verifier \(M=\frac{600-300}{2-0.30}+1=51\) checkpoints that are 30 to 60 metres apart. For each candidate, a random checkpoint is selected from among the 51 available by the verifier. **Deadline selection:** In order to arrive at the given checkpoints safely, the deadlines may be chosen in any way. We consider a relative velocity differential \(U_{ref}\) (positive or negative) to travel the distance \(\left|\left|d_{i}-d_{ref}\right|\right|\) as an easy approach to pick a deadline for checkpoint \(d_{i}\). In this scenario, the time limit is set to \(t_{i}=\frac{d_{i}-d_{ref}}{\rho_{i}}+\epsilon\), where the candidate's motion may have a modest amount of tolerance (\(\epsilon\)) built in. Figure 5: Setting a range for candidate C’s checkpoint. Figure 6: ACC Parameters. In contrast to the automatic nature of platooning and customer engagement, this simplistic model assumes that the candidate's velocity changes quickly rather than gradually. Alternately, the verifier may use an ACC model that considers aspects such as safety and motion smoothing to compute deadlines for the system. An optimal control-based intersection CACC (iCACC) system was proposed by [PERSON] et al. According to the simulation results, the suggested solution reduces energy consumption by 45% and the average intersection latency by 90%, respectively [12]. A convex optimization problem with linear constraints was later created for a group of coordination leaders and their coordination followers by [PERSON] et al. to optimize the fuel savings of a Truck CACC system's coordination leaders [13]. To reduce energy use and pollutant emissions at various phases of the CACC operation, [PERSON] et al. suggested a platoon-wide Eco-CACC system [14]. The intra-platoon vehicle sequence was the subject of another investigation using optimization methods [15]. To penalize relative position mistakes between nearby CACC vehicles, [PERSON] et al. constructed centralized linear quadratic optimal control formulations [16]. They concluded that stability and detectability would decline as the size of the CACC system increased. To determine the ideal engine speed to reduce fuel consumption, [PERSON] et al. explored the cooperative look-ahead control of a heavy-duty CACC system [17]. It is possible to use any ACC controller here; however, we prefer the one provided in [18]. Our ACC parameter in simulation is presented in Figure 6.  
The deadline is computed as follows using this model. We allow for a challenge d that corresponds to a time gap of \(T=d/\dot{x}_{C}\), where \(\dot{x}_{C}\) represents the person's current pace. \(\Delta_{t}\) is the number of iterations in the algorithm. 1.