## 3 Neighbor Verification through Low-Power Beacons
### Range Extension  
One obvious question will be about the appropriate value of the whisper range \(d_{W}\). It should depend on applications that require contents plausibility checks. What if an application requires a wider checking range? One may argue that we could increase the Tx power of whispers to extend the range, but it would increase the channel utilization as well. As a consequence, it can trigger the BSM congestion control [24] so that fewer BSMs are transmitted and the vehicle position tracking error increases. In essence, it can have safety ramifications. In order to extend the range of whisper check to two hops without such side effects, we could take an approach similar to [PERSON] et al. [5]. Namely, when \(W_{V}\) passes the whisper check at \(U\), we can let \(U\) not only trust BSMs from \(V\), but also those from the vehicles in \(L_{V}\). So \(U\) can identify two-hop trusted neighbors \(N_{U}^{t^{2}}=\bigcup L_{x}\), where \(x\in N_{U}^{t}\).  
Unfortunately, under the two-hop whisper check, when the distance \(d_{K}\) between the attacker's true position and the message receiving vehicles is less than \(d_{W}\), the attacker can also exploit the overheard whisper identifiers (WIDs) to extend the attack range. Figure 2 depicts the situation. Here, the attacker \(K\) can obtain \(I_{V}\) from \(L_{A}\), for \(A\in N_{V}^{t}\) and \(d(A,\ K)\leq d_{W}\). Echoing this overheard \(I_{V}\) in its whisper \(W_{K}\), the attacker can extend its attack range from \(d_{W}\) to \(2d_{W}\). Not only that, after \(V\) passes \(K\), a similar situation can happen if there is another intermediate vehicle (e.g., \(B\)) between the attacker and the victim.  
Figure 2: Distances in credit-based whisper.  
Furthermore, there are two more factors that can extend the attacker's reach even beyond \(2d_{W}\). The first is the whisper ID update. Recollect that the WID is changed every \(t_{u}\) (see Section 3.3). If vehicle \(V\) moves at speed \(v\), it can add as much as \(vt_{u}\) to \(d_{K}\) because \(V\) can continue to use the same \(I_{v}\) even after moving more than 2 \(d_{W}\) away from \(K\), before the next update instant. The second factor is the message gap between consecutive whispers. Suppose \(V\) changes its WID from \(I_{v}\) to \(I_{v}^{\prime}\). Since the update will be reflected in the next whisper to transmit, a neighbor \(U\) can send its BSM containing the old WID \(I_{v}\). If \(V\) performs the whisper check against its new WID \(I_{v}^{\prime}\), this legitimate BSM from \(U\) will be filtered. Therefore, before whispering with the new WID, each vehicle should accept BSMs with its old WID. Assuming the whispering rate of \(c\) Hz, neighbors BSM with the old WID can arrive as late as \(1/c\) second after the update, which we reflect to the attacker's overhearing range calculation. In total, the attacker can attempt to deceive a vehicle at distances  
\[d_{X}\leq 4\cdot d_{W}+v\cdot(t_{u}+1/c),, \tag{1}\]  
where \(d_{X}\) is the maximum distance that the attacker can exploit \(V\)'s WID. We stress that the extended attack range \(d_{X}\) is not where the attacker can mount the attack from. The attacker should still be physically within \(d_{W}\) of the road to overhear the whispers. In this paper, however, we shun away from the multi-hop whispering possibilities due to the potential to extend the attacker's capability. We leave it as future work and focus on exploring the efficacy of the single-hop whispering.  
Note that the changed mobility model can affect the attack distance \(d_{X}\). In particular, the increased vehicle speed \(v\) affects Equation (1), extending the attack distance. In this case, according to the same equation, more rapidly changing the whisper ID (namely, smaller \(t_{u}\)) can be used to counter it.