PoF: Proof-of-Following for Vehicle Platoons

Although a PoF primitive is general and can be applied to various mobile scenarios where verification of following is necessary, we explore it in the context of a vehicle platooning application. Platoons are led by a manually-operated or autonomous vehicle, which is followed by autonomous or semi-autonomous vehicles [11]. Platoon members coordinate driving by sensing the physical environment and also exchanging control messages that contain motion state information such as acceleration, velocity, steering, etc. [19]. Vehicles may be equipped with sensors (e.g., cameras, radar or LiDAR), and run control algorithms such as cooperative adaptive cruise control (CACC) [42, 25] to maintain a fixed distance.

To secure the platoon operation, the V2V messages are protected using cryptographic primitives. According to the C-V2X communication standard (3GPP TS 33.185 [3]), V2X communication is supported by a PKI that provides each vehicle a private/public key pair and a digital certificate as a proof of identity. These credentials can be used to establish trust among the platoon vehicles. We assume that digital signatures are used to prove the source authenticity of messages. Key management of digital identities and platoon secrets is beyond the scope of this work. A PoF involves the following entities.

Candidate ($\mathcal{C}$): The candidate vehicle wishes to join a moving platoon by sending a join request to the platoon verifier. The candidate is in possession of a public/private key pair $(pk_{\mathcal{C}},sk_{\mathcal{C}})$ and a certificate $cert_{\mathcal{C}}$ that is issued by a trusted certificate authority. The candidate vehicle is not allowed to receive or transmit any platoon coordination messages before it completes a PoF with the verifier.

Verifier ($\mathcal{V}$): The verifier is an existing platoon member that is responsible to verify the digital identity of the candidate and that he indeed physically follows the platoon. The verification process may involve the verifier alone or require interaction with other platoon members. Typically, the role of the verifier is assumed by the last platoon vehicle. Once a candidate is admitted, its public key is added to the list of platoon members by all the other vehicles in the platoon. The verifier is given a public/private key pair $(pk_{\mathcal{V}},sk_{\mathcal{V}})$ and a certificate $cert_{\mathcal{V}}.$

Attacker goals and capabilities. We consider an external attacker $\mathcal{M}$ who attempts to pass a PoF verification without following the platoon. The ultimate goal of the adversary is to be admitted into the platoon and inject falsified coordination messages. The attacker is assumed to be in possession of a valid public/private key pair $(pk_{M},sk_{M})$ and a certificate $cert_{M}$ issued by a trusted certificate authority. Further, the adversary can control the communication channel between ${\cal C}$ an ${\cal V}$ and inject, replay, modify, or delete messages of his own choosing. We consider three adversary models.

1. 1.

   Remote adversary. A remote adversary is stationed at some location away from the moving platoon and uses the existing infrastructure (cellular tower or road side units) to communicate with the platoon. The adversary is aware of the platoon’s route in advance and in real time. The adversary can use this knowledge to traverse and observe (e.g., measure the RF environment) the platoon’s route ahead of time. He requests to join the platoon, pretending to be a vehicle that follows the platoon.

2. 2.

   Following-afar adversary. A following-afar adversary tails the platoon from a long distance that does not meet the following distance requirement, but still allows him to communicate with the platoon. As an example, the adversary could be within a few hundred meters from the platoon. The adversary is also aware of the platoon’s route and can traverse it ahead of time. Moreover, since the adversary follows the platoon from afar, he can obtain more up-to-date RSS measurements in real time.

3. 3.

   Partially-following adversary. A partially-following adversary follows the platoon within the following distance only for a fraction of time and then trails the platoon from a far distance or becomes a remote adversary.

Man-in-the-middle attacks. For all three attack models, the adversary can launch man-in-the-middle (MiTM) attacks to gain admittance to the platoon. During a MiTM attack, $\mathcal{M}$ maintains parallel sessions with the candidate and the verifier in an attempt to pass a PoF verification while not following the platoon. A MiTM attack is shown in Fig. 3. A candidate $\mathcal{C}$ requests to join the platoon represented by verifier $\mathcal{V}.$ The adversary intercepts the request and opens parallel sessions with $\mathcal{C}$ and $\mathcal{V}$ in an attempt to be admitted to the platoon.

DoS attacks. We do not consider DoS attacks in which the adversary attempts to deny $\mathcal{C}$ from joining the platoon. Such attacks do not violate the PoF property.

To formally define the following property, we first give a definition of a route for a moving vehicle.

Based on the route definition, we now provide the definition of following.

Note that our PoF definition is a relaxed one as it only differentiates between the two extreme cases (always follows and always does not follow). The most strict PoF definition would output reject if the candidate $\mathcal{C}$ does not follow $\mathcal{V}$ for any of the $n$ time points (rather than all). However, even for legitimate following vehicles, some error or brief violation of following should be tolerated (e.g., when vehicles are human-driven, or not following using a strict CACC algorithm).

Because of this, our PoF definition is not simply a generalization of repeated distance bounding tests over a discretized route mobile setting. Note also that the definition does not place any restriction on the location sampling rate, which can be adjusted based on the application scenario. Moreover, the definition does not specify the relative positioning between the two moving objects. That is, the candidate can be around the verifier (either leading or following). This is to allow for a more general definition, which can be further restricted based on the application requirements.

Another aspect of the definition is that it only requires one-way PoF, from ${\cal C}$ to ${\cal V}.$ This provides protection of the platoon from non-following candidates. However, it does not protect candidates from joining fictitious verifiers. The same PoF definition can be applied with the roles of ${\cal C}$ and ${\cal V}$ reversed to allow for mutual verification of the PoF property.

The chief idea of constructing our PoF primitive is to exploit the randomness of the continuously changing environment due to mobility to prove continuous vehicle proximity. The selected modality for perceiving the environment should satisfy two important criteria.

1. 1.

   The environment should exhibit spatial and temporal decorrelation.

2. 2.

   The environment should exhibit high entropy and should not be repeatable.

Several modalities such as sound, vision, and RF may meet the two criteria. For instance, ambient sound while travelling on a freeway decorrelates rapidly with distance. Moreover, it varies significantly with time at the same location.

We have opted to exploit both the spatial and temporal correlation of ambient wireless signals. Specifically, a legitimate candidate who is closely following the platoon will observe a similar RF environment as the verifier. Besides, the RF environment is dynamic with time and location due to the constant change of the physical environment and the motion of other vehicles. The temporal variation (short channel coherence time) can prevent an adversary from pre-recording ambient RF signals and replaying them to a traveling platoon. Moreover, the RF modality is widely available for outdoor scenarios. Vehicles will already be retrofitted with cellular receivers to support the C-V2X standard [3]. In our PoF, vehicles exploit the ambient RF signals transmitted by cellular base stations (eNBs) along the traversed route.

In this section, we conduct a feasibility study on exploiting large-scale fading as a PoF modality.

Why large-scale fading? Large-scale fading is the result of signal attenuation due to signal propagation through large distances and diffraction around large objects in the propagation path. The wireless signal propagation loss can be represented using the well-known log-distance path loss model [31]:

where $L(d_{tr})$ is the propagation loss (or large-scale fading), $d_{tr}$ is the distance between the transmitter (TX) and receiver (RX), $d_{0}$ is the reference distance, $\overline{L}(d_{0})$ is the path loss at $d_{0}$, $\beta$ is the path loss exponent, and $X_{\sigma}$ is the shadow fading.

Since the large-scale fading is impacted by terrain configuration between the TX and RX, it brings randomness and unpredictability as the vehicles move. It is more stable when two closely-located vehicles sense ambient RF signals from far-away cellular base stations because the distance and diffraction from a base station to the two vehicles is approximately the same. Moreover, large-scale fading in mobile outdoor scenarios decorrelates more gracefully with distance and time than small-scale fading [12, 40].

Several models have been proposed to capture the spatial decorrelation of large-scale fading [12, 34, 40]. The exponential model is the one that has been most widely adopted [12, 31, 10]. In Fig. 4, let two vehicles $A$ and $B$ simultaneously measure the large-scale fading from the same base station, denoted by $L_{A}$ and $L_{B}$, respectively. The correlation $\rho_{d}$ between $L_{A}$ and $L_{B}$ is expressed as

where $d_{corr}$ is the decorrelation distance, which depends on the physical environment [4, 17]. From this model, we expect the correlation to be high for vehicles with distances smaller than $d_{corr}$, but to drop significantly for larger distances. Several $d_{corr}$ values have been empirically determined for different mobile environments [4, 17].

Experimental validation. To validate the spatial and temporal correlation properties of large-scale fading, we collected measurements of LTE signals in a freeway environment, which is the most relevant for platooning applications. The data was collected by driving a platoon of two vehicles $A$ and $B$ and simultaneously measuring the RSS (Note that, since RSS (in dB) is the difference between the transmit power and path loss, measuring RSS is equivalent to measuring the fading). from eNBs. The location and timestamp of each sample was also recorded to allow for time sample alignment and the computation of the separation $d.$ Figure 4 shows the topology used in the experiments, along with a sample realization of the measured large scale fading samples and the correlation model in eq. (2). The experimental setup is described in detail in Sec. V-A. We tested the following two main hypotheses.

1. 1.

   Spatial correlation decreases with distance. Here, we seek to verify the correlation model in [12] and determine the decorrelation distance $d_{corr}$.

2. 2.

   Temporal correlation decreases with time. Here, we seek to verify that the correlation of RF signals collected at the same location but different times decreases with the time difference.

To extract the large-scale fading and filter out the small-scale fading, we apply an $M$-point moving RSS average $\overline{\gamma}_{A}(i)$. We then compute the Pearson’s correlation coefficient $\rho$ as the correlation metric, defined as:

where $\overline{\gamma_{A}}$ and $\overline{\gamma_{B}}$ are the mean values of the RSS moving average over $n$ RSS entries for $A$ and $B$, respectively.

In this section, we analyze the security of our PoF protocol against different types of adversaries.

We developed two setups based on the NI USRP platform [1]. The first setup was employed in the freeway and urban driving experiments whereas the second setup was employed in the highway driving experiments.

Setup 1. We used a Nissan Sentra and a BMW X5 acting as $\mathcal{V}$ and $\mathcal{C}$, respectively. The two vehicles had cruise control capabilities (not adaptive), but were otherwise manually operated. We placed at the trunk of each vehicle the equipment shown in Fig. 9. A USRP N200 radio device was connected to a VERT900 antenna. The USRP was programmed to implement an OFDM receiver for LTE signals. It operated at 1.972GHz with a 4MHz bandwidth, which is the frequency used for personal communications service (PCS) in LTE. We set the gain of the antenna to 10dB and the sample rate to 20Hz. A Razer blade stealth laptop was connected to the USRP for recording the RSS data. The laptop was also connected to a GPS receiver to record positioning information at 5Hz sampling rate. The synchronization between the RSS and GPS data was achieved via the laptop clock.

Setup 2. In setup 2, we formed a two-vehicle platoon for driving in a highway environment. Here, ${\cal V}$ (Honda Pilot) led the platoon with cruise control engaged, whereas ${\cal C}$ (Toyota RAV-4) followed ${\cal V}$ with adaptive cruise control engaged. The candidate was equipped with a LiDAR to measure the distance to ${\cal V}$. This allowed for an easier and more accurate control of the separation distance between the two vehicles at highway speeds. Although setup 2 is superior to setup 1 from a platooning perspective, it was not always available to us to conduct the experiments that spanned many hours and days, so we limited it to highway experiments were maintaining constant distance presents more challenges. The data collection setup was identical to that of Setup 1, with the central frequency set to 875MHz with 4 MHz bandwidth and the antenna gain was 20 dB. The new frequency was selected based on the signal availability at the specific part of the highway were experiments were conducted.

The PoF test is controlled by the selection of the $N$, $M$, $K$, $\tau$, and $\alpha$ parameters. For clarity, we summarize the definition of these parameters in Table I. In this section, we show how to select the parameter in practice and then evaluate the PoF protocol in three driving environments.

To select $N$ and $M$, we performed experiments on a freeway section of length 1.4 miles using Setup 1. The particular section was not accessible to other traffic and was located next to a highway. This presented an ideal situation for safely controlling the following distance. The two vehicles were driven at 30Mph over multiple runs and at different following distances. We collected RSS data using the radio testbed and processed the collected data using various test parameters.

Selecting $N$. The subset size $N$ determines the number of samples used per correlation test. It must be long enough to ensure that RSS values exhibit high correlation, but should not prolong the test duration. We experimented with different lengths $N$. For each $N$, we reused the second-half samples in each subset to form the first-half samples for the following subset to reduce the test duration. Figure 10(a) shows $\rho$ as a function of the following distance $d$. Generally, when a larger $N$ is selected, the correlation increases (except for ranges over 90m where the two RSS sequences are uncorrelated). From Fig. 10(a), we can see that beyond $N=400$ the gains in correlation are relatively small. Therefore, we fix $N=400$ for all the following evaluations.

Selecting $M$. The length of the moving average window impacts the elimination of small-scale fading. Intuitively, a larger window leads to a more stable moving average, and a higher correlation $\rho$, but the moving average becomes more predictable. In Fig. 10(b), we show the correlation $\rho$ as a function of the following distance for different $M$. As expected, we observe an increase in correlation with $M$ at short distances, whereas the impact of $M$ is small for large distances because the two RSS sequences are uncorrelated. Moreover, the increase in correlation diminishes after $M=20$. Based on these observations, we set $M=20$.

Selecting $\tau$, $K$, and $\alpha$. Let $f=\Pr(\rho_{k}(d)\geq\tau)$ denote the probability of passing a single correlation test when an RSS subset $\Gamma_{k}$ is used to compute $\rho_{d}(k)$. This probability depends on the selection of $\tau$ and the following distance $d$. For a total of $K$ tests, a PoF is passed if $\sum_{k=1}^{K}\frac{I(\rho(k)\geq\tau)}{K}\geq\alpha.$ Assuming independent tests due to the use of different subsets, the probability of passing a PoF verification consisting of $K$ correlation tests is

where ${K\choose x}$ is the binomial coefficient. Let $F_{C}$ denote the probability of passing the PoF verification for ${\cal C}$ and $F_{M}$ to be the passing probability for $\mathcal{M}$. Probability $F_{C}$ is derived from Eq. (4) by substituting the probability $f$ of passing a single correlation test at $d<d_{ref}$, given the selection of $\tau.$ Similarly, $F_{M}$ is derived from Eq. (4) by substituting the probability $f$ of passing a single correlation test at some distance $d>d_{ref}$, The equal error rate ($EER$) is defined as

We aim at selecting $\tau^{*}$ that minimizes the $EER$. To understand the interplay between $\tau,$ $K$, $\alpha$ and $F$, we generated the PDF of the correlation $\rho$ for three representative following distances. The respective PDFs are shown in Fig. 10(c). From the PDF, one can select a desired $\tau$ to satisfy a required passing rate for valid candidates for a given $d_{ref}.$ For instance, we chose $\tau=0.54$ for $d=20m$ and $\tau=0.28$ for $d=40m.$ A $d=90m$ is representative of a following-afar adversary.

Given $\tau$, we performed an exhaustive search over the two remaining free variables $K$ and $\alpha$ to minimize the $EER.$ Here, we limit $K$ to 40 to ensure that a PoF test adheres to a time limit and also limited $\alpha$ such that $\lceil\alpha K\rceil$ takes integer values between 1 and $K$. Figure 10(d) shows the $EER$ as a function of $K$ when the optimal $\alpha$ is selected. As expected, the $EER$ decreases with $K$. Here, a $K$ that satisfied a desired $EER$ requirement can be selected at the expense of a PoF test duration. For the freeway experiments, we set $K=20.$

An alternative method for selecting $\tau$ and $\alpha$ under fixed $K$ is to first determine two following distances from the platooning requirements. The first distance is that of the valid candidate, namely $d_{ref}$, whereas the second is that of the afar adversary that we try to prevent against. We then compute the threshold $\tau$ for a single correlation test from the exponential model in Eq. (2) by setting $d=d_{ref}$. Once $\tau$ is fixed, we select $\alpha$ to maximize the gap between $F_{C}$ and $F_{M}$. Given that the average correlation model may not hold for all driving environments, we opted to use the exhaustive search method to explore the performance of the PoF. These methods require the use of at least one trusted vehicle besides the verifier in the platoon to calculate passing rate $f$. If there is only one vehicle in the platoon, ${\cal V}$ has to select $\tau$ from eq. (2). Except $\tau$, all other parameters ($N,M,K,\alpha$) can be preset since they are stable in different environments.

For the freeway experiments, we employed Setup 1, with the two vehicles driving at approximately at 30Mph. Because the specific freeway section was closed, we were able to control the following distance between the two vehicles. We drove the vehicles at following distances between 10m - 115m.

Based on the parameter selection we discussed in the previous section, we set $N=400,$ $M=20$, and $K=20.$ We then performed an exhaustive search to find the optimal threshold values $\tau^{\ast}$ and $\alpha^{\ast}$ that minimize the $EER.$ Figure 11 shows the minimum EER for different values of valid following distance $d_{ref}$ when the adversary follows at 90m. The optimal values of $\tau^{\ast}$ and $\alpha^{\ast}$ that minimize the $EER$ for each following distance are also shown. First, we observe that our method achieves a fairly low $EER$. Moreover, the optimal $\tau^{\ast}$ and $\alpha^{\ast}$ do not vary significantly with the change of $d_{ref}.$

In Fig. 12, we show the PoF passing rate as a function of the following distance for the optimal $\tau^{\ast}$ and $\alpha^{\ast}$ values obtained from minimizing the $EER$. When a candidate is within a following distance between 10m-40m the passing rate is close to 1. The passing rate drops to zero for distances larger than 90m. The method leaves a “guard” zone between 40-90 where the passing rate is from 0.2 to 0.4. This zone cannot be considered to be secure as an adversary following in this zone could pass a PoF test with non-negligible probability. This is because the correlation degrades gracefully with distance and does not exhibit a step-function type of behavior.

Ideally, for any environment, we estimate the distribution of $\rho$ with different distance, and set $\tau,N,\alpha$. However, in practice, the distance between two vehicles is difficult to control due to the traffic, especially in urban and highway areas, which thwarts us from selecting $\tau$ with CDF of $\rho$. Instead, we are interested in evaluating PoF for certain given distance bound, from which we select $\tau$ based on the statistically relationship between the passing rate of a single correlation and the threshold $\tau$. After that, $K$ and $\alpha$ can be chosen with minimum $EER$. For all the following results, we also use 30$\%$ of experimental data as a training sequence for parameter selection, and the remaining 70$\%$ for testing.

For the urban area experiments, we used Setup 1 to drive the two vehicles along a 2.5-mile route inside Tucson city from River to Grant road, as shown in Fig. 14(a), several rounds for one hour. Except stops at red lights, the vehicles normally run at a speed up to 40Mph and always followed each other. Figure 13(a) shows the following distance $d$ over time. The following distance was fairly stable with an average of about 11 meters. Since the mixed traffic did not allow us to precisely control the following distance $d$, we did not obtain the PDF of the correlation for different distances as we did for the freeway experiments. Thus, we select optimal values of $\tau$, $K$, and $\alpha$ by minimizing the $EER$.

We ran experiments on a highway environment using Setup 2. Two platooning vehicles were driven on the piece of I-10 highway, shown in Fig. 14(b), from exit 250 to 257 for 6.4-mile back and forth over a period of 1.5 hours. The distance between ${\cal V}$ and ${\cal C}$ was maintained using ACC and remained quite stable (see Fig. 13(c)), with a 53.4m average.

We further implemented a partially-following adversary who was within following distance for a fraction $\theta$ of a PoF duration, whereas he remained outside the following distance for the remaining PoF time. In Fig. 17, we show the PoF passing rate as a function of $\theta$. The test parameters ($N,K,M,\tau,\alpha$) were set to the values indicated in Sec. V-D for the urban environment and Sec. V-E for the highway environment, assuming a following-afar adversary. The passing rates are averaged over 11 PoF runs for the urban and 13 runs for the highway environment, respectively. We observe that to pass the authentication with non-zero probability, the adversary has to follow the platoon at least 50% of the PoF duration (in the order of 100 seconds). For the urban environment where the RSS fluctuates more rapidly, the adversary is guaranteed to pass the PoF (passing rate equal to one) if he follows 90% of the time, whereas this percentage drops to around 70% on the highway environment. This indicates that a partially-following adversary could be successful, if he dedicates a significant portion of time in truly following the verifier.

Another approach for a remote adversary is to predict real-time RSS data from pre-recorded data. We use approximate entropy $AE(\cdot)$ to evaluate the randomness of the moving average values used to compute the correlation. Approximate entropy is preferred to sample entropy because it is a more accurate randomness measure when the number of samples is limited [29]. We calculate the approximate entropy of $\overline{\gamma_{V}}$ following standard steps in [48, 29]. For the two parameters $m$ and $R$ required for approximation entropy calculation (i.e., the length of compared run of data and the similarity criterion, respectively), we use typical values $m=2$ and $R=0.2\times std(\overline{\gamma_{V}})$ as done in [29], where $std(\overline{\gamma_{V}})$ is the standard deviation of $\overline{\gamma_{V}}$. The $ApEn(\overline{\gamma_{V}})$ for the urban and highway environment is 0.4730 and 0.3088, respectively. The $ApEn$ of a perfectly repeatable time series is about 0 [48], and is around 0.6 for binary expansions of some common irrational numbers [32]. Hence, our results indicated that the large-scale fading in dynamic traffic is random and unpredictable enough. Furthermore, it would be difficult for the attacker to pass the verification by predicting the RSS measurement of verifier $\mathcal{V}$.

The duration of each PoF protocol is dominated by the RSS collection phase. The number of the RSS samples needed for the test is decided by the parameters we select. Since we reuse $N/2$ RSS samples for two consecutive subsets, it requires $(K+1)\times N/2$ RSS samples to complete $K$ correlation tests, which takes $\frac{(K+1)\times N}{2\times\text{(Sampling Rate)}}$ seconds for data collection. For the urban and highway environments, we fixed $N=400$, $K=20$, and our sampling rate was 20Hz. Therefore, about 200 seconds are required for each PoF protocol run. This is a reasonable cost as vehicle platoons are intended to travel for relatively long periods of time.