# Achieving Differentially Private Location Privacy in Edge-assistant Connected Vehicles

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6 IEEE INTERNET OF THINGS JOURNAL 6 Fig. 4: Privacy-preserving Location Usage Framework Ï Ï Ï Ï Fig. 5: Ensuring the differential privacy in different ranges definition restricts the advantage that an adversary can get from observing the obfuscated location l 0. Note that we should ensure the differential privacy in a circle with a radius of r = r, rather than r. We prove its reasonableness by the Fig. 5. We consider the extreme circumstance that the real location l is located in the circle, as shown in Fig. 5. If we ensure the (r, ɛ, δ)-geo-indistinguishability (Fig. 5 (left)), only part of the circle S can meet the privacy guarantee (the shadowed part). Therefore, it is reasonable to achieve (r, ɛ, δ)-geo-indistinguishability. ) A Mechanism for (r, ɛ, δ)-geo-indistinguishability: In this section, we will propose the concrete method to add the noise which can fit the (r, ɛ, δ)-geo-indistinguishability. We propose a scheme to generate the noisy location which follows two dimensional Gaussian Distribution. The probability density function of two dimensional Gaussian distribution is given by x + y f(x, y) = πσ e σ () where σ is standard deviation. Then we give the the privacy loss which is bounded by ɛ to obtain σ which fits the (r, ɛ, δ)- Geo-indistinguishability. The privacy loss P ri loss is defined as follows: P ri loss = ln + y e x σ e (x x) + (y y) σ = x + y σ + (x x) + (y y) σ (x x + y y) + ( x) + ( y) = σ ɛ (3) Which can be converted into: (x x + y y) + ( x) + ( y) σ x x + y y + ( x) + ( y) ɛσ According to the Cauchy-Buniakowsky-Schwarz and ( x) + ( y) ) r, we can obtain: x + y ɛσ r r As defined by the (r, ɛ, δ)-geo-indistinguishability, we ensure the privacy loss bounded by ɛ with probability at least δ, which means: (4) (5) P [ x + y ɛσ r r ] < δ (6) σ r ɛ ln δ + ɛ (7) The Guassian nosie with parameter σ r ɛ ln δ + ɛ is (r, ɛ, δ)-geo-indistinguishability.

7 IEEE INTERNET OF THINGS JOURNAL 7 3) Obfuscation with Gaussian Noise Fitting (r, ɛ, δ)-geoindistinguishability: In this section, we explore how to add the Gaussian noise fitting (r, ɛ, δ)-geo-indistinguishability to an actual location. The basic idea is that we shift the location by adding the noise generated randomly from the following two dimensional Gaussian distribution: f(x, y) = x + y πσ e σ, σ r ln ɛ δ + ɛ (8) which can be transformed into the following form under the polar coordinates: f(r, θ) = r r πσ e σ (9) where r is the distance between the actual location l and the noisy location l 0, and θ is the angle that indicates the direction of the line l l 0. The joint probability density of r and θ are described as follows: f(r ) = π 0 f(θ) = r r πσ e 0 σ dθ = r r r πσ e σ e r σ dr = π σ (0) () From the above equations we can see that these two variables are independent, which means we can draw them separately. Assuming the actual location is l = (s, t), the noisy location that follows two dimensional Gaussian distribution can be generated as l 0 = (s + r cos θ, t + r sin θ) () 4) Optimal Privacy Mechanism Under the Tolerable Service Quality Loss: By deploying the differential privacy protection mechanism M, we can ensure the attacker cannot infer the actual location even if the attacker has the prior knowledge that the vehicles location must be within the coverage of the edge node. However, the noisy location must have the impact on the service quality. It is reasonable to obtain the maximum privacy level under the tolerable service quality loss. In this section, we formalize the problem as an optimization problem between the privacy and the service quality. First, we define the service quality based on the utility notion which is introduced in [0]. The service quality can be represented by the tolerable maximum offset distance D and the probability γ: Definition. ((D, γ)-service Quality) Let d(,) denote the Euclidean metric and l be the actual location of the vehicle, the differential privacy protection mechanism M satisfies ((D, γ)-service Quality) if: P [d(l, M(l )) D] γ (3) Note that d(l, M(l )) = r. Therefore, the probability can be computed by the cumulative distribution function (cdf) F (r ): F (r ) = e r σ (4) P [d(l, M(l )) D] = F (D) = e D σ γ (5) We assume the tolerable service quality loss is (D, γ ), which means the minimum service quality that the vehicle can tolerate. This constraints the privacy level, which can be used as a threshold for the mechanism M. Therefore, the optimization problem (find the optimal privacy level) under the given service quality could be described as follows: Minimize P ri loss (6) subject to P [d(l, M(l )) D ] = e D σ γ (7) σ r ln ɛ δ + ɛ (8) P ri loss ɛ (9) From the optimization problem, we can get the optimal two tuples (ɛ, δ ) (ensuring P (pri loss ɛ ) δ ) under the specified (D, γ ), which has the following relationship: ɛ ln γ (r ln r δ = 4 ln γ ) D r ln γ D (0) Similarly, we can set the optimization problem for finding the optimal service quality (D, γ ) (ensuring P [d(l, M(l )) D ] γ ) under the given privacy loss bound (ɛ, δ ) with the same constraint conditions: D = r ln γ ɛ (ln δ + ) () ɛ B. Privacy Level Adjustment (PLA) Note that, under different situations users have different privacy requirements. For example, when people stays at their top locations (e.g., home and office) where they always go, they want to protect these sensitive locations with a higher level of privacy at the expense of the service quality. However, when they are in public regions, it is not reasonable to sacrifice so many service quality to protect their location privacy. Therefore, it is reasonable to adjust the privacy level ɛ which is bounded by the (ɛ, δ) to obtain the better service quality. This requirement can be achieved by the context-based privacy protection scheme proposed in [33], which can automatically learn users privacy preferences based on the users habits by using a decision tree model. VII. EVALUATION In this section, we demonstrate the effectiveness and efficiency of the proposed differentially privacy-preserving location-based service usage mechanism by evaluating its accuracy on different applications. Then, we explain its efficiency under different parameters with respect to privacy level and service quality.

8 IEEE INTERNET OF THINGS JOURNAL 8 Weather APP POI Query POI query with Extended Radius δ = 0.05, γ = 0.05 δ = 0.05, γ = 0.0 δ = 0.0, γ = 0.05 δ = 0.0, γ = 0.0 Accuracy r/d ln() 5ln(3) 5ln(4) ε Fig. 6: The impact of the deployment of the framework on different applications A. The Effectiveness of Pri-EVN We consider the proposed location-based subscription applications in the edge-assistant vehicular networking scenario. In our setting, drivers communicate with the honest-butcurious service provider via an edge node. In this paper, we consider two types of applications which have the different requirements for location accuracy: low-location-sensitive applications and high-location-sensitive applications. We implement the proposed privacy-preserving mechanism using Java, including random parameters generation, coordinate transformation, and the result analysis. First, we evaluate the accuracy of the proposed framework when using the different types of applications. To assess the impact of our framework on different scenarios, we deploy the differential privacy-preserving location-based service usage mechanism on two typical vehicular applications: Weather APP and POI query. Note that, we use the API provided by the Baidu Map for POI query. We evaluate how much accuracy will be reduced when deploying our mechanism with different privacy loss with bound ɛ. In particular, the accuracy refers to the difference between the query results by these two locations (actual location and the noisy location) and we use multiple (e.g., 0) query results as the average accuracy to eliminate the error. We choose the different ɛ as used in [0], and the result between the accuracy and ɛ under different applications is shown in Fig. 6. In this figure, we can see that our mechanism has no effect on lowlocation-sensitive applications. For the high-location-sensitive applications, the accuracy decreases by approximately 5% when deploying our differential privacy-preserving locationbased service usage mechanism. Therefore, it is better to use the alternative method: increasing the query radius to ensure the accuracy. We know the maximum offset ratio under the specific ɛ, therefore we can extend the query radius by the maximum offset distance D. Note that, the offset can be eliminated by filtering the results. The accuracy under this query radius is shown by the third bar (POI query with extended radius). Then, we evaluate the relationship between the privacy loss bound ɛ (where ɛ is the privacy loss bound) and service privacy loss bound ε Fig. 7: The relationship between ɛ and r D quality r D, where r is the radius and D is the maximum offset distance with the privacy protection mechanism M (D is bounded by P [d(l, M(l )) D] γ). We evaluate the relationship with very small parameters δ and γ, which means a very strong bound in the range of D and ɛ. The result under different parameters (δ = 0.0, 0.05 and γ = 0.0, 0.05) is shown in Fig. 7. As shown in this figure, the privacy loss bound ɛ and the service quality r D have the linear relationship, which means with the increase of privacy protection level, the service quality will not be drop too fast. Therefore, under different scenarios as described in the previous section, drivers could adjust the privacy level to find the tradeoff with the service quality. B. The Efficiency Under Different Parameters As described in the previous subsection, different applications have different requirements with respect to the privacy level and the service quality. However, because the differential privacy-preserving mechanism has the probabilistic nature, it is impossible to guarantee the privacy level and the service quality with 00% probability. In this section, we further evaluate the impact of parameters (δ, γ) on privacy level and the service quality under the optimal situation, and discuss how to adjust them to fit different scenarios. First, we illustrate the relationship of (ɛ, δ) under the given service quality, which is shown in Fig. 8. From this figure we have the following insight: with the decrease of δ (the confidence of the privacy loss bound), the privacy loss bound ɛ will decrease under the given service quality. Therefore, we can slightly increase δ to get the higher privacy level ɛ when deploying our mechanism on applications which do not need the strong confidence. For example, when deploying the mechanism on the users traces, attackers cannot recover the trace even if a small portion of the locations has the risk of leakage. Fig. 9 shows the relationship of D and γ under the specified privacy level and the fixed r = 0. (the same parameter as used in [0]). When ɛ = 5 ln(), δ = 0.0, the offset distance can be controlled within 500m with a probability of 0.95, within 440m with a probability of 0.9. Similar to the privacy level, we can also adjust γ to obtain the higher service quality.

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