# Track Me If You Can: On the Effectiveness of Context-based Identifier Changes in Deployed Mobile Networks

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8 Algorithm 2 Position Estimation Input: P[] is the list of positions of sniffing stations observing the message. P[i] = (P x [i], P y [i]) are the x and y coordinates of the i th sniffing station observing the message Input: D[] is the list of distances (computed from signal strength indicator) from each sniffing station observing the message Output: p, the estimated position of the message 1: n = P, the number of sniffing stations 2: m = D, the number of distances 3: if not (n = m) OR n = 0 then 4: return error 5: else if n = 1 then Only sniffing station i observes the message 6: return P[i] 7: else if n = 2 then Only sniffing stations i and j observe the message 8: return (P x [i] + P y [i] + P y [ j] P y [i] ( D[i] + D[ j])/ D[i] ) P x [ j] P x [i] ( D[i] + D[ j])/ D[i], 9: else if n = 3 then Only sniffing stations i, j and k observe the message 10: return trilateration(p[i], D[i], P[ j], D[ j], P[k], D[k]) 11: else 12: Let l, m, n be the three sniffing stations in P[] with the smallest distances 13: return trilateration(p[l], D[l], P[m], D[m], P[n], D[n]) 14: end if 4.1. Probabilistic Tracking Framework We model the daily observations by the adversarial AP mesh network by using a Markov chain, where a state of the system is defined as the set of ordered observations with the same pseudonym and the transition probability gives the probability of going from one set of observations to the next. As the total number of observations is finite and the transitions probabilities are time-invariant (as discussed below) with a fixed probability distribution on the initial states, the proposed model can be characterized as a finite state first order Markov chain. Let S be the state space and each state s S be represented as a triple of the form s = (π, e start, e end ), where π Π is a pseudonym and e start, e end are temporally 1 the first and last event respectively using the pseudonym π. Here, t start (s) = t(e start (s)) and t end (s) = t(e end (s)) are the corresponding start and end times of the state s, respec- 1 An implicit assumption here is that no pseudonym is reused. tively. A similar notation is used for the observers and received signal strengths of the state. The transition probability matrix is defined by a transition function P : S S [0, 1] that satisfies the following two constraints: 1) Valid- s j S P(s i, s j ) = 1 s i ity: S and 2) Time monotonicity: P(s i, s j ) = 0 s i, s j S such that t end (s i ) > t start (s j ). Each entry in the transition probability matrix P[i, j] represents how likely the adversary considers state s j to follow s i ; it gives the likelihood of the adversary to observe events in s j immediately after observing events in s i for any user. The transition probability matrix is user-invariant, i.e., the adversary s transition function is the same for all users. The tracking success of the adversary depends on how well the transition function is defined and how close it is to the actual transitions. In this work, we estimate the transition function by using two heuristics that intuitively capture the likelihood of observing a set of events from some previous events. 1. Common sniffing stations: The probability that a state s is the next state of state s is proportional to the number of common sniffing stations in the events observed in s and in s. The higher the number of common sniffing stations between s and s, the higher the probability of transitioning from s to s. 2. Speed matching: As each event has position and time information, a notion of speed between two events can be defined as the Euclidean distance between the (position of) two events divided by the time difference between the events. Then, according to our speedmatching heuristic, the probability that a state s follows state s is 1 v(s) v(s ) /v max, where v(s) is the speed of state s and v max is the maximum speed (5m/s in our case). The tracking framework and the transition probabilities described above are for a single user, given his initial state (or some probability distribution on it). In this case, the attacker wants to determine a single (most probable) path in the state space corresponding to the user in the initial state. It is also possible to track multiple users simultaneously using the above model, i.e., the attacker will attempt to find several non-overlapping paths in the state space, given the initial states of multiple users. As the transitions in this case are between sets of states or multi-states (one state for each user being tracked), the transition probability function needs to be accordingly modified. The transition probability of one multi-state to the next can be estimated by normalizing the sum of the individual transition probabilities in the multi-set. Specific details of the single user and multi-user transition probability matrix computations can be found in [11].

9 4.2. Tracking Strategies We propose two straightforward adversarial tracking strategies based on the above tracking framework Locally Optimal Walk (L-WALK) The L-WALK algorithm (Alg. 3) reconstructs the user trace by performing a locally-optimal walk in the state space. In other words, at each state (of the walk), starting from the initial state, the next state candidate with the highest probability is selected, until there are no further candidates. L-WALK produces an ordered sequence of states T = (s 0, s 1,..., s k ) (k > 0) such that P(s i, s i+1 ) > P(s i, s ) s S \ s i+1 i = 0, 1,..., k. Algorithm 3 Locally optimal walk (L-WALK) Input: Initial state s 0, heuristic function P Output: Trace T = (s 0,..., s k ) 1: T (s 0 ), continue True 2: repeat 3: Let c be the next state candidate with the highest probability 4: Append c to T 5: until no more candidates 6: return T From Alg. 3, we can see that L-WALK iteratively builds a walk by selecting the probabilistically best next state at each iteration and stops when no more states are available. It is possible to improve L-WALK by using additional reference points along the walk. For instance, if the adversary is able to ascertain that some state s j is associated to a given user, she can use s j to better direct her search in cases where multiple next states are equally probable at a given state. Due to this additional knowledge, paths that do not pass through s j can also be discarded by the adversary. More than one such reference point will further improve the accuracy of the adversary s walk. Algorithm 4 Globally optimal walk (G-WALK) Input: Initial state s 0, transition function P, maximum evaluation count c max, initial temperature t initial and temperature decrease factor k [0, 1] Output: Trace T = (s 0,..., s k ) T L-WALK(s 0 ), v Π k 1 i=0 P(s i, s i+1 ) Initial solution and likelihood T best T, v best v Best solution and likelihood c 0 Initial evaluation count while c < c max do T new mutate(t), v new Πi=0 k 1P(s new,i, s new,i+1 ) t temperature(c), c c + 1 if random( ) < accept probability(v, v new, t) then Randomly move to a new state T T new, v v new end if if v new > v best then T best T new, v best v new end if end while return T best function mutate(t) Let T be a random mutation of T. return T end function function temperature(c) return t initial (k) c end function function accept probability(v, v new, t) return min(1, e (v new v)/t ) end function Globally Optimal Walk (G-WALK) The G-WALK algorithm (Alg. 4) reconstructs the user trace by performing a walk in the state space such that the probability over the entire walk is maximized over all walks. In other words, G-WALK produces an ordered sequence of states T = (s 0, s 1,..., s k ) (k > 0) such that Π k 1 i=0 P(s i, s i+1 ) > Π l 1 j=0 P(s j, s j+1 ) : T = (s 0, s 1,..., s l ) with T T and s 0 = s 0. Unlike L-WALK, G-WALK does not rely on locally optimal choices but makes a globally optimal choice. An exhaustive search for a globally optimal path is infeasible due to the large number of paths in the state space. In order to obtain a fairly good approximation of the global optimum, we use a randomized search heuristic called Simulated Annealing (SA) [33]. In G-WALK, the current solution in each iteration is replaced by a random nearby solution chosen with a probability that depends both on the difference between the values of those solutions and a global parameter t, called the temperature, which is gradually decreased in each iteration. The nearby solution or path is chosen by the MUTATE function, which replaces one of the state transitions in the current solution by an alternate one. The temperature parameter enables the algorithm to escape local optima throughout the simulation, while slowly converging to a near-optimal solution.

10 5. Empirical Results and Evaluation We evaluate the success of the L-WALK and G-WALK algorithms in tracking users by using well-known metrics for location privacy Privacy Metrics We use four metrics in our evaluation; each uniquely captures the extent to which users can be tracked Traceability Metrics (τ-metrics) Traceability metrics, originally proposed by Hoh et al. [32], capture the extent to which the user can be tracked in time or distance. In our setting, we define two traceability metrics: the percentage of time τ t and the percentage of space τ d during which tracking is successful. Formally, these metrics are defined as follows: Definition 2 (Traceability metrics). Let r = ( π 0, π 1,..., π l ) denote the reconstruction of user pseudonyms as obtained by a reconstruction attack and r = (π 0, π 1,..., π k ) be the real sequence (groundtruth) of pseudonyms. The time- and distance-traceability metrics are: τ t (r, r) = τ d (r, r) = min(k,l) i=0 t match (π i, π i ) ki=0 t used (π i ) min(k,l) i=0 d match (π i, π i ) ki=0 d used (π i ) where t used (π) and d used (π) are the actual time and distance that pseudonym π was used by the user being tracked, and t match (π, π) and d match (π, π) are the time and distance during which pseudonym π is correctly matched to π in the reconstructed trace by the adversary for that user Uncertainty Metrics (u-metrics) Uncertainty metrics, originally proposed by Diaz et al. [18], capture the uncertainty of the adversary to correctly predict the next pseudonym used by the user. We define three uncertainty metrics as follows. Definition 3 (Uncertainty metrics). Let r = ( π 0, π 1,..., π l ) denote the reconstruction of user pseudonyms obtained by a reconstruction attack. Let Y(π) be the random variable denoting the next possible pseudonym (selected by the adversary) of pseudonym π and H denote the entropy operator. Then, we have the following uncertainty metrics that give the average, maximum and minimum entropy for all pseudonym changes: u avg ( r) = 1 l 1 l H(Y(π i )) i=0 u max ( r) = max{h(y(π i )) π i r \ π l } u min ( r) = min{h(y(π i )) π i r \ π l } Traceability-Uncertainty Metrics (µ-metrics) Traceability-Uncertainty metrics combine the advantages of the traceability and uncertainty metrics by capturing both the extent to which the user can be tracked, as well as the difficulty (or uncertainty) in tracking. They can be defined as follows. Definition 4 (Traceability-uncertainty metric). Let r = ( π 0, π 1,..., π l ), r = (π 0, π 1,..., π k ), Y(π) be defined as above. Let H max (Y(π)) = log 2 Y(π) denote the maximum achievable entropy for pseudonym π. Then, the corresponding time- (µ t ) and distance-traceability-uncertainty (µ d ) metrics are: µ t (r, r) = µ d (r, r) = min(k,l) i=1 min(k,l) i= Clustering Metrics (c-metrics) H(Y(π i 1 )) H max (Y(π i 1 )) t match(π i, π i ) min(k,l) i=1 t used (π i ) H(Y(π i 1 )) H max (Y(π i 1 )) d match(π i, π i ) min(k,l) i=1 d used (π i ) Clustering c-metrics, as proposed by Hoh et al. [31], capture the extent to which one user was confused with another in the context of multiple user tracking. We define the clustering error metric as a measure of the average distance-error between the reconstructed and real sequence of pseudonym over all users. We first define the clustering error for a single user as follows: Definition 5 (Clustering error for single user). For any user u, let r = ( π 0,..., π l ) and r = (π 0,..., π k ) be defined as above and p start (π) be the position of the start event of the subtrace with pseudonym π. Then, the clustering error c u for user u is the average distance between the start events in the reconstruction and in the groundtruth: c u (r, r) = min(k,l) 1 min(k, l) 1 p start ( π i ) p start (π i ) Then, the multi-user clustering error metric can be defined as follows. i=0 Definition 6 (Clustering error metric). Let R be the set of reconstructed sequences of user pseudonyms as obtained

11 Traceability [%] % 61% 46% time tracking L-WALK with common sniffing stations heuristic L-WALK with speed matching heuristic G-WALK with common sniffing stations heuristic G-WALK with speed matching heuristic 43% 47% 50% 31% distance tracking 28% Traceability [%] % 88% 83% time tracking L-WALK with common sniffing stations heuristic L-WALK with speed matching heuristic G-WALK with common sniffing stations heuristic G-WALK with speed matching heuristic 81% 65% 70% 67% distance tracking 64% (a) (b) Traceability [%] L-WALK time tracking L-WALK distance tracking G-WALK time tracking G-WALK distance tracking Number of sniffing stations Traceability [%] L-WALK time tracking L-WALK distance tracking G-WALK time tracking G-WALK distance tracking Number of sniffing stations (c) (d) Figure 2. Traceability success: 2(a) single user tracking results; 2(b) multiple user tracking results. Adversary strengths using L-WALK and G-WALK: 2(c) single user; 2(d) multiple users. by a multi-user reconstruction attack, R be the set of real sequences (groundtruth) of pseudonyms for the same users and U be the set of all users. Then, the the clustering error metric C is defined as the average clustering error over all users: C(R, R) = 1 U c u (r, r) u U,r R, r R The evaluation of the proposed tracking algorithms with more sophisticated privacy metrics, such as the one by Shokri et al. [45, 44], is left as part of future work Results Overview Fig. 2(a) shows the results for the single-user tracking using time and distance traceability metrics, which are averaged across all users and all tracking attempts over the entire 4-month duration. We can observe that the success ratio of L-WALK is around 60% with the time traceability metric and roughly 50% with the distance traceability metric. Also, both the speed and common station heuristics fared more or less equally well. The high success ratio of the simple L-WALK algorithm shows that the current PCA parameters (Table 1), althought realistic, do not perform very well in networking scenarios with slow or limited mobility, such as a network of smartphone users. In our setting, it is indeed rare to observe users move significantly during a mixing attempt. Consequently, even simple algorithms, such as L-WALK, are very effective in providing a correct ordering on candidates for the next state, despite the fact that transition probability estimates are not extremely precise. In order to have an equivalent performance comparison of the G-WALK with L-WALK for the single user case, we need to slightly adapt G-WALK s maximization criterion. In the single-user case, simply maximizing the product of probabilities for each complete walk is inherently prone to selecting shorter walks (as their products tend to be larger than those of longer walks). In our implementation, rather than simply maximizing the product of proba-

13 Table 2. Complete tracking results using the time, distance and clustering privacy metrics. Users Method Heuristic τ t τ d u avg µ t µ d c avg common stations 62% 47% % 37% - L-WALK speed matching 61% 51% % 41% - Single User common stations 46% 31% % 17% - G-WALK speed matching 43% 28% % 25% - Multiple Users L-WALK G-WALK common stations 84% 65% speed matching 88% 70% common stations 83% 67% speed matching 81% 64% ing case are very similar to those in single user tracking, except that in multiple user tracking, the success rate is around 20% higher compared to single user tracking over all the adversary strengths. In fact, by processing multiple users at the same time, we observe that the algorithms perform better even with significant inaccuracies in the user positions. Table 3. Adversary strengths. # stations Density [/1000m 2 ] Strength % % % % % % There might be other adversary models for tracking that are significantly weaker than (even the passive version of) the omni-potent Dolev-Yao model but relevant from the practical point of view. To be more widely useful, such an adversary model should, of course, be applicable to many different kinds of scenarios. Finding such a model is an interesting research challenge Impact on Network Efficiency While providing privacy protection, one major concern for pseudonym change mechanisms is the effect it can have on the network performance. We analyze the effect of our pseudonym change mechanism on the network performance by computing the average time spent by devices in a mixzone and the resulting packet loss rate. We estimate the average time of a device in a mix-zone by computing the ratio of the average mixing time to the average time between two mixings for that device. We estimate the packet loss between two mix attempts by computing the ratio of the average number of packets that would be sent during a mix attempt to the average number of packets sent between two mix attempts. In our experiments, we observe that between two mixing attempts, devices spend an average of 1.5% of their network time in mix-zones, resulting in a packet loss rate of approximately 2.4%. These results show that PCA with the current parameters does not have a major effect on the network performance. However, these values do not consider the costs involved in re-establishing connections or the effect on transport protocols with congestion control mechanisms Traceability in Large User Clusters Intuitively, when users organize themselves in large clusters (each cluster consisting of many mix-zones close to each other), user density within individual mix-zones also increases, thus leading to larger anonymity sets. Technically, this should result in better protection against trace reconstruction or tracking attacks. To verify this intuition, we measure the traceability of users on some selected days when the user-density is comparatively higher, for example, around the time when participants have lectures. Specifically, we define two tracking intervals, each of approximately 10 minutes, one at the beginning and the other at the end of the monitored lecture. We plot (Fig. 4) the average time traceability, as defined in Section 5.1, and the picked-up ratio during these two tracking intervals. The picked-up ratio is the ratio of the number of users for which the subtraces in the first and the second tracking interval match the ground truth to the total number of users in both the intervals. The horizontal axis in the plot denotes the number of users, during a particular lecture, that can be followed by our multiple target tracking algorithm. This number is also indicative of the size of the user cluster on that particular day, although it does not directly represent the size of each mix-zone within that cluster. We plot tracking results for 9 different lectures of the same course. We can see from the results that an increase in the number of users present in the cluster decreases both the traceability and the picked-up ratio. In other words, large clusters enable users to hide from the adversary. Note that these results include users (not necessarily in equal num-

17 [47] Theodore S. Rappaport. Wireless Communications: Principles and Practice, 2 nd Edition, chapter Mobile Radio Propagation: Large-Scale Path Loss. Pearson Education, Inc., [48] B. Wiedersheim, Z. Ma, F. Kargl, and P. Papadimitratos. Privacy in Inter-Vehicular Networks: Why simple pseudonym change is not enough. In IEEE/IFIP WONS, [49] H. Yoon, J. Kim, F. Tan, and R. Hsieh. On-demand video streaming in mobile opportunistic networks. In PERCOM, [50] X. Zhang, H. Heys, and C. Li. An analysis of link layer encryption schemes in wireless sensor networks. In ICC, Appendix Symbol Table 5. Symbol Table. Definition m User s actual message t(m) Device time when the message m is sent p(m) Device position when message m is sent π(m) Device identifier when message m is sent c Message content M Set of all actual messages (sent by all users) Q f Quota for forced identifier changes t f Forced timer Q c Quota for context-based identifier changes t c Context check timer t silent Radio silence period Q Total identifier-change quota ˆm Copy of the m observed by the adversary ô( ˆm) Adversary AP observing ˆm ŝ( ˆm) Received signal strength of ˆm r Actual sequence of pseudonyms ẽ Event constructed from observed messages ˆT Set of time-stamps in the event Ô Set of observing APs in the event r Reconstructed sequence of pseudonyms m Message reconstructed from an event ẽ S State space P State transition function v(s) Speed associated with the state s τ Traceability metric u Uncertainty metric µ Traceability-uncertainty metric C Clustering metric

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