Dynamic distribution method for privacy budget

Abstract

According to the method, time-space extended real-time trajectory data is abstracted into a streaming data structure, geographic indistinguishability is expanded into w-event geographic indistinguishability to measure the privacy intensity of a real-time trajectory, and a dynamic privacy budget allocation strategy supporting an infinite trajectory data stream is designed on the basis of the method. Firstly, a budget manager theta equally divides a privacy budget epsilon into two parts: epsilon 1 is used for a detection mechanism, and epsilon 2 is used for a disturbance mechanism; secondly, pre-distributing epsilon 1 and epsilon 2 to position data of each sampling moment according to a certain sequence; and if the privacy budget is not used, the privacy budget is recovered and then averagely allocated to two subsequent positions, and the consumption of the privacy budget is reduced through a recovery and reutilization method. According to the dynamic privacy budget allocation strategy designed by the invention, the length of a preset track is not needed, and the utilization rate of the privacy budget is effectively increased by recovering the unused privacy budget and overlapping and reallocating the unused privacy budget, so that the availability of published data is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of real-time trajectory data publishing based on differential privacy, and in particular to a method for dynamically allocating a privacy budget. Background Art

[0002] Real-time trajectory data has dynamic characteristics in which data distribution characteristics and time series regularities change over time, making it difficult to allocate privacy budgets in a coordinated manner based on fixed statistical structures. Therefore, it is extremely challenging to reasonably measure the strength of privacy protection and dynamically allocate privacy budgets. For static trajectory data, the trajectory can be made to satisfy ε-differential privacy by allocating privacy budgets in a coordinated manner. However, the dynamic characteristics of real-time trajectories make the length of trajectories unpredictable, making it difficult to globally optimize the allocation strategy. Existing publishing algorithms mainly allocate privacy budgets by presetting trajectory lengths, but this allocation strategy has certain limitations: if the trajectory length is greater than the preset value, the part of the trajectory that exceeds the preset value cannot be protected; if the trajectory length is less than the preset value, the privacy budget will be wasted, affecting the availability of published data. Designing a dynamic privacy budget allocation strategy that supports arbitrary trajectory lengths is the key to publishing real-time trajectory data.

[0003] The relevant concepts involved in the above technical solution are described and explained:

[0004] Definition 1. ε-Differential Privacy: Given datasets D and D′, the two datasets have the same data structure and differ by only one record, i.e., |D′ΔD|≤1. Given an algorithm A, Range(A) is the value range of A, if the output O(O∈Range(A)) of algorithm A on datasets D and D′ satisfies the inequality Pr[A(D)=O]≤e ε ×Pr[A(D′)=O], then A satisfies ε-differential privacy.

[0005] Where Pr[·] represents the probability of user privacy leakage, ε is the privacy budget, which represents the degree of privacy protection. The smaller ε is, the higher the degree of privacy protection is.

[0006] Definition 2. Global sensitivity: Let the query function f: D→R d , for any adjacent data sets D and D′, the global sensitivity of function f is Where R is the real space mapped by the data set D, d represents the query dimension of the function f, and p is the norm distance used to measure Δf, generally p=1.

[0007] Definition 3. Laplace mechanism: Given a data set D, there is a query function f: D→R d, its global sensitivity is Δf. For a random algorithm A that satisfies differential privacy, the algorithm output is A(D) = f(D) + Lap(Δf / ε). Among them, Lap(Δf / ε) is an independent Laplace distribution. The amount of noise added is proportional to Δf and inversely proportional to the privacy budget ε. The smaller ε is, the larger Δf is, the greater the added noise is, and the higher the privacy protection is. And vice versa.

[0008] Property 1. Sequential compositionality: Given a data set D and n sequences satisfying ε i (1≤i≤n)-Differentially Privacy Preserving Randomized Algorithm A i (1≤i≤n), these algorithms constitute the combined algorithm A(A1(D), A2(D), ..., A n (D) Satisfaction -Differential privacy protection.

[0009] Property 2. Parallel Combinability: A given data set D is partitioned into n disjoint subsets, D = {D1, D2, ..., D n}, let A i For a set of i -Differential privacy protection random algorithm, A is used for D To implement privacy protection, the combination algorithm A(A1(D), A2(D), ..., A n (D)) satisfies max(ε i )-Differential privacy protection.

[0010] Definition 4. Geographic Indistinguishability

[0011] Let X be the point of interest, i.e. the possible real location of the user. Let Z be the published location after disturbance. For all x, x′ ∈ X, Z ∈ Z, if the following inequality exists, then K is said to satisfy ε-geographic indistinguishability.

[0012] K(x)(Z)≤e εd(x，x′) K(x′) (Z)

[0013] Where K(x)(Z) represents the probability that the output of the perturbation mechanism K is Z when the input is x. d(x, x′) is the Euclidean distance between x and x′, representing the level of indistinguishability between x and x′. The smaller d(x, x′) is, the higher the level of indistinguishability between the real locations is, that is, the stronger the privacy is. The larger d(x, x′) is, the higher the degree to which the attacker can distinguish these real locations is, and the weaker the privacy is.

[0014] Definition 5. Planar Laplace distribution

[0015] Given parameters And the actual location For any The probability density function of the planar Laplace noise distribution is:

[0016]

[0017] in, is the normalization factor, and d(x0, x) represents the Euclidean distance between x0 and x.

[0018] Currently, differential privacy protection for real-time data streams can be divided into three levels: event-level, user-level, and w-event-level. Their adjacent data streams and corresponding differential privacy protection are defined as follows:

[0019] Assume that S = {x1x2x1x1x3…} is a continuously observed data stream, X represents the value range of the elements in the data stream S, and x i ∈X represents an event of a certain user.

[0020] Definition 6. Event-level differential privacy

[0021] Under continuous observation, if there exists x, x′∈X, and any x in S is replaced by x′ to become S′, then S and S′ are called event-level adjacent data streams. That is, an event of a user is added or deleted from the continuously observed data stream.

[0022] Given a random algorithm A, Range(A) is the set of all possible outputs of algorithm A. If any output result O(O∈Range(A)) of random algorithm A on event adjacent data streams S and S′ satisfies the following inequality, then random algorithm A is said to satisfy ε-differential privacy:

[0023] Pr[A(S)=O]≤e ε ×Pr[A(S′)=O]

[0024] Where Pr[·] represents the probability of user privacy leakage, and ε is the privacy budget.

[0025] Event-level differential privacy protects a user's event in the data stream by differential privacy with a privacy budget of ε.

[0026] Definition 7. User-Level Differential Privacy

[0027] Under continuous observation, if there exists x, x′∈X, and all events x corresponding to a certain user are replaced by x′ from S to become S′, then S and S′ are called user-level adjacent data streams. That is, all participating events of a certain user are added or deleted from the continuously observed data stream.

[0028] Given a random algorithm A, Range(A) is the set of all possible outputs of algorithm A. If any output result o(o∈Range(A)) of random algorithm A on user adjacent data streams S and S′ satisfies the following inequality, then random algorithm A is said to satisfy ε-differential privacy:

[0029] Pr[A(S)=O]≤e ε ×Pr[A(S′)=O]

[0030] Where Pr[·] represents the probability of user privacy leakage, and ε is the privacy budget.

[0031] All the participation events of a user in the user-level differential privacy protection data stream are protected by differential privacy with a privacy budget of ε.

[0032] Definition 8.w-adjacent

[0033] Given a positive integer w, if two data stream prefixes S t and S′ t Satisfies: (1) For every i∈[t] and S t [i]≠S′ t [i], both have S t [i] and S′ t [i] are adjacent; (2) for each i1<i2, S t [i1]≠S′ t [i1],S t [i2]≠S′ t [i2], and i2-i1+1≤w, then these two flow prefixes are called S t and S′ t are w-adjacent.

[0034] Definition 9. w-event-level differential privacy

[0035] Given a random algorithm A, Range(A) is the set of all possible outputs of algorithm A. If random algorithm A is in w-adjacent data streams S t and S′ t If any output O(O∈Range(A)) on A satisfies the following inequality, then the random algorithm A is said to satisfy ε-differential privacy:

[0036] Pr[A(S)=O]≤e ε ×Pr[A(S′)=O]

[0037] Where Pr[·] represents the probability of user privacy leakage, and ε is the privacy budget.

[0038] w-event-level differential privacy realizes user-level differential privacy for users in any w sliding window. The w-event level is in the middle of the event level and the user level. When w = 1, it degenerates to event-level differential privacy; when w = |T|, it belongs to user-level differential privacy. Summary of the invention

[0039] The present invention provides a method for dynamically allocating a privacy budget, which does not require a preset trajectory length and effectively improves the utilization rate of the privacy budget by recycling and reusing the allocated privacy budget.

[0040] In order to achieve the purpose of the present invention, the technical solution adopted is: a method for dynamically allocating a privacy budget, characterized in that it includes the following steps:

[0041] S1, the budget manager Θ divides the privacy budget ε into two parts: ε1 is used for the detection mechanism, and ε2 is used for the perturbation mechanism, ε = ε1 + ε2;

[0042] S2, pre-allocate the privacy budgets ε1 and ε2 to the location data at each sampling time according to the sequence ε / 2, ε / 4, ..., 3ε / [(n+1)(n+2)];

[0043] S3. If the detection mechanism or the perturbation mechanism is not activated at a certain moment, the unused privacy budget is recycled and evenly distributed to the next two positions. The privacy budget is dynamically adjusted through recycling and reuse.

[0044] As an optimization solution of the present invention, in step S2, since the user's location cannot be predicted at time t1, the disturbance mechanism is enabled to add noise to the real location and then publish it. The detection mechanism is enabled from time t2, then t i The privacy budget allocated to the detection mechanism at any time is Right now:

[0045]

[0046] in, is the privacy budget allocated to the detection mechanism at time t1, t i (t i ≥2) The privacy budget allocated to the detection mechanism at any time, t j (t j ≥1) The privacy budget allocated to the perturbation mechanism at any given moment.

[0047] As an optimization solution of the present invention, in step S3, the unused privacy budget is recovered and evenly distributed to the next two positions as follows:

[0048]

[0049] As an optimization scheme of the present invention, whether to enable the disturbance mechanism is determined according to the prediction of the prediction mechanism and the driving status of the user. If the disturbance mechanism is not enabled, the pre-allocated privacy budget is recovered and then allocated to the next two positions. Even if the privacy budget pre-allocated to the end of the trajectory is small, the privacy budget at the end of the trajectory is increased by continuously recovering the unused budget.

[0050] As an optimization solution of the present invention, the threshold η is set to 10 -3 ,when or When , the budget manager Θ, the detection mechanism, and the perturbation mechanism all stop working. Since the prediction mechanism does not consume the privacy budget, it can still make predictions. At this time, the predicted position will be directly released.

[0051] As an optimization scheme of the present invention, the real-time trajectory T published by the dynamic allocation method of the privacy budget satisfies the w-event geographic indistinguishability, that is, within the sliding window of length w at any time, the privacy budget sum is less than or equal to ε.

[0052] As an optimization solution of the present invention, given a random algorithm A, Range(A) is the set of all outputs of A, if A is in the w-adjacent position data stream S i and S′ i If any output O(O∈Range(A)) on A satisfies the following inequality, then the random algorithm A is said to satisfy w-event geographic indistinguishability:

[0053]

[0054] Where Pr[·] represents the probability of user privacy leakage, ε is the privacy budget, and d max =max d(S t [i],S′ t [i]), i∈(0, t], that is, the adjacent position data stream S t and S′ t At the same time t i The position pair (S t [i],S′ t [i])’s maximum Euclidean distance.

[0055] As an optimization solution of the present invention, mechanism A prefixes the position data stream S t As input, S t [i]=L i ∈L, and then perturb it to output o=(o1,...,o t )∈O. Decompose mechanism A into t sub-mechanisms A1,...,At , so that A i (L i )=o i , each sub-mechanism A i Generate independent random noise and satisfy ε i -Geographic indistinguishability. If A satisfies the following inequality, then the mechanism A is said to satisfy w-event geographic indistinguishability:

[0056]

[0057] Proof: Since there are t sub-mechanisms A i Both generate independent random noise, and A i (L i )=o i ,but:

[0058]

[0059] Similarly, with S t w-adjacent arbitrary position data stream S′ t , for the same output:

[0060]

[0061] When 1≤k≤iw and i+1≤k≤t, there exists i∈(0,t] such that L k =L′ k . According to the above two equations, we have:

[0062]

[0063] Because A k Satisfy ε k -Geographically indistinguishable, according to Definition 4:

[0064]

[0065] Then we have:

[0066]

[0067] therefore, When , mechanism A satisfies the w-event geographical indistinguishability.

[0068] As an optimization solution of the present invention, in order to make the real-time trajectory publishing mechanism A satisfy the w-event geographical indistinguishability, each location loc in the real-time trajectory T i All must satisfy ε i -Geographic indistinguishability, where 1≤i≤|T|. And the sum of the privacy budgets in any sliding window of length w is less than or equal to ε, that is

[0069] As an optimization scheme of the present invention, the real-time trajectory published by the privacy budget dynamic allocation method proposed in the present invention satisfies the 4-event geographic indistinguishability, that is, at any time in the sliding window of w=4, the sum of the allocated privacy budgets is less than or equal to ε.

[0070] Proof: t n The privacy budget pre-allocated at each moment is 3ε / (t n +1)(t n +2). Let a n = 3 / (n+1)(n+2), then the sum of the sequence S n for:

[0071]

[0072] When n→∞, S n =3 / 2 It can be seen that the privacy budget pre-allocated by infinite real-time trajectory T tends to ε sum =3ε / 2.

[0073] Since the pre-allocated privacy budget follows the decreasing principle, the sum of the privacy budgets in the sliding window of length w = 4 at any time is no greater than ε, and we only need to calculate the maximum value of the budget sum in the worst case.

[0074] (1) If the prediction mechanism fails completely, each position needs to use both the detection mechanism and the prediction mechanism at the same time, then when w = 4;

[0075] The privacy budget for the perturbation mechanism is:

[0076]

[0077] The privacy budget for the detection mechanism is:

[0078]

[0079] That is, in this case, the privacy budget within the sliding window w=4 is less than ε at any time.

[0080] (2) If the user is always in a static state, at time t1, the privacy budget allocated to the detection mechanism is Enable the perturbation mechanism, and publish the real location after perturbation. The privacy budget consumed at time t1 is At time t2, the prediction mechanism sends the location published at time t1 to the detection mechanism, which consumes The privacy budget protection detection process, then the privacy budget consumed at time t2 is ε1 / 2;

[0081] When t ≥ t3, the privacy budget is continuously added backwards, and the real-time trajectory T ends at t n-3 to n The privacy budget sum is the maximum value. When n→∞, the total pre-allocated privacy budget ε sum =3ε / 2, the budget of ε2 / 2+ε1 / 2=ε / 2 is consumed at t1 and t2, then when t≥t3, the total budget consumed is 3ε / 2-ε / 2=ε.

[0082] That is, in this case, the privacy budget within the sliding window w=4 at any time is no greater than ε.

[0083] In summary, the real-time trajectory published by the privacy budget dynamic allocation method proposed in this invention satisfies the 4-event geographic indistinguishability.

[0084] The present invention has positive effects:

[0085] 1) The present invention abstracts the spatiotemporally extended real-time trajectory data into a streaming data structure and extends geographic indistinguishability into w-event geographic indistinguishability to measure the privacy strength of real-time trajectories.

[0086] 2) The present invention designs a dynamic privacy budget allocation method that supports unlimited trajectory data. It does not need to pre-set the trajectory length. By recycling the unused privacy budget and redistributing it backward, the utilization rate of the privacy budget is effectively improved;

[0087] 3) The present invention avoids the degradation of data quality caused by excessive privacy protection through a reasonable privacy budget allocation and recovery mechanism, ensuring that the published real-time trajectory data maintains high availability while protecting privacy;

[0088] 4) The present invention can adapt to real-time trajectory data of different lengths and dynamically adjust the allocation of privacy budget according to the prediction situation and the user's driving status, making the published data more flexible and practical, and enhancing the adaptability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0090] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0091] Figure 2 It is an embodiment diagram of the present invention;

[0092] Figure 3 (a)-(f) are the maximum distance comparison diagrams of the privacy budget shown in the present invention when ε=0.5, 1.0, and 2.0;

[0093] Figure 4 (a)-(b) are comparison diagrams of relative errors of frequent patterns when the privacy budget is ε=0.5, 1.0, and 2.0 as shown in the present invention. DETAILED DESCRIPTION

[0094] like Figure 1 As shown, the present invention discloses a method for dynamically allocating a privacy budget, so that the published real-time trajectory meets the w-event geographic indistinguishability. The strategy does not require a preset trajectory length, and by recycling and reusing the allocated privacy budget, the utilization rate of the privacy budget is effectively improved.

[0095] Inspired by the inverse principle of triangular numbers, this allocation strategy pre-allocates the privacy budget ε to each location according to the following sequence:

[0096] (ε / 2), (ε / 4), ....(3ε / [(n+1)(n+2)])

[0097] That is t i = 1, loc1 is pre-allocated to the privacy budget of ε / 2; when t i = n, loc n Pre-allocated to 3ε / [(t n +1)(t n +2)]; when n→∞, the total privacy budget of the sequence tends to 3ε / 2.

[0098] This allocation strategy adopts the principle of decreasing allocation, gradually reducing the share of the privacy budget over time. The reasons for this allocation are as follows:

[0099] (1) Since the length of the real-time trajectory cannot be predicted, allocating the privacy budget earlier can reduce the waste of privacy budget caused by shorter trajectories.

[0100] (2) Determine whether to enable the perturbation mechanism based on the prediction of the prediction mechanism and the user's driving status. If the perturbation mechanism is not enabled, the pre-allocated privacy budget is recovered and then allocated to the next two positions. Even if the privacy budget pre-allocated to the end of the trajectory is small, the privacy budget at the end of the trajectory can be increased by continuously recovering the unused budget.

[0101] The dynamic allocation method strategy of the privacy budget proposed in this invention is described as follows:

[0102] (1) The privacy budget is ε. The budget manager Θ divides the privacy budget ε into two parts: ε1 is used for the detection mechanism and ε2 is used for the perturbation mechanism.

[0103] (2) Pre-assign ε1 and ε2 to the position of each sampling time according to the above sequence:

[0104] Since the prediction mechanism cannot make a prediction at time t1, the perturbation mechanism is enabled at this time to add noise to the real position and then publish it. The detection mechanism is enabled from time t2, then t i The privacy budget allocated to the detection mechanism at any time is Right now:

[0105]

[0106] And t j The privacy budget allocated to the perturbation mechanism at any given moment is Right now:

[0107]

[0108] (3) If the detection mechanism or the perturbation mechanism is not activated at a certain moment, the unused privacy budget is recovered and evenly distributed to the next two positions, namely:

[0109]

[0110] Through the recycling and reuse method, the privacy budget can be dynamically adjusted to effectively reduce the consumption of the privacy budget.

[0111] It should be noted that the allocated privacy budget cannot be infinitely approaching 0. The threshold η is set to 10 -3 ,when or When θ is less than θ, the budget manager Θ, the detection mechanism, and the perturbation mechanism all stop working. However, since the prediction mechanism does not consume the privacy budget, prediction can still be made. At this time, the predicted position will be directly released.

[0112] Example 1

[0113] like Figure 2 As shown, the privacy budget pre-allocated to the detection mechanism by the budget manager Θ is: Then at t2 and t3, the privacy budget allocated by Θ to the detection mechanism is ε1 / 2 and ε1 / 4 respectively.

[0114] Assuming that the user's driving speed and direction at t2 and t3 have not changed significantly, the detection frequency is reduced, and the detection mechanism is not enabled at t3, and the predicted location is directly released. The privacy budget will be pre-allocated to t3 Evenly distributed to t4 and t5. At this time, the privacy budget used for the detection mechanism at t4 is: the pre-allocated 3ε1 / 20 plus the privacy budget recovered at t3 Half of , that is, 3ε1 / 20+ε1 / 8=11ε1 / 40. Similarly, the privacy budget for the detection mechanism at time t5 is ε1 / 10+ε1 / 8=9ε1 / 40.

[0115] Assuming that the prediction mechanism succeeds at time t2, that is, the distance between the predicted position and the actual position is within the set threshold, the perturbation mechanism is skipped and the predicted position is directly released. Therefore, the privacy budget allocated to the perturbation mechanism at time t2 is recovered and evenly distributed to t3 and t4. The privacy budget used for the perturbation mechanism at time t3 is: 3ε2 / 20 plus half of the pre-allocated budget at time t2, that is, 3ε2 / 20+ε2 / 8=11ε2 / 40. Similarly, the privacy budget used for the perturbation mechanism at time t4 is ε2 / 10+ε2 / 8=9ε2 / 40. Since the detection mechanism was not enabled at time t3, the predicted position was directly released. Therefore, the perturbation mechanism still does not need to be enabled at time t3, and the privacy budget 11ε2 / 40 used for the perturbation mechanism at time t3 is recycled again and evenly distributed to t4 and t5. At this time, the privacy budget used for the perturbation mechanism at time t4 is: 9ε2 / 40+11ε2 / 80=29ε2 / 80, and the privacy budget used for the perturbation mechanism at time t5 is: ε2 / 14+11ε2 / 80=117ε2 / 560.

[0116] The pseudo code of the dynamic allocation method of privacy budget is as follows:

[0117]

[0118]

[0119] Example 2

[0120] The real-time trajectories published by this privacy budget allocation method satisfy 4-event geographic indistinguishability.

[0121] Proof: To make the real-time trajectory T satisfy the w-event geographical indistinguishability, each location published in the real-time trajectory data stream must satisfy ε i - Geographic indistinguishability, and That is, at any time in a sliding window of length W, the sum of the privacy budgets is less than or equal to ε. The following proves that at any time in a sliding window of length w = 4, the sum of the allocated privacy budgets is less than or equal to ε.

[0122] In the dynamic privacy budget allocation strategy proposed in this invention, t n The privacy budget pre-allocated at each moment is 3ε / (t n +1)(t n +2). Let a n =3 / (n+1)(n+2), then the sum of the sequence S n for:

[0123]

[0124] When n→∞, S n =3 / 2. It can be seen that the privacy budget pre-allocated by infinite real-time trajectory T tends to ε sum =3ε / 2.

[0125] Since the pre-allocated privacy budget follows the decreasing principle, the sum of the privacy budgets in the sliding window of length w = 4 at any time is no greater than ε, and we only need to calculate the maximum value of the budget sum in the worst case. The following analyzes the privacy budgets of the two cases:

[0126] (1) Assuming that the prediction mechanism fails completely, both the detection mechanism and the prediction mechanism need to be enabled at each location.

[0127] Since the initial allocation budget follows the decreasing principle, when w=4, the sum of the privacy budgets from t1 to t4 is the maximum.

[0128] The privacy budget for the perturbation mechanism is:

[0129]

[0130] The privacy budget for the detection mechanism is:

[0131]

[0132] Therefore, in this case, the privacy budget within the sliding window w=4 is less than ε at any time.

[0133] (2) Assume that the user is always stationary.

[0134] At time t1, the privacy budget allocated to the detection mechanism Enable the perturbation mechanism, and publish the real location after perturbation. The privacy budget consumed at time t1 is

[0135] At t2, the running speed is still 0, so the prediction mechanism sends the position published at t1 to the detection mechanism, which consumes The privacy budget protection detection process is obviously successful, and the predicted position is published. Since there is no need to enable the perturbation mechanism, the budget consumed at time t2 is ε1 / 2.

[0136] Since the user is always in a static state, neither the detection mechanism nor the disturbance mechanism is enabled. Therefore, when t ≥ t3, the privacy budget is continuously added backwards, and the real-time trajectory T ends at t n-3 to n The privacy budget and is the maximum value.

[0137] From the above, we can see that when n→∞, the sum of the pre-allocated privacy budget ε sum=3ε / 2, and the budget of ε2 / 2+ε1 / 2=ε / 2 is consumed at t1 and t2. When t≥t3, the total consumed budget is 3ε / 2-ε / 2=ε. Obviously, the privacy budget in the sliding window of w=4 at any time is not greater than ε.

[0138] In summary, the real-time trajectories published by this privacy budget dynamic allocation method satisfy the 4-event geographic indistinguishability.

[0139] Figure 3 (a)-(f) are the maximum distance comparison diagrams based on the public datasets Porto-Taxi and T-drive, with privacy budget ε = 0.5, 1.0, and 2.0. The maximum distance measures the maximum difference between two trajectories, and its formal definition is: given two trajectories T and T′, P i is the position point on trajectory T, is a position point in trajectory T′, then the maximum distance between them is:

[0140]

[0141] Since there is a temporal and spatial correlation between trajectory positions, it is easy for an attacker to identify the entire trajectory of a user based on a specific position. The experiment measures the difference between two trajectories by the maximum distance. Figure 3 As shown in (a)-(f), the maximum distances of all algorithms on the T-drive dataset are larger than those on the Porto-Taxi dataset. The reason is that the sampling interval and the average length of the trajectory of the T-drive dataset are longer than those of the Porto-Taxi dataset, and the maximum distance is also larger than that of the Porto-Taxi dataset.

[0142] As ε increases, the maximum distance decreases. Since the maximum distance is mainly determined by the privacy budget of the perturbation mechanism The decision is the published position after adding noise to the true position. The value of increases with the increase of ε, so the maximum distance also decreases. Under all parameters, the maximum distance value of the method of the present invention is smaller than that of the comparison algorithm. This is because the comparison algorithm is implemented by setting a fixed privacy consumption rate or a fixed trajectory length, while the method of the present invention uses a dynamic privacy budget allocation strategy to more reasonably utilize the privacy budget and reduce the amount of added noise.

[0143] Figure 4(a)-(b) are comparisons of the relative error of frequent patterns based on the public datasets Porto-Taxi and T-drive with a privacy budget of ε = 0.5, 1.0, and 2.0. The formal definition of the relative error of frequent patterns is: project each trajectory in the trajectory dataset onto a uniform grid U to obtain the sequence of cells that the trajectory passes through. Define pattern P as an ordered list of cells, such as: P: C2→C4→C3, define supp(D, P) as the number of times pattern P appears in dataset D, and define is the top-k pattern in the dataset D. For each pattern P∈F, the frequent pattern relative error represents supp(D, P) and sup(S D , P) between:

[0144]

[0145] Among them, S D A synthetic dataset.

[0146] like Figure 4 As shown in (a)-(b), the relative errors of the frequency modes of the method of the present invention on the two data sets are smaller than those of the comparison algorithms. This shows that the proposed method of the present invention recovers the unused privacy budget and redistributes it backward, which effectively increases the utilization rate of the privacy budget and improves the availability of the published trajectory. The errors of the N-grams and DPT algorithms in the frequent mode are large. This is because the hierarchical prefix tree of DPT changes the density distribution of the original data, making the distribution of the synthetic data set tend to be uniform. When N-grams are processed by high-pass filtering and the trajectory prefix tree is synthesized, the nodes with statistical numbers less than the threshold are pruned, so that the synthetic data are only from high-density areas, making the dense areas denser and the sparse areas sparser, which affects the relative error value of the frequent mode.

[0147] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A dynamic allocation method for privacy budget, Features: The steps include: S1. The budget manager Θ divides the privacy budget ε into two parts: ε 1 For the detection mechanism, ε 2 For the perturbation mechanism, ε = ε 1 +ε 2 ; S2: According to the sequence ε / 2, ε / 4, ..., 3ε / [(n+1)(n+2)], the privacy budget ε is increased. 1 and ε 2 Position data pre-assigned to each sampling moment; S3. If the detection mechanism or the perturbation mechanism is not activated at a certain moment, the unused privacy budget is recycled and evenly distributed to the next two positions. The privacy budget is dynamically adjusted through recycling and reuse.

2. A method for dynamically allocating a privacy budget according to claim 1, Features: In step S2, since it is impossible to 1 The user's location is predicted at all times. At this time, the perturbation mechanism is enabled to add noise to the real location and then publish it. The detection mechanism starts from t 2 Start to use at time t i The privacy budget allocated to the detection mechanism at any time is Right now: in, t 1 The privacy budget allocated to the detection mechanism at all times, t i (t i ≥2) The privacy budget allocated to the detection mechanism at any time, t j (t j ≥1) The privacy budget allocated to the perturbation mechanism at any given moment.

3. A method for dynamically allocating a privacy budget according to claim 2, Features: In step S3, the unused privacy budget is recycled and evenly distributed to the next two positions, specifically:

4. A method for dynamically allocating a privacy budget according to claim 3, Features: Based on the prediction of the prediction mechanism and the user's driving status, it is determined whether to enable the perturbation mechanism. If the perturbation mechanism is not enabled, the pre-allocated privacy budget is recovered and then allocated to the next two positions. Even if the privacy budget pre-allocated to the end of the trajectory is small, the privacy budget at the end of the trajectory is increased by continuously recovering the unused budget.

5. A method for dynamically allocating a privacy budget according to claim 4, Features: Set the threshold η = 10 -3 ,when or When , the budget manager Θ, the detection mechanism, and the perturbation mechanism all stop working. Since the prediction mechanism does not consume the privacy budget, prediction can still be made. At this time, the predicted position will be directly released.

6. A method for dynamically allocating a privacy budget according to claim 5, Features: The real-time trajectory T published by the dynamic allocation method of the privacy budget satisfies the w-event geographic indistinguishability, where the w-event geographic indistinguishability means that the sum of the privacy budgets is less than or equal to ε within a sliding window of length w at any time.

7. A method for dynamically allocating a privacy budget according to claim 6, Features: Given a random algorithm A, Range(A) is the set of all outputs of A. If A is in the w-adjacent position data stream S t and S′ t Any output result O on o∈Range(A) satisfies the following inequality, then the random algorithm A is said to satisfy w-event geographical indistinguishability: Where Pr[·] represents the probability of user privacy leakage, ε is the privacy budget, and d max =maxd(S t [i],S′ t [i]), i∈(0, t], that is, the adjacent position data stream S t and S′ t At the same time t i The position pair (S t [i],S′ t [i])’s maximum Euclidean distance.

8. A method for dynamically allocating a privacy budget according to claim 7, Features: Mechanism A prefixes the location data stream with S t As input, S t [i]=L i ∈L, and then perturb it to output o=(o 1 , ..., o t )∈O, decompose mechanism A into t sub-mechanisms A 1 , ..., A t , so that A i (L i )=o i , each sub-mechanism A i Generate independent random noise and satisfy ε i -Geographic indistinguishability. If A satisfies the following inequality, then the mechanism A is said to satisfy w-event geographic indistinguishability: Among them, ε k is the privacy budget within an arbitrary sliding window of length w.

9. A method for dynamically allocating a privacy budget according to claim 8, Features: To make the real-time trajectory publishing mechanism A satisfy the w-event geographical indistinguishability, each location loc in the real-time trajectory T i All must satisfy ε i - Geographic indistinguishability, where 1≤i≤|T|, and the sum of the privacy budgets in any sliding window of length w is less than or equal to ε, i.e.

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