Location information hiding method based on active opaqueness of random discrete event system

Abstract

The invention provides a random discrete event system active opaqueness-based position information hiding method, which comprises the following steps of: modeling a position information hiding system into a random discrete event system, constructing a k-step active opaqueness verifier VG according to a modeled mathematical model, and further constructing a Markov chain M, calculating the probability of exposing the secret position after each position information hiding scheme is forced to be executed, judging whether the probability corresponding to at least one position information hiding scheme is smaller than a preset threshold value or not, if so, determining that the mathematical model of the random discrete event system has random k-step active opaqueness, and completing hiding of the position information; otherwise, regenerating a new position information hiding scheme; according to the method, multiple sets of position information hiding schemes are preset at the same time, active control is introduced into opaqueness research, k-step active opaqueness is verified, the opaqueness control capacity is improved, the active opaqueness application range is widened, and reliable hiding of position information can be effectively achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of location information hiding, and more specifically, to a location information hiding method based on active opacity of a random discrete event system. Background Art

[0002] Discrete Event Systems (DESs) are a type of dynamic system whose state evolves due to the interaction of discrete events according to certain rules. Due to its significant advantages in optimization control, fault diagnosis and prediction, information security verification, etc., DESs have been widely used in industrial manufacturing, software engineering, traffic control, computer integrated manufacturing systems, electronic communication networks, robotics and other fields.

[0003] In recent years, the study of the opacity of discrete event systems has attracted widespread attention from many scholars at home and abroad. In the literature [5], Lin first proposed the concept of opacity under the DESs framework and studied the application of opacity in observability, anonymity, diagnosability, etc. Intuitively, an opaque system satisfies: for any path to the secret state of the system, there is at least another path to the non-secret state, so that these two paths have the same observation value. Therefore, an opaque system can effectively resist the attack of intruders and protect privacy, because the intruder cannot determine whether the state reached by the system is a secret state or a non-secret state based on its observation results. For this reason, it has achieved important applications in information security mechanisms such as digital signatures, confidential communications, information authentication, intrusion detection, and data encryption.

[0004] In order to solve the problem that opacity is difficult to ensure in complex systems with multiple secret states, the paper "TAN JX, LIU F, ZBIGNIEW D. Active opacity of discrete-event systems[J]. International Journal of Control, 2023, 96(8): 2090-2099" introduced controllable events, proposed the concept of active opacity, and constructed an active opacity verifier, giving a necessary and sufficient condition for verifying the active opacity of the system; however, this paper only studies the active opacity of the current state of DESs under the framework of DESs modeled on deterministic automata, lacks the ability of dynamic analysis, and has a narrow scope of application of active opacity.

[0005] Traditional opacity research is mainly based on a binary representation method, which divides the opacity of all systems into two forms: completely transparent or completely opaque. However, in real-world application scenarios, due to unforeseen factors (such as sensor failures, etc.), it is often difficult to ensure that the system achieves absolute opacity. In this case, the system may have a small probability of violating opacity. In addition, some application systems may not necessarily need to achieve complete opacity, but only need to ensure that the probability of violating opacity remains below a certain acceptable threshold.

[0006] As for the positioning system, with the popularity of mobile devices and online transaction systems, more and more applications begin to require users to provide real-time location information in order to provide users with personalized and timely information. This service is called Location Based Services (LBS). For example, food delivery and navigation services require LBS. While LBS provides users with better services, it also increases the risk of privacy exposure. Intruders can use this information to learn about users' home addresses, workplaces, and even physical conditions. In order to protect users' location privacy, the most commonly used technology for LBS is location anonymizers based on location anonymization services. Location anonymizers convert users' accurate location information into a location area that contains multiple false location information and is larger than the accurate location range, and then provide it to the LBS server. Its workflow is as follows: Figure 1 As shown;

[0007] When the user is in motion, since the LBS data provided is only some location areas, the user's trajectory may be incoherent or unclear. Therefore, in addition to setting a false location, it is also necessary to set a false path, that is, to arrange the same trajectory path as the user between false locations, especially for those sensitive locations. In order to better protect privacy, users may further require that they will not reveal that they have been to these sensitive locations for a period of time (or forever) after passing through them.

[0008] Based on the above considerations, many researchers have begun to use stochastic discrete event systems (SDESs) to evaluate and quantify the opacity of the system. For example, in the paper "YIN X, LI Z, WANG W, LI S, Infinite-step opacity and K-step opacity of stochastic discrete event systems [J]. Automatica, 2019, 99: 266-274", Yin et al. discussed almost k-step opacity and almost infinite step opacity under the SDESs framework and proposed an effective algorithm to verify these opacities; however, this paper did not consider active opacity based on event controllability and is not applicable to the above positioning system. In the SDESs framework modeled on random automata, when the system has multiple secret states, opacity is still difficult to guarantee. Summary of the invention

[0009] In order to overcome the defects in the above-mentioned prior art that opacity is difficult to ensure when SDESs (such as location hiding systems) have multiple secret states, and the narrow scope of application of active opacity, the present invention provides a location information hiding method based on active opacity of random discrete event systems, models the location information hiding system as a random discrete event system, and presets multiple sets of location information hiding schemes, introduces active control into opacity research, verifies k-step active opacity, greatly improves the control ability of opacity, and broadens the scope of application of active opacity, which can effectively realize the reliable hiding of location information.

[0010] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0011] A method for hiding location information based on active opacity of a random discrete event system comprises the following steps:

[0012] S1: Obtain a map, determine several real locations and real paths of the user on the map according to the LBS, and use at least one real location as a secret location to be concealed;

[0013] S2: randomly generating a number of false locations within a preset range around each of the real locations, and converting each real location into a corresponding location area;

[0014] S3: randomly generating a number of false paths between each of the location areas, and saving each false path that can reach the secret location as a location information hiding scheme;

[0015] S4: Construct a mathematical model of a random discrete event system and construct a k-step active opaque verifier V based on the mathematical model G , where k is a preset non-negative integer;

[0016] S5: According to the k-step active opaque verifier V G Construct the corresponding Markov chain M and calculate the probability of exposing the secret location after each location information hiding scheme is enforced;

[0017] S6: Determine whether there is at least one location information hiding scheme with a corresponding probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, and all false paths are saved to complete the hiding of the location information; otherwise, re-execute step S3 to regenerate a new location information hiding scheme.

[0018] Preferably, in step S4, the random discrete event system includes: a state set, an event set, a partial state transition probability function and an initial state, wherein the event set includes observable events and unobservable events.

[0019] Preferably, the unobservable events also include controllable events, and each of the controllable events corresponds to one of the location information hiding schemes.

[0020] Preferably, in step S4, the mathematical model of the random discrete event system is:

[0021] G=(X,Σ,p,x0)

[0022] Where G represents a random discrete event system, X represents a set of states, each state corresponds to a real location or a false location; Σ represents a set of events, each event corresponds to a state transition process, in which the migration of a user from one location area to another is recorded as an observable event, and the location migration of a user within the same location area is recorded as an unobservable event; among unobservable events, the movement of a user from an initial location to a virtual location closest to a secret location is recorded as a controllable event; p represents a partial state transition probability function; x0 represents the initial state of the random discrete event system G.

[0023] Preferably, in step S4, the k-step active opaque verifier V G Specifically:

[0024] V G =(Q,∑,f,q0)

[0025] Among them, Q is the state set after the controllable event, satisfying represents the ordered set of controllable events; f is the state transition function, satisfying f:Q×∑→Q; q0 is the k-step active opaque verifier V G The initial state satisfies UR({x0}) represents the set of states that state x0 can reach through unobservable events;

[0026] For any and σ∈∑, there are:

[0027]

[0028] r′=UR(Next σ (r))

[0029]

[0030] Where q is the state after the controllable event; x is the current state of the random discrete event system G; u is the controllable event sequence that runs to the current state; r is the current state estimate corresponding to the unobservable event after path s occurs; r is the current state estimate corresponding to the observable event after path s occurs; ρ i is the state estimate before the i-th step corresponding to the unobservable event, i = 1,…,k; ρ i ′ is the state estimate before the i-th step corresponding to the observable event; ∑ uo is the set of unobservable events; o is a collection of observable events; Next σ (r) represents the set of states that state r can reach through observable events; Ξ(σ) represents the set of state pairs consisting of states that can execute event σ and states that can be reached through event σ; is the preset operator;

[0031] For any ρ i ∈2 X×X ,have I1(ρ i ) represents the delayed state estimate of the i-th step of the random discrete event system G.

[0032] Preferably, the necessary and sufficient conditions for the random discrete event system G to have k-step active opacity are:

[0033] If and only if the k-step active opaque verifier V G Any state q after a controllable event, that is, q=(x,u,r,ρ1,...,ρ k ) and u≠φ, and at the same time:

[0034] and I1(ρ i )≠φ, and

[0035] Among them, X S A collection of secret locations.

[0036] Preferably, in step S5, according to the k-step active opaque verifier V G Constructing the corresponding Markov chain M includes:

[0037] For all possible locations x that can reach the secret position i ∈X S The path s∈∑ * Make a controllable projection and get the secret state x i A set of controllable events It is expressed as:

[0038]

[0039] Among them, P c (s) represents a controllable projection of s;

[0040] If there are n secret locations in the system, then the set of secret controllable events L kc It is expressed as:

[0041] Define the state set Q KS :

[0042]

[0043] Eliminate the state set Q in the random discrete event system G KS After the part that can be migrated to, the state space obtained is Indicates that the Markov chain is constructed Among them, π0 is the initial state probability vector, satisfying π0(q0)=1; p M : is the state transition function of the Markov chain, defined as: for any q=(x,u,r,ρ1,...,ρ k ), have:

[0044]

[0045] Calculate the probability of exposing the secret location after each location information hiding scheme is enforced Specifically:

[0046]

[0047] Among them, π0(q) represents the probability of migrating from the initial state q0 to the state q; represents the probability of transitioning from state q to the exposed state, is the minimum non-negative solution of the following equation:

[0048]

[0049] Preferably, the necessary and sufficient conditions for the random discrete event system G to have random k-step active opacity are:

[0050] Given a preset threshold θ, if and only if: for any There is at least one controllable event string satisfy

[0051] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method are implemented.

[0052] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the processor, the steps in the above method are executed.

[0053] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0054] The present invention provides a location information hiding method based on active opacity of a random discrete event system. First, a map is obtained, and several real locations and real paths of a user are determined on the map according to an LBS, and at least one real location is used as a secret location to be hidden; then, several false locations are randomly generated within a preset range around each of the real locations, and each real location is converted into a corresponding location area; several false paths are randomly generated between each of the location areas, and each false path that can reach the secret location is saved as a location information hiding scheme; then, a mathematical model of the random discrete event system is constructed, and a k-step active opaque verifier V is constructed according to the mathematical model. G , where k is a preset non-negative integer; according to the k-step active opaque verifier V G Construct the corresponding Markov chain M, calculate the probability of exposing the secret location after each location information hiding scheme is enforced; finally, determine whether there is at least one location information hiding scheme with a probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, save all false paths, and complete the hiding of location information; otherwise, regenerate a new location information hiding scheme;

[0055] The present invention solves the problem that opacity is difficult to ensure in a complex system with multiple secret states by introducing controllable events into random k-step active opacity. By applying it to a positioning system, multiple sets of location concealment schemes are actively introduced to ensure the effectiveness and reliability of location information concealment. In addition, the present invention generalizes active opacity from discrete event systems to random discrete event systems, and also generalizes active opacity from current state opacity to k-step opacity, greatly broadening the scope of application of active opacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a schematic diagram of the LBS workflow provided in the background technology.

[0057] Figure 2 This is a flow chart of a method for hiding location information based on active opacity of a random discrete event system provided in Example 1.

[0058] Figure 3 This is a schematic diagram of a map of a certain area provided in Example 2.

[0059] Figure 4 This is a schematic diagram of the generation location area provided in Example 2.

[0060] Figure 5 Schematic diagram of two sets of location information hiding solutions provided in Example 2.

[0061] Figure 6 Schematic diagram of the random discrete event system G provided in Example 2.

[0062] Figure 7 is the k-step active opaque verifier V provided in Example 2 G Schematic diagram.

[0063] Figure 8 This is a schematic diagram of the Markov chain M provided in Example 2.

[0064] Fig. 9 Schematic diagram of the random discrete event system G in the verification experiment provided in Example 3.

[0065] Fig.10 is the k-step active opaque verifier V in the verification experiment provided in Example 3 G Schematic diagram.

[0066] Fig.11 Schematic diagram of the Markov chain M in the verification experiment provided in Example 3. DETAILED DESCRIPTION

[0067] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0068] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0069] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0070] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0071] Example 1

[0072] like Figure 2 As shown, this embodiment provides a method for hiding location information based on active opacity of a random discrete event system, comprising the following steps:

[0073] S1: Obtain a map, determine several real locations and real paths of the user on the map according to the LBS, and use at least one real location as a secret location to be concealed;

[0074] S2: randomly generating a number of false locations within a preset range around each of the real locations, and converting each real location into a corresponding location area;

[0075] S3: randomly generating a number of false paths between each of the location areas, and saving each false path that can reach the secret location as a location information hiding scheme;

[0076] S4: Construct a mathematical model of a random discrete event system and construct a k-step active opaque verifier V based on the mathematical model G , where k is a preset non-negative integer;

[0077] S5: According to the k-step active opaque verifier V G Construct the corresponding Markov chain M and calculate the probability of exposing the secret location after each location information hiding scheme is enforced;

[0078] S6: Determine whether there is at least one location information hiding scheme with a corresponding probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, and all false paths are saved to complete the hiding of the location information; otherwise, re-execute step S3 to regenerate a new location information hiding scheme.

[0079] In the specific implementation process, firstly, a map is obtained, and several real locations and real paths of the user are determined on the map according to the LBS, and at least one real location is used as a secret location that needs to be hidden;

[0080] Then, a number of false locations are randomly generated within a preset range around each real location, and each real location is converted into a corresponding location area;

[0081] A number of false paths are randomly generated between each location area, and each false path that can reach the secret location is saved as a location information hiding scheme;

[0082] Then, a mathematical model of a random discrete event system is constructed. In this embodiment, the random discrete event system includes: a state set, an event set, a partial state transition probability function, and an initial state, wherein the event set includes observable events and unobservable events; the unobservable events also include controllable events, and each of the controllable events corresponds to one of the location information hiding schemes;

[0083] The mathematical model of the random discrete event system is:

[0084] G=(X,Σ,p,x0)

[0085] Where G represents a random discrete event system, X represents a state set, each state corresponds to a real location or a false location; Σ represents an event set, each event corresponds to a state transition process, wherein the migration of a user from one location area to another is recorded as an observable event, and the location migration of a user within the same location area is recorded as an unobservable event; among unobservable events, the movement of a user from an initial location to a virtual location closest to a secret location is recorded as a controllable event; p represents a partial state transition probability function, for example, state A may have three events a, b and c, with probabilities of 0.3, 0.3 and 0.4 respectively, then p(A,a)=0.3; x0 represents the initial state of the random discrete event system G;

[0086] In this embodiment, random k-step active opacity is defined as: given a random discrete event system G = (X, Σ, p, x0), for any secret state x∈X S , a non-negative integer k ≥ 0 and a threshold θ > 0, there exists a controllable event string u∈Λ x The following conditions must be met:

[0087] 1)

[0088] 2)

[0089] Then the random discrete event system G is said to have random k-step active opacity;

[0090] Intuitively, random k-step active opacity requires that for every secret state in the system G, there exists at least one controllable event string u, and the probability Pr that the path s taken by the system G satisfies k-step opacity after enforcing u isk u (s) is greater than a given threshold θ; a system G with random k-step active opacity only requires that there exists a path that satisfies k-step opacity for each secret state (rather than requiring that each path passing through the secret state satisfies k-step opacity), so that an intruder cannot determine whether the system G has reached the secret state within k steps after passing through the secret state;

[0091] For "k-step opacity", k refers to the number of steps, and the specific value is determined by the user according to specific needs. In short, k steps means that within k steps after an event occurs, the intruder does not know whether the event has occurred, that is, information protection within k steps is provided; for example, a user goes to the hospital first, then to the post office, and finally returns home. Taking the event of going to the hospital as an example, k = 0 means that the user hopes that the intruder does not know that the user has been to the hospital when he arrives at the hospital; k = 1 means that the user hopes that the intruder does not know that the user has been to the hospital when he arrives at the post office, and when the user returns home, it is already the second step, so the intruder may know that the user has been to the hospital, that is, information protection within 1 step is provided;

[0092] Constructing a k-step active opaque verifier V according to the mathematical model G , where k is a preset non-negative integer; V G Specifically:

[0093] V G =(Q,∑,f,q0)

[0094] Among them, Q is the state set after the controllable event, satisfying ∑c represents the set of controllable events, represents a sorted set of controllable events. For example, if there are controllable events c1, c2, and c3 in the system, then represents the possible ordering of all controllable events, such as c1c2c3, empty set, c1c3c2, etc.; f is the state transition function, satisfying f:Q×∑→Q; q0 is the k-step active opaque verifier V G The initial state satisfies

[0095] For the state set r∈2 X and event σ∈∑ o , UR(r) is defined as:

[0096]

[0097] Among them, UR(r) represents the set of states that state x′∈X can reach through unobservable events; therefore, UR({x0}) represents the set of states that state x0 can reach through unobservable events;

[0098] For any and σ∈∑, there are:

[0099]

[0100] u={P c (s):f(q0,s)=q}

[0101] r′=UR(Next σ (r))

[0102]

[0103] ρ0=⊙(r)

[0104] Among them, q is the state after the controllable event; state q=(x,u,r,ρ1,...,ρ k ) where x is the current state of the tracking system G; u is the controllable event sequence that runs to the current state; r is the current state estimate after path s occurs. If s is migrated to q = (x,u,r,ρ1,...,ρ k ), then r is the state estimate after s occurs, that is, ρ i is the state estimate before the i-th step, i=1,…,k;∑ uo is the set of unobservable events; o is a collection of observable events; Next σ (r) represents the set of states that state r can reach through observable events. Next σ (r) is defined as:

[0105]

[0106] For observable event strings Operator Ξ: Defined as:

[0107]

[0108] Ξ(α) represents the state pair set consisting of the state x that can execute the event string α and the state x′ that can be reached through the event string α;

[0109] For a set of state pairs Operators 2 X×X ×2 X×X →2 X×X Defined as:

[0110]

[0111] For the state set r∈2 X , operator ⊙: 2X →2 X×X is defined as:

[0112]

[0113] The difference between r′ and r is that r′ includes the states that may be reached through unobservable events after reaching the states in r. For example, in r, there are two states 1 and 2, and an invisible event a may occur in state 2, and after occurrence, it will migrate to state 3. Then r′ is the three states 1, 2, and 3, ρ i ′ is the same;

[0114] In order to use the k-step active opacity verifier V G to verify the k-step active opacity of system G, first define that for any ρ i ∈2 X×X , there is I1(ρ i ) represents the delayed state estimation of the i-th step of the stochastic discrete event system G;

[0115] Lemma 1:

[0116] For any s ∈ L(V G ) = L(G), if it can migrate from the initial state q0 to q = (x, u, r, ρ1,..., ρ K ) through the string s, that is, f(q0, s) = {x, u, r, ρ1,..., ρk}, then there are:

[0117] 1) u = P c (s)

[0118] 2)

[0119] 3) For the string α < P(s), if i := |P(s)| - |α| ≤ k, then there is

[0120] Among them, 1) can be obtained by performing a controllable mapping P c (s) on the event string s; 2) can be constructed by UR(Next(·)); 3) can be proved by induction;

[0121] Intuitively, Lemma 1 means that for any event string s ∈ L(V G ) that satisfies f(q0, s) = q, I1(ρ |P(s)|-|α| ) is the delayed state estimation of the previous i steps, that is, the states that may be passed through in the k steps before migrating to the x state;

[0122] Therefore, if the string s does not belong to L k , it only needs to satisfy one of the following conditions: 1) 2) For i = 1, ..., k, and I1(ρ i )≠φ, there is Therefore, define the state set Q KS :

[0123]

[0124] State set Q KS The meaning is: all satisfying (i.e. the current state estimate set is a subset of the secret state set) or k:I1(ρ i )≠φ and A set of states where the estimated state set one step ago is a subset of the secret state.

[0125] Lemma 2:

[0126] For any s∈L(V G )=L(G), we have:

[0127]

[0128] Proof of Lemma 2: Lemma 1 gives:

[0129]

[0130] We can further get:

[0131]

[0132] Therefore, Lemma 2 is proved;

[0133] Then we get Theorem 1: The necessary and sufficient condition for a random discrete event system G to have k-step active opacity is:

[0134] If and only if the k-step active opaque verifier V G Any state q after a controllable event, that is, q=(x,u,r,ρ1,...,ρ k ) and u≠φ, and at the same time:

[0135] 1)

[0136] 2)i∈{1,...,k}, I1(ρ i )≠φ, and

[0137] Among them, X S is a collection of secret locations;

[0138] Theorem 1 can be proved by contradiction:

[0139] Suppose that there exists a state q=(x,u,r,ρ1,...,ρ k ), and u≠φ, That is, condition 1) in Theorem 1 is violated; let f(q0,s)=q, because Indicates that the current possible states are all secret states, then There is no non-secret state and path s'∈P -1 P(s) satisfies f(x0,s')=x', so the system G does not have active opacity; and active opacity is a special case of k-step active opacity when k=0, that is, it does not have k-step active opacity either, 1) is proved;

[0140] In addition, suppose that there is a state q=(x,u,r,ρ1,...,ρ k ), satisfying u i ≠φ and for I1(ρ i )≠φ That is, condition 2 in Theorem 1 is violated; let f(q0,s)=q, the prefix And |P(t) / P(s)|=i and i≤k, I1(ρ i ) represents the state estimate of the system before the i-th step when the system reaches the q state, that is Then there is This means that the language s passes through the secret state and there is no s′∈Σ in the system * and prefix At the same time, P(s) = P(s′), P(t) = P(t′) and A language s is a language that violates k-step opacity, that is, a language s∈L(G,u,x) and Therefore, the system G does not have k-step active opacity, 2) is proved;

[0141] This method constructs a k-step active opaque verifier V G The associated Markov chain M is used to calculate the arrival time of Q KS The probability of the violation path s occurring in the state

[0142] First, for all possible locations x that can be reached i ∈X S The path s∈∑ * Make a controllable projection and get the secret state x iA set of controllable events It is expressed as:

[0143]

[0144] Among them, P c (s) represents a controllable projection of s;

[0145] If there are n secret locations in the system, then the set of secret controllable events L kc It is expressed as:

[0146] Intuitively speaking, L kc is the set of all controllable events that can reach the secret state;

[0147] Since the system runs to Q KS After the state in the state, it cannot be separated and will stay in the state for an infinite loop. Therefore, the random discrete event system G is eliminated from the state set Q KS The part that can be transferred to, and then the state space obtained is used Indicates that a new validator is constructed at the same time And further construct the Markov chain M and The state space is the same as that of , where π0 is the initial state probability vector, satisfying π0(q0)=1; p M : is the state transition function of the Markov chain, defined as: for any q=(x,u,r,ρ1,...,ρ k ), have:

[0148]

[0149] Because M excludes the system from Q KS The part to which the state can be transferred in, so if the system reaches If any state in the system is reached, the subsequent states will be merged, that is, the system will always stay in In this embodiment, Indicates that after a controllable event string u, the system stays in a The probability of a state can be calculated using the following formula:

[0150]

[0151] Among them, π0(q) represents the probability of migrating from the initial state q0 to the state q; represents the probability of transitioning from state q to the exposed state, is the minimum non-negative solution of the following equation:

[0152]

[0153] Because M is obtained by tracking the migration probability of the initial system and L(V G )=L(G), we can get Therefore, the following theorem can be obtained:

[0154] Theorem 2: The necessary and sufficient conditions for a random discrete event system G to have random k-step active opacity are:

[0155] Given a preset threshold θ, if and only if: for any There is at least one controllable event string satisfy

[0156] Specifically for the location information anonymity in the positioning system, this method is based on the k-step active opaque verifier V G Construct the corresponding Markov chain M, calculate the probability of exposing the secret location after each location information hiding scheme is enforced; finally, determine whether there is at least one location information hiding scheme with a probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, save all false paths, and complete the hiding of location information; otherwise, regenerate a new location information hiding scheme;

[0157] This embodiment solves the problem that opacity is difficult to ensure in a complex system with multiple secret states by introducing controllable events into random k-step active opacity. By applying it to a positioning system, multiple sets of location concealment schemes are actively introduced to ensure the effectiveness and reliability of location information concealment. In addition, this embodiment generalizes active opacity from discrete event systems to random discrete event systems, and also generalizes active opacity from current state opacity to k-step opacity, greatly broadening the scope of application of active opacity.

[0158] Example 2

[0159] This embodiment provides a method for hiding location information based on active opacity of a random discrete event system, including the following steps:

[0160] S1: Obtain a map, determine several real locations and real paths of the user on the map according to the LBS, and use at least one real location as a secret location that needs to be hidden;

[0161] S2: randomly generating a number of false locations within a preset range around each of the real locations, and converting each real location into a corresponding location area;

[0162] S3: randomly generating a number of false paths between each of the location areas, and saving each false path that can reach the secret location as a location information hiding scheme;

[0163] S4: Construct a mathematical model of a random discrete event system and construct a k-step active opaque verifier V based on the mathematical model G , where k is a preset non-negative integer;

[0164] S5: According to the k-step active opaque verifier V G Construct the corresponding Markov chain M and calculate the probability of exposing the secret location after each location information hiding scheme is enforced;

[0165] S6: Determine whether there is at least one location information hiding scheme with a corresponding probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, and all false paths are saved to complete the hiding of the location information; otherwise, re-execute step S3 to regenerate a new location information hiding scheme.

[0166] In the specific implementation process, this embodiment takes a map of a certain area as an example. Figure 3 As shown in , the user's motion trajectory is: starting from state 0, passing through state 1 to state 2, such as Figure 3 As shown, the three states represent three real locations, and the connecting lines represent real paths. Assume that state 1 is a sensitive location, and the user wants to keep the information “whether the user has reached state 1” secret until state 2 (that is, before reaching state 2, the outside world does not know whether the user has reached state 1).

[0167] In LBS, when the user's specific location (real location) is uploaded to the location anonymity server, several false locations are randomly generated and the specific location is converted into location areas. Suppose state 0, state 1, and state 2 are converted into area 0, area 1, and area 2, respectively. Figure 4 As shown; Figure 4 Positions 5 to 7 in zone 0, positions 3 and 8 in zone 1, and position 4 in zone 2 are all randomly generated false positions. Then, false paths are generated between states 0, 1, 2 and false positions 3, 4, 5, 6, 7, 8. The false paths are as follows: Figure 4 As shown by the black line path in ; In order to keep the confidentiality of “whether it has reached state 1”, it is assumed that the location anonymity system includes two sets of location anonymity schemes, such as Figure 5 As shown in the two paths in;

[0168] The location anonymity system is modeled as Figure 6 The random discrete event system G shown in the figure, where the event set is ∑ = {γ, α, β, c1, c2, u}, and each event corresponds to a state transition process;

[0169] The meaning of each event is shown in Table 1, where α, β, γ are observable events, representing movement to area 0, area 1, and area 2, respectively. c1, c2, and u are unobservable events, where c1 and c2 are controllable events. c1 and c2 represent anonymous scheme 1 and anonymous scheme 2, respectively. The state set is X = {0, 1..., 8}. The set of controllable events that can reach secret state 1 is

[0170] Table 1 Event description table of location anonymity system

[0171]

[0172] If you want to effectively hide your location information, you need to meet the following conditions: Among the two location anonymity schemes, at least one scheme can ensure that the probability of "the system revealing that the user has been through state 1 before reaching state 2" does not exceed 0.2;

[0173] according to Figure 6 Constructing a k-step active opaque verifier V for a random discrete event system G in G ,like Figure 7 As shown; by the formula

[0174] It can be seen that Figure 7 The states marked in the box belong to Q KS state set;

[0175] According to V G Construct the corresponding Markov chain M and calculate the set of controllable event sequences The probability that the system exposes the secret state after each controllable event string is enforced is: Figure 8 As shown, the violation rates of the two schemes c1 and c2 can be calculated respectively. and That is, in the two solutions c1 and c2, c1 satisfies the condition that the probability that the exposed user has reached state 1 before reaching state 2 does not exceed 0.2;

[0176] Therefore, when k = 1 and threshold θ = 0.2, the random discrete event system G has random 1-step active opacity, which means that the scheme c1 in this location anonymity system can ensure that the probability of "the system reveals that the user has passed through state 1 before reaching state 2" does not exceed 0.2;

[0177] This embodiment solves the problem that opacity is difficult to ensure in a complex system with multiple secret states by introducing controllable events into random k-step active opacity. By applying it to a positioning system, multiple sets of location concealment schemes are actively introduced to ensure the effectiveness and reliability of location information concealment. In addition, this embodiment generalizes active opacity from discrete event systems to random discrete event systems, and also generalizes active opacity from current state opacity to k-step opacity, greatly broadening the scope of application of active opacity.

[0178] Example 3

[0179] This embodiment provides a verification experiment for verifying whether the determination process of random k-step active opacity of the random discrete event system provided in Embodiment 1 is correct and effective;

[0180] like Fig. 9 As shown, given a random discrete event system G = (X, Σ, p, x0), the state set X = {0, 1..., 11}, where the secret state set is X S = {4,5}, event set ∑ = {α, β, γ, u, c1, c2, c3}, where ∑ o ={α,β,γ} is the observable event set, ∑ uo = {u,c1,c2,c3} is the set of unobservable events, ∑ c ={c1,c2,c3} is a set of controllable events.

[0181] In the specific implementation process, 1) verify whether the system G has active opacity: Taking the secret state 5 in the system G as an example, it can be seen that Λ 5 ={c1c3,c2c3}, if u=c1c3, u′=c1, s=c1αβγ * , we know that s∈L(G,u′), and P c (s) = c1, that is Violation of the definition of active opacity That is, G does not have active opacity;

[0182] 2) Verify whether the system G has k-step opacity: Let k = 1, take s = c1αγ, the prefix of s t = c1α, and |P(s) / P(t)| = 1, satisfying |P(s) / P(t)| ≤ k, and State 4 is a secret state, satisfying There is no path s′∈Σ in the system G. * and prefix At the same time, P(s) = P(s′), P(t) = P(t′) and Therefore, when k = 1, the system G does not have k-step opacity;

[0183] 3) Verify whether the system G has random k-step active opacity: Let k = 1, θ = 0.8. When the secret state x = 4, Λ 4 ={c1,c2}. When u = c2, all paths in system G with controllable projection equal to u will pass through secret state 4, satisfying There is a line belonging to L k The path s2=c2αβγ * , the execution probability of s1 can be obtained by formula (14) Then the path taken by the system after the forced execution of control u belongs to L k The probability of k c2 (s2) = 1.0 × 0.9 × 1.0 = 0.9; Therefore, when the secret state x = 4, u = c2, it satisfies and Two conditions;

[0184] When the secret state x = 5, we can get Λ 5 ={c1c3,c2c3}, when u = c1c3, there is a path belonging to L k Paths 13 =c1c3αβγ * , the execution probability is Therefore, when the secret state x=5,u=c1c3,then and Two conditions;

[0185] Therefore, for each secret state in the random discrete event system G, there exists a controllable event string u, and the probability that the path s taken by the system satisfies the k-step opacity after enforcing u is Therefore, when k = 1, the random discrete event system G has random k-step active opacity;

[0186] Then, the method provided in Example 1 is used to determine whether the random discrete event system G has random k-step active opacity;

[0187] When k = 1, G's k-step active opaque verifier V G like Fig.10 As shown, V G The initial state q0={0,φ,{0,1,2,3,6},{φ}};

[0188] When the event string c1α occurs, the system will migrate to a new state, represented by q=(x,u,r,ρ1), where q=(4,c1,{4,5,7},{(0,4),(1,4),(2,4),(0,7),(6,7),(0,5),(2,5),(3,5)}); u=c1 here means that the controllable event string before reaching this state is c1; r={4,5,7} means that after observing the occurrence of the observable event string α, the current possible state of the system is state 4, state 5 or state 7; ρ1 represents the delayed state estimate of the previous step, such as (0,4) in ρ1 means that the previous step estimate of state 4 is state 0;

[0189] pass Fig. 9 System G and Fig.10 V G Constructing a Markov chain like Fig.11 As shown; the system G contains two secret states 4 and 5, then the controllable event sequences that can reach states 4 and 5 are and Then the set of G's secret controllable events L kc ={{c1,c2},{c1c3,c2c3}}; Fig.11 The ones marked in the box belong to Q ks The state of, such as state (9,C1,{9},{(4,9),(5,9)})∈Q ks ;

[0190] For convenience, we move each state in M ​​from M1 to M 22 Number, what needs to be calculated is the secret controllable event series L kc The probability of each controllable event string exposing the secret state in The controllable event string c2c3 in the example has M4,M 17 ,M 18 ,M 19 and M 20 , plus the initial state M1, the probability that the state after c2c3 will eventually expose the secret state is calculated by the following equation:

[0191]

[0192] The above equations have infinite solutions. In order to obtain the minimum result, we take the free variable Can get Respectively represent from M1 to M 22 The probability that the state migrates to the marked state through the controllable event string c2c3; therefore, we can get That is, the probability of forcing the c2c3 event to be exposed is 0.1;

[0193] Similarly, the probability of exposing the secret state of executing c2 can be obtained as The probability of exposing the secret state when executing c1 is The probability of exposing the secret state when executing c1c3 is

[0194] Therefore, in In the example above, the path with controllable projection c2c3 is selected for forced execution. We choose to enforce the path through the controllable projection c2, then when k = 1, for all thresholds θ> 0.1, G has random k-step active opacity;

[0195] This embodiment uses the method proposed in Example 1, and the final verification result is correct. By constructing a k-step active opaque verifier V for the random discrete event system G G , introduce controllable events, and further construct the Markov chain M, and finally calculate the probability of the secret state being exposed after the controllable event is enforced. It can be seen that the judgment method proposed in Example 1 (i.e., Theorems 1 and 2) is effective and can solve the problem that opacity is difficult to ensure in a complex system with multiple secret states. At the same time, it expands the scope of application of active opacity, applies it to the positioning system, and actively introduces multiple sets of location hiding schemes, which can ensure the effectiveness and reliability of location information hiding.

[0196] The same or similar reference numerals correspond to the same or similar components;

[0197] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0198] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for hiding location information based on active opacity of a random discrete event system, characterized in that: The following steps are involved: S1: Obtain a map, determine several real locations and real paths of the user on the map according to the LBS, and use at least one real location as a secret location that needs to be hidden; S2: randomly generating a number of false locations within a preset range around each of the real locations, and converting each real location into a corresponding location area; S3: randomly generating a number of false paths between each of the location areas, and saving each false path that can reach the secret location as a location information hiding scheme; S4: Construct a mathematical model of a random discrete event system and construct a k-step active opaque verifier V based on the mathematical model G , where k is a preset non-negative integer; S5: According to the k-step active opaque verifier V G Construct the corresponding Markov chain M and calculate the probability of exposing the secret location after each location information hiding scheme is enforced; S6: Determine whether there is at least one location information hiding scheme with a corresponding probability less than a preset threshold. If so, the mathematical model of the random discrete event system has random k-step active opacity, and all false paths are saved to complete the hiding of the location information. Otherwise, step S3 is executed again to regenerate a new location information hiding scheme.

2. According to claim 1, a method for hiding location information based on active opacity of a random discrete event system is characterized in that: In step S4, the random discrete event system includes: a state set, an event set, a partial state transition probability function and an initial state, wherein the event set includes observable events and unobservable events.

3. The method for hiding location information based on active opacity of a random discrete event system according to claim 2 is characterized in that: The unobservable events also include controllable events, and each of the controllable events corresponds to a location information hiding scheme.

4. The method for hiding location information based on active opacity of a random discrete event system according to claim 3 is characterized in that: In step S4, the mathematical model of the random discrete event system is: G=(X,Σ,p,x0) Where G represents a random discrete event system, X represents a set of states, each state corresponds to a real location or a false location; Σ represents a set of events, each event corresponds to a state transition process, in which the migration of a user from one location area to another is recorded as an observable event, and the location migration of a user within the same location area is recorded as an unobservable event; among unobservable events, the movement of a user from an initial location to a virtual location closest to a secret location is recorded as a controllable event; p represents a partial state transition probability function; x0 represents the initial state of the random discrete event system G.

5. The method for hiding location information based on active opacity of a random discrete event system according to claim 4 is characterized in that: In step S4, the k-step active opaque verifier V G Specifically: IN G =(Q,∑,f,q0) Among them, Q is the state set after the controllable event, satisfying represents the ordered set of controllable events; f is the state transition function, satisfying f:Q×∑→Q; q0 is the k-step active opaque verifier V G The initial state satisfies UR({x0}) represents the set of states that state x0 can reach through unobservable events; For any and σ∈∑, there are: r′=UR(Next σ (r)) Where q is the state after the controllable event; x is the current state of the random discrete event system G; u is the controllable event sequence that runs to the current state; r is the current state estimate corresponding to the unobservable event after path s occurs; r is the current state estimate corresponding to the observable event after path s occurs; ρ i is the state estimate before the i-th step corresponding to the unobservable event, i = 1,…,k; ρ i ′ is the state estimate before the i-th step corresponding to the observable event; ∑ uo is the set of unobservable events; o is a collection of observable events; Next σ (r) represents the set of states that state r can reach through observable events; Ξ(σ) represents the set of state pairs consisting of states that can execute event σ and states that can be reached through event σ; is the preset operator; For any ρ i ∈2 X×X ,have I1(ρ i ) represents the delayed state estimate of the i-th step of the random discrete event system G.

6. The method for hiding location information based on active opacity of a random discrete event system according to claim 5, characterized in that: The necessary and sufficient conditions for the random discrete event system G to have k-step active opacity are: If and only if the k-step active opaque verifier V G Any state q after a controllable event, that is, q=(x,u,r,ρ1,...,ρ k ) and u≠φ, and at the same time: Among them, X S A collection of secret locations.

7. A method for hiding location information based on active opacity of a random discrete event system according to claim 5 or 6, characterized in that: In step S5, according to the k-step active opaque verifier V G Constructing the corresponding Markov chain M includes: For all possible locations x that can be reached i ∈X S The path s∈∑ * Make a controllable projection and get the secret state x i A set of controllable events It is expressed as: Among them, P c (s) represents a controllable projection of s; If there are n secret locations in the system, then the set of secret controllable events L kc It is expressed as: Define the state set Q KS : Eliminate the state set Q in the random discrete event system G KS After the part that can be migrated to, the state space obtained is Indicates that the Markov chain is constructed Wherein, π0 is the initial state probability vector, satisfying π0(q0)=1; is the state transition function of the Markov chain, defined as: for any q=(x,u,r,ρ1,...,ρ k ), have: Calculate the probability of exposing the secret location after each location information hiding scheme is enforced Specifically: Among them, π0(q) represents the probability of migrating from the initial state q0 to the state q; represents the probability of transitioning from state q to the exposed state, is the minimum non-negative solution of the following equation:

8. The method for hiding location information based on active opacity of a random discrete event system according to claim 7, characterized in that: The necessary and sufficient conditions for the random discrete event system G to have random k-step active opacity are: Given a preset threshold θ, if and only if: for any There is at least one controllable event string satisfy 9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps in the method according to any one of claims 1 to 8 are implemented.

10. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores computer-readable instructions. When the computer-readable instructions are executed by the processor, the steps in the method according to any one of claims 1 to 8 are executed.

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