CN-119622802-B - Position information hiding method based on active opacity of random discrete event system

CN119622802BCN 119622802 BCN119622802 BCN 119622802BCN-119622802-B

Abstract

The invention provides a position information hiding method based on active opacity of a random discrete event system, which comprises the steps of modeling a position information hiding system as a random discrete event system, constructing a k-step active opacity verifier V G according to a modeled mathematical model, further constructing a Markov chain M, calculating the probability of exposing a secret position after forced execution of each position information hiding scheme, judging whether at least one position information hiding scheme exists, if so, the mathematical model of the random discrete event system has random k-step active opacity, completing position information hiding, otherwise, regenerating a new position information hiding scheme, and meanwhile, presetting a plurality of sets of position information hiding schemes, introducing active control into opacity research, verifying k-step active opacity, improving the control capability of the opacity, widening the application range of the active opacity, and effectively realizing the reliable hiding of the position information.

Inventors

LIU FUCHUN
LIU WEIQI

Assignees

广东工业大学

Dates

Publication Date: 20260508
Application Date: 20241122

Claims (10)

1. A method for hiding position information based on active opacity of a random discrete event system, comprising the steps of: S1, acquiring a map, determining a plurality of real positions and real paths of a user on the map according to LBS, and taking at least 1 real position as a secret position to be hidden; s2, randomly generating a plurality of false positions in a preset range around each real position, and converting each real position into a corresponding position area; S3, randomly generating a plurality of false paths between each position area, and storing each false path which can reach the secret position as a position information hiding scheme; s4, constructing a mathematical model of a random discrete event system, and constructing a k-step active opaque verifier according to the mathematical model Wherein k is a preset non-negative integer; s5, initiative opaque verifier according to the k steps Constructing corresponding Markov chains Calculating the probability of exposing the secret position after the forced execution of each position information hiding scheme; And S6, judging whether at least one probability corresponding to the position information hiding scheme is smaller than a preset threshold value, if yes, enabling a mathematical model of the random discrete event system to have random k-step active opacity, storing all false paths to complete hiding of the position information, otherwise, re-executing the step S3, and regenerating a new position information hiding scheme.
2. The method for hiding position information based on active opacity of a random discrete event system according to claim 1, wherein in step S4, the random discrete event system comprises a state set, an event set, a partial state transition probability function and an initial state, wherein the event set comprises observable events and unobservable events.
3. The method for hiding position information based on active opacity of random discrete event system according to claim 2, wherein said unobservable events further comprise controllable events, each of said controllable events corresponding to one of said position information hiding schemes.
4. A method for hiding position information based on active opacity of a random discrete event system according to claim 3, wherein in step S4, the mathematical model of the random discrete event system is: Wherein, the Representing a system of random discrete events, Representing a set of states, each state corresponding to a real or false location; Representing an event set, wherein each event corresponds to a state migration process, wherein migration of a user from one location area to another location area is recorded as an observable event, and location migration of the user in the same location area is recorded as an unobservable event; representing a partial state transition probability function; Representing a random discrete event system Is set in the initial state of (2).
5. The method for hiding position information based on active opacity of random discrete event system according to claim 4, wherein in step S4, k steps are performed by an active opacity verifier The method comprises the following steps: Wherein, the To pass the state set of the controllable event, satisfy , Representing an ordered set of controllable events; Is a state transition function, satisfies ; Active opaque verifier for k steps Is satisfied with , Representing the status A set of states reachable through an unobservable event; for any one And The method comprises the following steps: Wherein, the Is the state of passing a controllable event; system for random discrete events Is the current state of (2); a string of controllable events passed for running to a current state; Is a path Estimating the current state corresponding to the unobservable event after occurrence; Is a path Estimating the current state corresponding to the observable event after occurrence; for state estimation before the i-th step corresponding to the unobservable event, ; Estimating the state before the i-th step corresponding to the observable event; Is a collection of unobservable events; is a set of observable events; Representing the status A set of states reachable through observable events; representing executable events Status and passable events of (a) A set of state pairs consisting of the reached states; Is a preset operator; for any one There is , Representing a random discrete event system And (3) estimating the delay state in the i step.
6. The method for hiding location information based on active opacity of random discrete event system according to claim 5, wherein said random discrete event system The full requirements for active opacity with k steps are: active opaque verifier if and only if k steps The status of any one passing a controllable event I.e. And is also provided with Simultaneously satisfies: And Wherein, the Is a collection of secret locations.
7. The method for hiding position information based on active opacity of random discrete event system according to claim 6, wherein in step S5, according to said k-step active opacity verifier Constructing corresponding Markov chains Comprising the following steps: for all reachable secret locations Is a path of (a) Controllable projection is performed to obtain a secret state Controllable event cluster of (a) Expressed as: Wherein, the Representation pair Performing controllable projection; If n secret locations exist in the system, a secret controllable event string set Expressed as: ; defining a set of states : System for eliminating random discrete event From a set of states After the part which can be migrated to, the obtained state space is used for Representation, construction of the Markov chain , wherein, Is an initial state probability vector, satisfies ; The state transition function of the Markov chain is defined as, for any arbitrary , The method comprises the following steps: Calculating the probability of exposing the secret location after enforcement of each location information concealment scheme The method specifically comprises the following steps: Wherein, the Representing from the initial state Transition to State Probability of (2); Representing slave states The probability of migrating to the exposed state is that, Is the least nonnegative solution of the following equation: 。
8. The method for hiding position information based on active opacity of random discrete event system according to claim 7, wherein said random discrete event system The full requirements for active opacity with random k steps are: Given a preset threshold If and only if for any There is at least one controllable event string Satisfies the following conditions 。
9. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
10. An electronic device comprising a processor and a memory storing computer readable instructions which, when executed by the processor, perform the steps of the method of any of claims 1-8.

Description

Position information hiding method based on active opacity of random discrete event system Technical Field The invention relates to the technical field of position information hiding, in particular to a position information hiding method based on active opacity of a random discrete event system. Background Discrete event systems (DISCRETE EVENT SYSTEMS, DESs for short) are a type of dynamic system in which discrete events interact according to a certain rule, resulting in state evolution. Due to the significant advantages in optimizing control, fault diagnosis and prediction, information security verification, and the like, DESs have been widely used in a number of fields such as industrial manufacturing, software engineering, traffic control, computer integrated manufacturing systems, electronic communication networks, robotics, and the like. In recent years, opacity (opacity) research of discrete event systems has attracted a great deal of attention from many students at home and abroad, and in document [5], lin first proposes an opacity concept under the DESs framework, and researches on applications of opacity in aspects of observability, anonymity, diagnosability and the like. Intuitively, a system with opacity satisfies that for any one path to reach the system secret state, there is at least one other path to reach the non-secret state, so that the two paths have the same observation value. Therefore, a system with opacity can effectively resist an attack of an intruder to protect privacy, because the intruder cannot determine whether the state reached by the system is a secret state or a non-secret state only from the observation result thereof. As such, it finds important application in information security mechanisms such as digital signature, secure communications, information authentication, intrusion detection, data encryption, and the like. Aiming at the problem that opacity is difficult to guarantee in a complex system with a plurality of secret states, controllable events are introduced in a document "TAN J X, LIU F, ZBIGNIEW D. Active opacity of discrete-event systems[J]. International Journal of Control, 2023, 96(8): 2090-2099", an active opacity concept is provided, an active opacity verifier is constructed, and a sufficient requirement for checking the active opacity of the system is provided, however, the document only researches the active opacity of the current state of DESs under the DESs frame taking a deterministic automaton as a model, lacks the capability of dynamic analysis, and has a narrow application range. Traditional opacity studies are based mainly on binary representation methods, i.e. the opacity of all systems is divided into two forms, completely transparent or completely opaque. However, in real world application scenarios, it is often difficult to ensure that the system achieves absolute opacity due to unforeseen factors (e.g., sensor failure, etc.). 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 some acceptable threshold. With the popularity of mobile devices and online transaction systems for positioning systems, more and more applications are beginning to require users to provide real-time location information in an effort to provide personalized and timely information to the users, such services being referred to as location-based services (Location Based Services, LBS), which are required for example, take-away and navigation services. LBS increases the harm of privacy exposure while providing better service to users, and intruders can learn about the home address, work place, and even physical condition of users through the information. In order to protect the location privacy of the user, the most commonly used technology of LBS is a location anonymizer (location anonymizers) based on location anonymizing service, the location anonymizer converts the accurate location information of the user into a location area which contains a plurality of false location information and is larger than the accurate location range, and then the location area is provided to the LBS server, and the workflow of the location area is shown in fig. 1; When the user is in a motion state, since the LBS data is provided only in some location areas, a situation that the user trajectory is not consistent or clear may occur. Thus, in addition to setting up false locations, there is a need to set up false paths, i.e. to arrange the same trajectory paths as the user between false locations, especially for those sensitive locations, which the user may further require in order to better protect privacy, that the sensitive locations have not been reached for a certain period of time (or ever) after passing through them are exposed. Based on the above considerations, numerous researchers began to