A Current State Opacity Verification Method Based on Labeled Timed Petri Nets

Abstract

The present invention belongs to the field of information security technology, and specifically relates to a current state opacity verification method based on a labeled time Petri net, including establishing a labeled time Petri net model of a system to be verified, proposing a method based on linear programming to determine a logical transition sequence consistent with a given time by utilizing time constraints related to transition sequences, constructing a key MSCG consistent with the given time, seeking state classes whose identifiers belong to a secret set and are observable identifiers in the key MSCG, and determining observable label sequences that can reach these state classes, and based on the key MSCG, judging whether a logical identifier set consistent with a given time and an observable label sequence is included in a secret set. The present invention proposes a method for judging whether a system is opaque about a secret set within a given time without enumerating state classes consistent with a given time and all observed label sequences, which greatly reduces the risk of attacks on systems with time requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of information security, and in particular relates to a current state opacity verification method based on a label time Petri net. Background Art

[0002] With the rapid development of network communications and the improvement of information level, information security issues have become increasingly prominent. In this context, a novel concept, information flow, has emerged in the information field, which describes the transmission of secret data from high-level users to low-level users (possibly indirectly). Opacity is a key aspect of information security. The opacity of a system refers to the inability of external intruders to observe the secret state of the system. In recent years, many domestic and foreign scholars have devoted themselves to combining discrete event systems (DES) with opacity and have made significant research progress.

[0003] In DES, current state opacity is a manifestation of system opacity. Assuming that the intruder knows the structure and initial identification of the system and can only observe the occurrence of some events, if the intruder cannot determine that the current state obtained based on the observed event sequence is a subset of the secret state, the system is said to be current state opaque with respect to the secret state. In recent years, research on current state opacity has mainly focused on DES that is not assigned time information (referred to as untimed DES). For example, Tong et al. in the paper "Verification of Current-state Opacity Using PetriNets" constructed a reduced reachability graph (basic reachability graph) based on the algorithm of the basic reachability graph, enumerated a set of reachable identifications, expressed other identifications by a set of linear equations related to the reachable identifications, and proposed a necessary and sufficient condition for verifying the current state opacity of bounded Petri nets. This verification method does not need to enumerate all reachable states of the system, thereby reducing the computational cost of the system state space. However, the current state opacity of DES assigned time information (referred to as timed DES) will change over time. Therefore, the research method of the current state opacity of the untimed DES cannot be directly applied to the timed DES. In order to solve the problem of verifying the current state opacity of a real-time observation of a timed DES based on labeled time Petri nets, Qin et al. designed a key observer based on parallel SCG in the paper "Verification of Current-state Opacityin Time Labeled Petri Nets with Its Application to Smart Houses" to solve the current state consistent with the real-time observation. However, since the number of real-time observations of a timed DES is infinite, this research method cannot be used to verify the current state opacity of the entire timed DES.

[0004] The current state opacity of the real-time system ensures that specific information of the system will not be known to intruders, thereby avoiding privacy leakage or security accidents, especially in communication protocol systems or railway systems. However, there are few studies that consider the impact of time factors on the current state opacity of the entire real-time system, and there is still a lack of effective solutions to the current state opacity verification problem of timed DES.

[0005] Therefore, it is necessary to propose a new current state opacity verification method based on labeled time Petri nets. Summary of the invention

[0006] The purpose of the present invention is to provide a method for verifying the current state opacity of a timed DES based on a labeled time Petri net without enumerating the state classes that are consistent with a given time and all observed label sequences, thereby reducing the computational cost of solving the current state and greatly reducing the risk of the system being attacked, so that the system has a higher resistance to potential attacks and provides reliable protection for the security of data and information.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A method for verifying the opacity of a current state based on a labeled time Petri net comprises the following steps:

[0009] S1: Establish a label time Petri net model of the system to be verified;

[0010] S2: By utilizing the time constraints related to the transition sequence, a linear programming-based method is proposed to determine the logical transition sequence consistent with the given time and construct the key MSCG consistent with the given time;

[0011] S3: Find the state classes whose identities belong to the secret set and are observable in the key MSCG, and determine the observable label sequences that can reach these state classes;

[0012] S4: Based on the key MSCG, by determining whether the set of logical identifiers consistent with the given time and observable tag sequence is included in the secret set, verify whether the system is opaque about the current state of the secret set at a given time.

[0013] The technical effects achieved by the present invention are:

[0014] The present invention proposes a key MSCG construction algorithm for representing a partial state space of a labeled time Petri net system by analyzing the satisfaction of a set of time constraints associated with transitions, in order to seek state classes and paths consistent with a given time, and accurately represents all state classes that the system can reach and the observation label sequences that can be triggered within a given time.

[0015] The method proposed in this invention verifies the opacity of the current state of the timed DES system under the label time Petri net modeling. It greatly reduces the damage of the system being attacked, makes the system more resistant to potential attacks, and provides reliable protection for the security of data and information. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of current state opacity verification based on label time Petri net of the present invention;

[0017] Figure 2It is a model diagram of the label time Petri net system in the present invention;

[0018] Figure 3 It is the key MSCG diagram that the labeled time Petri net system in the present invention is consistent with τ=3. DETAILED DESCRIPTION

[0019] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0020] Example

[0021] like Figure 1-3 As shown, a current state opacity verification method based on labeled time Petri nets. An embodiment of the present invention provides a current state opacity verification method of timed DES based on labeled time Petri nets. This method does not need to list state classes consistent with a given time and all observed label sequences, reduces the number of current states to be solved, and greatly reduces the risk of attacks on the system, so that the system has a higher resistance to potential attacks, providing reliable protection for the security of data and information.

[0022] The code implementation of the key MSCG construction algorithm can be generated by running in Python language in the Pycharm interpretation environment, or can be implemented using other software tools such as Matlab, which is not limited here. In addition, the key MSCG construction algorithm used in the present invention is not limited to the embodiments provided in this method, but can also be applied to other embodiments;

[0023] The following steps are involved:

[0024] S1: Establish a label time Petri net model of the system to be verified;

[0025] A Petri net is represented by the following quadruple:

[0026] N={P,T,Pre,Post}

[0027] Where P = {p1, p2, ..., p m} represents a finite set of m places, T = {t1, t2, …, t n} represents a finite set of n transitions, Pre / Post: is the pre- or post-correlation function of N, p1, p2, …, p m represents the m places in the Petri net place set P, t1, t2, …, t nrepresents n transitions in the Petri net transition set T;

[0028] The association matrix of a Petri net is represented by C = Post-Pre. Indicates that a non-negative token number is assigned to each place, which reflects the state of the system;

[0029] Where C represents the incidence matrix of the Petri net;

[0030] The enabling transition t is emitted at M, generating a new identity:

[0031] M'=M+C(·,t)

[0032] Where C(·,t) represents the column vector corresponding to the transition t in the incidence matrix C;

[0033] The set of logically enabled transitions at M is expressed as:

[0034] E(M)={t∈T|M≥Pre(·,t)}

[0035] Where Pre(·,t) represents the column vector corresponding to the transition t in the pre-correlation function Pre;

[0036] The labeled time Petri net consists of two tuples Indicates that, N t =(N,Q) represents the time Petri net, represents a labeled time Petri net, where N t represents the time Petri net, represents the label function associated with the transition, where N t =(N,Q) represents a time Petri net, N represents the Petri net, Q represents the time function associated with the Petri net transition, which is the time function for each transition t in the Petri net. i Assign two rational numbers l i and u i , and is the transition t i Assign two rational numbers l i and u i The time function is:

[0037]

[0038] represents the set of non-negative rational numbers, Representing a collection and collection The Cartesian product of is the set of non-negative rational numbers, is the union of the set of non-negative rational numbers and the element +∞. The time function Q is the transition t in the Petri net transition set T. i Assign two rational numbers l i and u i , to form a static transmission delay interval [l i ,u i ],in is a non-negative rational number, is a non-negative rational number or +∞;

[0039] And, Q(t i )=[l i ,u i ] indicates t i The static transmission delay interval, where 0≤l i ≤u i ,l i ≠∞;

[0040] The label function associated with the transition is:

[0041]

[0042] In which, the above formula specifies an empty string ε or a symbol belonging to the label set Υ for each transition t∈T, and represents the set of unobservable transitions labeled ε, represents the set of observable transitions. Secondly, the temporal Petri net system considered in S1 is bounded, and there is no unobservable transition cycle that can be emitted in zero duration. In addition, the unobservable subnet of the system is acyclic.

[0043] Combine the following Figure 2 The step S1 in this embodiment is explained.

[0044] The system considered is a simple data transmission program, which consists of a buffer and two addresses. Address 1 is the actual address of the user, which contains a lot of private information. An intruder can infer the existence of address 1 by observing some activities of the system, thereby accessing sensitive data and tracking the user's privacy behavior. In addition, address 2 is an arbitrarily generated address without any substantial information, and the intruder cannot obtain any relevant information.

[0045] In order to hide the activity of address 1, the database transfers data to address 1 and address 2. Specifically, the transmission process can be simplified into the following steps: Data is stored in buffer 1. When address 1 and address 2 are ready, the system starts data transmission. After receiving the data, buffer 1 can continue the next transmission. According to step 1, the above transmission process is established into a labeled time Petri net model, see Figure 2, where buffer 1 is modeled as place p1, the data transmission process is modeled as p2 and p4, address 1 and address 2 are modeled as p3 and p4, the data in buffer 1 starts to be transmitted to address 1 as t1 and the transmission time is calibrated as [0,2]. This process is calibrated as unobservable and labeled as ε, the end of p2 is modeled as t2 and the transmission time is calibrated as [2,3]. This process is calibrated as observable and labeled as a, the data in buffer 1 starts to be transmitted to address 2 as t3 and the transmission time is calibrated as [1,2]. This process is calibrated as observable and labeled as c, the end of p4 is modeled as t4 and the transmission time is calibrated as [2,4]. This process is calibrated as unobservable and labeled as ε, the data received at address 1 and address 2 are modeled as t5 and t6 respectively and the transmission time is calibrated as [3,4] and [3,5] respectively, t5 is calibrated as unobservable and labeled as ε, t6 is calibrated as observable and labeled as b, the practical significance of each element in the model is given in the following table:

[0046] Repository / Change meaning Static time interval Label <![CDATA[p1]]> Buffer 1 \ \ <![CDATA[p2]]> Data transmission process \ \ <![CDATA[p3]]> Address 1 \ \ <![CDATA[p4]]> Data transmission process \ \ <![CDATA[p5]]> Address 2 \ \ <![CDATA[t1]]> Start transferring data [0,2] ε <![CDATA[t2]]> End of data transfer [2,3] a <![CDATA[t3]]> Start transferring data [1,2] c <![CDATA[t4]]> End of data transfer [2,4] s <![CDATA[t5]]> Address 1 receives data [3,4] ε <![CDATA[t6]]> Address 2 receives data [3,5] b

[0047] The above table shows the practical significance of the places and transitions of the labeled time Petri net.

[0048] The initial identity of the given system is M0 =

[10101] T , if only address 1 receives data, there may be potential information leakage, and the intruder may track the user's activities, so this situation is marked as a secret behavior, that is:

[0049] H={[0 0 1 1 0] T ,[1 0 1 0 0] T ,[0 0 1 0 0] T}.

[0050] S2: By utilizing the time constraints related to the transition sequence, a linear programming-based method is proposed to determine the logical transition sequence consistent with the given time and construct the key MSCG (modified stateclass graph) consistent with the given time;

[0051] The time transition sequence of the time Petri net with initial identifier M0 is expressed as:

[0052]

[0053] Among them, σ represents the time-varying sequence, τ k Indicates change The trigger time, and τ1≤τ2≤…≤τ k , represents a set of non-negative real numbers, ignoring the time information τ in σ k, and k is a natural number, and its logic transition sequence (logic transition sequence, LTS) is expressed as:

[0054]

[0055] Among them, a time-varying sequence σ is emitted from M0 to generate a reachable marker M k The process is recorded as M0[σ>M k , the set of all identifiers reachable from M0 is denoted as R(N t ,M0), the set of all logical transition sequences LTS is represented as L(N t ,M0);

[0056] The state of the label time Petri net system is represented by Z k =(M k ,θ k ), where θ k Representation and identification M k A set of inequalities related to the emission intervals of all enabled transitions It is marked by the reachability symbol M k And the following inequality:

[0057]

[0058] where ξ i Indicates that in Z k Enabling Transition i The emission delay of each inequality indicates that the transition t i ∈E(M k ) can be passed through time units later, and must be time units ago, if the transition t i In state Z k If it can be launched, then the transition t i Satisfy M≥Pre(·,t) and time constraints Among them, j is used to distinguish the mark M k The next enabling transition set E(M k ) indices of different transitions, t j ∈E(M k ) indicates that in the mark M k The transition with index j in the set of enabled transitions is: It means that in the mark M k The enabled transition t with index j j The maximum transmission delay.

[0059] Furthermore, given a labeled time Petri net system and a given time τ, the set of logical transition sequences consistent with τ is defined as:

[0060]

[0061] in, express The emission time of the last transition in , T * Represents the set of all logical transition sequences consisting of the transitions in the Petri net transition set T.

[0062] The set of identities consistent with τ is defined as:

[0063]

[0064] The set of states consistent with τ is defined as:

[0065]

[0066] Among them, S k =(M k ,Θ k ) represents a state class, a state class represents a set of states with the same reachable identifier, is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S k The trigger delay below.

[0067] Furthermore, in order to determine the logical transition sequence consistent with a given time, it is necessary to analyze the satisfiability of the time constraints related to the transition by solving linear programming problems (LPPs) to determine the set of logical transition sequences E(τ) consistent with the time τ, and then construct the key MSCG consistent with the given time τ.

[0068] First, we construct the MSCG of the labeled time Petri net system. MSCG is a directed graph used to represent the state space of the labeled time Petri net system. Its nodes represent state classes. In addition, the edges of MSCG represent the connection information from the parent node to the child node, which is recorded as:

[0069]

[0070] in t i Tags, Indicates that from the parent node S k To the child node i The allowed transmission interval, Indicates the changei Tags, Indicates that from the parent node S k Emission transition i The allowed transmission time interval to the child nodes;

[0071] Based on MSCG, this application defines a The relevant paths are as follows:

[0072]

[0073] in, Representation and logical transition sequence The relevant path, that is, from the root node (state class) Start firing in sequence The transitions in the A path is formed, and Representation status class Transition through launch Arrival status class S kq+1 Connection information, where Indicates change Tags, Indicates change In the state class The allowed transmission time interval under Wherein, q is a natural number.

[0074] In order to calculate the state classes and paths consistent with a given time τ, we first give a set of state classes consistent with the path The time constraints associated with a given time τ are:

[0075]

[0076] In the above formula, the constraint (a1-a2) is related to the path The inequality related to the allowed emission interval of all transitions in , constraint (a3) ​​indicates that the system changes from state class To target state class The required time must be less than or equal to the given time τ, where q is a natural number.

[0077] By introducing the objective function in constraint (a3), the following LPP can be obtained:

[0078]

[0079] The existence of a feasible solution satisfying constraint (3) is tested by the LINGO package. If LPP (4) has no solution, then the path Obviously inconsistent with τ.

[0080] Furthermore, in the key MSCG construction algorithm consistent with a given time, at initialization, Π represents a set of paths consistent with a given time.

[0081] The specific steps include:

[0082] Input: a labeled time Petri net system with an initial state class S0 = (M0, Θ0) and a given time τ;

[0083] S21, initialization set S(τ):={S0}; in Mark as "new";

[0084] S22, MSCG of computing system;

[0085] S23. If there is a path marked as "new" in the UI, select any path marked as "new" from the UI.

[0086] S231. Searching for paths in a reachable graph For all enabled transitions t that can be emitted at the terminal node of the path, compare them with Splicing, thus expanding the new path to:

[0087]

[0088] For Path Construct the constraints as shown in formula (3). If there is a feasible solution to LPP (4), mark it as "new" and update the set

[0089] like The terminal node does not belong to S(τ), update the set

[0090] S232, remove Marking;

[0091] S24, removing the state classes and paths that are inconsistent with the given time in MSCG;

[0092] Output: Key MSCG corresponding to the given time.

[0093] To obtain a new path In step S231, search for a path in the reachable graph The old path Connect with all the emissible enabling transitions t under its terminal node to form a new path

[0094] In order to obtain the state class and path consistent with the given time, in step S231, for the path Construct the constraints as shown in formula (3). If there is a feasible solution about LPP (4), it means that the path is consistent with the given time.

[0095] To avoid repeated storage of state classes, step S231 is used to determine whether there is a state class in S(τ) If not, it will be stored

[0096] Combine the following Figure 3 Step S2 in this embodiment is explained.

[0097] If the system is in the initial state:

[0098] S0=(M0,Θ0)(M0=[1 0 1 0 1] T ,Θ0={0≤η1≤2,1≤η3≤2,3≤

[0099] η5≤4,3≤η6≤5})

[0100] Given a given time τ = 3, for the initial path Its terminal node is S0. The enabled transitions that can be transmitted under S0 are t1 and t3. For the enabled transition t1, compare it with Splicing to form new Expand to new path By obtaining the time constraints associated with transition δ, the following set of constraints can be obtained:

[0101]

[0102] By introducing the objective function From equation (5), a feasible solution can be found, which means that S1 and the path π(t1) are consistent with the given time τ=3.

[0103] For Path Its terminal node is S3. The enabling transitions that can be transmitted under S3 are t5 and t6. For enabling transition t5, combine it with Splicing to form new Expand to new path By obtaining the time constraints associated with transition δ, the following set of constraints can be obtained:

[0104]

[0105] By introducing the objective function According to equation (6), no feasible solution can be found, which means that S5 and the path π(t1t2t5) are inconsistent with the given time τ=3.

[0106] By repeating the same verification for all transition sequences consistent with time, we can obtain the key MSCG consistent with the given time τ = 3, as Figure 3 shown.

[0107] S3: Find the state classes whose identities belong to the secret set and are observable in the key MSCG, and determine the observable label sequences that reach these state classes;

[0108] Furthermore, given a labeled time Petri net system, the set of all observable identifiers reachable from M0 is defined as

[0109]

[0110] t o represents an observable transition and its label Υ is the label set, represents the set of observable transitions;

[0111] Furthermore, given a label-time Petri net system, a time label sequence is represented as:

[0112]

[0113] Among them, α h represents the hth label in the time label sequence ω, β h Represents the label α h The time observed, is a non-negative number and satisfies β1≤β2≤…≤β h , so α1 represents the first label in the time label sequence ω, and β1 represents the time when label α1 is observed;

[0114] The label sequence that is consistent with the ω logic is called an observable label sequence (OLS), which is expressed as:

[0115]

[0116] The set of all observable tag sequences reachable from M0 is defined as:

[0117]

[0118] Where Γ represents the set of all observable label sequences reachable from M0, Υ * represents the set of all label sequences consisting of labels in the label set Y, Representation and logical transition sequence The associated tag sequence;

[0119] Combine the following Figure 3 Step S3 in this embodiment is explained.

[0120] Through the key MSCG, we know that there are state classes S2, S8 and S9, whose identifiers belong to M o (G)∩H. For state class S2, the system can reach state class S2 through OLS c. For state class S8, the system can reach state class S8 through OLS ab. For state class S9, the system can reach state class S9 through OLS ba.

[0121] S4: Based on the key MSCG, by determining whether the set of logical identifiers consistent with the given time and observable tag sequence is included in the secret set, verify whether the system is opaque about the current state of the secret set at a given time.

[0122] In S4, given a label time Petri net system, a given time τ and a secret set H∈R(N t ,M0), for any If there is a state class Its logo is:

[0123] M f ∈(M o (G)∩H)

[0124] Among them, (M o (G)∩H) represents the set M of all observable identifiers reachable from M0 o (G) intersection with the secret set H;

[0125] in, is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S f The trigger delay is as follows: is a non-negative rational number, indicating that in the state class S f Down Enable Transition t i The minimum trigger delay of is a non-negative rational number or +∞, indicating that in the state class S f Down Enable Transition t i The maximum trigger delay.

[0126] Given a labeled time Petri net system, a given time τ and a and The set of logical identifiers consistent with τ is defined as:

[0127]

[0128] Representation and logical transition sequence The associated tag sequence, Represented as a set of logical identifiers;

[0129] and The set of states consistent with τ is defined as:

[0130]

[0131] Given a labeled time Petri net system, a given time τ, a secret set H∈R(N t ,M0) and a For the marker M f ∈(M o (G)∩H) state class With S f of The set of states consistent with τ is defined as:

[0132]

[0133] in, is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S d The trigger delay under the condition is expressed as in, is a non-negative rational number, indicating that in the state class S d Down Enable Transition t i The minimum trigger delay of is a non-negative rational number or +∞, indicating that in the state class S d Down Enable Transition t i The maximum trigger delay.

[0134] Furthermore, based on the key MSCG, if for any If there is a state class Its symbol is M f ∈(M o (G)∩H), if there is a state class in the key MSCG Its logo Make Then the system is opaque about the secret set H at time τ.

[0135] Combine the following Figure 3 S4 in this implementation step is explained.

[0136] Given a given time τ = 3, the system can reach state class S2 through OLS c, and S(c,τ) = {S2,S5,S6,S 10 ,S 11}, it can be seen that there is at least one state class, such as S5, whose identifier therefore The system can reach state class S8 through OLS ab, and S(ab,τ)={S8,S 13}, it can be seen that there is a state class S 13 , its identification therefore The system can reach state class S9 through OLS ba, and S(ba,τ)={S9,S 13}, it can be seen that there is a state class S 13 , its identification therefore

[0137] Furthermore, the system is opaque in its current state with respect to the secret set H at time τ=3.

[0138] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A current state opacity verification method based on labeled time Petri net, characterized in that: The following steps are involved: S1: Establish a label time Petri net model of the system to be verified; In S1, the Petri net is represented by the following four-tuple: N={P,T,Pre,Post} Where P = {p1, p2, ..., p m } represents a finite set of m places, T = {t1, t2, …, t n } represents a finite set of n transitions, Pre / Post: is the pre- or post-correlation function of N, and represents a set of non-negative integers, and N represents a Petri net, p1, p2, ..., p m represents the m places in the Petri net place set P, t1, t2, …, t n represents n transitions in the Petri net transition set T; The association matrix of a Petri net is represented by C = Post-Pre. Indicates that a non-negative token number is assigned to each place, which reflects the state of the system; Where C represents the incidence matrix of the Petri net; The enabling transition t is emitted at M, generating a new identity: M′=M+C(·,t) Where C(·,t) represents the column vector corresponding to the transition t in the incidence matrix C; The set of logically enabled transitions at M is expressed as: E(M)={t∈T|M≥Pre(·,t)} Where Pre(·,t) represents the column vector corresponding to the transition t in the pre-correlation function Pre; The labeled time Petri net consists of two tuples express, represents a labeled time Petri net, where N t represents the time Petri net, represents the label function associated with the transition, where N t =(N,Q) represents a time Petri net, N represents the Petri net, Q represents the time function associated with the Petri net transition, which is the time function for each transition t in the Petri net. i Assign two rational numbers l i and u i , and is the transition t i Assign two rational numbers l i and u i The time function is: represents the set of non-negative rational numbers, Representing a collection and collection The Cartesian product of is the set of non-negative rational numbers, is the union of the set of non-negative rational numbers and the element +∞. The time function Q is the transition t in the Petri net transition set T. i Assign two rational numbers l i and u i , to form a static transmission delay interval [l i ,u i ],in is a non-negative rational number, is a non-negative rational number or +∞; And, Q(t i )=[l i ,u i ] indicates t i The static transmission delay interval, where 0≤l i ≤u i ,l i ≠∞; The label function associated with the transition is: In which, the above formula specifies an empty string ε or a symbol belonging to the label set γ for each transition t∈T, and represents the set of unobservable transitions labeled ε, represents the set of observable transitions; S2: By utilizing the time constraints related to the transition sequence, a linear programming-based method is proposed to determine the logical transition sequence consistent with the given time and construct the key MSCG consistent with the given time; In S2, the time transition sequence of the time Petri net with the initial identifier M0 is expressed as: Among them, σ represents the time-varying sequence, τ k Indicates change The trigger time, and τ1≤τ2≤…≤τ k , represents a set of non-negative real numbers, ignoring the time information τ in σ k , and k is a natural number, its logical transition sequence is expressed as: Emit a time-varying sequence σ from M0 to generate a reachable marker M k The process is recorded as M0[σ>M k , the set of all identifiers reachable from M0 is denoted as R(N t ,M0), the set of all logical transition sequences is represented as L(N t ,M0); In S2, the state of the label time Petri net system is represented by Z k =(M k ,θ k ), where θ k Representation and identification M k A set of inequalities related to the emission intervals of all enabled transitions By reachability mark M k And the following inequality: Among them, ξ i Indicates that in Z k Enabling Transition i The emission delay of each inequality indicates that the transition t i ∈E(M k ) can be passed through time units later, and must be time units ago, if the transition t i In state Z k If it can be launched, then the transition t i Satisfy M≥Pre(·,t) and time constraints Among them, j is used to distinguish the mark M k The next enabling transition set E(M k ) indices of different transitions, t j ∈E(M k ) indicates that in the mark M k The transition with index j in the set of enabled transitions is: It means that in the mark M k The enabled transition t with index j j The maximum launch delay of In S2, given a label time Petri net system and a given time τ, the set of logical transition sequences consistent with τ is defined as: in, express The emission time of the last transition in * represents the set of all logical transition sequences consisting of the transitions in the Petri net transition set T; The set of identities consistent with τ is defined as: The set of states consistent with τ is defined as: Among them, S k =(M k ,Θ k ) represents a state class, and a state class represents a set of states with the same reachable identifier; is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S k The trigger delay of the following; Use MSCG to find the path of the system, and by using the time constraints related to the transition sequence, determine the logical transition sequence consistent with the given time based on the linear programming method, and construct the key MSCG consistent with the given time; First, we construct the MSCG of the labeled time Petri net system, whose nodes represent state classes. In addition, the edges of the MSCG represent the connection information from the parent node to the child node, which is recorded as: in t i Tags, Indicates that from the parent node S k To the child node i The allowed transmission interval, Indicates the change i Tags, Indicates that from the parent node S k Emission transition i The allowed transmission time interval to the child nodes; Based on MSCG, define a The relevant paths are: in, Representation and logical transition sequence The relevant path, that is, from the root node Start firing in sequence The transitions in the A path is formed, and Representation status class Transition through launch Arrival Status Connection information, where Indicates change Tags, Indicates change In the state class The allowed transmission time interval under Wherein, q is a natural number; Compute the state classes and paths consistent with a given time τ, giving a set of state classes and paths The time constraints associated with a given time τ are: Among them, the constraints a1-a2 are related to the path The inequality related to the allowed emission interval of all transitions in the system. Constraint a3 indicates that the system changes from state class To target state class The time required must be less than or equal to the given time τ, where q is a natural number; By introducing the objective function in constraint a3, we obtain: Test the existence of a feasible solution that satisfies constraint (3). If LPP (4) has no solution, then the path Obviously inconsistent with τ; Furthermore, in the key MSCG construction algorithm, at initialization, Π represents the set of paths consistent with a given time; The following steps are involved: Input: a labeled time Petri net system with an initial state class S0 = (M0, Θ0) and a given time τ; S21, initialization set S(τ):={S0}; in Mark as "new"; S22, MSCG of computing system; S23. If there is a path marked as "new" in the UI, select any path marked as "new" from the UI. S231. Searching for paths in a reachable graph For all enabled transitions t emitted at the terminal node of the path, compare them with Splicing, thus expanding the new path to: For Path Construct the constraints as shown in formula (3). If there is a feasible solution to LPP (4), mark it as "new" and update the set like The terminal node does not belong to S(τ), update the set S232, remove Marking; S24, removing the state classes and paths that are inconsistent with the given time in MSCG; Output: Key MSCG consistent with the given time; To obtain a new path In the step S231, a path is searched in the reachable graph. The old path Connect with all the emissible enabling transitions t under its terminal node to form a new path To obtain a state class and path consistent with a given time, in step S231, Construct the constraints as shown in formula (3). If there is a feasible solution about LPP (4), it means that the path is consistent with the given time; To avoid repeated storage of state classes, S231 is used to determine whether there is a state class in S(τ). If not, it will be stored S3: Find the state classes whose identities belong to the secret set and are observable in the key MSCG, and determine the observable label sequences that can reach these state classes; In S3, given a labeled time Petri net system, the set of all observable identifiers reachable from M0 is defined as: Among them, t o represents an observable transition and its label Υ is the label set, represents the set of observable transitions; In S3, the time tag sequence is expressed as: Among them, α h represents the hth label in the time label sequence ω, β h Represents the label α h The time observed, is a non-negative number and satisfies β1≤β2≤…≤β h , so α1 represents the first label in the time label sequence ω, and β1 represents the time when label α1 is observed; A label sequence that is consistent with ω logic is called an observable label sequence, which is expressed as: in, represents an observable label sequence; The set of all observable tag sequences reachable from M0 is defined as: Where Γ represents the set of all observable label sequences reachable from M0, Υ * represents the set of all label sequences consisting of labels in the label set Y, Representation and logical transition sequence The associated tag sequence; S4: Based on the key MSCG, by determining whether the logical identification set consistent with the given time and the observable tag sequence is included in the secret set, verify whether the system is opaque about whether the secret set is in the current state at a given time; In S4, given a label time Petri net system, a given time τ and a and The set of logical identifiers consistent with τ is defined as: Representation and logical transition sequence The associated tag sequence, Represented as a set of logical identifiers; and The set of states consistent with τ is defined as: is a state class set; In S4, given a label time Petri net system, a given time τ, and a secret set H∈R(N t ,M0) and a For the state class Its logo is: M f ∈(M o (G)∩H) Among them, (M o (G)∩H) represents the set M of all observable identifiers reachable from M0 o (G) intersection with the secret set H; in, is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S f The trigger delay is as follows: is a non-negative rational number, indicating that in the state class S f Down Enable Transition t i The minimum trigger delay of is a non-negative rational number or +∞, indicating that in the state class S f Down Enable Transition t i The maximum trigger delay of With S f of The set of states consistent with τ is defined as: in, is a set of time-constrained inequalities, η i Indicates enabling transition t i In the state class S d The trigger delay under the condition is expressed as in, is a non-negative rational number, indicating that in the state class S d Down Enable Transition t i The minimum trigger delay of is a non-negative rational number or +∞, indicating that in the state class S d Down Enable Transition t i The maximum trigger delay of In S4, given a label time Petri net system, a given time τ and a secret set H∈R(N t ,M0), for any If there is a state class Its logo is: M f ∈(M o (G)∩H) And meet The system is opaque about the current state of the secret set H at time τ.

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