System security real-time verification method and system for discrete event system

Abstract

The invention discloses a system security real-time verification method and system for a discrete event system, and the method comprises the steps: building a Time Labled Petri Nets model of the discrete event system according to the information of the discrete event system, and enabling the information of the discrete event system to comprise an event, a tag and time information; for the Time Labled Petri Nets model of the discrete event system, using the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system; constructing an integer linear programming mathematical problem model according to the discrete event system verification real-time security constraint condition; substituting the real-time observation of the discrete event system and the initial secret state of the discrete event system into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain a verification result; and judging the security of the discrete event system according to a verification result.

Description

Technical Field

[0001] The present invention belongs to the technical field of discrete event systems, and in particular relates to a system security real-time verification method and system for discrete event systems. Background Art

[0002] Discrete event system (DES) is a type of system driven by discrete events, which is widely used in industrial control, traffic management, computer networks and other fields. The technologies included include formal modeling, control theory, optimization algorithms, etc. As people's needs increase, in order to pursue more automated and intelligent discrete event systems, these technologies provide us with powerful tools for system analysis. By introducing information security technologies such as opacity, DES plays an important role in ensuring system privacy and security. In the future, with the development of technology, DES will be applied and promoted in more fields.

[0003] The occurrence of system events in discrete event systems is usually instantaneous and occurs at a specific point in time. When these events occur, the system information is inevitably leaked through communication hardware such as sensors, so it is very necessary to consider the information security of discrete event systems. Information security technology can provide information security protection for discrete event systems to reduce the risk of secret information leakage. Nowadays, verifying whether the occurrence of certain events will cause discrete event systems to fall into secret information leakage has gradually attracted people's attention. Real-time verification of discrete event system security usually assumes that the system model is known, the secret initial state information, and the real-time information is known, including label information and corresponding time information.

[0004] Under a known precise system model, there have been many studies on verifying the information security of the system, mainly including state-based opacity and language-based opacity. However, these opaque technical studies mainly only consider events without considering the corresponding time. However, since the occurrence of events in actual discrete event systems often contains time information, and the leakage of time information will also cause the leakage of the event information to a certain extent. Therefore, the current research on verifying the system information security of discrete event systems faces the problem of not considering the leakage of time information. Summary of the invention

[0005] The purpose of the present invention is to overcome the problem that the prior art is still lacking in time information leakage of discrete event systems, and proposes a system security real-time verification method and system for discrete event systems.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme: A method for real-time verification of system safety of a discrete event system comprises the following steps: A Time Labelled Petri Nets model of a discrete event system is established based on the discrete event system information, wherein the discrete event system information includes events, labels and time information; The Time Labled Petri Nets model of the discrete event system uses the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system; Construct an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; The real-time observation of the discrete event system and the initial secret state of the discrete event system are brought into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The security of the discrete event system is judged based on the verification results.

[0007] Furthermore, the Time Labled Petri Nets model of discrete event system is as follows:

[0008] Where N represents the Petri net model, , and are place set and transition set respectively. and They represent the forward correlation function and the backward correlation function respectively, and specify the connection mode of directed arcs in the network; , The overall correlation matrix representing the network structure; A place in a Petri net model Represents a state of a discrete event system, and states represent different conditions of the discrete event system; A Transformation of Petri Net Model Represents an event of a discrete event system. An event represents the behavior of a discrete event system transitioning from one state to another. Represents the initial state identifier of the discrete event system; represents a time function, , is a positive rational number, each transition Associated with a static closed time interval, , , when a conversion When enabled, Can't Triggered before time units have passed, Must be in time units ago, unless another transition In a conversion Previously triggered and disabled ; Represents a set of tags; represents a function, , each change Assignment Tags or empty words in ; Will gather Partition into two disjoint sets , in, A collection of labels representing observable events, A collection of tags representing unobservable events; The transformation collection Partition into two disjoint sets , in, represents the set of observable transitions, represents a set of unobservable transitions; , ; The logical transition sequence of the trace of a discrete event system is , Function Generalize to sequence , express All elements in the set can form a sequence of any length; express All elements in the set can form a sequence of any length; , , .

[0009] Furthermore, the expression of real-time observation of discrete event system is as follows:

[0010] in, is the time-labeled observation, , , is the label of the observable event, , for A sequence of logical labels, It's a moment in time. , for The time of the last sequence of logical label sequences, , express and Closure operation of the Cartesian product; The expression for the initial secret state of a discrete event system is as follows:

[0011] { } in, represents the initial secret state of the discrete event system, represents the set of initial secret states without time; is a secret initial state element in the secret initial state set without time; is the trace of the discrete event system and is expressed as follows: , It is a transition The feasible launch time, and ; The initial state of the discrete event system is identified The set of reachable discrete event system states is expressed as follows:

[0012] is the state identifier of the discrete event system, is from Reachable identification, , Indicated in The number of transitions that are logically allowed to be triggered, Indicates transition Only in After time units have passed and time units before the transition is triggered, unless another enabled transition Already triggered, disable transition , express and Closure operation of the Cartesian product; express yes exist Inspiring change at all times The status indicator of arrival.

[0013] Furthermore, the sequence of transitions of observable labels and their timings consistent with real-time observations is as follows:

[0014]

[0015] in, is a set of observable labels and their transition sequences whose time is consistent with real-time observations, is the trace of a discrete event system. The trace of a discrete event system is a sequence of changes in observable labels and their times that are consistent with real-time observations. express and Closure operation of the Cartesian product; Is the system status indicator, It is the set of all state identifiers that can be reached from the initial state identifier of the discrete event system; Represents the trace of a discrete event system The time label observations generated below; yes The trigger time of the final transition in , is the feasible activation time of the last transition, yes is at the upper bound of unobservable transformations, Indicates in status The following can enable changes, Represents a set of unobservable transitions.

[0016] Furthermore, the objective function of the integer linear programming mathematical problem model is to minimize the total time spent on satisfying the constraints; The constraints for verifying the real-time safety of the discrete event system include the first constraint, the second constraint, the third constraint and the fourth constraint; The first constraint is the system status identifier The correctness of operation, The second constraint is the transition Follow time constraints; The third constraint is that the observable labels and their times are consistent with real-time observations; The fourth constraint is that the observable labels of real-time observations are consistent The initial state is inconsistent with the initial secret state.

[0017] Furthermore, the first constraint is as follows:

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[0024] in, and They are the unobservable identification of discrete event systems and the observable identification of discrete event systems. and is the state transition formula, Represents a set of 01 vectors corresponding to a transition sequence, Represents the 01 vector corresponding to another set of transition sequences, marking Indicates the previous mark pass Reachable identification, Indicates the previous mark pass Reachable identification, For change, Indicates m o A matrix of dimension, Indicates m u A matrix of dimension, is a constant, indicating and Maximum number of excitations; represents the set of observable transitions, represents a set of unobservable transitions; The second constraint is as follows: (2-1) (2-2) (2-3) (2-4) (2-5) (2-6) (2-7) (2-8) (2-9) (2-10) (2-11) (2-12) (2-13) (2-14) (2-15) (2-16) (2-17) (2-18)

[0025] Equations (2-1) to (2-8) are used to find the transitions that are still enabled before and after the i-th excitation of the discrete event system; Equations (2-9) to (2-18) are used to constrain the time of transitions that are still enabled before and after excitation; Equations (2-9) to (2-10) are used to constrain the instantaneous moment of transition excitation each time a transition is excited; Formulas (2-11) to (2-18) are used to represent the update of schedule I after each excitation; Formulas (2-15) to (2-18) are used to reset the schedule of the transition triggered for the i-th time and the transition that cannot be enabled before the i-th trigger to the initial schedule. ; in, and is an integer variable, Indicates the number of transitions in each place in the state identifier before the i-th transition is triggered, except for the transitions before the i-th transition is triggered. Indicates the number of transitions in each place in the state identifier after the i-th transition is triggered, except for the transitions before the i-th transition. Bold and is 01 variable, represents the excitable state of transitions before the i-th excitation, except for the transitions of the i-th excitation; It indicates the excitable state of transitions after the i-th excitation, except for the transitions of the i-th excitation; Indicates a set of transitions with multiple preceding places; is an integer variable, indicating the instant of the i-th excitation transition; Greater than or equal to the maximum value between the 0 time and the shortest excitation time and less than or equal to the minimum value of the latest excitation time of all simultaneously excitable transitions; schedule is an integer variable, represents a 2i-dimensional matrix, represents the initial schedule, Indicates the shortest initial excitation time for each transition, Indicates the latest triggering time of each initial transition, Subscript 2i When it is an odd number, it indicates the shortest activation time of each transition after the update of schedule I after the i-th activation transition. Subscript 2i When it is an even number, it indicates the latest activation time of each transition after the update of schedule I after the i-th activation transition. represents a maximum constant, is a minimum constant, is the number of cycles, Indicates the total number of transitions; The third constraint is as follows: (3-1) (3-2) (3-3) in, Indicates the cumulative time of triggering observable tags in sequence, Indicates the instantaneous moment of the sequential tags, real-time observation Represents the instantaneous moment of the global clock; Formula (3-1) represents the instantaneous moment of the observable tag and the real-time observation same; Formula (3-2) indicates that the trigger time of the observable tag is less than the global clock in the real-time observation , , The feasible activation time for the last transition; Formula (3-3) indicates that the observable label is constrained. The observable label is the same as the real-time observed label. , for A sequence of logical labels, for A logical label sequence of The fourth constraint is as follows: (4-1) (4-2) (4-3) (4-4) Formulas (4-1) to (4-4) are used to constrain the initial state to be inconsistent with the initial secret state, and at least one initial state is inconsistent with the initial secret state; in, is the secret initial state, is a non-secret initial state, yes dimensional vector, is the number of places in the Time Labled Petri Nets model of discrete event systems, and is 01 variable, Express Each initial secret state in is listed in equations (4-1) to (4-4).

[0026] According to the method for real-time system security verification of a discrete event system as claimed in claim 1, judging the security of the discrete event system according to the verification result is specifically as follows: comparing the verification result with the secret initial state, solving the initial state identifier of the discrete event system obtained by the verification result With a secret initial state ,like and Inconsistency means that the discrete event system is initially opaque under this secret state, and the discrete event system is secure.

[0027] A system safety real-time verification system for a discrete event system, comprising a system model building module, for building a Time Labled Petri Nets model of the discrete event system according to discrete event system information, wherein the discrete event system information includes event, label and time information; A real-time observation and initial secret state acquisition module is used to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system using the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system for the Time Labled PetriNets model of the discrete event system; A problem model building module is used to build an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; A verification result acquisition module is used to bring the real-time observation of the discrete event system and the initial secret state of the discrete event system into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The safety judgment module is used to judge the safety of the discrete event system according to the verification results.

[0028] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the system security real-time verification method of a discrete event system is implemented.

[0029] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the system security real-time verification method of a discrete event system is implemented.

[0030] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention proposes a method for real-time verification of system security of a discrete event system. Aiming at the problem of real-time information security verification of a discrete event system, a Time Labeled Petri Nets (TLPN) model is established according to the discrete event system information, and the model is used to perform real-time security verification in combination with real-time observation and initial secret state. TLPN adds time labels on the basis of traditional Petri nets, so that the model can describe the dynamic behavior of the system state changing over time, which is helpful for analyzing the time sensitivity of the discrete event system. TLPN can naturally represent the parallel and concurrent activities in the system, and the time relationship and logical dependency between activities can be clearly described through the TLPN model. By modeling the discrete event system as a Time Labeled Petri Net system, and performing integer linear programming on the Time Labeled Petri Net system according to constraint requirements, the integer linear programming mathematical problem is solved, and the real-time information security of the verification system is realized according to the solution results.

[0031] Furthermore, integer linear programming constructs a series of linear inequalities, which contain global constraints, including time constraints, label constraints, and state inconsistency constraints. By observing the system state in real time and combining the TLPN model for dynamic analysis, potential security threats can be discovered and responded to in a timely manner. The initial secret state is used as the starting point for security verification. Combined with the time information and system state changes in the TLPN model, the security state of the system at different time points can be more accurately evaluated, which helps to reduce the occurrence of false positives and false negatives. The TLPN model supports complex logical relationships and time constraints, allowing the system to implement more sophisticated and complex security strategies. Through real-time observation and dynamic analysis of the TLPN model, the system can discover potential security threats in a timely manner and take corresponding countermeasures, which helps to reduce the risk of the system being attacked and protect the system's key data and resources. Real-time security verification can ensure the normal operation of the system under various complex environments and conditions. By discovering and repairing security vulnerabilities in a timely manner, the system can avoid interruption of operation or data loss due to security issues. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are for explanation purposes only and are not intended to limit the scope of the present invention in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only for illustration purposes to help understand the present invention, and are not intended to specifically limit the shapes and proportional dimensions of the components of the present invention. In the drawings: Figure 1 The present invention is a flowchart of a method for real-time verification of system security of a discrete event system.

[0033] Figure 2 This is a structural diagram of a system security real-time verification system for a discrete event system of the present invention.

[0034] Figure 3 This is an electronic device diagram of a method for real-time verification of system security of a discrete event system of the present invention.

[0035] Figure 4 The present invention is a flowchart of a method for real-time verification of system security of a discrete event system.

[0036] Figure 5 Schematic diagram of a discrete event system in an embodiment of the present invention.

[0037] Figure 6 is the model of the discrete event system in the embodiment of the present invention Network model diagram .

[0038] Figure 7 It is a graph of integer linear programming solution results in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0040] Embodiment 1 See also Figure 1 , a system safety real-time verification method for a discrete event system, comprising the following steps: A Time Labelled Petri Nets model of a discrete event system is established based on the discrete event system information, wherein the discrete event system information includes events, labels and time information; The Time Labled Petri Nets model of the discrete event system uses the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system; Construct an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; The real-time observation of the discrete event system and the initial secret state of the discrete event system are brought into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The security of the discrete event system is judged based on the verification results.

[0041] This embodiment provides a systematic and automated solution for real-time information security verification of discrete event systems through precise modeling and efficient solution. It not only improves the accuracy and efficiency of verification, but also reduces the risk of human error, providing strong support for the security verification of complex systems. The TLPN model is established according to the discrete event system information, and real-time security verification is performed in combination with real-time observation and initial secret state. It has multiple benefits such as improving the real-time and accuracy of security verification and supporting the implementation of complex security policies. It helps to ensure the safe and stable operation of the system, reduce maintenance costs and improve overall efficiency. TLPN uses a graphical method to represent the system, so that the system status, events and the relationship between them are clear at a glance, which helps to quickly understand the system structure and working principle.

[0042] Embodiment 2 A system safety real-time verification method for a discrete event system, the main steps of which include: Step 1: Establish the corresponding discrete event system information Model; Step 2: Construct the corresponding integer linear programming mathematical problem model according to the constraints; Step 3: Real-time observation With the initial secret state Bring in the integer linear programming model to solve and verify its security; Step 4: Determine the security of the system based on the verification results; The step 1 is specifically as follows: The discrete event system is established as the corresponding Model, obtain its events, labels, and time information. The system model is established as .in, Indicates its corresponding Network model, where and are respectively a set of places and a set of transitions. , each change , and They represent the forward correlation function and the backward correlation function, which specify the connection mode of the directed arcs in the network and the overall correlation matrix of the network structure. ; Represents the initial state identifier of the discrete event system; is a time function that associates each transition with a static closed time interval ,in is a positive rational number, Specifically, when a conversion When enabled, it cannot be used in time units have passed before it fires. It must time units ago, unless another transition exist Previously triggered and disabled ; is a set of tags. is a function that, for each transition Assignment Tags or empty words in .

[0043] A discrete event system can be represented by a set of states and a set of events The state represents the different conditions of the system, and the event represents the behavior of the system from one state to another. Each state of the discrete event system is represented by the library Indicates that each event is represented by a transition Indicates that for Model, the state identification of the discrete event system can be expressed as ,in is from Reachable identification, is a set of inequalities, where Indicated in The number of transitions that are logically allowed to be triggered in the set In the inequality Means transition Only in After time units have passed and Time units before the transition is triggered, unless another enabled transition has already triggered, making the transition is disabled. The trace of the system is defined as a transition time series ,in It is a transition The feasible launch time, and .symbol Status indicator Is a status indicator exist Inspiring change at all times Arrived can be further written as ,use express The feasible triggering time of the last transition is defined as .

[0044] from The set of reachable discrete event system states is , the collection Partition into two disjoint sets ,in is the label set of observable events, corresponding to The label set representing the unobservable event. Similarly, the transition set Divide into observable and unobservable sets of changes and , ,in , . Tag function It can be extended to the sequence , that is to say , among which , .

[0045] Define a real-time observation , in are time-tagged observations, where any is the label of the observable event, It's a moment in time. for A sequence of logical labels, It is also a moment in time and In discrete mathematics, E×Q represents the Cartesian product of E and Q, represents all possible ordered pairs (e, t) of E×Q, and ()* represents the closure operation of this Cartesian product, that is, a sequence of any length of (e, t). Then the time series with consistent observations is: ,in yes The trigger time of the final transition in , yes is the upper bound of the unobservable transition, , It is the set of all state identifiers that can be reached from the initial state identifier. The initial state set is defined as , note that in this sense, is the observed initial state of the evolution, not the initial state identifier . Given the initial secret state of the discrete event system is , and its corresponding initial secret state set without time is express, { }.

[0046] The step 2 is specifically as follows: The objective function of the integer linear programming mathematical problem model is to minimize the total time required to satisfy the following constraints, namely:

[0047] The constraints for real-time safety verification of discrete event systems are: Constraint 1) System status identification needs to be guaranteed To ensure the correctness of the operation, an integer linear programming model is established based on this constraint as follows: (1) (2) (3) (4) (5) (6) (7) in and They are the unobservable and observable marks of the system, and the state transition formula ( ), ( ) represents a set of 01 vectors corresponding to a transition sequence, and identifies ( ) is the previous mark ( )pass ( ) accessible identification, is a constant, indicating and Maximum number of excitations.

[0048] Constraint 2) Changes must be guaranteed Following the time constraint, the corresponding integer linear programming constraints are as follows: (2-1) (2-2) (2-3) (2-4) (2-5) (2-6) (2-7) (2-8) (2-9) (2-10) (2-11) (2-12) (2-13) (2-14) (2-15) (2-16) (2-17) (2-18)

[0049] in and is an integer variable, indicating that when the i-th excitation occurs, The state identifiers of each library before and after the excitation Quantity (except the token before the i-th trigger transition), the bold and are all 01 variables, representing the excitable states of the transitions before and after the i-th excitation (except the transitions of the i-th excitation). The purpose of equations (2-1)-(2-8) is to find the transitions that are still enabled before and after the i-th excitation of the system, because the transitions that are still enabled before and after the excitation need to further constrain their time. Specifically, they are equations (2-9)-(2-18). Note that here It represents a set of transitions with multiple preceding places. is an integer variable, which indicates the instant of the i-th excitation transition. Equations (2-9)-(2-10) are constraints on the instant of the excitation of each transition. It needs to satisfy the maximum value between the time 0 and the shortest excitation time (Formula (2-9)), and less than or equal to the minimum value of the latest excitation time of all simultaneously excitable transitions (Formula (2-10)). Formulas (2-11)-(2-18) represent the update of schedule I after each excitation. Schedule is an integer variable, represents the initial schedule, Indicates the shortest initial excitation time for each transition, Indicates the latest triggering time of each transition at the beginning. Further extension, when the subscript is an odd (even) number, it indicates the shortest (latest) triggering time of each transition after the schedule I is updated after the i-th triggering transition. Formulas (2-15)-(2-18) reset the schedule of the i-th triggered transition and the transition that cannot be enabled before the i-th trigger to the initial schedule. , Represents the total number of transitions. j can be regarded as the number of loops required in an algorithm. Because the elements in all formulas are basically matrix operations, if you need to be specific to a certain row, you need a number j to represent the row.

[0050] Constraint 3) Observable tags and their corresponding time and real-time observation The corresponding integer linear programming constraints are as follows: (3-1) (3-2) (3-3) in Indicates the cumulative time of triggering observable tags in sequence, represents the instantaneous moment of the sequential label, and formula (3-1) represents the instantaneous moment of the observable label and the real-time observation are the same, note that in real-time observation represents the instantaneous moment of the global clock, and represents the instant of the triggering transition; Formula (3-2) indicates that the triggering time of the observable tag is smaller than the global clock in the real-time observation , that is, satisfy ; Formula (3-3) constrains the observable label so that the observable label is the same as the real-time observed label .

[0051] Constraint 4) requires consistency with observable labels observed in real time The initial state of is inconsistent with the initial secret state, and the corresponding integer linear programming constraints are as follows: (4-1) (4-2) (4-3) (4-4) Formulas (4-1)-(4-4) are used to constrain two initial states (a secret A non-secret ), that is, it is guaranteed that there is at least one initial state that is inconsistent with the initial secret state, which also ensures the security of the initial secret state information of the system. is a dimensional vector, The number of places after modeling the system, is 01 variable, It means For each initial secret state in , equations (4-1)-(4-4) must be listed.

[0052] Embodiment 3 See also Figure 2 , a system safety real-time verification system for a discrete event system, comprising a system model building module for building a Time Labled Petri Nets model of the discrete event system according to discrete event system information, the discrete event system information including event, label and time information; A real-time observation and initial secret state acquisition module is used to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system using the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system for the Time Labled PetriNets model of the discrete event system; A problem model building module is used to build an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; A verification result acquisition module is used to bring the real-time observation of the discrete event system and the initial secret state of the discrete event system into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The safety judgment module is used to judge the safety of the discrete event system according to the verification results.

[0053] Embodiment 4 See also Figure 3 An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, a system security real-time verification method for a discrete event system as described in Example 2 is implemented.

[0054] Embodiment 5 A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for real-time verification of system security of a discrete event system described in Embodiment 2 is implemented.

[0055] Embodiment 6 like Figure 4 As shown in the figure, a real-time verification method for system security of discrete event systems is shown. Taking the military system as an example, the specific steps are as follows: Step 1: Establish the corresponding discrete event system information Model; In this example, the discrete event system is a military system. The commander issues instructions from the military command vehicle. To protect the commander's life, the military command vehicle has a signal jammer. The specific system is as follows: Figure 5 As shown. The military command vehicle where the commander is located is very important (that is, it is in an initial secret state). The commander issues orders to the infantry squadron, tank squadron, and air force squadron, and each squadron can also communicate with each other. Construct the corresponding discrete event system Model, such as Figure 6 As shown, there are libraries Represents each camp and team respectively. The commander can use the military command vehicle to The time required to shuttle back and forth between the two is 3 minutes to 10 minutes, and the movement during this period is changed Respectively, in particular, this example is the commander in the middle of the military command vehicle with a warehouse Issued an order, the Air Force used the warehouse It means that the commander issues instructions to the air force and the air force is ready to use it. It means that the time required is 5-10 minutes, and the observable signal is The Air Force will complete the relevant instructions and give feedback to the commander. It means that the time required is 10min-20min, and the observable signal is ; Tank corps warehouse It means that the commander issues orders to the tank team and the tank team is ready to use it. It means that the time required is 10min-15min, and the observable signal is The tank team completes the relevant instructions and feeds back to the commander. It means that the time required is 15min-20min, and the observable signal is ; Infantry Corps warehouse It means that the commander issues orders to the infantry squadron and the infantry squadron is ready to use It means that the time required is 3min-8min, and the observable signal is The infantry squad completes the relevant instructions and feeds back to the commander. It means that the time required is 5-10 minutes, and the observable signal is ; The communication signal between each team is , communication between teams using transitions It is said that the Air Force team's ability to receive signals is slightly slower than the other two teams due to environmental factors, with the communication time between them being 3min-5min and 5min-10min respectively. Step 2: Construct the corresponding integer linear programming mathematical problem model according to the constraints; The constructed integer linear programming mathematical problem model is as follows: Objective function:

[0056] Constraints:

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[0088] Step 3: Real-time observation With the initial secret state Bring in the integer linear programming model to solve and verify its security; The initial secret state of the known embodiment requires only one ,in , , assuming that there is an intruder who observes the signal of the system (the ability is to observe only observable signals). The real-time observation of the intruder for , According to this initial secret state and real-time observation, the integer linear programming problem model in step 2 is introduced and solved using the Gurobi solver. The solution obtained is for , such as Figure 4 shown.

[0089] Step 4: Determine the security of the system based on the verification results; Compare the result with the secret initial state and solve the result. , with the secret initial state , , if they are inconsistent, then the initial state of the system in this secret state is opaque, that is, the discrete event system is secure.

[0090] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0091] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0092] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0093] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention is described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation of the present invention can still be modified or replaced by equivalents, and any modification or equivalent replacement that does not deviate from the spirit and scope of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for real-time verification of system security of a discrete event system, characterized in that: The following steps are involved: A Time Labelled Petri Nets model of a discrete event system is established based on the discrete event system information, wherein the discrete event system information includes events, labels and time information; The Time Labled Petri Nets model of the discrete event system uses the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system; Construct an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; The real-time observation of the discrete event system and the initial secret state of the discrete event system are brought into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The security of the discrete event system is judged based on the verification results.

2. A method for real-time verification of system security of a discrete event system according to claim 1, characterized in that: The Time Labled Petri Nets model of discrete event systems is shown below: Where N represents the Petri net model, , and are place set and transition set respectively. and They represent the forward correlation function and the backward correlation function respectively, and specify the connection mode of directed arcs in the network; , The overall correlation matrix representing the network structure; A place in a Petri net model Represents a state of a discrete event system, and states represent different conditions of the discrete event system; A Transformation of Petri Net Model Represents an event of a discrete event system. An event represents the behavior of a discrete event system transitioning from one state to another. Represents the initial state identifier of the discrete event system; represents a time function, , is a positive rational number, each transition Associated with a static closed time interval, , , when a conversion When enabled, Can't Triggered before time units have passed, Must be in time units ago, unless another transition In a conversion Previously triggered and disabled ; Represents a set of tags; represents a function, , each change Assignment Tags or empty words in ; Will gather Partition into two disjoint sets , in, A collection of labels representing observable events, A collection of tags representing unobservable events; The transformation collection Partition into two disjoint sets , in, represents the set of observable transitions, represents a set of unobservable transitions; ， ； The logical transition sequence of the trace of a discrete event system is , Function Generalize to sequence , express All elements in the set can form a sequence of any length; express All elements in the set can form a sequence of any length; ， ， 。 3. A method for real-time verification of system security of a discrete event system according to claim 2, characterized in that: The expression for real-time observation of discrete event system is as follows: in, is the time-labeled observation, , , is the label of the observable event, , for A sequence of logical labels, It's a moment in time. , for The time of the last sequence of logical label sequences, , express and Closure operation of the Cartesian product; The expression for the initial secret state of a discrete event system is as follows: { } in, represents the initial secret state of the discrete event system, represents the set of initial secret states without time; is a secret initial state element in the secret initial state set without time; is the trace of the discrete event system and is expressed as follows: , It is a transition The feasible launch time, and ; The initial state of the discrete event system is identified The set of reachable discrete event system states is expressed as follows: is the state identifier of the discrete event system, is from Reachable identification, , Indicated in The number of transitions that are logically allowed to be triggered, Indicates transition Only in After time units have passed and time units before the transition is triggered, unless another enabled transition Already triggered, disable transition , express and Closure operation of the Cartesian product; express yes exist Inspiring change at all times The status indicator of arrival.

4. A method for real-time verification of system security of a discrete event system according to claim 3, characterized in that: The sequence of observable labels and their transitions that are consistent with real-time observations is as follows: in, is a set of observable labels and their transition sequences whose time is consistent with real-time observations, is the trace of a discrete event system. The trace of a discrete event system is a sequence of changes in observable labels and their times that are consistent with real-time observations. express and Closure operation of the Cartesian product; Is the system status indicator, It is the set of all state identifiers that can be reached from the initial state identifier of the discrete event system; Represents the trace of a discrete event system The time label observations generated below; yes The trigger time of the final transition in , is the feasible activation time of the last transition, yes is at the upper bound of unobservable transformations, Indicates in status The following can enable changes, Represents a set of unobservable transitions.

5. A method for real-time verification of system security of a discrete event system according to claim 4, characterized in that: The objective function of the integer linear programming mathematical problem model is to minimize the total time spent on making the constraints meet; The constraints for verifying the real-time safety of the discrete event system include the first constraint, the second constraint, the third constraint and the fourth constraint; The first constraint is the system status identifier The correctness of operation, The second constraint is the transition Follow time constraints; The third constraint is that the observable labels and their times are consistent with real-time observations; The fourth constraint is that the observable labels of real-time observations are consistent The initial state is inconsistent with the initial secret state.

6. A method for real-time verification of system security of a discrete event system according to claim 5, characterized in that: The first constraint is as follows: in, and They are the unobservable identification of discrete event systems and the observable identification of discrete event systems. and is the state transition formula, Represents a set of 01 vectors corresponding to a transition sequence, Represents the 01 vector corresponding to another set of transition sequences, marking Indicates the previous mark pass Reachable identification, Indicates the previous mark pass Reachable identification, For change, represents a matrix of dimension mo, represents a matrix of mu dimensions, is a constant, indicating and Maximum number of excitations; represents the set of observable transitions, represents a set of unobservable transitions; The second constraint is as follows: （2-1） （2-2） （2-3） （2-4） （2-5） （2-6） （2-7） （2-8） （2-9） （2-10） （2-11） （2-12） （2-13） （2-14） （2-15） （2-16） （2-17） （2-18） Equations (2-1) to (2-8) are used to find the transitions that are still enabled before and after the i-th excitation of the discrete event system; Equations (2-9) to (2-18) are used to constrain the time of transitions that are still enabled before and after excitation; Equations (2-9) to (2-10) are used to constrain the instantaneous moment of transition excitation each time a transition is excited; Formulas (2-11) to (2-18) are used to represent the update of schedule I after each excitation; Formulas (2-15) to (2-18) are used to reset the schedule of the transition triggered for the i-th time and the transition that cannot be enabled before the i-th trigger to the initial schedule. ; in, and is an integer variable, Indicates the number of transitions in each place in the state identifier before the i-th transition is triggered, except for the transitions before the i-th transition is triggered. Indicates the number of transitions in each place in the state identifier after the i-th transition is triggered, except for the transitions before the i-th transition. Bold and is 01 variable, represents the excitable state of transitions before the i-th excitation, except for the transitions of the i-th excitation; It indicates the excitable state of transitions after the i-th excitation, except for the transitions of the i-th excitation; Indicates a set of transitions with multiple preceding places; is an integer variable, indicating the instant of the i-th excitation transition; Greater than or equal to the maximum value between the 0 time and the shortest excitation time and less than or equal to the minimum value of the latest excitation time of all simultaneously excitable transitions; schedule is an integer variable, represents a 2i-dimensional matrix, represents the initial schedule, Indicates the shortest initial excitation time for each transition, Indicates the latest triggering time of each initial transition, When the subscript 2i is an odd number, it means the shortest activation time of each transition after the schedule I is updated after the i-th activation transition. When the subscript 2i of is an even number, it indicates the latest activation time of each transition after the update of schedule I after the i-th activation transition. represents a maximum constant, is a minimum constant, is the number of cycles, Indicates the total number of transitions; The third constraint is as follows: (3-1) (3-2) (3-3) in, Indicates the cumulative time of triggering observable tags in sequence, Indicates the instantaneous moment of the sequential tags, real-time observation Represents the instantaneous moment of the global clock; Formula (3-1) represents the instantaneous moment of the observable tag and the real-time observation same; Formula (3-2) indicates that the trigger time of the observable tag is less than the global clock in the real-time observation , , The feasible activation time for the last transition; Formula (3-3) indicates that the observable label is constrained. The observable label is the same as the real-time observed label. , for A sequence of logical labels, for A logical label sequence of The fourth constraint is as follows: （4-1） （4-2） （4-3） （4-4） Formulas (4-1) to (4-4) are used to constrain the initial state to be inconsistent with the initial secret state, and at least one initial state is inconsistent with the initial secret state; in, is the secret initial state, is a non-secret initial state, yes dimensional vector, is the number of places in the Time Labled Petri Nets model of discrete event systems, and is 01 variable, Express Each initial secret state in is listed in equations (4-1) to (4-4).

7. The method for real-time verification of system security of a discrete event system according to claim 1, characterized in that: The security of the discrete event system is judged based on the verification results. Specifically, the verification results are compared with the secret initial state, and the initial state identifier of the discrete event system obtained by solving the verification results is obtained. With a secret initial state ,like and Inconsistency means that the discrete event system is initially opaque under this secret state, and the discrete event system is secure.

8. A system safety real-time verification system for a discrete event system, characterized in that: It includes a system model building module, which is used to build a Time Labelled Petri Nets model of a discrete event system according to discrete event system information, wherein the discrete event system information includes event, label and time information; A real-time observation and initial secret state acquisition module is used to obtain the real-time observation of the discrete event system and the initial secret state of the discrete event system using the real-time observation expression of the discrete event system and the expression of the initial secret state of the discrete event system for the Time Labled Petri Nets model of the discrete event system; A problem model building module is used to build an integer linear programming mathematical problem model based on the constraints of real-time safety verification of discrete event systems; A verification result acquisition module is used to bring the real-time observation of the discrete event system and the initial secret state of the discrete event system into the integer linear programming model to solve and verify the security of the integer linear programming model to obtain the verification result; The safety judgment module is used to judge the safety of the discrete event system according to the verification results.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the system security real-time verification method for a discrete event system as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the method for real-time verification of system security of a discrete event system as claimed in any one of claims 1 to 7.

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