Innovation-based false data injection attack strategy generation method and system

Abstract

The invention provides an innovation-based false data injection attack strategy generation method and system, and belongs to the technical field of information physical system security defense. The method comprises the following steps: acquiring priori knowledge of a cyber-physical system (CPS), and storing information modified by an attacker at the previous moment and system information at the current moment; collecting auxiliary information by using a sensor in the information physical system; constructing a false data injection attack strategy based on the information modified by the attacker at the previous moment, the system information at the current moment and the auxiliary information; according to the false data injection attack strategy, calculating an error covariance of attacked information; and representing the error covariance in a convex optimization form to obtain a covariance of a maximized remote estimation variance, and finally obtaining an information-based optimal attack strategy. According to the method, the optimal false data injection attack strategy can be generated on the basis of remarkably reducing the priori knowledge complexity of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of information-physical system security defense, and in particular, relates to a method and system for generating a false data injection attack strategy based on new information. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the advancement of technology, the application of cyber-physical systems (CPS) has become more and more extensive and has been applied to many fields such as smart grids, smart factories, and unmanned aerial vehicles. With this expansion, ensuring the security of CPS has become a pressing issue. Therefore, some research has begun to develop specific attack strategies from the perspective of attackers. This provides defenders with unique perspectives and tools to better understand the thought process and action plan of potential attackers.

[0004] Malicious attacks against CPS can be divided into two categories: denial of service (DoS) attacks and spoofing attacks. DoS attacks can tamper with the data in the data packet and interfere with the signal transmission, thereby preventing information exchange. In contrast, the design of spoofing attacks is more covert, and one of the most representative is the false data injection (FDI) attack. Formulating specific attack strategies from the attacker's perspective is crucial to helping defenders actively establish effective defense measures and develop effective mitigation strategies.

[0005] On the other hand, unlike the above-mentioned attacks that directly inject into the system, attacks based on innovation have become increasingly prominent in the research community in recent years. Innovation refers to the difference between the actual measured value and the predicted value of the system model. At present, in addition to the research on some control algorithms, the research results of attack strategies based on innovation have also developed the Kullback-Leible (KL) divergence, chi-square (χ 2 ) detection and interval observation methods.

[0006] The inventors found that when designing an attack strategy based on new information, the existing technology only uses one historical new information, which limits the effect of the attack. Therefore, it is necessary to obtain more prior knowledge in the information-physical system, which makes the attack strategy design process computationally complex and the attack strategy is not concealed. Summary of the invention

[0007] In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a method and system for generating a false data injection attack strategy based on new information, which can generate an optimal false data injection attack strategy on the basis of significantly reducing the complexity of the system's prior knowledge.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0009] A first aspect of the present invention provides a method for generating a false data injection attack strategy based on new information.

[0010] A method for generating a false data injection attack strategy based on new information, comprising:

[0011] Acquire prior knowledge of the cyber-physical system (CPS) and store the new information modified by the attacker at the last moment and the new information of the system at the current moment; use sensors in the cyber-physical system to collect auxiliary information;

[0012] Construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and auxiliary information;

[0013] According to the false data injection attack strategy, the error covariance of the attacked new information is calculated; the error covariance is expressed in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally the optimal attack strategy based on information is obtained.

[0014] Furthermore, the sensor measurement data is transmitted to a remote estimator based on a wireless communication network.

[0015] Furthermore, according to the false data injection attack strategy, the error covariance of the attacked new information is calculated, including: obtaining parameter data of the linear discrete time-invariant system when the sensor is attacked by the new information.

[0016] Furthermore, based on the parameter data, a Kalman filter with a safety preselector is used to perform filter estimation to obtain a system filter estimation vector.

[0017] Furthermore, an estimation error vector is obtained according to the difference between the system estimation vector under the attack of the new information and the system's own estimation vector.

[0018] Furthermore, according to the estimated error vector, the system estimation vector under the new information attack and the Kalman filter gain, a recursive form of the linear discrete time-invariant system under the new information attack and the long-range error covariance is obtained.

[0019] Furthermore, the Schur's complement lemma is applied to transform the concealment constraint into a convex optimization problem, and the optimal concealed attack strategy is solved under the condition of the concealment constraint by solving the convex optimization problem.

[0020] A second aspect of the present invention provides a false data injection attack strategy generation system based on new information.

[0021] A false data injection attack strategy generation system based on new information, comprising:

[0022] The data acquisition module is configured to: obtain prior knowledge of the cyber-physical system CPS, store the new information modified by the attacker at the last moment and the new information of the system at the current moment; use sensors in the cyber-physical system to collect auxiliary information;

[0023] The attack strategy generation module is configured to: construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and the auxiliary information;

[0024] The attack strategy optimization module is configured to: calculate the error covariance of the attacked new information according to the false data injection attack strategy; express the error covariance in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally obtain the optimal attack strategy based on information.

[0025] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in a method for generating a false data injection attack strategy based on new information as described in the first aspect of the present invention.

[0026] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in a method for generating a false data injection attack strategy based on new information as described in the first aspect of the present invention are implemented.

[0027] One or more of the above technical solutions have the following beneficial effects:

[0028] The present invention uses auxiliary information to perform optimal design strategies for novelty-based attacks in cyber-physical systems (CPSs). By combining novelty modified by the attacker, novelty of the current system, and auxiliary information measured by sensors to construct a false data injection attack strategy, the optimal false data injection attack strategy with stronger concealment can be generated on the basis of significantly reducing the complexity of acquiring system prior knowledge.

[0029] The present invention transforms the optimal attack strategy formula of false data injection attack into a convex optimization problem, which can maximize the covariance of remote estimation error while ensuring the concealment of the attack strategy.

[0030] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0032] Figure 1 This is a flow chart of a method for generating a false data injection attack strategy based on new information in Embodiment 1 of the present invention.

[0033] Figure 2 FIG. 1 is a schematic diagram of an architecture of a remote estimation system in Embodiment 1 of the present invention.

[0034] Figure 3 The figure is a flowchart of obtaining system information and the attack design intention in the first embodiment of the present invention. DETAILED DESCRIPTION

[0035] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0036] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0037] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0038] Embodiment 1

[0039] This embodiment discloses a novel method for generating a false data injection attack strategy based on new information that requires less prior knowledge. It combines the system new information and auxiliary information at the current moment that have been modified by the attacker at the previous historical moment. It is suitable for scenarios where malicious attackers can intercept and tamper with original data packets and obtain auxiliary information through additional sensors.

[0040] like Figure 1 As shown, a method for generating a false data injection attack strategy based on new information includes:

[0041] Step S1: Acquire prior knowledge of the cyber-physical system CPS, and store the new information modified by the attacker at the last moment and the new information of the system at the current moment; use the sensors in the cyber-physical system to collect auxiliary information; the above operations reduce the complexity of obtaining system information and prior knowledge, significantly reduce the parameters required, and make the attack easier to initiate;

[0042] Step S2: construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and the auxiliary information; since it is less difficult for the attacker to obtain the auxiliary information, a higher degree of freedom is provided for the design of the attack strategy;

[0043] Step S3, according to the false data injection attack strategy, calculate the error covariance of the attacked new information; express the error covariance in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally obtain the optimal attack strategy based on information. This processing provides a clearer description of the designed attack strategy, proving that the designed attack strategy can maximize the damage to the system while maintaining stealth.

[0044] As introduced in the background technology, potential attack mechanisms and strategies are deeply studied and understood from the perspective of security defense. The purpose of the attack is to formulate specific attack strategies and analyze potential vulnerabilities in CPS, which is of great significance for defenders to proactively establish effective defense measures such as attack detection, security state estimation, and elastic control methods. By constructing and analyzing innovative attack strategies, our goal is to provide defenders with a unique perspective and tools that enable users to better understand the thought process and action plans of potential attackers. This process is a key step in identifying, preventing and defending against actual attacks. To facilitate understanding of the technical solution of the present invention, this solution is further explained as follows:

[0045] In step S1, before obtaining the prior knowledge in the cyber-physical system CPS, it is necessary to first construct a dynamic model of the linear discrete time-invariant system, which is expressed as follows:

[0046]

[0047] Where k∈N represents the time index, and the state of the discrete-time linear time-invariant process is represented by x k ∈R n Indicated by y, the sensor measurement value is k ∈R m Indicates. k ∈R n and v k ∈R m denote process noise and measurement noise respectively, which are independent zero-mean Gaussian distributions with the same covariance Q>0 and R≥0, which means that ω k ~N(0,Q) and υ k ~N(0,R). In addition, we assume is controllable, (A, C) is observable. This embodiment considers a discrete system, and the value of the latter term can be obtained by iterating the attack strategies of the previous n terms (it is later known that the attack starts from a stable state, that is, the attacker can obtain the state estimation error of the system at the initial moment, so the first n terms can be iterated to x0) to obtain the attack strategy corresponding to the current moment. In other words, the attack strategies at historical moments are stored in the attack strategy at the current moment.

[0048] Furthermore, when obtaining prior knowledge in the cyber-physical system CPS, it is assumed that the attacker has the ability to inject attacks into the communication channel, so that the attacker can obtain perfect system information, namely: the state transfer matrix A, the output matrix C, the Gaussian random noise Q and R with covariance, and the Kalman filter gain K are all known to the attacker.

[0049] Furthermore, the attacker can install additional sensors in the system to observe the system status and collect auxiliary information, namely:

[0050]

[0051] in, and denote the additional sensor measurements and their corresponding measurement noise, respectively.

[0052] Furthermore, at each time step, the sensor measurement data is transmitted to the remote estimator via the wireless communication network. A standard Kalman filter is used for state estimation based on sensor measurements, as shown in the following equation:

[0053]

[0054] in and Represent the state x on the remote estimator respectively k The corresponding a priori and a posteriori minimum mean square error estimates, and P k represents the corresponding estimation error covariance, z k Represents the new information of the system, K k represents the Kalman filter gain.

[0055] It is common sense that the Kalman filter converges exponentially fast for any initial condition. The steady-state values ​​of the state error covariance and the Kalman filter gain are given by:

[0056]

[0057] in, represent is the only positive semidefinite solution of , and K is defined as the steady-state Kalman filter gain.

[0058] In step S2, a false data injection attack strategy is constructed based on the new information modified by the attacker at the previous moment, the new information of the system at the current moment, and the auxiliary information. Specifically, based on the system in the above formula model (1), the following new information attack design scheme is proposed:

[0059] Condition 1: A malicious attacker installs additional sensors in the system to observe the system status and collect auxiliary information. Assume that the adversary has access to all system information, including monitoring and intercepting system updates. k ,Right now:

[0060]

[0061] in, and denote the additional sensor measurements and their corresponding measurement noise, respectively; The corresponding covariance are independent and have zero-mean Gaussian distributions, expressed as

[0062] Based on condition 1, the local Kalman filter generated by sensor 2 is as follows:

[0063]

[0064] For the attacker, the attacker's plan is to further increase the covariance of the estimation error, thereby reducing the estimation performance of the system. Therefore, the corrected state estimation can be described as:

[0065]

[0066] in, and denote the states modified by the attacker at the remote estimator The minimum mean square error (MMSE) of the prior and posterior estimates of . At the same time, it can be inferred that the estimation equations (2) and (6) have the same initial state It means that the attack starts from a stable state. Therefore, in the absence of data loss and FDI attack, and are the same.

[0067] By using the new information, auxiliary information and system new information modified by the attacker at the previous moment, an imperceptible FDI attack strategy model is constructed, namely:

[0068]

[0069] Where T∈R m×m , and L∈R m×m is the matrix chosen by the attacker, i.e., the attack matrix. In addition, b k ∈R m Obey independent of new information k The same distribution of Gaussian distribution, and b k ~N(0,ρk ); and when k≤0, also follows a Gaussian distribution with mean zero, i.e. At the same time, k and z k-1 Independent of each other.

[0070] In step S3, according to the false data injection attack strategy, the error covariance of the attacked new information is calculated; specifically, by obtaining the parameter data of the linear discrete time-invariant system when the sensor is attacked by the new information; based on the parameter data, a Kalman filter with a safety preselector is used to perform filtering estimation to obtain a system filter estimation vector. The estimated error vector is obtained based on the difference between the system estimation vector under the attack of the new information and the estimation vector of the system itself. According to the estimated error vector, the system estimation vector under the attack of the new information and the Kalman filter gain, a recursive form of the linear discrete time-invariant system under the attack of the new information and the remote error covariance is obtained. The error covariance is expressed in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally the optimal attack strategy based on information is obtained. Figure 3 As shown, step S3 can be implemented by the following process:

[0071] Step S3-1: Based on the set attack model, recursively obtain the remote estimation error covariance, specifically:

[0072] From the above information, we can infer that z k ~N(0,Σ). Furthermore, It also has a mean of zero, so the covariance is expressed as:

[0073]

[0074] In order to keep the FDI attack hidden, the covariance of the new information after the attack must be the same as the covariance of the new information under normal circumstances, that is:

[0075] Σ a =Σ(9)

[0076] Step S3-2: Convert the theoretically designed attack strategy into a convex optimization problem to satisfy the constraints and maximize the trace of the estimated error covariance. Specifically:

[0077] The attacker’s goal is to degrade the estimation performance by manipulating the posterior estimation error covariance while satisfying the concealment constraint. Therefore, it is necessary to transform the theoretical result into an optimization problem, namely:

[0078]

[0079] in, represents the covariance matrix of the remote estimation error, and its purpose is to make The trace of maximization.

[0080] The sensor transmits the received new information to the remote state estimator on the system through the network layer. Therefore, for the safety of the system, 2 The detector can be placed on the same side as the remote state estimator and utilizes innovative features to identify potential anomalies. The corresponding detection metric is defined as follows:

[0081]

[0082] Among them, τ is the size of the detection window, ξ is the detection threshold; H0 indicates the normal operation of the system, while H1 indicates that the system is under attack. When ξ is exceeded, the detector will trigger an alarm.

[0083] Step S3-3, attack performance analysis. As mentioned above, the attacker's goal is to maximize the trace of the estimation error covariance while maintaining concealment. Next, the estimation error covariance is studied.

[0084] Starting from (1) and (2), the a priori estimation error of the normal operating system is expressed as

[0085]

[0086] In this case, you can get new information about the system:

[0087]

[0088] Similarly, the prior estimation error and innovation obtained by the additional sensor are:

[0089]

[0090] According to equations (2), (6) and (7), after the attack is injected into the system, the following information can be obtained:

[0091]

[0092] The posterior error covariance matrix of the remote estimator is:

[0093]

[0094] because are independent and identically distributed Gaussian random variables, so Therefore, the first two terms in formula (16) are consistent with the new information modified by the attacker. In this case, the calculation of the last two terms in formula (18) becomes crucial.

[0095] From formula (1), we can know the weight dynamic model:

[0096]

[0097] Formula (a) is valid because And the last term in formula (16) is 0. Formula (b) is valid because υ i and b i For i∈{1,2,...,k} and ω i and z k-i For i∈{1,2,...,k}, it is independent. The validity of formula (c) is based on and are the unique solutions to the positive semidefinite equations, as follows:

[0098]

[0099] in,

[0100] The same method can easily obtain This expected value is calculated as follows:

[0101]

[0102] The focus of the attacker is to minimize the performance of the system, and the goal is to maximize the derived In order to more clearly demonstrate the effectiveness of the designed attack strategy, the optimal covert attack strategy is derived under the constraints by solving the convex optimization problem (10).

[0103] According to the property of trace tr(A) = tr(A T ), the estimated error covariance matrix P k a The trace of can be expressed as:

[0104]

[0105] in,

[0106]

[0107] Obviously, the attack matrix T, and L do not participate in the first term of (20). Therefore, the analysis should focus on the specific terms in the following terms:

[0108]

[0109] Introduction The above hidden constraint can be rewritten as follows:

[0110]

[0111] By applying Schur's complement lemma, the constraints in equation (25) are transformed into a convex optimization problem of the following form:

[0112]

[0113] Therefore, by combining (22) and (23), we can obtain:

[0114]

[0115] in

[0116]

[0117] In summary, the attacker can obtain the measured information y of system parameters based on k and auxiliary information Calculate the true innovation value z k Then, combined with the new information modified by the attacker The ultimate goal is to manipulate the measured values Right now This means generating manipulated measurements Equivalent to generating tampered new information

[0118] The convex optimization problem with constraints is solved by MATLAB. Its objective function involves optimizing the attack matrix T, and L, it is known that the optimal linear attack strategy is T = 0, L = -I and ρ k = 0. Under these conditions, simulations prove that the designed attack strategy can minimize the system performance.

[0119] At present, no similar solutions have been proposed for the safety control system of linear discrete time-invariant systems based on new information attacks, and the design of optimal attack strategies that combine information from both the current moment and the previous historical moment; and there is still a lack of effective theoretical design solutions for the problem of new information-based attacks involving historical moments in the prior art. The present invention explores the optimal design strategy for new information-based attacks on cyber-physical systems, in which malicious attackers use auxiliary information. The attacker only needs to know the new information modified by the opponent at the previous moment, the new information of the current system, and the auxiliary information obtained through additional sensor measurements, which significantly reduces the complexity of obtaining prior knowledge. This method formulates the optimal attack strategy as a convex optimization problem, maximizing the covariance of remote estimation errors while ensuring concealment.

[0120] Embodiment 2

[0121] This embodiment discloses a false data injection attack strategy generation system based on new information, including:

[0122] The data acquisition module is configured to: obtain prior knowledge of the cyber-physical system CPS, store the new information modified by the attacker at the last moment and the new information of the system at the current moment; use sensors in the cyber-physical system to collect auxiliary information;

[0123] The attack strategy generation module is configured to: construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and the auxiliary information;

[0124] The attack strategy optimization module is configured to: calculate the error covariance of the attacked new information according to the false data injection attack strategy; express the error covariance in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally obtain the optimal attack strategy based on information.

[0125] Embodiment 3

[0126] The purpose of this embodiment is to provide a computer-readable storage medium.

[0127] A computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps in a method for generating a false data injection attack strategy based on new information as described in the first embodiment of the present disclosure.

[0128] Embodiment 4

[0129] The purpose of this embodiment is to provide an electronic device.

[0130] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in a method for generating a false data injection attack strategy based on new information as described in Embodiment 1 of the present disclosure are implemented.

[0131] The steps involved in the apparatuses of the above embodiments 2, 3 and 4 correspond to the method embodiment 1, and the specific implementation methods can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0132] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0133] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for generating a false data injection attack strategy based on new information, characterized in that: include: Acquire prior knowledge of the cyber-physical system (CPS) and store the new information modified by the attacker at the last moment and the new information of the system at the current moment; Using sensors in cyber-physical systems to collect auxiliary information; Construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and auxiliary information; According to the false data injection attack strategy, the error covariance of the attacked new information is calculated; The error covariance is expressed in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally the optimal attack strategy based on information is obtained.

2. A method for generating a false data injection attack strategy based on new information as claimed in claim 1, characterized in that: The sensor measurement data is transmitted to the remote estimator based on the wireless communication network.

3. A method for generating a false data injection attack strategy based on new information as claimed in claim 1, characterized in that: According to the false data injection attack strategy, the error covariance of the attacked new information is calculated, including: obtaining parameter data of the linear discrete time-invariant system when the sensor is attacked by the new information.

4. A method for generating a false data injection attack strategy based on new information as claimed in claim 3, characterized in that: Based on the parameter data, a Kalman filter with a safety preselector is used to perform filter estimation to obtain a system filter estimation vector.

5. A method for generating a false data injection attack strategy based on new information as described in any one of claims 3-4, characterized in that: The estimated error vector is obtained according to the difference between the system estimated vector under the attack of new information and the system's own estimated vector.

6. A method for generating a false data injection attack strategy based on new information as described in any one of claims 3 to 5, characterized in that: According to the estimated error vector, the system estimation vector under the new information attack and the Kalman filter gain, the recursive form of the linear discrete time-invariant system under the new information attack and the long-range error covariance is obtained.

7. A method for generating a false data injection attack strategy based on new information as claimed in claim 1, characterized in that: The concealment constraint is transformed into a convex optimization problem by applying Schur's complement lemma. The optimal concealed attack strategy is obtained under the condition of concealment constraint by solving the convex optimization problem.

8. A false data injection attack strategy generation system based on new information, characterized by: include: The data acquisition module is configured to: obtain prior knowledge of the cyber-physical system CPS and store the new information modified by the attacker at the last moment and the new information of the system at the current moment; Using sensors in cyber-physical systems to collect auxiliary information; The attack strategy generation module is configured to: construct a false data injection attack strategy based on the new information modified by the attacker at the last moment, the new system information at the current moment, and the auxiliary information; The attack strategy optimization module is configured to: calculate the error covariance of the attacked new information according to the false data injection attack strategy; The error covariance is expressed in the form of convex optimization to obtain the covariance that maximizes the remote estimation variance, and finally the optimal attack strategy based on information is obtained.

9. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps in the method for generating a false data injection attack strategy based on new information as described in any one of claims 1 to 7 are implemented.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the method for generating a false data injection attack strategy based on new information as described in any one of claims 1 to 7 are implemented.

Images