A Neural Network-Based Secure Artificial Noise Encryption Method

Abstract

The present invention discloses a security artificial noise encryption method based on a neural network. The local end and the remote end adopt the same artificial noise sequence Γ(k) with time as the independent variable, and also adopt the same periodic function f(x) with a period of T and a periodic function g(x) with a period not equal to T. In the local end, f(Γ(k)) is used as the input of the local neural network N(θ(k)), and the sum of the output security artificial noise at the current moment and the original observation value is used as the encrypted observation information transmitted by the communication network. Using the artificial noise sequence Γ(k) as the input, the output generated by passing through the periodic function g(x) is used as the target value of the local neural network N(θ), the loss function value is calculated, and the network weight θ(k) is updated using the gradient descent algorithm. In the remote end, the encrypted artificial noise is obtained by the same method, and the original observation value is obtained by subtracting the encrypted artificial noise from the data obtained through network transmission. This method adds artificial noise to the observation information transmitted through the wireless network for encryption, which is safe and reliable.

Description

Technical Field

[0001] The present invention belongs to the technical field of remote state estimation, relates to a method for secure transmission of observation information, and mainly relates to a secure artificial noise encryption method based on a neural network. Background Art

[0002] The rapid development of computing, control, and communication has expanded the scale of interconnection between devices in cyber-physical systems. However, such an open physical access system is more vulnerable to attacks by malicious attackers targeting a certain vulnerability. Among them, eavesdropping is a typical passive attack method, which does not affect the performance of the system but poses a threat to the security of information.

[0003] There are many ways to prevent eavesdropping. The most common and intuitive method is to encrypt the original information. Adding artificial noise to the original information is a simple and effective method. Adding a random number as artificial noise can confuse eavesdroppers to a certain extent. If the random number is a pseudo-random number, that is, actually generated by a computer according to a certain function, the eavesdropper has the ability to estimate the function through a large amount of statistical information and then decrypt the information. If a true random number is generated by a process similar to thermal noise, the generation result of the noise cannot be restored at the remote end.

[0004] In order to restore the encrypted information at the local end at the remote end, the currently adopted technologies mainly include the null space method and the coding matrix method: The null space method uses additive artificial noise, and the added artificial noise is within a certain null space predetermined at the remote end and the local end. During decoding, only need to multiply by the corresponding matrix to offset the influence of the artificial noise; The coding matrix method aggregates the original information and artificial noise with an invertible coding matrix. At the remote end, only need to multiply by the inverse of the coding matrix to obtain the original signal. The artificial noise adopted by these two methods is a random signal, but a definite coding scheme is required to be able to restore at the remote end. If the eavesdropper masters the details of the coding scheme through a loophole, then the data encrypted with this artificial noise is also insecure. Even if a time-varying coding scheme is adopted, if the time-varying rule can be obtained by the eavesdropper through a backdoor loophole or statistical information, it is also insecure. Therefore, if a more secure and reliable encryption method is designed, it has been the main research direction of those skilled in the art. Summary of the Invention

[0005] In view of the security problems existing in information transmission in the prior art, the present invention provides a secure artificial noise encryption method based on a neural network. The local end and the remote end adopt the same artificial noise sequence Γ(k) with time as the independent variable, and the same periodic function f(x) with period T and periodic function g(x) with a period not equal to T. In the local end, f(Γ(k)) is used as the input of the local neural network N(θ(k)), and the output is the secure artificial noise at the current moment. This is added to the original observation value to be the encrypted observation information transmitted by the communication network. Using the artificial noise sequence Γ(k) as the input, the output generated by passing through the periodic function g(x) is used as the target value of the local neural network N(θ), the loss function value is calculated, and the gradient descent algorithm is used to update the weight θ(k) of the network N(θ(k)). In the remote end, the encrypted artificial noise is obtained using the same method, and the data obtained through network transmission is subtracted by the encrypted artificial noise to obtain the original observation value. The Kalman filter algorithm is executed to update the posterior covariance matrix and the state estimation value, and the weight θ′(k) of the neural network N′(θ′(k)) at the remote end is updated. Repeat the steps until the estimation time ends. This method encrypts the observation information transmitted through the wireless network by adding artificial noise. Even if a powerful eavesdropper masters the entire coding process and details, they cannot restore the added artificial noise, which is safe and reliable.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a secure artificial noise encryption method based on a neural network, including the following steps:

[0007] S1: The local end and the remote end adopt the same artificial noise sequence Γ(k) with time as the independent variable, and the same periodic function f(x) with period T and periodic function g(x) with a period not equal to T; initialize the neural networks N(θ) and N’(θ) at the local end and the remote end; initialize the posterior covariance matrix and the state estimation value at the remote end;

[0008] S2: At the local end, use f(Γ(k)) as the input of the neural network N(θ(k)), and the output is the secure artificial noise at the current moment;

[0009] S3: Add the secure artificial noise at the current moment obtained in step S2 to the original observation value to be the encrypted observation information transmitted by the communication network;

[0010] S4: Using the artificial noise sequence Γ(k) as the input, the output generated by passing through the periodic function g(x) is used as the target value of the neural network N(θ), calculate the loss function value, and use the gradient descent algorithm to update the weight θ(k) of the network N(θ(k));

[0011] S5: The remote end repeats the method in steps S2 - S3 to obtain encrypted artificial noise, subtracts the encrypted artificial noise from the data obtained through network transmission to get the original observation value; executes the Kalman filtering algorithm to update the posterior covariance matrix and the state estimation value, and then updates the weight θ′(k) of the neural network N′(θ′(k)) at the remote end through the method in step S4;

[0012] S6: Repeat steps S2 - S5 until the estimation time ends.

[0013] As an improvement of the present invention, in step S1, when initializing the neural networks N(θ) and N′(θ) at the local end and the remote end, exactly the same hyperparameters are adopted, and the hyperparameters at least include network structure, learning rate, loss function, optimization method, and initial weights; the period T is less than the range of the artificial noise Γ(k).

[0014] As an improvement of the present invention, in step S3, the encrypted observed information y * (k) transmitted by the communication network at time k is:

[0015]

[0016] where, represents the output generated after passing f(Γ(k)) as the input through the neural network with parameters θ(k); y(k) ∈ R p represents the original system observation value at time k.

[0017] As another improvement of the present invention, in step S4, the neural network N(θ) selects the L 2 loss function:

[0018]

[0019] where, y Loss is the loss function value, is the output value of the neural network, y target is the target value given by the neural network. At time k, and y target = g(Γ(k)).

[0020] As another improvement of the present invention, the gradient descent algorithm is adopted to update the network weight in step S4, and the specific calculation formula is:

[0021]

[0022] where, η is the learning rate.

[0023] As a further improvement of the present invention, the original observation value y(k) at time k in step S5 is specifically:

[0024]

[0025] Among them, the remote end generates artificial noise at time k which represents the output generated after taking f(Γ(k)) as the input and passing through the neural network N’(θ) with parameter θ′(k).

[0026] As a further improvement of the present invention, in the step S5, the specific method for updating the posterior covariance matrix and the state estimate value is as follows:

[0027]

[0028] P(k|k - 1) = AP(k - 1|k - 1)A T + Q,

[0029] K(k) = P(k|k - 1)C T (CP(k|k - 1)C T + R) -1 ,

[0030]

[0031] P(k|k) = P(k|k - 1) - K(k)CP(k|k - 1),

[0032] wherein, and respectively represent the prior estimate and the posterior estimate of the state by the remote estimator at time k, P(k|k - 1) and P(k|k) are the corresponding prior estimate error covariance matrix and posterior estimate error covariance matrix, and K(k) is the Kalman filter gain at time k; after the remote state estimation algorithm runs, the remote end updates the weight θ′(k) of the neural network N′(θ′(k)) in the same way as the local end.

[0033] Compared with the prior art, the present invention provides a secure artificial noise encryption method based on a neural network, having the beneficial effects:

[0034] (1) The periods of the periodic functions f(x) and g(x) adopted by the present invention are different, and the periods are much smaller than the extreme values of the original artificial noise Γ(k). Therefore, it is a multi - valued mapping for the input and output of the neural network, so that the weight update of the neural network cannot converge, and the neuron weights are constantly changing, which is equivalent to a time - varying non - linear function.

[0035] (2) For the legal remote estimator, the generation method of the secure artificial noise and the weight update algorithm of the neural network are determined, so it will not affect the estimation performance of the remote estimator.

[0036] (3) For an eavesdropper who appears at time t in the present invention, even if its estimation of Γ(k) is asymptotically convergent and it knows the coding method, the hyperparameters of the neural network, and the weights at time t, as long as it does not know Γ(k) precisely, its estimation of the secure artificial noise is still large. Description of the Drawings

[0037] Figure 1 is the flowchart of the steps of a secure artificial noise encryption method based on neural network according to the present invention;

[0038] Figure 2 is the graph of the change of the loss function during the neural network training process in Embodiment 2 of the present invention;

[0039] Figure 3 is the schematic diagram of the two-norm of the estimation error of the legitimate remote estimator in step S5 of the method of the present invention;

[0040] Figure 4 is the schematic diagram of the relative estimation error of the secure artificial noise by the eavesdropper when the estimation of the original artificial noise is asymptotically convergent after the test for Embodiment 2 of the present invention. Detailed Embodiments

[0041] The present invention will be further clarified below in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0042] Embodiment 1

[0043] A secure artificial noise encryption method based on neural network is used for a remotely estimated system that may be wiretapped. Assume that the dynamic equation of the system to be remotely estimated is:

[0044] x(k + 1) = Ax(k) + ω(k), (1)

[0045] where x(k) ∈ R n represents the system state at time k, A ∈ R n×n represents the system matrix, ω(k) ∈ R n is the process noise at time k, which is Gaussian white noise independent of the initial state value, and the covariance matrix is Q ∈ R n×n . ω(k 1 ) and ω(k 2 ) are also uncorrelated at k 1 ≠ k 2 ;

[0046] Correspondingly, its observation equation can be described as:

[0047] y(k) = Cx(k) + v(k), (2)

[0048] where y(k) ∈ R p represents the system measurement value at time k, C ∈ R p×n represents the observation matrix, and v(k) ∈ R p is the process noise at time k, which is Gaussian white noise independent of both the initial state value and the process noise, and its covariance matrix is R ∈ R p×p . v(k 1 ) and v(k 2 ) are also uncorrelated when k 1 ≠ k 2 ;

[0049] At time k, the local end transmits the encrypted observation information to the remote end to prevent potential eavesdroppers from stealing the corresponding observation information. The specific method steps are as Figure 1 shown

[0050] Step S1: The local end and the remote end agree to use the same vector function Γ(k) with the same dimension as the observation vector and time as the independent variable as the artificial noise at time k, and use the same periodic function f(x) with period T and the periodic function g(x) with period not T; The selection of T should be much smaller than the range of the artificial noise Γ(k); Initialize the posterior covariance matrix and the state estimate value of the remote estimation end; Initialize the neural networks N(θ) and N’(θ) of the local end and the remote end. When initializing, use exactly the same hyperparameters, including the network structure, learning rate, loss function, and optimization method, as well as exactly the same initial weights.

[0051] Step S2: At the local end, use f(Γ(k)) as the input of the neural network N(θ(k)).

[0052] Step S3: Use the output of the neural network N(θ(k)) as the artificial noise at the current time, and add it to the original observation value as the encrypted observation information transmitted by the communication network. That is, the encrypted observation information transmitted through the wireless network at time k is:

[0053]

[0054] where y * (k) represents the encrypted information, represents the output generated after passing through the neural network with parameters θ(k) with f(Γ(k)) as the input. f(Γ(k)) is the function value with Γ(k) as the input, and f(x) is a periodic function with period T. Here, the selection of T should be much smaller than the range of the original artificial noise Γ(k).

[0055] Step S4: Using Γ(k) as the input and the output generated by g(x) as the target value of the neural network, calculate the loss function value and update the network weights using the gradient descent algorithm. The neural network selects L 2 Loss function:

[0056]

[0057] where y Loss is the loss function value, is the output value of the neural network, y target is the target value given by the neural network. At time k, and y target = g(Γ(k)).

[0058] Update the network weights using the gradient descent algorithm. The specific calculation formula is:

[0059]

[0060] where η is the learning rate.

[0061] Step S5: At the remote end, obtain the added artificial noise in the same way and subtract it to get the original observed value. Perform the Kalman filtering algorithm to obtain the posterior estimate of the state, and then update the neural network weights in the same way. The remote end generates the artificial noise at time k in the same way, that is and obtain the original observed value at time k through the following formula

[0062]

[0063] Then update the posterior covariance and posterior state estimate according to the following formula:

[0064]

[0065] P(k|k - 1) = AP(k - 1|k - 1)A T + Q, (8)

[0066] K(k) = P(k|k - 1)C T (CP(k|k - 1)C T + R) -1 , (9)

[0067]

[0068] P(k|k) = P(k|k - 1) - K(k)CP(k|k - 1), (11)

[0069] where, and They respectively represent the prior estimate and the posterior estimate of the state by the remote estimator at time k. P(k|k - 1) and P(k|k) are the corresponding prior estimate error covariance matrix and posterior estimate error covariance matrix, and K(k) is the Kalman filter gain at time k.

[0070] After the remote state estimation algorithm runs, the remote end updates the weight θ′(k) of the neural network N′(θ′(k)) in the same way as the local end.

[0071] Step S6: Repeat the above steps S2 - S5 until the estimation time ends. The method of the present invention designs secure artificial noise so that even if the eavesdropper obtains the coding change method and the corresponding coding weights at the eavesdropping moment through the backdoor vulnerability, the observed information cannot be completely restored.

[0072] Embodiment 2

[0073] A secure artificial noise encryption method based on a neural network specifically includes the following steps:

[0074] First, perform parameter settings:

[0075] Considering the IEEE4 bus power grid system, considering the observation period is 0.05 ms, and its system matrix is

[0076]

[0077] Assume that the covariance matrix of the process noise is

[0078]

[0079] The system uses two local sensors to monitor the first state and the second state respectively. Their measurement variances are 0.008 and 0.002 respectively, and the measurement noises of the two sensors are uncorrelated. The joint observation matrix can be written as

[0080]

[0081] Design artificial noise So that its range is infinite. Design the periodic functions f(x) = sin(x) and g(x) = sin(πx). These two functions have different periods. The neural network uses one hidden layer with 32 neurons. The activation function from the input layer to the hidden layer is the Relu function, and the hidden layer to the output layer is linear. Such a small network will not bring too much burden to the encryption calculation.

[0082] The initial value of the local system is generated by Gaussian white noise with a mean of 0 and a covariance matrix of the identity matrix. The initial value of the estimator at the remote estimation end is 0, and the initial value of the posterior estimate error covariance matrix is the identity matrix.

[0083] At the local end, with Γ(k) as the input, the output generated by f(x) is used as the input of the neural network. The generated output is used to generate the encrypted information during the transmission process according to formula (3).

[0084] Take g(Γ(k)) as the target value y of the neural network target , and update the network weights at the local end according to formula (4) and formula (5). Figure 2 The change of the loss function value is shown. Figure 2 As can be seen from

[0085] Update of the remote state estimate value and the posterior estimate error covariance matrix: Restore the original state estimate value according to formula (6), and perform the Kalman filtering algorithm according to formula (7) - formula (11) to obtain the posterior estimate and the posterior estimate error covariance. The posterior estimate error is as Figure 3 shown. Figure 3 As can be seen from

[0086] Update the neural network weights at the remote end: Similar to the local end, that is, take g(Γ(k)) as the target value y of the neural network target , and update the network weights at the remote end according to formula (4) and formula (5).

[0087] Repeat the above steps until the estimation time ends.

[0088] Test the solution of Embodiment 2. Assume that the estimation error of the powerful eavesdropper for the artificial noise Γ(k) is Start eavesdropping at time t and master the weights of the neural network at time t and all hyperparameters. Its relative error in the estimation of the secure artificial noise is as Figure 4 shown. The test results show that even if the coding method is leaked, there is still a large error in the eavesdropper's estimation of the secure artificial noise. Therefore, this method encrypts the observed information transmitted through the wireless network by adding artificial noise. Even if a powerful eavesdropper masters the entire coding process and details, it is impossible to completely restore the added artificial noise, which is safe and reliable.

[0089] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A security artificial noise encryption method based on a neural network, characterized in that, it includes the following steps: S1: The local end and the remote end adopt the same artificial noise sequence Γ(k) with time as the independent variable, and the same periodic function f(x) with a period of T and a periodic function g(x) with a period not equal to T; initialize the neural networks N(θ) and N’(θ) of the local end and the remote end; initialize the posterior covariance matrix and the state estimate value of the remote end; S2: At the local end, take f(Γ(k) as the input of the neural network N(θ(k)), and the output is the security artificial noise at the current moment; S3: Add the security artificial noise at the current moment obtained in step S2 to the original observation value as the encrypted observation information transmitted by the communication network; S4: Take the artificial noise sequence Γ(k) as the input, and use the output generated by the periodic function g(x) as the target value of the neural network N(θ), calculate the loss function value, and use the gradient descent algorithm to update the weight θ(k) of the network N(θ(k)); S5: At the remote end, repeat the methods of steps S2 - S3 to obtain the encrypted artificial noise, subtract the encrypted artificial noise from the data obtained through network transmission to obtain the original observation value; execute the Kalman filter algorithm to update the posterior state estimate value and the covariance matrix, and then update the weight θ′(k) of the neural network N′(θ′(k)) of the remote end through the method of step S4; S6: Repeat steps S2 - S5 until the estimation time ends.

2. The security artificial noise encryption method based on a neural network according to claim 1, characterized in that: In step S1, when initializing the neural networks N(θ) and N’(θ) of the local end and the remote end, exactly the same hyperparameters are adopted, and the hyperparameters at least include the network structure, learning rate, loss function, optimization method, and initial weight; the period T is less than the range of the artificial noise Γ(k).

3. The security artificial noise encryption method based on a neural network according to claim 2, characterized in that: In the step S3, the encrypted observed information y transmitted by the communication network at the k-th moment * (k) is as follows: Among them, represents the output generated after passing f(Γ(k)) as the input through a neural network with parameters θ(k); y(k) ∈ R p represents the original system observation value at time k.

4. The security artificial noise encryption method based on a neural network according to claim 2, characterized in that: In the step S4, the neural network N(θ) selects L 2 Loss function: Among them, y Loss is the loss function value, is the output value of the neural network, and y target is the target value given by the neural network. At time k, and y target = g(Γ(k)).

5. The security artificial noise encryption method based on a neural network according to claim 4, characterized in that: In step S4, the gradient descent algorithm is used to update the network weight, and the specific calculation formula is: where η is the learning rate.

6. The security artificial noise encryption method based on a neural network according to claim 5, characterized in that: In step S5, the original observation value y(k) at time k is specifically: Among them, the remote end generates artificial noise at time k represents the output generated after passing the input f(Γ(k)) through the neural network N'(θ) with parameter θ'(k).

7. The security artificial noise encryption method based on a neural network according to claim 6, characterized in that: In step S5, the specific method for updating the posterior covariance matrix and the state estimate value is: P(k|k - 1) = AP(k - 1|k - 1)A T + Q, K(k) = P(k|k - 1)C T (CP(k|k - 1)C T + R) -1 , P(k|k)={(k|k - 1)-K(k)CP(k|k - 1), Among them, and respectively represent the prior estimate and posterior estimate of the state by the remote estimator at time k. P(k|k - 1) and P(k|k) are the corresponding prior estimate error covariance matrix and posterior estimate error covariance matrix, and K(k) is the Kalman filter gain at time k; A represents the system matrix, Q represents the covariance matrix of the system, C represents the observation matrix, and R represents the covariance matrix in the observation equation. After the remote state estimation algorithm runs, the remote end updates the weight θ′(k) of the neural network N′(θ′(k)) in the same way as the local end.

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