Image encryption method based on memristor chaotic system

Abstract

The invention relates to the technical field of image processing, in particular to an image encryption method based on a memristor chaotic system, which comprises the following steps: acquiring a to-be-encrypted image; replacing the first neuron resistance connection weight of the HNN model with the adaptive memristor weight, and constructing a DM-HNN model; generating an encryption key by using a true random number generator; pixel coordinates and pixel value information of a plaintext image act on the DM-HNN model, and nonlinear transformation is performed on plaintext information by using a nonlinear function; bidirectional diffusion is executed, and image encryption is completed. According to the invention, image encryption is carried out based on the memristor state, and the problems of weak encryption performance, weak anti-attack ability and poor encryption security and efficiency of the existing method are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to an image encryption method based on a memristive chaotic system. Background Art

[0002] As an important means to ensure the security of image information, the encryption process usually includes two key stages: scrambling and diffusion. In the scrambling stage, the original structure of the image is disrupted by changing the pixel positions, while in the diffusion stage, the subtle changes of a single pixel are propagated to multiple surrounding pixels through specific mathematical operations, thus significantly changing the statistical characteristics of the ciphertext image and making it significantly different from the plaintext image.

[0003] Discrete chaotic systems have shown extremely high adaptability in digital hardware and industrial application scenarios due to their significant advantages such as fast iteration speed, low implementation cost, and strong randomness, and have great potential value in image encryption and ensuring the security of image information. For example, in "Multi-Image Encryption Algorithm Based on Novel Spatiotemporal Chaotic System and Fractal Geometry", a shift table is generated through the iteration of a chaotic sequence, and a random shift amount is extracted from the chaotic value using bit operations to achieve the cyclic shift diffusion of pixel values; another example is in "Image Encryption Algorithm Based on Chaotic Mapping and Binary Bidirectional Zigzag Transform", where a pseudo-random sequence is generated through the iteration of a chaotic system, and diffusion encryption is achieved through an exclusive OR operation with the original image data. Although discrete chaotic systems have shown significant advantages in the field of image encryption, the above methods mainly focus on using chaotic sequences for diffusion operations, but there are problems such as weak encryption performance, weak anti-attack ability, and poor security and efficiency of encryption. Summary of the Invention

[0004] Aiming at the deficiencies of the existing methods, the present invention encrypts images based on the memristive state, solving the problems of weak encryption performance, weak anti-attack ability, and poor security and efficiency of the existing methods.

[0005] The technical solution adopted by the present invention is: an image encryption method based on a memristive chaotic system includes the following steps:

[0006] Step 1: Obtain the image to be encrypted;

[0007] As a preferred embodiment of the present invention, the image to be encrypted is a plaintext image.

[0008] Step 2: Use the adaptive memristor weight to replace the first neuron resistance connection weight of the HNN model to construct a DM-HNN model;

[0009] As a preferred embodiment of the present invention, the formula of the DM-HNN model is:

[0010]

[0011] where n is a natural number, x n and y n represent two state variables at the nth iteration, represents the cosine magneto-controlled memristor state variable at the nth iteration, μ is the neuron attenuation, g 12 , g 21 and g 22 are connection weights, ε is the internal control parameter of the memristor, and k is a specified parameter.

[0012] Step 3: Use a true random number generator to generate an encryption key;

[0013] As a preferred embodiment of the present invention, the encryption key includes: the initial states of the memristors in forward and backward diffusion and the input parameters of the nonlinear function.

[0014] Step 4: Apply the pixel coordinates and pixel value information of the plaintext image to the DM-HNN model, and use a nonlinear function to perform a nonlinear transformation on the plaintext information;

[0015] As a preferred embodiment of the present invention, the formula of the nonlinear function is:

[0016]

[0017] where (i, j) are pixel coordinates, p is the pixel value at the corresponding position associated with the memristor offset control factor, ∈ is a perturbation factor, represents the global state of the memristor, and D() is the nonlinear transformation function of the DM-HNN model.

[0018] As a preferred embodiment of the present invention, round the nonlinear function M and perform an exclusive OR operation to obtain the corresponding binary number.

[0019] Step 5: Perform bidirectional diffusion on the output value of the nonlinear function to complete image encryption;

[0020] As a preferred embodiment of the present invention, the formula of the bidirectional diffusion is:

[0021]

[0022] where ⊙ represents a modulo operation, represents an exclusive OR operation, Pi,j is the pixel value of the original image, is the pixel value of the image after forward diffusion. i and j are the positions of the pixels, and P 1,1 is the first pixel of the image, is the last pixel of the image after forward diffusion.

[0023] As a preferred embodiment of the present invention, it further includes: decrypting the image.

[0024] As a preferred embodiment of the present invention, an image encryption system based on a memristive chaotic system includes: a memory for storing instructions executable by a processor; a processor for executing the instructions to implement an image encryption method based on a memristive chaotic system.

[0025] As a preferred embodiment of the present invention, a computer-readable medium storing computer program code, the computer program code implementing an image encryption method based on a memristive chaotic system when executed by a processor.

[0026] Advantages of the present invention:

[0027] 1. The DM-HNN model proposed by the present invention has highly complex dynamic characteristics, can exhibit chaotic / hyperchaotic attractors with complex structures, and a uniform attractor with enhanced memristive initials, and is suitable for applications in image encryption based on chaotic systems;

[0028] 2. The present invention does not rely on chaotic sequences, but fully utilizes the chaotic transformation method of nonlinear systems to replace traditional sequences, improving the resource utilization efficiency;

[0029] 3. The present invention has excellent security. The memristive state offset regulation of DM-HNN can achieve jumps between multiple chaotic attractor domains, so as to realize nonlinear transformation of different pixel values using different attractors, enhancing the security;

[0030] 4. The present invention realizes one-to-many mapping through the memristive state, and uses the dynamically adjusted global memristive state to improve the encryption complexity and randomness, effectively enhance the anti-attack ability, and significantly improve the security and efficiency of image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a schematic diagram of the image encryption method based on a memristive chaotic system of the present invention;

[0032] Figure 2 is the chaotic dynamic behavior generated by the chaotic system under typical parameters of the present invention;

[0033] Figure 3Homogeneous coexisting chaotic / hyperchaotic attractors generated by the chaotic system under typical parameters of the present invention;

[0034] Figure 4 Schematic diagram of the non-linear converter based on the memristor state in the image encryption method of the present invention. Detailed implementation manners

[0035] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic way. Therefore, it only shows the components related to the present invention.

[0036] As Figure 1 shown, an image encryption method based on a memristor chaotic system includes the following steps:

[0037] Step 1: Obtain the image to be encrypted;

[0038] The size of the image to be encrypted is W×H, which is the plaintext image P. Here, W and H represent the number of rows and columns of P.

[0039] Step 2: Improve the Hopfield neural network (HNN), that is, the DM-HNN model. The DM-HNN model is composed of two neurons equipped with sine activation functions connected to each other. Replace the resistance connection weight g 11 of its first neuron with an adaptive memristor weight. The formula of the DM-HNN model is:

[0040]

[0041] where n is a natural number, x n and y n represent the two state variables of the nth iteration, μ is the neuron attenuation, g 12 , g 21 and g 22 are connection weights, ε is the memristor internal control parameter, and k is a specified parameter; represents the cosine magneto-controlled memristor state variable of the nth iteration.

[0042] That is, replace g 11 in the original HNN model with

[0043] Set the parameters (k, ε) = (1, 0.1), the connection weights (g 12 , g 21, g 22 ) = (1, -2, 2), and the initial state is fixed μ are respectively equal to 0.6, 0.7, 0.8, 0.9; Figure 2The chaotic dynamic behavior generated by the chaotic system under typical parameters is demonstrated through the phase trajectory diagram.

[0044] Due to the introduction of the cosine magneto-controlled memristor model with memristive internal control parameters, the DM-HNN can enhance the complexity of its bifurcation behavior through the internal state of the memristor.

[0045] The cosine magneto-controlled memristor model can adopt the literature 2021 - IEEE TII - Memristor-Based Hyperchaotic Maps and Application in AC - GANs.

[0046] Set the initial state (k, ε) = (1, 0.1), (g 12 , g 21, g 22 ) = (1, -2, 2) and (x0, y0) = (1, 1); when setting the initial state of the memristor m to be (0, ±1, ±2), the DM-HNN can generate two groups of coexisting homogeneous chaotic / hyperchaotic attractors, as Figure 3 shown; it can be seen that for different initial states of the memristor these coexisting homogeneous chaotic / hyperchaotic attractors have exactly the same fractal structure, but their positions in the phase space are different, and adjacent attractors have a 2π shift in the direction.

[0047] Step 3: Use a true random number generator to generate 4 encryption keys keys = {K1, K2, K3, K4};

[0048] Among them, K1 is the initial state of the memristor in forward diffusion, K3 is the initial state of the memristor in backward diffusion, and K2 and K4 are used as the input parameters of the nonlinear function M; each K i is a double-precision floating-point number, and the key space required to resist brute-force attacks should be no less than 2 100 , while the key space obtained by the keys generated in the present invention is (10 16 ) 4 ≈2 214 , which is more than twice larger than the key space required to resist attacks.

[0049] Step 4: Define a nonlinear transformation function M. Since the DM-HNN has the initial value offset regulation characteristic driven by the memristive internal state, its offset regulation factor will offset with a period of 2π according to the initial state of the memristor ; based on this, by applying the plaintext pixel coordinates and pixel value information to the DM-HNN, the nonlinear transformation of the plaintext information can be realized by using the chaotic nonlinear ability of the DM-HNN.

[0050] The non - linear transformation function M is defined as:

[0051]

[0052] where (i, j) is the pixel coordinate, p is the pixel value at the corresponding position associated with the memristor offset regulation factor, ∈ = 1 + 10 -9 is the perturbation factor, represents the global state of the memristor, which evolves continuously during the entire encryption process.

[0053] D is the non - linear transformation function based on DM - HNN, and the formula is:

[0054]

[0055] where x', y', are the single - step iteration outputs of DM - HNN. After completing the non - linear transformation, the global state of the memristor is updated to prepare for the next update of the memristor state;

[0056] Its core feature is that: before each non - linear transformation, it will be lifted to a new attractor region under the drive of the offset regulation factor associated with the pixel value, and after the transformation is completed, it will return to the original attractor region, thus forming a complete dynamic regulation loop, realizing the use of different chaotic attractor spaces for non - linear transformation of different pixel values and enhancing the complexity of the transformation.

[0057] Subsequently, by taking the integer part of x' and y' and performing an exclusive - or operation, a binary number is obtained as the output of the M function, which can be described as:

[0058]

[0059] where m = 10 9 is the amplification factor, represents the floor operation, and ⊕ represents the bit - wise operation.

[0060] Utilizing the non - linearity of the DM - HNN model, non - linear transformations of coordinate values, pixel values, and global states are realized. Based on the principle of the non - linear converter of the memristor state, as Figure 4 shown.

[0061] Step 5: Perform two - way diffusion on the output value of the non - linear function M to complete image encryption;

[0062] First, forward diffusion gives Then backward diffusion gives The diffusion algorithm is expressed as:

[0063]

[0064] Among them, ⊙ represents modulo operation, represents exclusive-or operation, P i,j is the pixel value of the original image, is the pixel value of the image after forward diffusion, i and j are the positions of the pixels, P 1,1 is the first pixel of the image, is the last pixel of the image after forward diffusion.

[0065] The decryption diffusion process of this method is the opposite of the encryption process.

[0066] Inspired by the ideal embodiments of the present invention described above, through the above description, relevant staff can completely make various changes and modifications without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. An image encryption method based on a memristive chaotic system, characterized in that, It includes the following steps: Step 1, obtain the image to be encrypted; Step 2, use the adaptive memristive weight to replace the first neuron resistance connection weight of the HNN model to construct the DM-HNN model; Step 3, use a true random number generator to generate an encryption key; Step 4, apply the pixel coordinates and pixel value information of the plaintext image to the DM-HNN model, and use a non-linear function to perform non-linear transformation on the plaintext information; Step 5, perform two-way diffusion on the output value of the non-linear function to complete image encryption.

2. The image encryption method based on a memristive chaotic system according to claim 1, wherein The formula of the DM-HNN model is: where n is a natural number, x n and y n represent two state variables of the n-th iteration, represents the cosine magneto-controlled memristor state variable of the n-th iteration, μ is the neuron attenuation, g 12 , g 21 and g 22 are connection weights, ε is the memristor internal control parameter, and k is a specified parameter.

3. The image encryption method based on a memristive chaotic system according to claim 1, characterized in that The formula of the non-linear function is: where (i, j) are pixel coordinates, p is the pixel value at the corresponding position associated with the memristor offset regulation factor, ∈ is the perturbation factor, represents the global state of the memristor, and D() is the nonlinear transformation function of the DM-HNN model.

4. The image encryption method based on a memristive chaotic system according to claim 3, wherein Round and perform an exclusive OR operation on the non-linear function M to obtain the corresponding binary number.

5. The image encryption method based on a memristive chaotic system according to claim 3, wherein The formula of two-way diffusion is: Among them, ⊙ represents modular arithmetic, represents exclusive OR operation, P i,j is the pixel value of the original image, is the pixel value of the image after forward diffusion, i and j are the positions of the pixels, P 1,1 is the first pixel of the image, is the last pixel of the image after forward diffusion.

6. The image encryption method based on a memristive chaotic system according to claim 1, wherein The encryption key includes: the initial states of the memristors in forward and backward diffusion and the input parameters of the non-linear function.

7. The image encryption method based on a memristive chaotic system according to claim 1, characterized in that It also includes: Decrypt the image.

8. The image encryption method based on a memristive chaotic system according to claim 1, wherein The image to be encrypted is a plaintext image.

9. An image encryption system based on a memristive chaotic system, characterized in that, It includes: A memory for storing instructions executable by a processor; A processor for executing instructions to implement the image encryption method based on a memristive chaotic system as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code implements the image encryption method based on a memristive chaotic system as described in any one of claims 1-8 when executed by the processor.

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