Medical image encryption hiding method and system based on fractional order memristor Hopfield neural network

Abstract

The invention discloses a medical image encryption hiding method and system based on a fractional order memristor Hopfield neural network. The method comprises the following steps: acquiring a medical image to be encrypted and hidden; constructing an image encryption model based on a Hopfield neural network; and encrypting and hiding the medical image by using the constructed image encryption model. According to the method, known plaintext attacks and selective plaintext attacks can be effectively resisted, and the security of chaotic system application data encryption is improved. Meanwhile, the number of secret keys in the encryption algorithm is increased due to the increase of the control parameters of the chaotic system, so that the secret key space is greatly expanded. According to the method, a chaotic sequence of a fractional order memristor Hopfield neural network is adopted to randomly embed a ciphertext image into a carrier image, so that the purpose that the ciphertext image and the carrier image have no difference visually is achieved, and a dual-protection effect is achieved; even if a large degree of information loss or various noises occur, the ciphertext image can still be decrypted from the carrier image.

Description

Technical Field

[0001] The present invention relates to the field of image security, and in particular to a medical image encryption and hiding method and system based on a fractional-order memristor Hopfield neural network. Background Art

[0002] With the rapid development of network communication technology and digital medicine, information technology has been widely used in telemedicine. As the most intuitive information carrier, digital images have become an important means of information dissemination and communication. In the medical Internet of Things and mobile terminals (such as smart phones and medical devices), medical images contain a large amount of private information. This information is easily stolen or lost during the transmission and storage process, resulting in serious privacy leakage risks for medical images. Therefore, the issue of protecting the security of medical image information has received widespread attention.

[0003] Neural networks are composed of a variety of neurons and can exhibit complex and rich discharge patterns and dynamic behaviors like the brain. In order to better simulate and study biological neural networks, researchers have abstracted and simplified biological neural networks and proposed many artificial neural networks, such as the Hopfield neural network, the BAM neural network, and the Cellular neural network. Among them, the Hopfield neural network has been widely studied because of its network structure similar to that of real biological neural networks, and can produce complex and rich dynamic behaviors.

[0004] In 1971, Cai Shaotang first proposed the fourth electrical component, the memristor. Due to the characteristics of the memristor and certain transmission and memory functions, it has important application prospects in chaotic circuits, secure communications and neural networks. In neural networks, neurons transmit information through synapses, so memristors can act as synapses or self-synapses, and can also be used as electromagnetic radiation signals to stimulate neurons. At the same time, fractional calculus is a generalization of traditional integer calculus. It introduces non-integer derivatives and integral operations, and is widely used in control theory, biomedical engineering and other fields, providing a more flexible and accurate modeling method. Compared with integer-order systems, fractional-order nonlinear systems can more accurately describe behaviors with complex dynamics and memory characteristics, and have the same memory characteristics as memristors. Therefore, in order to better describe the dynamic behavior of neural networks, fractional calculus is introduced in the memristor neural network model.

[0005] At present, Hopfield neural networks have been widely studied in many application fields, such as information security, pattern recognition, synchronous control, etc. Since Hopfield neural networks have complex dynamic characteristics that enhance their performance, many researchers study image information security based on Hopfield neural networks. Image encryption and image hiding are two ways to protect image security. They are not contradictory, but promote each other and can provide dual protection for images. However, due to the characteristics of high redundancy, large capacity, and high correlation between pixels of medical image data, traditional encryption methods cannot meet the needs of medical image encryption. Therefore, chaotic systems that are very sensitive to initial conditions can improve the security of encryption algorithms. At present, there are few studies on the application of Hopfield neural networks in medical image encryption, and even fewer studies on the combination of medical image encryption and hiding. Therefore, medical image encryption and hiding based on Hopfield neural networks is a very worthy topic to study. Summary of the invention

[0006] In order to solve the problem that existing medical image encryption and hiding algorithms cannot achieve a balance in multiple performances such as complexity, security and efficiency, the present invention provides a fractional-order memristor Hopfield neural network, which uses the chaotic sequence generated by the fractional-order memristor Hopfield neural network to achieve medical image encryption, hiding and decryption.

[0007] To achieve the above object, the present invention provides a medical image encryption and hiding method based on a fractional-order memristor Hopfield neural network, the steps comprising:

[0008] Collect medical images to be encrypted and hidden;

[0009] Based on the Hopfield neural network, an image encryption model is constructed. The construction method includes: using a memristor with a nonlinear function as a connecting synapse between the second neuron and the third neuron of the Hopfield neural network, and also as an external electromagnetic induction current of the second neuron of the Hopfield neural network; the mathematical model expression of the constructed image encryption model is as follows:

[0010]

[0011] Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight.

[0012] The constructed image encryption model is used to encrypt and hide medical images. The method includes: using the image encryption model as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; hiding the ciphertext image E in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q.

[0013] Preferably, the method for encrypting the original medical image Γ includes: first inputting the medical image, then calculating the information entropy of the medical image to evaluate its randomness and complexity; then, using the SHA-512 function to generate a 512-bit hash value K, and the hash value K is divided into 16 blocks to obtain a key; then, the key is input into the image encryption model, a chaotic sequence is generated through iteration, and processed into a pseudo-random sequence; using these pseudo-random sequences, the medical image is subjected to mirror scrambling and finite field bidirectional diffusion operations, and finally an unrecognizable ciphertext image E is obtained.

[0014] Preferably, the method for hiding the ciphertext image E in the original carrier image Q includes: first, converting the ciphertext image E and the carrier image Q into a one-dimensional pixel matrix, then performing bit plane decomposition on the pixel values ​​of the ciphertext image E, extracting each bit in each pixel value, and forming a longer matrix; then, preprocessing the chaotic sequence generated by the image encryption model to obtain an index matrix, and embedding the pixel values ​​of the ciphertext image E into the least significant bits of the pixel values ​​of the original carrier image Q according to the index matrix; finally, obtaining a new carrier image C that is visually indistinguishable from the original carrier image Q but contains the information of the ciphertext image E through bit reconstruction, thereby completing the image hiding.

[0015] The present invention also provides a medical image encryption and hiding system based on fractional-order memristor Hopfield neural network, the system is used to implement the above method, including: an acquisition module, a construction module and an encryption and hiding module;

[0016] The acquisition module is used to acquire medical images to be encrypted and hidden;

[0017] The building module is used to build an image encryption model based on the Hopfield neural network;

[0018] The encryption and hiding module is used to encrypt and hide the medical image using the constructed image encryption model.

[0019] Preferably, the workflow of the construction module includes: using a memristor with a nonlinear function as a connecting synapse between the second neuron and the third neuron of the Hopfield neural network, and also as an external electromagnetic induction current of the second neuron of the Hopfield neural network; the mathematical model expression of the constructed image encryption model is as follows:

[0020]

[0021] Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight.

[0022] Preferably, the workflow of the encryption and hiding module includes: using the image encryption model as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; hiding the ciphertext image E in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention provides a medical image encryption method, which applies a newly designed fractional-order memristor Hopfield neural network to improve the complexity and security of the encryption system. The initial parameters of the system generated by the SHA-512 function are very sensitive to the original image, so the present invention also provides a medical image hiding method, which uses a chaotic sequence of a fractional-order memristor Hopfield neural network to randomly embed the ciphertext image into a carrier image, so as to achieve the purpose of being visually indistinguishable from the carrier image, and play a dual protection role.

[0025] The present invention uses the chaotic sequence of the fractional-order memristor Hopfield neural network to randomly embed the ciphertext image into the carrier image, so as to achieve the purpose of being visually indistinguishable from the carrier image, thus playing a dual protection role. In addition, during the communication process, even if a large degree of information loss or various noises occur in the image generated by the encryption hiding method, the ciphertext image can still be decrypted from the carrier image to achieve high-definition image restoration. The method has strong robustness and is suitable for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0027] Figure 1 A schematic diagram of a method flow chart of an embodiment of the present invention;

[0028] Figure 2 This is a structural diagram of the memristor Hopfield neural network used in the present invention;

[0029] Figure 3 A structural diagram of medical image encryption and hiding based on medical Internet of Things provided in an embodiment of the present invention;

[0030] Figure 4 A flowchart of a method for encrypting and hiding an image provided in an embodiment of the present invention;

[0031] Figure 5 A diagram of a scrambling method used in an embodiment of the present invention;

[0032] Figure 6 A diagram of a diffusion method used in an embodiment of the present invention;

[0033] Figure 7 A bit plane decomposition diagram used in an embodiment of the present invention;

[0034] Figure 8 LSB algorithm diagram used in the embodiment of the present invention;

[0035] Fig. 9 The sample images and their encryption, hiding and decryption results in the performance test process of the embodiment of the present invention; wherein, (a) represents the original image of "Adenocarcinoma"; (b) represents the ciphertext image; (c) represents the carrier image of "Chest"; (d) represents the carrier image containing the ciphertext image; (e) represents the decrypted image; (f) represents the original image of "Large Cell Carcinoma"; (g) represents the ciphertext image; (h) represents the carrier image of "Man"; (i) represents the carrier image containing the ciphertext image; (j) represents the decrypted image; (k) represents the original image of "Squamous Cell Carcinoma"; (l) represents the ciphertext image; (m) represents the carrier image of "House"; (n) represents the carrier image containing the ciphertext image; (o) represents the decrypted image;

[0036] Fig.10: are histograms of sample images and ciphertext images during the performance test of the embodiment of the present invention; wherein (a) represents three groups of original images; (b) represents the histograms of three groups of original images; (c) represents three groups of ciphertext images; (d) represents the histograms of three groups of ciphertext images;

[0037] Fig.11 The histograms of the original image and the carrier image containing the ciphertext image during the performance test of the embodiment of the present invention; wherein, (a) represents the original carrier image of "Chest"; (b) represents the histogram of the original carrier image; (c) represents the carrier image containing the ciphertext image; (d) represents the histogram of the carrier image containing the ciphertext image; (e) represents the original carrier image of "Man"; (f) represents the histogram of the original carrier image; (g) represents the carrier image containing the ciphertext image; (h) represents the histogram of the carrier image containing the ciphertext image; (i) represents the original carrier image of "House"; (j) represents the histogram of the original carrier image; (k) represents the carrier image containing the ciphertext image; (l) represents the histogram of the carrier image containing the ciphertext image;

[0038] Fig.12 The following is a distribution diagram of the correlation of adjacent pixels of sampled pixels in the plaintext image and the ciphertext image in the horizontal, vertical and diagonal directions during the performance test of the embodiment of the present invention; wherein (a) represents the correlation of adjacent pixels of the original image of "Adenocarcinoma"; (b) represents the correlation of adjacent pixels of the ciphertext image; (c) represents the correlation of adjacent pixels of the original image of "Large Cell Carcinoma"; (d) represents the correlation of adjacent pixels of the ciphertext image; (e) represents the correlation of adjacent pixels of the original image of "Squamous Cell Carcinoma"; (f) represents the correlation of adjacent pixels of the ciphertext image;

[0039] Fig.13 The key generation process of the performance test of the embodiment of the present invention is 10 -16 Decrypted images after changes; (a) represents the decrypted image with the correct key key0; (b) represents the decrypted image with the key key1; (c) represents the decrypted image with the key key1; (d) represents the decrypted image with the key key2; (e) represents the decrypted image with the key key3; (f) represents the decrypted image with the key key4;

[0040] Fig.14The decryption results of the carrier image containing the ciphertext image cropped by 1 / 16, 1 / 8 and 1 / 4 during the performance test of the embodiment of the present invention; wherein, (a) represents the carrier image containing the ciphertext image cropped by 1 / 16; (b) represents the carrier image containing the ciphertext image cropped by 1 / 8; (c) represents the carrier image containing the ciphertext image cropped by 1 / 4; (d) represents the decryption result of the 1 / 16 cropping attack; (e) represents the decryption result of the 1 / 8 cropping attack; (f) represents the decryption result of the 1 / 4 cropping attack;

[0041] Fig.15 These are the decryption results of the carrier image containing the ciphertext image after adding 0.001%, 0.01% and 0.1% salt and pepper noise during the performance test of the embodiment of the present invention; wherein, (a) represents the carrier image containing the ciphertext image after adding 0.001% salt and pepper noise; (b) represents the carrier image containing the ciphertext image after adding 0.01% salt and pepper noise; (c) represents the carrier image containing the ciphertext image after adding 0.1% salt and pepper noise; (d) represents the decryption result after adding 0.001% salt and pepper noise; (e) represents the decryption result after adding 0.01% salt and pepper noise; (f) represents the decryption result after adding 0.1% salt and pepper noise. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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 are within the scope of protection of the present invention.

[0043] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Embodiment 1

[0045] like Figure 1 As shown, it is a flow chart of the medical image encryption and hiding method based on the fractional-order memristor Hopfield neural network provided in this embodiment, and the steps include:

[0046] S1. First, collect the medical image to be encrypted and hidden.

[0047] S2. Build an image encryption model based on the Hopfield neural network.

[0048] A memristor with a nonlinear function is used as the connecting synapse between the second neuron and the third neuron of the Hopfield neural network, and also as the external electromagnetic induction current of the second neuron of the Hopfield neural network; therefore, the mathematical model of the constructed fractional-order memristor Hopfield neural network model (image encryption model) is as follows:

[0049]

[0050] Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight.

[0051] Figure 2 This is a structural diagram of the memristor Hopfield neural network used in the present invention. Since the higher the complexity and randomness of the sequence generated by the chaotic system, the more difficult it is to restore the original sequence, the SE spectral entropy and C0 complexity measurements are performed on the chaotic system of this embodiment, verifying that the chaotic system of this embodiment has a high complexity.

[0052] S3. Use the constructed image encryption model to encrypt and hide medical images.

[0053] The image encryption model constructed above is used as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; the ciphertext image E is hidden in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q; Figure 3 A structural diagram of medical image encryption and hiding based on the medical Internet of Things provided in this embodiment.

[0054] The encryption and hiding of the image is completed in two steps, and the method for image encryption includes: first, inputting a medical image, and then calculating the information entropy of the medical image to evaluate its randomness and complexity; then, using the SHA-512 function to generate a 512-bit hash value K, and the hash value K is divided into 16 blocks to initialize the parameters of the chaotic system (fractional-order memristive Hopfield neural network model) to obtain the key; then, the key is input into the chaotic system, and a chaotic sequence is generated through iteration, and processed into a pseudo-random sequence; using these pseudo-random sequences, the medical image is subjected to mirror scrambling and finite field bidirectional diffusion operations, and finally an unrecognizable ciphertext image E is obtained.

[0055] The specific steps of the above image encryption are as follows Figure 4 As shown, including:

[0056] S301: Input a plaintext image Γ (original medical image) of size M×N, and calculate the information entropy entropy(Γ) of the plaintext image Γ to evaluate its randomness and complexity. Wherein, M and N are the number of rows and columns of the plaintext image Γ, respectively, and entropy() is a function for calculating the information entropy of the image.

[0057] S302: Use the SHA-512 function to generate a 512-bit hash value K, which is divided into 16 blocks in turn and used to initialize the parameters of the chaotic system (fractional-order memristor Hopfield neural network model) to obtain the key. The initial values ​​and parameters of the chaotic system x0, y0, z0, Generated by the following formula:

[0058] K=K1,K2,...,K 16

[0059]

[0060] Among them, SHA-512 is very sensitive to the original image and can effectively resist known and selective plaintext attacks. i (i=1,2,...,32) consists of 16 bits, corresponding to the decimal numbers from 0 to 255, ⊕ represents the exclusive OR operation, and bi2de(x) represents the conversion of the binary number x to decimal.

[0061] S303: Input the key into the chaotic system, iterate M×N+1000 times to obtain the chaotic sequence X1, X2, X3, X4, X5, discard the first 1000 values ​​of the chaotic sequence X1, X2, X3, X4, X5 to obtain the pseudo-random sequence S1, S2, S3, S4, S5 of length M×N. Among them, mod() is the remainder function, floor() is the integer function, and pow2() is the power operation and scaling of the floating point number with base 2.

[0062]

[0063] S304: Apply the processed pseudo-random sequence to the scrambling and diffusion process, wherein the scrambling process is mirror scrambling, and the specific process is as follows:

[0064] S304-1: Calculate according to the following formula to obtain the position index matrix A for scrambling:

[0065] A=mod(floor((S1(1:M*N)+100)*10 10 ),M*N)+1.

[0066] S304-2: Convert the input image Γ into a one-dimensional pixel matrix X, sort it in ascending order according to the index matrix A, shuffle X in a non-repeating manner, and obtain a one-dimensional matrix Y.

[0067] S304-3: Convert the one-dimensional matrix Y into a two-dimensional matrix Z to obtain the final scrambled image Γ1. The reshape function is a reconstruction function:

[0068] Z = reshape(Y,M,N),

[0069] Figure 5 FIG. 4 is a diagram of the scrambling method adopted by the present invention.

[0070] S305: Perform finite field bidirectional diffusion on the scrambled image Γ1 to obtain a ciphertext image E. Figure 6 This is a diagram of the diffusion method used in the present invention. The diffusion operation process is as follows:

[0071] S305-1: Create a matrix T of size 256×256, take values ​​between (0 and 255) and define matrices B and Π. Where a is a 256×1 column vector, b is a 1×256 row vector, and the values ​​of both vectors are between (0 and 255).

[0072] T = mod(ab,256),

[0073] B=zeros(1,M*N), ∏=zeros(1,M*N).

[0074] Among them, zeros means starting from 0.

[0075] S305-2: Perform positive diffusion on the image Γ1 using the pseudo-random sequence S2, i is cycled from 2 to M×N, and the matrix B(i) is obtained by the following formula:

[0076] B(i)=T(T(B(i-1)+2,S2(i)+2))+1,Z(i)+2)-1.

[0077] S305-3: According to the pseudo-random sequence S3, the matrix B performs reverse diffusion, i cycles from M×N-1 to 1, and the matrix Π is obtained:

[0078] ∏(i)=T(T(∏(i+1)+2, S3(i)+2))+1, B(i)+2)-1.

[0079] S306: According to the pseudo-random sequence S4, the pixel matrix Π is non-repeatedly arranged to obtain the final ciphertext image E.

[0080] After the image encryption is completed, the ciphertext image E is hidden in the carrier image Q to obtain the carrier image C containing the ciphertext image E:

[0081] C = reshape(C,M,N).

[0082] The hiding process includes: first, converting the ciphertext image E and the carrier image Q into a one-dimensional pixel matrix, then performing bit plane decomposition on the pixel values ​​of the ciphertext image E, extracting each bit in each pixel value, and forming a longer matrix; then, using the chaotic sequence preprocessing generated by the fractional-order memristor Hopfield neural network model (image encryption model) to obtain an index matrix, and embedding the pixel values ​​of the ciphertext image E into the least significant bit of the pixel value of the original carrier image Q according to the index matrix; finally, through bit reconstruction, a new carrier image C is obtained that is visually indistinguishable from the original carrier image Q but contains the information of the ciphertext image E, completing the image hiding. The specific steps are as follows:

[0083] S3301: Input the ciphertext image E and the carrier image Q, calculate the size of the ciphertext image E M1×N1 and the size of the carrier image Q M×N, and convert the pixel values ​​of the ciphertext image E and the carrier image Q into one-dimensional matrices H and P respectively:

[0084] [M,N]=size(Q),

[0085] [M1, N1] = size(E).

[0086] S3302: Perform bit plane decomposition on the matrix H, loop i from 1 to M1×N1, extract each bit in each pixel value, and form a matrix A with a length of M1×N1×8:

[0087]

[0088] Among them, bitget(Q,k) represents the bit function of obtaining the specified position of the original carrier image Q.

[0089] Figure 7 This is the bit plane decomposition diagram used in this embodiment. If the carrier image is in color, the bit plane is decomposed into 24 planes.

[0090] S3303: Preprocess the chaotic sequence S5 to obtain the index matrix S. i circulates from 1 to M1×N1, indexes and decomposes the pixel values ​​of the matrix P, embeds the pixel values ​​of the ciphertext image E into the least significant bit (LSB) of the original carrier image Q, and then obtains the carrier image C containing the ciphertext image E through bit reconstruction:

[0091]

[0092] Figure 8This is a diagram of the LSB algorithm used in this embodiment.

[0093] Embodiment 2

[0094] To restore the ciphertext image to the plaintext image, first extract the ciphertext image from the carrier image, then decrypt the ciphertext image, and finally get the plaintext image. The extraction process is as follows:

[0095] S1: According to the chaotic sequence S5, i circulates from 1 to M1×N1, performs bit plane decomposition on the carrier image C containing the ciphertext image, extracts the least significant bit and assigns it to the one-dimensional matrix F:

[0096]

[0097] S2: Reshape the one-dimensional matrix F into a two-dimensional matrix G, loop i from 1 to M1×N1, convert the binary to decimal and assign it to the one-dimensional matrix I, and then reconstruct it to obtain the ciphertext image E of the lowest bit plane:

[0098]

[0099] In the decryption process, inverse diffusion is performed first, and then inverse scrambling is performed to obtain the decrypted image. The decryption process is as follows:

[0100] S1: The steps of generating the pseudo-random sequence are the same as S2 and S3 in the encryption method and will not be described in detail.

[0101] S2: Perform finite field bidirectional inverse diffusion on the ciphertext image E to obtain the matrix Ψ, the rules of which are as follows:

[0102] S2-1: Backward inverse diffusion, i cycles from M×N-1 to 1, and the matrix Ψ is obtained:

[0103] Ψ(i)=T(T(E(i+1)+2, S3(i)+2))+1, E(i)+2)-1.

[0104] S2-2: Forward reverse diffusion, i circulates from 2 to M×N, and the matrix F is obtained:

[0105] F(i)=T(T(Ψ(i-1)+2, S2(i)+2))+1, Ψ(i)+2)-1.

[0106] S3: After the diffusion operation is completed, the mirror inverse scrambling is performed to convert the two-dimensional matrix F into a one-dimensional matrix E for inverse scrambling, and then reconstructed into a two-dimensional matrix G to obtain the decrypted image:

[0107] G = reshape(E,M,N).

[0108] Embodiment 3

[0109] In order to verify the performance of the image encryption, hiding and decryption method provided by the present invention, a corresponding performance test experiment is designed below, and the performance advantages of the image encryption, hiding and decryption method provided by the present invention are analyzed based on the experimental results.

[0110] 1. Analysis of simulation results

[0111] Take the grayscale images “Adenocarcinoma”, “Large Cell Carcinoma”, and “Squamous CellCarcinoma” as sample images, and the grayscale images “Chest”, “Man”, and “House” as carrier images. The encrypted, hidden, and decrypted images are as follows: Fig. 9 As shown in the figure, it can be seen that the encrypted image cannot extract the relevant information of the plaintext image. There is no visual change between the original carrier image and the carrier image containing the ciphertext image, and the plaintext image can be decrypted, which verifies the effectiveness and integrity of this method.

[0112] 2. Histogram analysis

[0113] The histogram is an intuitive indicator for evaluating the pixel information of an image. For a meaningful image, the distribution of the histogram is usually uneven. A good encryption algorithm must be able to make the histogram distribution of the ciphertext image uniform, and a good hiding algorithm must be able to make the carrier image containing the ciphertext image slightly different from the original image, but not obviously different. The medical images "Adenocarcinoma", "Large Cell Carcinoma", and "Squamous CellCarcinoma" are used as sample images, and the grayscale images "Chest", "Man", and "House" are used as carrier images for the test of the present invention. Fig.10 and Fig.11 Obviously, the histogram of the ciphertext image is evenly distributed, while the histogram of the carrier image containing the secret is very similar to the histogram of the original carrier image.

[0114] 3. Correlation analysis between adjacent pixels

[0115] The correlation analysis between adjacent pixels is how adjacent pixels are related to each other in the horizontal, vertical and diagonal directions. The correlation value of the original image is very close to 1, indicating that the pixels are highly correlated. The encrypted image has a very low correlation value, close to zero, indicating that the pixels of the encrypted image are unrelated to each other, so it is almost impossible to detect information from this image. The correlation distribution diagram of adjacent pixels in the horizontal, vertical and diagonal directions of the original image and the ciphertext image is shown in Figure 1. Fig.12As shown in the figure, the adjacent pixels of the original image have strong correlation in the horizontal, vertical and diagonal directions, which can be fitted into a straight line, and are shown as a linear regular distribution close to the diagonal line on the image, while the correlation between adjacent pixels of the ciphertext image is close to 0. Therefore, the image encryption method provided in this embodiment can effectively conceal the features between adjacent pixels in the image and resist differential attacks.

[0116] 4. Key sensitivity analysis

[0117] If the key is slightly changed, the decryption algorithm will not be able to restore the normal image. Therefore, the key sensitivity of the algorithm is tested by slightly modifying the value of the initial key. Set the initial key key0: x0, y0, z0, u0, Increase the values ​​of x0, y0, z0 and u0 by 10 respectively -16 , and get four new keys key1, key2, key3, and key4. First, use the original key key0 to encrypt the grayscale image and get the encrypted image. Then, use key1, key2, key3, and key4 to decrypt the image encrypted by key0, respectively. Fig.13 As shown in the figure, if the key is slightly modified, the algorithm will not be able to restore the original image. Therefore, the algorithm is very sensitive to the key.

[0118] 5. Robustness analysis

[0119] During the transmission of ciphertext images, there are varying degrees of noise interference or information loss, and even intentional attacks by attackers. Therefore, the provided solution must be highly robust, that is, it can still be successfully decrypted when part of the ciphertext image information is lost or changed. In this regard, this embodiment uses the solution in Example 4 to decrypt the ciphertext image, and designs the following cropping attack and salt and pepper noise test.

[0120] (1) Clipping attack

[0121] In the carrier image containing the ciphertext image, the information is cropped to 1 / 16, 1 / 8, and 1 / 4, and then the image is extracted and decrypted to obtain the carrier images containing the ciphertext image with three different cropping degrees and their corresponding decrypted images as shown in the figure. Fig.14 As shown in Figure 2. Therefore, the proposed algorithm can diffuse the influence of the cropped part to the entire image, thereby minimizing the impact of cropping on the local area and obtaining the original image information. Therefore, the algorithm can effectively resist cropping attacks and has strong robustness.

[0122] (2) Salt and pepper noise attack

[0123] 0.001%, 0.01% and 0.1% salt and pepper noise were added to the carrier image with the ciphertext image, and then the image was extracted and decrypted. Finally, the three carrier images with ciphertext images and their corresponding decrypted images with different proportions of noise added are shown in Figure 1. Fig.15 As shown in the figure, the less noise an image contains, the clearer the decrypted image is. Therefore, the scheme has strong anti-noise attack capability and strong robustness.

[0124] Embodiment 4

[0125] This embodiment also provides a medical image encryption and hiding system based on a fractional-order memristor Hopfield neural network, including: an acquisition module, a construction module and an encryption and hiding module; the acquisition module is used to acquire medical images to be encrypted and hidden; the construction module is used to construct an image encryption model based on the Hopfield neural network; the encryption and hiding module is used to use the constructed image encryption model to encrypt and hide the medical image.

[0126] The workflow of the construction module includes: using a memristor with a nonlinear function as the connecting synapse between the second and third neurons of the Hopfield neural network, and also as the external electromagnetic induction current of the second neuron of the Hopfield neural network; the mathematical model expression of the constructed image encryption model is as follows:

[0127]

[0128] Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight.

[0129] The constructed image encryption model is used to encrypt and hide medical images. The process includes: using the image encryption model as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; hiding the ciphertext image E in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q.

[0130] The workflow of the encryption and hiding module includes encryption and hiding of medical images.

[0131] The process of encrypting the original medical image Γ includes: first inputting the medical image, then calculating the information entropy of the medical image to evaluate its randomness and complexity; then, using the SHA-512 function to generate a 512-bit hash value K, which is divided into 16 blocks to obtain the key; then, inputting the key into the image encryption model, generating a chaotic sequence through iteration, and processing it into a pseudo-random sequence; using these pseudo-random sequences, performing mirror scrambling and finite field bidirectional diffusion operations on the medical image, and finally obtaining an unrecognizable ciphertext image E.

[0132] The process of hiding the ciphertext image E in the original carrier image Q includes: first, converting the ciphertext image E and the carrier image Q into a one-dimensional pixel matrix, then performing bit plane decomposition on the pixel values ​​of the ciphertext image E, extracting each bit in each pixel value, and forming a longer matrix; then, preprocessing the chaotic sequence generated by the image encryption model to obtain an index matrix, and embedding the pixel values ​​of the ciphertext image E into the least significant bits of the pixel values ​​of the original carrier image Q according to the index matrix; finally, through bit reconstruction, a new carrier image C is obtained that is visually indistinguishable from the original carrier image Q but contains the information of the ciphertext image E, thereby completing the image hiding.

[0133] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A medical image encryption and hiding method based on fractional-order memristor Hopfield neural network, characterized in that the steps include: Collect medical images to be encrypted and hidden; Based on the Hopfield neural network, an image encryption model is constructed. The construction method includes: using a memristor with a nonlinear function as a connecting synapse between the second neuron and the third neuron of the Hopfield neural network, and also as an external electromagnetic induction current of the second neuron of the Hopfield neural network; the mathematical model expression of the constructed image encryption model is as follows: Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight; The constructed image encryption model is used to encrypt and hide medical images. The method includes: using the image encryption model as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; hiding the ciphertext image E in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q.

2. The medical image encryption and hiding method based on fractional-order memristor Hopfield neural network according to claim 1 is characterized in that: The method for encrypting the original medical image Γ includes: first inputting the medical image, then calculating the information entropy of the medical image to evaluate its randomness and complexity; then, using the SHA-512 function to generate a 512-bit hash value K, and the hash value K is divided into 16 blocks to obtain a key; then, the key is input into the image encryption model, a chaotic sequence is generated through iteration, and processed into a pseudo-random sequence; using these pseudo-random sequences, the medical image is subjected to mirror scrambling and finite field bidirectional diffusion operations, and finally an unrecognizable ciphertext image E is obtained.

3. The medical image encryption and hiding method based on fractional-order memristor Hopfield neural network according to claim 2 is characterized in that: The method for hiding a ciphertext image E in an original carrier image Q includes: first, converting the ciphertext image E and the carrier image Q into a one-dimensional pixel matrix, then performing bit plane decomposition on the pixel values ​​of the ciphertext image E, extracting each bit in each pixel value, and forming a longer matrix; then, preprocessing the chaotic sequence generated by the image encryption model to obtain an index matrix, and embedding the pixel values ​​of the ciphertext image E into the least significant bits of the pixel values ​​of the original carrier image Q according to the index matrix; finally, obtaining a new carrier image C that is visually indistinguishable from the original carrier image Q but contains the information of the ciphertext image E through bit reconstruction, thereby completing the image hiding.

4. A medical image encryption and hiding system based on fractional-order memristor Hopfield neural network, the system being used to implement the method according to any one of claims 1 to 3, characterized in that: include: Acquisition module, construction module and encryption and hiding module; The acquisition module is used to acquire medical images to be encrypted and hidden; The building module is used to build an image encryption model based on the Hopfield neural network; The encryption and hiding module is used to encrypt and hide the medical image using the constructed image encryption model.

5. The medical image encryption and hiding system based on fractional-order memristor Hopfield neural network according to claim 4 is characterized in that: The workflow of the construction module includes: using a memristor with a nonlinear function as a connecting synapse between the second neuron and the third neuron of the Hopfield neural network, and also as an external electromagnetic induction current of the second neuron of the Hopfield neural network; the mathematical model expression of the constructed image encryption model is as follows: Where x, y and z represent the state vector of the Hopfield neuron; and They represent the internal state of the memristor state function; a represents the neuron activation gradient; b1 and b2 represent the internal parameters of the memristor; k1 represents the coupling coefficient between the memristor and the neuron; k2 represents the feedback gain of the induced current; is a nonlinear periodic function; D represents integral derivative; q represents fractional product; k represents synaptic weight.

6. The medical image encryption and hiding system based on fractional-order memristor Hopfield neural network according to claim 5 is characterized in that: The workflow of the encryption and hiding module includes: using the image encryption model as an encryption and hiding tool to generate a ciphertext image E with the same size as the original medical image Γ; hiding the ciphertext image E in the original carrier image Q to obtain a carrier image C containing the ciphertext image E, and the carrier image C is visually indistinguishable from the original carrier image Q.

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