Image encryption method and system based on five-dimensional memristor chaotic system and cellular automaton

Abstract

The invention belongs to the technical field of image encryption, and discloses an image encryption method and system based on a five-dimensional memristor chaotic system and a cellular automaton, and the method comprises the steps: 1, building a memristor model; step 2, establishing a five-dimensional memristor chaotic system based on the memristor model; step 3, acquiring a secret key based on the five-dimensional memristor chaotic system; 4, acquiring a pixel value matrix of the original gray level image, and scrambling the positions of pixel points by using an Arnod scrambling method; step 5, taking the obtained secret key binary stream as first generation data, converting the obtained scrambled pixel value matrix into a binary stream and taking the binary stream as second generation data, and performing iterative evolution by using an evolution rule of a Wolfler reversible cellular automaton to obtain an encrypted binary stream; and step 6, converting the obtained encrypted binary stream into a pixel value matrix, and obtaining a grayscale image after bit-level encryption.

Description

Technical Field

[0001] The present invention belongs to the technical field of image encryption, and particularly relates to an image encryption method and system based on a five-dimensional memristive chaotic system and a cellular automaton. Background Art

[0002] With the rapid development of information technology, images, as important information carriers, are widely used in various fields. However, the security risks existing in the process of image transmission and storage are becoming increasingly prominent. Traditional image encryption methods, such as DES, AES, etc., although they can protect the security of image data to a certain extent, still have problems such as low security and high computational complexity, and it is difficult to meet the growing demand for image encryption.

[0003] In recent years, the development of memristor technology has provided new ideas for image encryption. A memristor is a new type of electronic device with characteristics such as non-volatility, high density, and low power consumption. It can store analog signals and change its resistance value according to the change of the input voltage. This characteristic makes it show great potential in the field of image encryption. Especially for the chaotic system based on memristors, due to the non-periodic, non-linear characteristics of chaotic signals, as well as high randomness and unpredictability, it has become an ideal key for image encryption.

[0004] On the basis of the chaotic system, the five-dimensional memristive chaotic system further enhances the complexity and unpredictability of chaotic behavior. Compared with traditional low-dimensional systems, the five-dimensional system has richer dynamic behaviors and a larger key space, thus being able to provide a higher level of security. In addition, the five-dimensional memristive chaotic system can also generate a variety of different chaotic sequences by adjusting system parameters, providing more selectivity and flexibility for image encryption.

[0005] On the other hand, as a grid dynamics model with discrete time, space, and state, a cellular automaton has the ability to simulate the spatio-temporal evolution process of complex systems. A cellular automaton consists of a regular grid of cells, and each cell is synchronously updated according to a definite local rule, thus showing rich dynamic behaviors.

[0006] In summary, by combining the advantages of the five-dimensional memristive chaotic system and the cellular automaton, an image encryption method and system based on the five-dimensional memristive chaotic system and the cellular automaton are proposed. Summary of the Invention

[0007] To address the deficiencies of existing image encryption methods in terms of security, efficiency, and adaptability, the present invention provides an image encryption method and system based on a five-dimensional memristive chaotic system and cellular automata. This method uses the five-dimensional memristive chaotic system to generate complex chaotic sequences as encryption keys, and combines the evolution rules of cellular automata to achieve bit-level encryption of grayscale images. This method not only has high security, but also is computationally simple and easy to implement, and can meet the high requirements of modern image encryption. By implementing this method, the security of image data can be effectively protected, preventing unauthorized persons from accessing or understanding the content of the image, thereby ensuring the security of the image during transmission, storage, or processing.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] An image encryption method based on a five-dimensional memristive chaotic system and cellular automata, the method comprising:

[0010] Step 1: Establish a memristor model;

[0011] Step 2: Based on the memristor model, establish a five-dimensional memristive chaotic system;

[0012] Step 3: Based on the five-dimensional memristive chaotic system, obtain a secret key;

[0013] Step 4: Obtain the pixel value matrix of the original grayscale image, and use the Arnold scrambling method to scramble the positions of the pixels;

[0014] Step 5: Use the obtained secret key binary stream as the first-generation data, convert the obtained scrambled pixel value matrix into a binary stream and use it as the second-generation data, and perform iterative evolution using the evolution rules of the Wolfram reversible cellular automata to obtain the encrypted binary stream;

[0015] Step 6: Convert the obtained encrypted binary stream into a pixel value matrix to obtain the grayscale image after bit-level encryption.

[0016] Preferably, in step 1, establishing the memristor model includes:

[0017]

[0018] where a, b, and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge quantity of the new memristor and the magnetic flux, represents the memductance value of the new memristor.

[0019] Preferably, in step 2, based on the memristor model, establishing the five-dimensional memristive chaotic system includes:

[0020]

[0021] W(v) = a - bsin(2v) + 3cv 2 ,

[0022] W(w) = a - bsin(2w) + 3cw 2 ,

[0023] Wherein, x, y, z, w, and v are state variables of the system, α, β, ξ, and γ are system parameters, and W(v) and W(w) are intermediate variables.

[0024] Preferably, in step 3, obtaining the secret key based on the five-dimensional memristive chaotic system includes:

[0025] K i = [(v i + |v min |)·M] mod A,

[0026] Wherein, K i represents the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

[0027] Preferably, in step 4, obtaining the pixel value matrix of the original grayscale image and scrambling the positions of the pixels using the Arnold scrambling method includes:

[0028]

[0029] Wherein, (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j, and k are elements in the transformation matrix, and the four elements in the transformation matrix need to satisfy the condition e*k - f*j = 1, and n is the number of rows or columns in the original pixel value matrix.

[0030] The present invention also provides an image encryption system based on a five-dimensional memristive chaotic system and a cellular automaton. The system is used to implement any one of the above methods, and the system includes: a first construction module, a second construction module, a first conversion module, a scrambling module, an iterative evolution module, and a second conversion module;

[0031] The first construction module is used to establish a memristor model;

[0032] The second construction module is used to establish a five-dimensional memristive chaotic system based on the memristor model;

[0033] The first conversion module is used to obtain a secret key based on the five-dimensional memristive chaotic system;

[0034] The scrambling module is used to obtain the pixel value matrix of the original grayscale image and scramble the positions of the pixel points using the Arnold scrambling method;

[0035] The iterative evolution module is used to use the obtained secret key binary stream as the first-generation data, convert the obtained scrambled pixel value matrix into a binary stream and use it as the second-generation data, and perform iterative evolution using the evolution rules of the Wolfram reversible cellular automaton to obtain the encrypted binary stream;

[0036] The second conversion module is used to convert the obtained encrypted binary stream into a pixel value matrix to obtain a grayscale image encrypted at the bit level.

[0037] Preferably, in the first construction module, establishing a memristor model includes:

[0038]

[0039] where a, b, and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge quantity and the magnetic flux of the new memristor, represents the memductance value of the new memristor.

[0040] Preferably, in the second construction module, based on the memristor model, establishing a five-dimensional memristive chaotic system includes:

[0041]

[0042] W(v) = a - bsin(2v) + 3cv 2 ,

[0043] W(w) = a - bsin(2w) + 3cw 2 ,

[0044] where x, y, z, w, and v are the state variables of the system, α, β, ξ, and γ are the system parameters, and W(v) and W(w) are intermediate variables.

[0045] Preferably, in the first conversion module, obtaining a secret key based on the five-dimensional memristive chaotic system includes:

[0046] K i = [(v i + |v min |)·M] mod A,

[0047] where K idenotes the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

[0048] Preferably, in the scrambling module, obtaining the pixel value matrix of the original grayscale image and using the Arnold scrambling method to scramble the positions of the pixels includes:

[0049]

[0050] where (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j, and k are the elements in the transformation matrix, and the four elements in the transformation matrix need to satisfy the condition e*k - f*j = 1, and n is the number of rows or columns in the original pixel value matrix.

[0051] Compared with the prior art, the beneficial effects of the present invention are:

[0052] By combining the five-dimensional memristive chaotic system and the cellular automaton, the present invention realizes a significant improvement in image encryption technology. The main benefits include: the five-dimensional chaotic system improves the complexity and unpredictability of the key, and the memristor characteristics ensure a fast and secure encryption process. Utilizing the parallel processing capabilities of the memristor and the cellular automaton significantly reduces the computational complexity and speeds up the encryption speed. By adjusting the system parameters and the cellular automaton rules, it can be flexibly applied to different types of image encryption. The high-dimensional chaos and the scrambling algorithm enhance the resistance of the encrypted image to various attack means. It brings new technologies to the field of image encryption and promotes the application and development of memristors and cellular automata in information security. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0054] Figure 1 is the encryption and decryption flow chart in the embodiment of the present invention;

[0055] Figure 2 is the volt-ampere characteristic curve of the new memristor in the embodiment of the present invention, where (a) is the volt-ampere characteristic curve with increasing frequency, and (b) is the volt-ampere characteristic curve with increasing amplitude;

[0056] Figure 3 is the fifth-order memristive chaotic circuit in the embodiment of the present invention;

[0057] Figure 4 This is the phase trajectory diagram of the five-dimensional memristive chaotic system in the embodiments of the present invention. Among them, (a) x-y phase plane, (b) y-v phase plane, (c) z-w phase plane;

[0058] Figure 5 This is the phase trajectory diagram of the discrete five-dimensional memristive chaotic system in the embodiments of the present invention. Among them, (a) x-y phase plane, (b) y-v phase plane, (c) z-w phase plane;

[0059] Figure 6 This is the demonstration diagram of Arnold scrambling in the embodiments of the present invention. Among them, (a) untransformed matrix, (b) transformed matrix;

[0060] Figure 7 This is the 30th rule of the Wolfram reversible cellular automaton in the embodiments of the present invention;

[0061] Figure 8 This is the evolution process of the 30th rule of the Wolfram reversible cellular automaton in the embodiments of the present invention. Among them, (a) forward evolution, (b) reverse evolution;

[0062] Figure 9 This is the original image in the embodiments of the present invention. Among them, (a) five-pointed star, (b) planet, (c) boy;

[0063] Figure 10 This is the encrypted image in the embodiments of the present invention. Among them, (a) five-pointed star, (b) planet, (c) boy;

[0064] Figure 11 This is the decrypted image in the embodiments of the present invention. Among them, (a) five-pointed star, (b) planet, (c) boy;

[0065] Figure 12 This is the pixel distribution diagram, histogram and correlation diagram of the five-pointed star in the original image in the embodiments of the present invention. Among them, (a) pixel distribution diagram, (b) histogram, (c) correlation diagram;

[0066] Figure 13 This is the pixel distribution diagram, histogram and correlation diagram of the encrypted image of the five-pointed star in the embodiments of the present invention. Among them, (a) pixel distribution diagram, (b) histogram, (c) correlation diagram;

[0067] Figure 14 This is the encrypted image under attack in the embodiments of the present invention. Among them, (a) 15% shearing attack, (b) salt-and-pepper noise attack with a density of 0.1;

[0068] Figure 15This is the decrypted image after being attacked in the embodiment of the present invention, where (a) is a 15% shearing attack and (b) is a salt-and-pepper noise attack with a density of 0.1. Detailed implementation manners

[0069] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0070] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0071] Embodiment 1

[0072] As Figure 1 shown, the present invention proposes an innovative image encryption technology, which combines the advantages of a five-dimensional memristive chaotic system and a cellular automaton, aiming to solve the deficiencies of existing image encryption methods in terms of security, efficiency, and adaptability. The embodiment of the present invention discloses an image encryption method based on a five-dimensional memristive chaotic system and a cellular automaton. The encryption process includes the following steps:

[0073] Step 1: Establish a new memristor model: Introduce the cosine square term into the third-order passive smooth magneto-controlled memristor, and the mathematical model of the new memristor is:

[0074]

[0075] where a, b, and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge quantity and the magnetic flux of the new memristor, represents the memductance value of the new memristor.

[0076] Step 2: Establish a five-dimensional memristive chaotic system: Replace the resistor and the Chua diode in the Chua's circuit (a fourth-order chaotic circuit) with the new memristor, and the state equation of the five-dimensional memristive chaotic system is:

[0077]

[0078] W(t) = a - bsin(2v) + 3cv 2 ,

[0079] w(w) = a - bsin(2w) + 3cw 2 . (2)

[0080] Among them, x, y, z, w, and v are the state variables of the system, α, β, ξ, and γ are the system parameters, and W(v) and W(w) are intermediate variables.

[0081] Step 3: Obtain the secret key: The chaotic system shown in formula (2) can generate five groups of chaotic sequences. Arbitrarily select one group and convert it into a binary data stream to obtain the secret key. The conversion formula is:

[0082] K i =[(v i +|v min |)·M]mod A. (3)

[0083] Among them, K i represents the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

[0084] Step 4: Scramble the positions of the original image pixel points: Obtain the pixel value matrix of the original grayscale image, and use the Arnold scrambling method to scramble the positions of the pixel points. The rules of the Arnold scrambling method are:

[0085]

[0086] Among them, (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j, and k are the elements in the transformation matrix, and n is the number of rows or columns in the original pixel value matrix. It should be noted that the four elements in the transformation matrix need to satisfy the condition e*k - f*j = 1, which ensures that the Arnold scrambling is reversible.

[0087] Step 5: Encrypt the pixel values of the original image: Use the binary stream of the secret key obtained in Step 3 as the first-generation data, convert the scrambled pixel value matrix obtained in Step 4 into a binary stream and use it as the second-generation data, and perform iterative evolution using any one of the 256 evolution rules of the Wolfram reversible cellular automaton. First, an initial cellular configuration needs to be set, which is usually a grid of finite size, and each grid (i.e., cell) has an initial state. Then, apply a transformation function (i.e., any one of the 256 evolution rules) to update the state of each cell. This transformation function usually depends on the current state of the cell and the states of its neighboring cells. In a reversible cellular automaton, this transformation function is carefully designed to ensure that there is an inverse transformation function that can restore the original state. According to the transformation function, all cells will synchronously update their states.

[0088] Step 6: Generate the encrypted image: Convert the encrypted binary stream obtained in Step 5 into decimal numbers and arrange them in order as a pixel value matrix to obtain a grayscale image encrypted at the bit level.

[0089] Furthermore, for the image encryption method based on the five-dimensional memristive chaotic system and cellular automata, the decryption process includes the following steps:

[0090] Step 1: Decrypt the pixel values of the encrypted image: Use the secret key binary stream obtained in Step 3 of the encryption process as the first-generation data, and use the encrypted binary stream obtained in Step 5 of the encryption process as the second-generation data, and perform inverse iterative evolution using the evolution rule of the Wolfram reversible cellular automata used in Step 5 of the encryption process.

[0091] Step 2: Restore the scrambling of the positions of the encrypted image pixel points: Convert the decrypted binary stream obtained in Step 1 into a pixel value matrix, and use the Arnold scrambling method to restore the scrambling of the positions of the pixel points. It should be noted that the transformation matrix used for scrambling restoration should be the same as the transformation matrix used for scrambling.

[0092] Step 3: Generate the decrypted image: Read the pixel value matrix after scrambling restoration obtained in Step 2 to obtain the decrypted grayscale image.

[0093] (1) In the present invention, by introducing a cosine-squared term into the magnetron memristor model, a new memristor model is obtained. Due to its more unique non-linear characteristics, it can be used to construct a chaotic system with richer dynamic behaviors. (2) By introducing two new memristors into the Chua's circuit (a fourth-order chaotic circuit), a fifth-order memristive chaotic system is obtained. (3) Using the pseudo-random sequence generated by the new system as the key, a bit-level image encryption algorithm is designed by combining reversible cellular automata with Arnold scrambling. After testing and comparison, the designed algorithm exhibits high security and reconstruction accuracy.

[0094] Embodiment 2

[0095] The following further details the implementation process of the present invention in combination with specific drawings and examples. The programming software used is Matlab R2020a.

[0096] As Figure 1 shown, an image encryption method based on a five-dimensional memristive chaotic system and cellular automata includes three main parts: key generation, Arnold scrambling, and pixel value encryption based on cellular automata. The complete encryption process is as follows:

[0097] Step 1: Key Generation: Introduce the cosine squared term into the third-order passive smoothing memristor, and the mathematical model of the new memristor is obtained as follows:

[0098]

[0099] There is also a known formula:

[0100]

[0101] Let \(u(t)=\sin(2\pi t)\), \(a = 1\), \(b = 3\), \(c = 1\). The voltage-current characteristic curve of the new memristor is as Figure 2 shown.

[0102] Replace the resistor and Chua's diode in the Chua's circuit (a fourth-order chaotic circuit) with the new memristor, and a fifth-order chaotic circuit is obtained as Figure 3 shown. According to Kirchhoff's law and the characteristics of each component, list the state equations of the fifth-order chaotic circuit:

[0103]

[0104] Let \(u_1 = x\), \(u_2 = y\), \(i_1 = z\), \(1 / C_1=\alpha\), \(C_2 = 1\), \(G=\xi\), \(1 / L=\beta\), \(r / L=\gamma\), the formula (6) can be sorted out as:

[0105]

[0106] \(W(v)=a - b\sin(2v)+3cv\) 2 ,

[0107] \(W(w)=a - b\sin(2w)+3cw\) 2 . (2)

[0108] Set the system parameters \(a = 1\), \(b = 3\), \(c = 1\), \(\alpha = 10\), \(\beta = 100 / 7\), \(\gamma = 0.1\), \(\xi = 9 / 7\), and given the initial state of the system \(x_0 = 0\), \(y_0 = 0.1\), \(z_0 = 0\), \(w_0 = 0\), \(v_0 = 0\), the phase trajectory of the five-dimensional memristive chaotic system can be obtained as Figure 4 shown.

[0109] In order to obtain the chaotic sequence, use the Gaussian discretization algorithm to discretize the five-dimensional memristive chaotic system, and the following can be obtained:

[0110] \(x(i + 1)=x(i)+h*\{\alpha\cdot[(y(i)-x(i)\cdot W(v(i))+x(i)\cdot\xi - x(i)\cdot W(w(i))]\}\),

[0111] \(y(i + 1)=y(i)+h*\{\left((x(i)-y(i))\cdot W(v(i))+z(i)\right)\}\),

[0112] z(t + 1)=z(i)+h*{-β·y(i)-γ·z(i)},

[0113] w(t + 1)=w(t)+h*x(i),

[0114] v(i + 1)=v(i)+h*{y(i)-x(i)},

[0115] W(v(i)) = a - bsin(2v(i))+3cv(i) 2 ,

[0116] w(w(i)) = a - bsin(2w(i))+3cw(i) 2 . (7)

[0117] Set the step size h = 0.0001, and iterate equation (7) 1,250,000 times. The phase trajectory obtained is as Figure 5 shown.

[0118] Select the chaotic sequence in the v direction and convert it into a pseudo - random sequence using formula (6). Set A = 256 and M = 10 9 , a pseudo - random sequence with a length of 1,250,000 can be obtained. Convert it into an 8 - bit binary stream, and a binary key with a length of 10,000,000 can be obtained.

[0119] K i =[(v i +|v min |)·M]mod A. (3)

[0120] To test the randomness of the key, use the NIST (National Institute of Standards and Technology) SP800 - 22 test suite to test the key. The test results are shown in Table 1 below.

[0121] Table 1

[0122]

[0123] Step 2: Scramble the pixel positions of the original image: Obtain the pixel value matrix of the original grayscale image, and use the Arnold scrambling method to scramble the pixel positions. The rules of the Arnold scrambling method are as follows:

[0124]

[0125] To more intuitively feel the Arnold scrambling, set e = 1, f = 1, g = 2, k = 3, and convert a 10 - row and 10 - column matrix 5 times, as Figure 6as shown

[0126] Step 3: Encrypt the pixel values of the original image: Use the binary stream key generated in Step 1 as the first-generation data, convert the scrambled pixel value matrix in Step 2 into an 8-bit binary stream and use it as the second-generation data, and use Rule No. 30 of the Wolfram reversible cellular automaton to encrypt the pixel values of the original image. Rule No. 30 of the Wolfram reversible cellular automaton is as Figure 7 shown. During decryption, only need to perform reverse evolution using the key binary stream and the ciphertext binary stream as the first-generation and second-generation data respectively.

[0127] To more intuitively understand the evolution process of Rule No. 30 of the Wolfram reversible cellular automaton, use a 1-row and 100-column all-zero data as the first-generation data, use a 1-row and 100-column data (where the 50th and 51st columns are 1 and all other columns are 0) as the second-generation data, and evolve it for 50 generations. The results of each generation are as Figure 8 shown.

[0128] The image decryption process is the reverse process of Step 2 and Step 3.

[0129] Use the above encryption steps to Figure 9 encrypt and decrypt the original image as shown. The encrypted image and the decrypted image are as Figure 10 and Figure 11 shown.

[0130] To evaluate the encryption performance of the designed encryption method, the pixel distribution maps, histograms, and correlation maps of the original grayscale image and the encrypted image are plotted, as Figure 12 and Figure 13 shown.

[0131] To evaluate the robustness of the designed method, a 15% shear attack and a salt-and-pepper noise attack with a density of 0.1 are added to the encrypted image, as Figure 14 shown. Subsequently, use the designed method to decrypt the attacked image, and the results are as Figure 15 shown.

[0132] Example 3

[0133] The present invention also provides an image encryption system based on a five-dimensional memristive chaotic system and a cellular automaton. The system is used to implement any one of the methods described above. The system includes: a first construction module, a second construction module, a first conversion module, a scrambling module, an iterative evolution module, and a second conversion module;

[0134] The first construction module is used to establish a memristor model;

[0135] A second construction module, configured to establish a five-dimensional memristive chaotic system based on the memristor model;

[0136] A first conversion module, configured to obtain a secret key based on the five-dimensional memristive chaotic system;

[0137] A scrambling module, configured to obtain a pixel value matrix of an original grayscale image and scramble the positions of pixel points using the Arnold scrambling method;

[0138] An iterative evolution module, configured to use the obtained binary stream of the secret key as the first-generation data, convert the obtained scrambled pixel value matrix into a binary stream and use it as the second-generation data, and perform iterative evolution using the evolution rule of the Wolfram reversible cellular automaton to obtain an encrypted binary stream;

[0139] A second conversion module, configured to convert the obtained encrypted binary stream into a pixel value matrix to obtain a grayscale image encrypted at the bit level.

[0140] In this embodiment, in the first construction module, establishing the memristor model includes:

[0141]

[0142] where a, b, and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge quantity and the magnetic flux of the new memristor, represents the memductance value of the new memristor.

[0143] In this embodiment, in the second construction module, establishing the five-dimensional memristive chaotic system based on the memristor model includes:

[0144]

[0145] W(v) = a - bsin(2v) + 3cv 2 ,

[0146] W(w) = a - bsin(2w) + 3cw 2 , (2)

[0147] where x, y, z, w, and v are state variables of the system, α, β, ξ, and γ are system parameters, and W(v) and W(w) are intermediate variables.

[0148] In this embodiment, in the first conversion module, obtaining the secret key based on the five-dimensional memristive chaotic system includes:

[0149] K i = [(v i + |v min|)·M] mod A, (3)

[0150] Among them, K i represents the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

[0151] In this embodiment, in the scrambling module, obtaining the pixel value matrix of the original grayscale image and using the Arnold scrambling method to scramble the positions of the pixels includes:

[0152]

[0153] Among them, (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j, and k are the elements in the transformation matrix, and the four elements in the transformation matrix need to satisfy the condition e*k - f*j = 1, and n is the number of rows or columns in the original pixel value matrix.

[0154] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An image encryption method based on a five-dimensional memristor chaotic system and a cellular automaton, characterized in that: The method comprises: Step 1: Build a memristor model; Step 2: Based on the memristor model, a five-dimensional memristor chaotic system is established; Step 3: Based on the five-dimensional memristive chaotic system, obtain a secret key; Step 4: Get the pixel value matrix of the original grayscale image and scramble the positions of the pixels using the Arnold scrambling method; Step 5: Use the obtained secret key binary stream as the first generation data, convert the obtained scrambled pixel value matrix into a binary stream and use it as the second generation data, and use the evolution rule of Wolfram reversible cellular automaton to iteratively evolve to obtain the encrypted binary stream; Step 6: Convert the encrypted binary stream into a pixel value matrix to obtain a grayscale image after bit-level encryption.

2. The method according to claim 1, characterized in that In the step 1, establishing a memristor model includes: Among them, a, b and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge and magnetic flux of the new memristor, represents the memristor value of the new memristor.

3. The method according to claim 2, characterized in that In the step 2, based on the memristor model, establishing a five-dimensional memristor chaotic system includes: W(v)=a-bsin(2v)+3cv 2 , <h2 style=";text-align:left;direction:ltr">W(w) = a - bsin(2w) + 3cw<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> , Among them, x, y, z, w and v are the state variables of the system, α, β, ξ and γ are system parameters, and W(v) and W(w) are intermediate variables.

4. The method according to claim 1, characterized in that: In the step 3, based on the five-dimensional memristive chaotic system, obtaining the secret key includes: K i =[(v i +|v min |)·M]mod A, Among them, K i represents the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

5. The method according to claim 1, characterized in that In step 4, obtaining the pixel value matrix of the original grayscale image and scrambling the positions of the pixels using the Arnold scrambling method comprises: Among them, (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j and k are elements in the transformation matrix, the four elements in the transformation matrix need to satisfy the condition e*kf*j=1, and n is the number of rows or columns in the original pixel value matrix.

6. An image encryption system based on a five-dimensional memristor chaotic system and a cellular automaton, the system being used to implement the method of any one of claims 1 to 5, characterized in that: The system comprises: a first construction module, a second construction module, a first conversion module, a scrambling module, an iterative evolution module, and a second conversion module; The first building block is used to establish a memristor model; The second building module is used to establish a five-dimensional memristor chaotic system based on the memristor model; The first conversion module is used to obtain a secret key based on the five-dimensional memristor chaotic system; The scrambling module is used to obtain the pixel value matrix of the original grayscale image and scramble the positions of the pixels using the Arnold scrambling method; The iterative evolution module is used to use the obtained secret key binary stream as the first generation data, convert the obtained scrambled pixel value matrix into a binary stream as the second generation data, and use the evolution rule of Wolfram reversible cellular automaton to iteratively evolve to obtain the encrypted binary stream; The second conversion module is used to convert the encrypted binary stream into a pixel value matrix to obtain a grayscale image after bit-level encryption.

7. The system according to claim 6, characterized in that In the first building block, establishing a memristor model includes: Among them, a, b and c are real constants, is the magnetic flux flowing through the new memristor, represents the relationship between the charge and magnetic flux of the new memristor, represents the memristor value of the new memristor.

8. The system according to claim 7, characterized in that In the second building module, building a five-dimensional memristor chaotic system based on the memristor model includes: W(v)=a-bsin(2v)+3cv 2 , <h2 style=";text-align:left;direction:ltr">w(w) = a - bsin(2w) + 3cw<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> , Among them, x, y, z, w and v are the state variables of the system, α, β, ξ and γ are system parameters, and W(v) and W(w) are intermediate variables.

9. The system according to claim 6, characterized in that In the first conversion module, based on the five-dimensional memristor chaotic system, obtaining a secret key includes: K i =[(v i +|v min |)·M]mod A, Among them, K i represents the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min | represents the absolute value of the minimum value in the chaotic sequence, M is a positive integer, A is the maximum amplitude value in the K sequence, and mod represents the modulo operation.

10. The system according to claim 6, characterized in that In the scrambling module, obtaining the pixel value matrix of the original grayscale image and scrambling the positions of the pixels using the Arnold scrambling method include: Among them, (x, y) represents the original pixel value matrix, (x′, y′) represents the scrambled pixel value matrix, e, f, j and k are elements in the transformation matrix, the four elements in the transformation matrix need to satisfy the condition e*kf*j=1, and n is the number of rows or columns in the original pixel value matrix.

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