An image encryption method and system based on a five-dimensional chaotic system and a cellular automaton

Abstract

The application 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, wherein step 1 is to establish a memristor model; step 2 is to establish a five-dimensional memristor chaotic system based on the memristor model; step 3 is to obtain a secret key based on the five-dimensional memristor chaotic system; step 4 is to obtain a pixel value matrix of an original gray image, and to use an Arnold scrambling method to scramble the positions of pixel points; step 5 is to use the obtained secret key binary stream as first-generation data, to convert the obtained scrambled pixel value matrix into a binary stream and use the binary stream as second-generation data, to use the evolution rule of a Wolfram reversible cellular automaton to perform iterative evolution, and to obtain an encrypted binary stream; and step 6 is to convert the obtained encrypted binary stream into a pixel value matrix, and to obtain a gray image that has been encrypted at a bit level.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of image encryption, and particularly relates to an image encryption method and system based on a five-dimensional memristor chaotic system and a cellular automaton. BACKGROUND

[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 transmission and storage process of images are increasingly prominent. Traditional image encryption methods such as DES, AES, etc. can protect the security of image data to a certain extent, but still have problems such as low security and complex calculation, which are difficult to meet the growing demand for image encryption.

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

[0004] On the basis of chaotic system, the five-dimensional memristor chaotic system further enhances the complexity and unpredictability of chaotic behavior. Compared with traditional low-dimensional systems, the five-dimensional system has more rich dynamic behavior and larger key space, so as to provide higher level of security. In addition, the five-dimensional memristor chaotic system can also produce a variety of different chaotic sequences by adjusting the 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, cellular automaton has the ability to simulate the spatio-temporal evolution process of complex systems. Cellular automaton is composed of regular cell grids, and each cell is updated synchronously according to the determined local rules, thus showing rich dynamic behavior.

[0006] In summary, combining the advantages of five-dimensional memristor chaotic system and cellular automaton, an image encryption method and system based on five-dimensional memristor chaotic system and cellular automaton is proposed. SUMMARY

[0007] To solve the deficiencies of the existing image encryption methods in security, efficiency and adaptability, the application provides an image encryption method and system based on a five-dimensional memristor chaotic system and a cellular automaton, which uses the five-dimensional memristor chaotic system to generate a complex chaotic sequence as an encryption key, and combines the evolution rule of the cellular automaton to realize bit-level encryption of a grayscale image. This method not only has high security, but also is simple to calculate and easy to implement, and can meet the high requirements of modern image encryption. Through the implementation of the method, the security of image data can be effectively protected, unauthorized persons are prevented from accessing or understanding the content of the image, and the security of the image in the transmission, storage or processing process is ensured.

[0008] To achieve the above object, the application provides the following scheme:

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

[0010] Step 1: establishing a memristor model;

[0011] Step 2: based on the memristor model, establishing a five-dimensional memristor chaotic system;

[0012] Step 3: based on the five-dimensional memristor chaotic system, obtaining a secret key;

[0013] Step 4: obtaining a pixel value matrix of an original grayscale image, and using an Arnold scrambling method to scramble the positions of the pixel points;

[0014] Step 5: using the obtained secret key binary stream as first-generation data, converting the obtained scrambled pixel value matrix into a binary stream and using it as second-generation data, using the evolution rule of the Wolfram reversible cellular automaton for iterative evolution to obtain an encrypted binary stream;

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

[0016] Preferably, in step 1, the establishment of the memristor model comprises:

[0017]

[0018] wherein 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.

[0019] Preferably, in step 2, based on the memristor model, the establishment of the five-dimensional memristor chaotic system comprises:

[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, a, b, c and g are system parameters, W(v) and W(w) are intermediate variables.

[0024] Preferably, in the step 3, the key is obtained based on the five-dimensional memristor chaotic system, and the step 3 comprises the following steps:

[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 the step 4, the pixel value matrix of the original gray image is obtained, and the position of the pixel is scrambled using the Arnold scrambling method, and the step 4 comprises the following steps:

[0028]

[0029] wherein (x, y) represents the original pixel value matrix, (x', y') represents the pixel value matrix after scrambling, e, f, j and k are elements in the transformation matrix, the four elements in the transformation matrix need to satisfy the condition e*k-f*j=1, and n is the row number or column number in the original pixel value matrix.

[0030] The application further provides an image encryption system based on a five-dimensional memristor chaotic system and a cellular automaton, which is used for implementing any one of the methods, and 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.

[0031] The first construction module is used for establishing a memristor model.

[0032] The second construction module is used for establishing a five-dimensional memristor chaotic system based on the memristor model.

[0033] The first conversion module is configured to acquire a secret key based on the five-dimensional memristor chaotic system.

[0034] The scrambling module is configured to acquire a pixel value matrix of an original grayscale image, and scramble positions of pixel points using an Arnold scrambling method.

[0035] The iterative evolution module is configured to take the acquired secret key binary stream as first-generation data, convert the acquired scrambled pixel value matrix into a binary stream and take the binary stream as second-generation data, perform iterative evolution using an evolution rule of a Wolfram reversible cellular automaton, and obtain an encrypted binary stream.

[0036] The second conversion module is configured to convert the obtained encrypted binary stream into a pixel value matrix, and obtain a grayscale image that has been encrypted at a bit level.

[0037] Preferably, in the first construction module, the establishment of the memristor model comprises:

[0038]

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

[0040] Preferably, in the second construction module, the establishment of the five-dimensional memristor chaotic system based on the memristor model comprises:

[0041]

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

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

[0044] wherein x, y, z, w and v are state variables of the system, and a, b, c and d are system parameters.

[0045] Preferably, in the first conversion module, the acquisition of the secret key based on the five-dimensional memristor chaotic system comprises:

[0046] K i =[(v i +|v min |)·M]mod A,

[0047] wherein K idenotes the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min denotes 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 denotes the modulo operation.

[0048] Preferably, in the scrambling module, a pixel value matrix of an original grayscale image is obtained, and the positions of the pixel points are scrambled using an Arnold scrambling method, which includes:

[0049]

[0050] where (x, y) denotes the original pixel value matrix, (x', y') denotes the pixel value matrix after scrambling, e, f, j, and k are elements in the transformation matrix, 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 present application has the following beneficial effects:

[0052] The present application realizes a significant improvement in image encryption technology by combining a five-dimensional memristive chaotic system and a cellular automaton. 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. The parallel processing capability of the memristor and the cellular automaton significantly reduces the computational complexity and speeds up the encryption. By adjusting the system parameters and the cellular automaton rules, it can be flexibly applied to different types of image encryption. High-dimensional chaos and scrambling algorithm enhance the resistance of encrypted images to various attack methods. It brings new technology to the field of image encryption and promotes the application and development of memristors and cellular automata in information security. BRIEF DESCRIPTION OF DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0054] Figure 1 The encryption and decryption flowchart in the embodiment of the present application;

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

[0056] Figure 3 The five-order memristive chaotic circuit in the embodiment of the present application;

[0057] Figure 4 Phase trajectory plot of a five-dimensional memristive chaotic system in an embodiment of the present invention, where (a) x-y phase plane, (b) y-v phase plane, (c) z-w phase plane;

[0058] Figure 5 Phase trajectory plot of a discrete five-dimensional memristive chaotic system in an embodiment of the present invention, where (a) x-y phase plane, (b) y-v phase plane, (c) z-w phase plane;

[0059] Figure 6 Demonstration plot of Arnold scrambling in an embodiment of the present invention, where (a) untransformed matrix, (b) transformed matrix;

[0060] Figure 7 Rule 30 of Wolfram reversible cellular automata in an embodiment of the present invention;

[0061] Figure 8 Evolution process of Rule 30 of Wolfram reversible cellular automata in an embodiment of the present invention, where (a) forward evolution, (b) reverse evolution;

[0062] Figure 9 Original images in an embodiment of the present invention, where (a) pentacle, (b) star, (c) boy;

[0063] Figure 10 Encrypted images in an embodiment of the present invention, where (a) pentacle, (b) star, (c) boy;

[0064] Figure 11 Decrypted images in an embodiment of the present invention, where (a) pentacle, (b) star, (c) boy;

[0065] Figure 12 Pixel distribution plot, histogram, and correlogram of a pentacle in an original image in an embodiment of the present invention, where (a) pixel distribution plot, (b) histogram, (c) correlogram;

[0066] Figure 13 Pixel distribution plot, histogram, and correlogram of an encrypted image of a pentacle in an embodiment of the present invention, where (a) pixel distribution plot, (b) histogram, (c) correlogram;

[0067] Figure 14 Encrypted images under attack in an embodiment of the present invention, where (a) 15% cut attack, (b) salt and pepper noise attack with density 0.1;

[0068] Figure 15The images shown are decrypted images after being attacked in an embodiment of the present invention, wherein (a) is a 15% shearing attack and (b) is a salt and pepper noise attack with a density of 0.1. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0071] Example 1

[0072] like Figure 1 As shown, this invention proposes an innovative image encryption technology that combines the advantages of a five-dimensional memristor chaotic system and cellular automata, aiming to address the shortcomings of existing image encryption methods in terms of security, efficiency, and adaptability. An embodiment of this invention discloses an image encryption method based on a five-dimensional memristor chaotic system and cellular automata, the encryption process including the following steps:

[0073] Step 1: Establish a new memristor model: Introduce the square cosine term into the third-order passive smooth magnetically controlled memristor to obtain the mathematical model of the new memristor as follows:

[0074]

[0075] Where a, b, and c are real constants. It is the magnetic flux flowing through the new memristor. This indicates the relationship between the charge and magnetic flux of the new memristor. This indicates the memconductance value of the new memristor.

[0076] Step 2: Establish a five-dimensional memristor chaotic system: Replace the resistors and Chua's diodes in the Chua's circuit (a fourth-order chaotic circuit) with new memristors to obtain the state equation of the five-dimensional memristor chaotic system as follows:

[0077]

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

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

[0080] where x, y, z, w and v are state variables of the system, a, b, c and g are system parameters, W(v) and W(w) are intermediate variables.

[0081] Step 3: Obtain the secret key: the chaotic system shown in equation (2) can generate five groups of chaotic sequences, and any one of them is converted 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] where 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 rule of the Arnold scrambling method is:

[0085]

[0086] where (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 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 secret key binary stream 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 use any one of the 256 evolution rules of the Wolfram reversible cellular automaton for iterative evolution. First, an initial cell configuration needs to be set, which is usually a finite size grid, and each grid (i.e. cell) has an initial state. Then, a transformation function (i.e. any one of the 256 evolution rules) is applied to update the state of each cell. This transformation function usually depends on the current state of the cell and the state of its neighbor cells. In a reversible cellular automaton, this transformation function is carefully designed to ensure that an inverse transformation function can restore the original state. According to the transformation function, all cells will update their states simultaneously.

[0088] Step 6: Generate 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 gray-scale image after bit-level encryption.

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

[0090] Step 1: Decrypt the pixel value 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 use the evolution rule of the Wolfram reversible cellular automaton used in step 5 of the encryption process to perform inverse iteration evolution.

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

[0092] Step 3: Generate decrypted image: Read the pixel value matrix obtained in step 2 after scrambling recovery to obtain the decrypted gray-scale image.

[0093] The present application (1). By introducing the cosine square term into the magnetic control memristor model, a new memristor model is obtained, which can be used to construct a chaotic system with more rich dynamics due to its more unique nonlinear characteristics. (2). By introducing two new memristors into the Chua circuit (fourth-order chaotic circuit), a five-order memristor chaotic system is obtained. (3). With 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 shows high security and reconstruction accuracy.

[0094] Example two

[0095] The implementation process of the present application will be further described in detail below in combination with specific drawings and examples, and the programming software used is Matlab R2020a.

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

[0097] Step 1: Key generation: the cosine square term is introduced into the third-order passive smooth magnetic control 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(2πt), a = 1, b = 3, c = 1. The voltage-current characteristic curve of the new memristor is shown in Figure 2 .

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

[0103]

[0104] Let u1 = x, u2 = y, i1 = z, 1 / C1 = α, C2 = 1, G = ξ, 1 / L = β, r / L = γ, the formula (6) can be arranged as:

[0105]

[0106] W(v) = a - bsin(2v) + 3cv 2 ,

[0107] W(w) = a - bsin(2w) + 3cw 2 . (2)

[0108] Set the system parameters a = 1, b = 3, c = 1, α = 10, β = 100 / 7, γ = 0.1, ξ = 9 / 7, and the initial state of the system x0 = 0, y0 = 0.1, z0 = 0, w0 = 0, v0 = 0, the phase trajectory of the five-dimensional memristor chaotic system can be obtained as shown in Figure 4 .

[0109] In order to obtain chaotic sequence, the five-dimensional memristor chaotic system is discretized using Gaussian discretization algorithm, which can obtain:

[0110] x(i+1) = x(i) + h*{α·[(y(i)-x(i)·W(v(i))+x(i)·ξ-x(i)·W(w(i))]},

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

[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 - b sin(2v(i)) + 3c v(i) 2 ,

[0116] w(w(i)) = a - b sin(2w(i)) + 3c w(i) 2 . (7)

[0117] Setting step size h = 0.0001, formula (7) is iterated 1250000 times, and the phase trajectory obtained is shown in Figure 5 .

[0118] Selecting the chaotic sequence in the v direction, it is converted into a pseudo-random sequence using formula (6). Setting A = 256 and M = 10 9 , a pseudo-random sequence with a length of 1250000 can be obtained, which is converted into an 8-bit binary stream, and a binary key with a length of 10000000 can be obtained.

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

[0120] In order to test the randomness of the key, the key is tested using the NIST (National Institute of Standards and Technology) SP800-22 test suite, and the test results are shown in Table 1.

[0121] Table 1

[0122]

[0123] Step 2: Scramble the pixel position of the original image: obtain the pixel value matrix of the original gray image, and use the Arnold scrambling method to scramble the position of the pixel points. The rule of the Arnold scrambling method is:

[0124]

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

[0126] Step 3: Encryption of the pixel values of the original image: the binary stream key generated in step 1 is taken as the first generation data, the pixel value matrix after the permutation in step 2 is converted into an 8-bit binary stream and taken as the second generation data, and the pixel values of the original image are encrypted using rule No. 30 of the Wolfram reversible cellular automaton, as shown in Figure 7 As shown. When decrypting, only the key binary stream and the ciphertext binary stream are needed as the first and second generation data for reverse evolution.

[0127] In order to more intuitively understand the evolution process of rule No. 30 of the Wolfram reversible cellular automaton, 1 row of 100 columns of all-zero data is used as the first generation data, and 1 row of 100 columns of data (in which the 50th and 51st columns are 1, and all other columns are 0) is used as the second generation data, and it is evolved for 50 generations. The results of each generation are shown in Figure 8 As shown.

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

[0129] The above encryption steps are used to encrypt and decrypt the original image shown in Figure 9 As shown. Figure 10 And Figure 11 As shown.

[0130] In order to evaluate the encryption performance of the designed encryption method, the pixel distribution diagram, histogram and correlation diagram of the original gray image and the encrypted image are drawn, as shown in Figure 12 And Figure 13 As shown.

[0131] In order to evaluate the robustness of the designed method, 15% of the shear attack and the salt and pepper noise attack with a density of 0.1 are added to the encrypted image, as shown in Figure 14 As shown. Subsequently, the attacked image is decrypted using the designed method, and the results are shown in Figure 15 As shown.

[0132] Example Three

[0133] The application also provides an image encryption system based on a five-dimensional memristor chaotic system and a cellular automaton, which is used to implement any of the methods described above, and the system comprises a first construction module, a second construction module, a first conversion module, a permutation module, an iterative evolution module and a second conversion module.

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

[0135] The second construction module is configured to construct a five-dimensional memristor chaotic system based on the memristor model.

[0136] The first conversion module is configured to obtain a secret key based on the five-dimensional memristor chaotic system.

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

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

[0139] The second conversion module is configured to convert the obtained encrypted binary stream into a pixel value matrix to obtain a grayscale image that has been subjected to bit-level encryption.

[0140] In this embodiment, the first construction module includes constructing a memristor model.

[0141]

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

[0143] In this embodiment, the second construction module includes constructing a five-dimensional memristor chaotic system based on the memristor model.

[0144]

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

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

[0147] wherein x, y, z, w and v are state variables of the system, and a, b, c and d are system parameters.

[0148] In this embodiment, the first conversion module includes obtaining a secret key based on the five-dimensional memristor chaotic system.

[0149] K i =[(v i +|v minM mod A, (3)

[0150] wherein K i denotes the i-th element of the pseudo-random sequence, v i is the i-th element of the chaotic sequence, |v min denotes 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 denotes the modulo operation.

[0151] In the present embodiment, in the scrambling module, a pixel value matrix of an original gray-scale image is obtained, and the Arnold scrambling method is used to scramble the positions of the pixel points, including:

[0152]

[0153] wherein (x, y) denotes the original pixel value matrix, (x', y') denotes the pixel value matrix after scrambling, e, f, j, and k are elements in the transformation matrix, 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 above-described embodiments merely describe the preferred modes of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art shall fall within the protection scope defined by the claims of the present application.

Claims

1. An image encryption method based on a five-dimensional memristor chaotic system and cellular automata, characterized in that, The method includes: Step 1: Establish a memristor model; Step 2: Based on the memristor model, establish a five-dimensional memristor chaotic system; Step 3: Obtain the key based on the five-dimensional memristor chaotic system; 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; Step 5: Use the obtained 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 rules of the Wolfram reversible cellular automaton to perform iterative evolution to obtain the encrypted binary stream. Step 6: Convert the obtained encrypted binary stream into a pixel value matrix to obtain a grayscale image after bit-level encryption; In step 1, establishing the memristor model includes: ， ， in, a , b and c It is a real constant. φ It is the magnetic flux flowing through the new memristor. q ( φ This represents the relationship between the charge and magnetic flux of the new memristor. W ( φ This indicates the memconductance value of the new memristor; In step 2, establishing a five-dimensional memristor chaotic system based on the memristor model includes: ， ， ， ， ， ， ， in, x , y , z , w and v It is the system's state variable. α , β , ξ and These are system parameters. W ( v )and W ( w ) is an intermediate variable.

2. The method according to claim 1, characterized in that, In step 3, obtaining the key based on the five-dimensional memristor chaotic system includes: ， in, K i The first pseudo-random sequence represents the... i One element, v i It is the first chaotic sequence i One element, Represents the absolute value of the minimum value in a chaotic sequence. is a positive integer, yes K The maximum amplitude value in the sequence, where mod represents the modulo operation.

3. The method according to claim 1, characterized in that, In step 4, the pixel value matrix of the original grayscale image is obtained, and the Arnold scrambling method is used to scramble the positions of the pixels, including: ， in,( x , y ) represents the original pixel value matrix, ( x ′, y ′) represents the scrambled pixel value matrix, e , f , j and k These are the elements in the transformation matrix, and the four elements in the transformation matrix must satisfy the following conditions. e * k - f * j =1, n It is the number of rows or columns in the original pixel value matrix.

4. An image encryption system based on a five-dimensional memristor chaotic system and cellular automata, said system being used to implement the method described in any one of claims 1-3, characterized in that, 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; The first building module is used to build a memristor model; The second construction module is used to establish a five-dimensional memristor chaotic system based on the memristor model; The first conversion module is used to obtain the 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 take the acquired key binary stream as the first generation data, convert the acquired 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. The second conversion module is used to convert the obtained encrypted binary stream into a pixel value matrix to obtain a grayscale image after bit-level encryption; In the first construction module, establishing the memristor model includes: ， ， in, a , b and c It is a real constant. φ It is the magnetic flux flowing through the new memristor. q ( φ This represents the relationship between the charge and magnetic flux of the new memristor. W ( φ This indicates the memconductance value of the new memristor; In the second construction module, based on the memristor model, establishing a five-dimensional memristor chaotic system includes: ， ， ， ， ， ， ， in, x , y , z , w and v It is the system's state variable. α , β , ξ and These are system parameters. W ( v )and W ( w ) is an intermediate variable.

5. The system according to claim 4, characterized in that, In the first conversion module, obtaining the key based on the five-dimensional memristor chaotic system includes: ， in, K i The first pseudo-random sequence represents the... i One element, v i It is the first chaotic sequence i One element, Represents the absolute value of the minimum value in a chaotic sequence. is a positive integer, yes K The maximum amplitude value in the sequence, where mod represents the modulo operation.

6. The system according to claim 4, characterized in that, In the scrambling module, the pixel value matrix of the original grayscale image is obtained, and the Arnold scrambling method is used to scramble the positions of the pixels, including: ， in,( x , y ) represents the original pixel value matrix, ( x ′, y ′) represents the scrambled pixel value matrix, e , f , j and k These are the elements in the transformation matrix, and the four elements in the transformation matrix must satisfy the following conditions. e * k - f * j =1, n It is the number of rows or columns in the original pixel value matrix.

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