Image chaotic encryption method and system based on magnetic control memristor

Abstract

The invention relates to the technical field of image processing, in particular to an image chaotic encryption method and system based on a magnetic control memristor, and the method comprises the steps: obtaining a to-be-processed image; constructing a fractional order variable parameter hyper-chaos model through a magnetic control memristor; features of an image to be processed are used as initial parameters of the fractional order variable parameter hyper-chaos model, and a multi-dimensional key stream is dynamically generated through the fractional order variable parameter hyper-chaos model; performing preprocessing operation and blocking operation on the to-be-processed image; based on the multi-dimensional key stream, performing dual scrambling on the to-be-processed image after block processing to generate a scrambled image; performing dynamic diffusion and nonlinear confusion on the scrambled image through a fractional order difference feedback mechanism to generate a one-dimensional ciphertext vector; and remodeling the one-dimensional ciphertext vector to generate an encrypted image. According to the method, the security of the key stream can be remarkably improved, and a solid physical layer guarantee is provided for image encryption.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and in particular to an image chaos encryption method and system based on a magnetically controlled memristor. Background Art

[0002] Image encryption is a necessary means to protect the security of sensitive visual information in the digital society. Modern image data often contains biometric information such as faces and geographic locations, as well as sensitive content such as medical images.

[0003] Traditional chaos-based image encryption systems generally use low-dimensional, fixed-parameter chaotic systems to generate keys, which is difficult to meet the increasing security needs of image data. Therefore, it is crucial to develop an image encryption system with high security and high reconstruction quality to ensure data transmission security.

[0004] In addition, existing encryption methods usually rely on low-dimensional chaotic systems and high-dimensional chaotic systems. The key space of low-dimensional chaotic systems is small, and the chaotic behavior is not complex enough, which easily leads to residual pixel correlation and is easily attacked by plaintext, resulting in brute force cracking. Although high-dimensional chaotic systems can effectively resist quantum computing and known plaintext attacks, they have high computational complexity and significantly increase the hardware implementation cost. They lack the ability to generate keys based on dynamic evolution, resulting in insufficient randomness and complexity in the encryption process, and are easily cracked by modern attack methods. Existing encryption methods are difficult to effectively cope with environmental changes when implemented in hardware, and environmental noise can cause certain deviations in the key parameters of low-dimensional chaotic systems. Summary of the Invention

[0005] To solve the above-mentioned problems in the prior art, the present invention provides an image chaos encryption method and system based on a magnetically controlled memristor:

[0006] A first aspect of the present invention provides an image chaos encryption method based on a magnetically controlled memristor, comprising:

[0007] S1: Get the image to be processed;

[0008] S2: Constructing a fractional-order variable parameter hyperchaotic model using magnetically controlled memristors;

[0009] S3: using the features of the image to be processed as initial parameters of the fractional-order variable parameter hyperchaotic model, and dynamically generating a multidimensional key stream through the fractional-order variable parameter hyperchaotic model;

[0010] S4: performing preprocessing and block division operations on the image to be processed;

[0011] S5: Based on the multi-dimensional key stream, double-reset scrambling is performed on the image to be processed after the block processing to generate a scrambled image;

[0012] S6: Dynamically diffuse and nonlinearly obfuscate the scrambled image through a fractional-order differential feedback mechanism to generate a one-dimensional ciphertext vector;

[0013] S7: Reshape the one-dimensional ciphertext vector to generate an encrypted image.

[0014] A second aspect of the present invention provides an image chaos encryption system based on a magnetically controlled memristor, comprising: a processor and a memory;

[0015] The memory stores programs or instructions that can be run on the processor, and when the programs or instructions are executed by the processor, the steps of the image chaos encryption method based on magnetic controlled memristor as described in the first aspect are implemented.

[0016] The beneficial effects of the present invention are reflected in that, by constructing a high-dimensional fractional-order variable parameter hyperchaotic model and combining it with dynamic perturbations, a key stream with extremely high randomness and complexity can be generated, which greatly increases the key space and significantly improves the ability to resist brute force cracking. By using image features as the initial parameters of the fractional-order variable parameter hyperchaotic model, the key generated each time is closely related to the image content, ensuring a Figure 1 The key enables the same encryption algorithm to generate different key streams on different images, increasing security, enhancing the adaptability and complexity of the encryption system, and making it more difficult to crack. The magnetically controlled memristor has nonlinear resistance characteristics. By constructing a high-dimensional fractional-order variable parameter hyperchaotic model using the magnetically controlled memristor, the randomness and nonlinearity of the system are effectively enhanced, thereby improving the anti-interference ability, unpredictability and security of the encryption system, effectively solving the problems of environmental noise and temperature fluctuations in the hardware implementation process, and ensuring the stability and robustness of the encryption process. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of the flow of a chaotic image encryption method based on a magnetically controlled memristor provided by the present invention;

[0018] Figure 2 A schematic diagram of a process for generating a multi-dimensional key stream provided by the present invention;

[0019] Figure 3 A schematic diagram of a process for generating a scrambled image provided by the present invention;

[0020] Figure 4 A schematic diagram of a process for generating a one-dimensional ciphertext vector provided by the present invention;

[0021] Figure 5 This is a structural schematic diagram of an image chaos encryption system based on a magnetically controlled memristor provided by the present invention. DETAILED DESCRIPTION

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0023] Example 1:

[0024] Reference Manual Figure 1 , showing a flow chart of an image chaos encryption method based on a magnetically controlled memristor provided by the present invention.

[0025] An embodiment of the present invention provides a chaotic image encryption method based on a magnetically controlled memristor, comprising:

[0026] S1: Obtain the image to be processed.

[0027] S2: Construct a fractional-order variable parameter hyperchaotic model using magnetically controlled memristors.

[0028] Among them, a magnetoresistive memristor is a nonlinear electronic component with memory properties, whose resistance changes with the external magnetic field. Unlike traditional resistors, memristors can retain their state after power failure, exhibiting a memory effect. They are widely used in storage devices and chaotic systems. Fractional-order differential equations are a type of differential equation widely used in complex systems. The order is not an integer, but a fraction. Compared to conventional integer-order differential equations, fractional-order models have more complex dynamic behavior and can better simulate systems with memory and nonlocality. Hyperchaotic models are more complex than conventional chaotic systems, typically exhibiting multiple positive Lyapunov exponents and exhibiting more random and unpredictable behavior, making them suitable for key generation in encryption systems.

[0029] It should be noted that magnetically controlled memristors can generate highly complex and random chaotic signals. By utilizing their memory effect and nonlinear characteristics, they can generate constantly changing key streams by dynamically adjusting parameters, thereby increasing the unpredictability and randomness of encryption. The fractional-order hyperchaotic model introduces memory and nonlocality, making the system more sensitive to initial values, significantly enhancing the complexity and anti-attack capabilities of the key stream, and making the image encryption process more difficult to crack.

[0030] In a possible implementation, the fractional-order variable parameter hyperchaotic model is specifically:

[0031] ;

[0032] in, 、 、 and denote Caputo fractional derivatives, α, β, γ, and δ denote orders, (x, y, z, w) denote the four-dimensional state variables of the chaotic sequence, and a, b, c, and d denote the nonlinear coupling strength coefficients.

[0033] Among them, the nonlinear coupling intensity coefficient controls the complexity of chaotic behavior, and the chaos of the high-dimensional chaotic model is determined by the maximum Lyapunov exponent and other Lyapunov exponents.

[0034] In the present invention, the Lyapunov exponent spectrum can be obtained by calculating the eigenvalues ​​of the Jacobian matrix J:

[0035] ;

[0036] Where J represents the Jacobian matrix.

[0037] In a possible implementation manner, after S1, the method further includes:

[0038] Parameter perturbation is performed on the fractional-order variable parameter hyperchaotic model.

[0039] It's important to note that perturbing the parameters of the fractional-order variable-parameter hyperchaotic model significantly increases the system's complexity and randomness, making the key stream even more difficult to predict. This perturbation makes the system's dynamic behavior even more unpredictable, thereby enhancing the security of the encryption process. Even if an attacker knows part of the ciphertext and plaintext, they can't crack the key using conventional methods, significantly improving the system's resistance to attacks.

[0040] In this paper, a fractional-order hyperchaotic memristor circuit is constructed based on a magnetically controlled memristor. Using a chaotic model as a framework, the nonlinear elements are replaced with magnetically controlled memristors. Strong nonlinearity is introduced by exploiting their flux-charge relationship. The hardware circuit for fractional-order calculus is implemented using methods such as the Oustaloup recursive approximation method, enhancing the system's dynamics. A parameter perturbation mechanism is then introduced to dynamically modulate the memristor's characteristics through an external magnetic field while setting the fractional order as a time-varying parameter that varies with the state variable. Temperature compensation and dynamic calibration modules for the magnetically controlled memristor circuit effectively address environmental noise and temperature fluctuations during hardware implementation, ensuring the stability and robustness of the encryption process.

[0041] The fractional-order variable parameter hyperchaotic model after parameter perturbation is specifically:

[0042] ;

[0043] ;

[0044] Among them, (x1, x2, x3, x4) represents the four-dimensional state variables of the chaotic sequence, σ i (t) represents the function of the i-th chaotic sequence changing with time state t, σ i (t)0 represents the basic parameter, ε i represents the disturbance intensity coefficient of the i-th chaotic sequence, K i represents the coupling coefficient of the state of the i-th chaotic sequence and the state variable, ω represents the periodic disturbance frequency, δ i represents the amplitude of the i-th chaotic sequence.

[0045] The magnetically controlled memristor provides strong nonlinear characteristics, and the mathematical model of the dynamic change of resistance value with magnetic flux φ is:

[0046] ;

[0047] Among them, R M (φ) represents the resistance value of the memristor with a magnetic flux of φ, R on Indicates the on-state of the memristor, R off Indicates that the memristor is not conducting or in a blocking state. represents the nonlinear slope factor, φ represents the memristor flux, and φ0 represents the center flux.

[0048] Therefore, the fractional-order variable parameter hyperchaotic model is finally converted into:

[0049] ;

[0050] Among them, C a Represents a capacitance of order a, C β Indicates an inductor of order β, L γ represents an inductive element of order γ, represents the Caputo fractional derivative, a, β, and γ represent the order, v1 and v2 represent the capacitor voltage, δ1, δ2, δ3, and δ4 represent the amplitude coefficient of the external disturbance term, iL represents the inductor current, R M (φ) represents the resistance value of the memristor with a magnetic flux of φ, φ represents the magnetic flux of the memristor, i M represents the current through the memristor, k l represents the coupling gain coefficient of the flux change to the memristor current response, ω represents the angular frequency of the cosine perturbation, and R1 and R2 represent fixed resistor values.

[0051] Reference Manual Figure 2 , shows a schematic diagram of a process for generating a multi-dimensional key stream provided by the present invention.

[0052] S3: Using the features of the image to be processed as the initial parameters of the fractional-order variable parameter hyperchaotic model, a multi-dimensional key stream is dynamically generated through the fractional-order variable parameter hyperchaotic model.

[0053] It should be noted that using the features of the image to be processed as the initial parameters of the fractional-order variable parameter hyperchaotic model can ensure the close correlation between the encryption key stream and the image content, thus achieving a Figure 1 The key effect gives each image a unique key stream, thereby enhancing the security of encryption. At the same time, through fractional-order parameter variation, the nonlinear behavior of the system is enhanced, the key stream becomes more unpredictable, increasing the difficulty of cracking and ensuring the strength of image encryption.

[0054] In a possible implementation, S3 specifically includes:

[0055] S301: Using the features of the image to be processed as initial parameters of a fractional-order variable parameter hyperchaotic model, using the ABM algorithm to solve the fractional-order variable parameter hyperchaotic model, and determining a four-dimensional chaotic sequence.

[0056] The Adams-Bashforth-Moulton (ABM) algorithm is a commonly used numerical method for solving ordinary differential equations and fractional-order differential equations. It combines the Adams-Bashforth (explicit) and Adams-Moulton (implicit) methods to obtain high-precision solutions through iteration, while improving computational efficiency and stability during the solution process.

[0057] Specifically, the use of a fractional-order variable parameter model makes the encryption process more complex and dynamic, increasing the difficulty of cracking. Solving the fractional-order differential equation through the ABM algorithm not only ensures high-precision key stream generation, but also improves computational efficiency and stability, thereby enhancing the security and performance of the entire image encryption system.

[0058] In a possible implementation, the iterative formula of the ABM algorithm is specifically:

[0059] ;

[0060] ;

[0061] ;

[0062] Among them, n represents iterative compensation, h represents the time step, β m represents the weight coefficient of the kernel function at the mth historical point, Γ represents the Gamma function, x m ,y m ,z m ,w mRepresents the four-dimensional state variable of the chaotic sequence at the mth historical point.

[0063] S302: Normalize the four-dimensional chaotic sequence to determine the image replacement key and image diffusion key:

[0064] ;

[0065] ;

[0066] Among them, s i and t i Both represent the image permutation key of the i-th chaotic sequence, u i and v i All represent the image diffusion key of the i-th chaotic sequence, max represents maximization, {x i , y i , z i , w i} represents the four-dimensional state variable of the i-th chaotic sequence.

[0067] Specifically, normalization keeps the key values ​​within a uniform range, making image scrambling and diffusion more stable and effective. The generation of permutation and diffusion keys disrupts the spatial relationships and obfuscates pixel values, significantly improving the unpredictability and crack resistance of encrypted images.

[0068] S303: Convert the generated image replacement key and the generated image diffusion key into a multi-dimensional key stream.

[0069] The multi-dimensional key stream is specifically:

[0070] ;

[0071] Among them, k s (n) represents the nth key component of the chaotic sequence s, k t (n) represents the nth key component of chaotic sequence t, k u (n) represents the nth key component of the chaotic sequence u, k v (n) represents the nth key component of the chaotic sequence v.

[0072] After parameter perturbation, the multidimensional key stream is:

[0073] ;

[0074] Among them, σ(t) represents the function that changes with time state t.

[0075] S4: Perform preprocessing and block operations on the image to be processed.

[0076] It's important to note that preprocessing and segmenting the image provides an efficient and stable foundation for subsequent image encryption. Preprocessing ensures image standardization, protecting the encryption process from noise or inconsistent formats. Segmenting, by dividing the image into multiple small blocks, allows the encryption process to be executed in parallel, significantly increasing encryption speed. This also makes the encryption process for each pixel block more flexible and independent, effectively improving encryption security and efficiency.

[0077] In the present invention, after receiving the image to be processed, if it is a color image, it is converted into a grayscale image, the expression of pixel values ​​is unified, and the pixel values ​​are normalized to a specific interval. Subsequently, the image is divided into pixel blocks of fixed size to facilitate subsequent parallel encryption processing of the image;

[0078] In a possible implementation, the preprocessing operation is specifically as follows:

[0079] ;

[0080] Where P represents the flattened one-dimensional column vector, vec(I) represents the flattening of matrix I into a one-dimensional column vector in column priority order, I represents the grayscale matrix of the image to be processed, and p s Represents the value of the sth pixel in the original image, s=1,2,…,n, n represents the pixel value, T Indicates transposition processing.

[0081] Reference Manual Figure 3 , which shows a schematic diagram of a process for generating a scrambled image provided by the present invention.

[0082] S5: Based on the multi-dimensional key stream, the image to be processed after the block processing is double-reset and scrambled to generate a scrambled image.

[0083] It's important to note that the double-reset scrambling operation, which reorders the image's row and column indices twice, completely disrupts the order of its pixels. The introduction of a multidimensional key stream ensures a unique key stream for each encryption process, and the complexity of the key stream increases encryption strength. Double-reset scrambling enhances encryption effectiveness, resulting in a randomized pixel distribution and a complete destruction of the original structure of the encrypted image, making it more difficult to crack.

[0084] In the present invention, the image is dynamically permuted. First, the row permutation index is generated, and k s (1:512) Sort, record the original index R=[r1,r2,...,r 512 ), where r i Satisfy k s (r i )≤k s (ri +1). Similarly, we get the column index C, i,j∈[0,511].

[0085] In a possible implementation, S5 specifically includes:

[0086] S501: Generate row indexes and column indexes according to a multi-dimensional key stream.

[0087] S502: Perform a sorting operation on the row index and the column index to obtain a replacement rule.

[0088] Specifically, the sorting operation causes the pixel positions of the image to no longer follow the original order, ensuring that the image structure changes each time it is encrypted, thereby increasing the unpredictability and security of the image. By sorting the indexes, the spatial information of the image can be effectively disrupted.

[0089] S503: According to the permutation rule, the image to be processed after the block processing is subjected to double scrambling based on rows and columns to generate a scrambled image:

[0090] ;

[0091] Among them, P perm represents the scrambled image, i represents the row index of the target position, j represents the column index of the target position, r i and c j Both represent the permutation index generated by the chaotic sequence.

[0092] Reference Manual Figure 4 , which shows a schematic diagram of a process for generating a one-dimensional ciphertext vector provided by the present invention.

[0093] S6: Through the fractional-order differential feedback mechanism, the scrambled image is dynamically diffused and nonlinearly confused to generate a one-dimensional ciphertext vector.

[0094] Fractional-order differencing introduces memory and nonlocality, making the current state of a system dependent on its past state. Feedback involves feeding back a portion of the system output to the system input to adjust the current state. In image encryption, this feedback mechanism links the encryption process to previous pixel states, enhancing the complexity and randomness of the encryption.

[0095] It should be noted that dynamic diffusion and nonlinear obfuscation are implemented through a fractional-order differential feedback mechanism to further encrypt the scrambled image. Fractional-order differentials introduce memory, making the encryption result of each pixel dependent not only on the current pixel but also on the previous pixel state, increasing the complexity and unpredictability of the system. Dynamic diffusion and nonlinear obfuscation not only break the linear relationship between pixels but also enhance the randomness of the encrypted image, significantly improving its security.

[0096] In this paper, based on image scrambling, a fractional-order differential feedback mechanism is introduced. This mechanism takes into account the historical state information of image pixels, making the encryption result of the current pixel dependent on the states of multiple past pixels, thus achieving a non-local diffusion effect. The scrambled pixel values ​​are fused with the dynamic key stream, the fractional-order differential feedback term, and the external perturbation term, and the final ciphertext pixel value is obtained through operations such as modulo.

[0097] In a possible implementation, S6 specifically includes:

[0098] S601: Perform dynamic diffusion and nonlinear obfuscation on the scrambled image to generate a diffusion key stream.

[0099] Specifically, the scrambled image is further processed through dynamic diffusion and nonlinear obfuscation to generate a diffusion key stream, enhancing the unpredictability and security of the encrypted image. Dynamic diffusion introduces historical pixel states and key streams, ensuring that the encryption result of each pixel depends not only on the current pixel value, but also on the influence of surrounding pixels and the key, ensuring randomness. Nonlinear obfuscation eliminates the linear relationship between pixel values ​​in the image, breaking the image's locality and increasing the encryption strength, making it more difficult to crack or recover.

[0100] S602: Based on the diffusion key stream, perform nonlinear diffusion on the scrambled image to generate a one-dimensional ciphertext vector.

[0101] Specifically, the complexity and security of the encrypted image are significantly improved by performing nonlinear diffusion. This operation ensures that the relationships between pixel values ​​are more complex and unpredictable, preventing the original image from being recovered through traditional statistical methods. Converting the image into a one-dimensional ciphertext vector further destroys the spatial structure of the image, making the encryption result of each pixel even more irreversible, effectively increasing the encryption strength and anti-attack capabilities.

[0102] In a possible implementation, the diffusion key stream is specifically:

[0103] ;

[0104] Among them, k(n) represents the diffusion key stream, k u (n) represents the nth key component from the chaotic sequence u, k v (n) represents the nth key component from the chaotic sequence v, and mod represents limiting the range of the result;

[0105] The one-dimensional ciphertext vector is specifically:

[0106] ;

[0107] Among them, C(n) represents the one-dimensional ciphertext vector, P perm (n) represents the pixel value after scrambling the nth key component, k(n) represents the diffuse key value corresponding to the nth key component, and C(n-1) represents the ciphertext pixel value of the n-1th key component.

[0108] After parameter perturbation, the one-dimensional ciphertext vector is:

[0109] ;

[0110] Where C(n) represents the one-dimensional ciphertext vector of the nth key component, Δ represents the increment, represents a bitwise XOR operation, Ψ(n) represents the dynamic feedback coefficient of the nth key component, ξ(t) represents the external periodic disturbance corresponding to the time state t, and σ(t) represents the function that changes with the time state t.

[0111] S7: Reshape the one-dimensional ciphertext vector to generate an encrypted image.

[0112] It should be noted that by reshaping the one-dimensional ciphertext vector and restoring it to an encrypted image, it can be ensured that the final format of the image after encryption is consistent with the original image, maintaining the structure of the encrypted image, making it suitable for subsequent image storage and transmission. The reshaping operation can ensure that the nonlinear relationship and complexity between image pixels are retained, thereby improving the security of the image.

[0113] In the present invention, the one-dimensional ciphertext vector C is reshaped into a 512×512 matrix to obtain the encrypted image I enc .

[0114] Reference Manual Figure 5 , which shows a structural schematic diagram of an image chaos encryption system based on a magnetically controlled memristor provided by the present invention.

[0115] In the present invention, by deeply studying the unique flux-resistance control characteristics of magnetically controlled memristors and integrating them into fractional-order circuit design, a novel magnetically controlled memristor circuit is designed to construct a fractional-order hyperchaotic memristor circuit. The circuit uses magnetically controlled memristors as core nonlinear elements, and introduces strong nonlinearity by utilizing the characteristic that their resistance changes with magnetic flux. Fractional-order calculus units are constructed by combining fractional-order capacitors and inductors to give the system "memory". At the same time, through dynamic parameter perturbations, time-varying magnetic field signals are injected in real time to further enhance the complexity of chaotic signals. Compared with traditional chaotic circuits, the key stream generated by this hardware design has higher information entropy and lower autocorrelation, which significantly improves the security of the key stream and provides a solid physical layer guarantee for image encryption.

[0116] The present invention uses devices such as spin-transfer torque magnetoresistive memristors, and adopts temperature-compensated RC networks and dynamic calibration modules to enhance noise resistance. At the same time, disturbance source integration is achieved through micro-electromagnetic coils. After completion of the construction, the hyperchaotic behavior of the system is verified through numerical simulation and experiments to ensure the existence of at least two positive Lyapunov exponents. Finally, the system state variables, memristor states, fractional order and disturbance parameters are combined to generate a dynamic key stream, which is then combined with nonlinear diffusion operations and applied to encryption systems.

[0117] The embodiment of the present invention provides an image chaos encryption system 20 based on a magnetically controlled memristor, comprising: a processor 201 and a memory 202;

[0118] The memory 202 stores programs or instructions that can be run on the processor 201. When the programs or instructions are executed by the processor 201, the steps of the above-mentioned image chaos encryption method based on magnetically controlled memristors are implemented, and the same technical effects can be achieved. To avoid repetition, the present invention will not be described in detail.

[0119] It should be understood that the processor 201 in the embodiment of the present invention may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0120] It should also be understood that the memory 202 in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. The non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0121] In the description of the embodiments of the present invention, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "center", "top", "bottom", "top", "bottom", "inside", "outside", "inner side", "outer side" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. Among them, "inside" refers to an internal or enclosed area or space. "Periphery" refers to the area surrounding a specific component or specific area.

[0122] In the description of the embodiments of the present invention, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly specifying the number of the technical features indicated. Therefore, a feature specified as "first," "second," "third," or "fourth" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "plurality" means two or more.

[0123] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," "connected," and "assembled" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; they may refer to direct connections, indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention in specific circumstances.

[0124] In the description of the embodiments of the present invention, specific features, structures, materials or characteristics may be combined in an appropriate manner in any one or more embodiments or examples.

[0125] In describing the embodiments of the present invention, it should be understood that "-" and "~" represent a range between two values, and the range includes the endpoints. For example, "AB" represents a range greater than or equal to A and less than or equal to B. "A~B" represents a range greater than or equal to A and less than or equal to B.

[0126] In describing the embodiments of the present invention, the term "and / or" is used herein to describe a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. Furthermore, the character " / " is generally used herein to indicate that the associated objects are in an "or" relationship.

[0127] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A chaotic image encryption method based on magnetic controlled memristor, characterized in that: include: S1: Get the image to be processed; S2: Constructing a fractional-order variable parameter hyperchaotic model using magnetically controlled memristors; S3: using the features of the image to be processed as initial parameters of the fractional-order variable parameter hyperchaotic model, and dynamically generating a multidimensional key stream through the fractional-order variable parameter hyperchaotic model; S4: performing preprocessing and block division operations on the image to be processed; S5: Based on the multi-dimensional key stream, double-reset scrambling is performed on the image to be processed after the block processing to generate a scrambled image; S6: Dynamically diffuse and nonlinearly obfuscate the scrambled image through a fractional-order differential feedback mechanism to generate a one-dimensional ciphertext vector; S7: Reshape the one-dimensional ciphertext vector to generate an encrypted image.

2. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: The fractional-order variable parameter hyperchaotic model is specifically: ； in, 、 、 and denote Caputo fractional derivatives, α, β, γ, and δ denote orders, (x, y, z, w) denote the four-dimensional state variables of the chaotic sequence, and a, b, c, and d denote the nonlinear coupling strength coefficients.

3. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: After S1, the following steps are also included: Parameter perturbation is performed on the fractional-order variable parameter hyperchaotic model.

4. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: The S3 specifically includes: S301: using the features of the image to be processed as initial parameters of the fractional-order variable parameter hyperchaotic model, solving the fractional-order variable parameter hyperchaotic model using an ABM algorithm, and determining a four-dimensional chaotic sequence; S302: performing normalization processing on the four-dimensional chaotic sequence to determine an image replacement key and an image diffusion key: ； ； Among them, s i and t i Both represent the image permutation key of the i-th chaotic sequence, u i and v i All represent the image diffusion key of the i-th chaotic sequence, max represents maximization, {x i ,y i ,z i ,w i } represents the four-dimensional state variable of the i-th chaotic sequence; S303: Convert the generated image replacement key and the generated image diffusion key into the multi-dimensional key stream.

5. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: The iterative formula of the ABM algorithm is specifically: ； ； ； Among them, n represents iterative compensation, h represents the time step, β m represents the weight coefficient of the kernel function at the mth historical point, Γ represents the Gamma function, x m ,y m ,z m ,w m Represents the four-dimensional state variable of the chaotic sequence at the mth historical point.

6. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: The pre-processing operation is specifically as follows: ； Among them, P represents the flattened one-dimensional column vector, vec(I) represents the matrix I flattened into a one-dimensional column vector in column priority order, I represents the grayscale matrix of the image to be processed, p s Represents the value of the s-th pixel in the original image, s=1,2,…,n, n represents the pixel value, and T represents the transposition process.

7. The image chaos encryption method based on magnetic controlled memristor according to claim 5, characterized in that: The S5 specifically includes: S501: Generate a row index and a column index according to the multi-dimensional key stream; S502: performing a sorting operation on the row index and the column index to obtain a replacement rule; S503: According to the replacement rule, the image to be processed after the block processing is subjected to double scrambling based on rows and columns to generate the scrambled image: ； Among them, P perm represents the scrambled image, i represents the row index of the target position, j represents the column index of the target position, r i and c j Both represent the permutation index generated by the chaotic sequence.

8. The image chaos encryption method based on magnetic controlled memristor according to claim 5 is characterized in that: The S6 specifically includes: S601: Perform dynamic diffusion and nonlinear obfuscation on the scrambled image to generate a diffusion key stream; S602: Based on the diffusion key stream, perform nonlinear diffusion on the scrambled image to generate a one-dimensional ciphertext vector.

9. The image chaos encryption method based on magnetic controlled memristor according to claim 1, characterized in that: The diffusion key stream is specifically: ； Among them, k(n) represents the diffusion key stream, k u (n) represents the nth key component from the chaotic sequence u, k v (n) represents the nth key component from the chaotic sequence v, n represents the position index of the key stream, and mod represents limiting the range of the result; The one-dimensional ciphertext vector is specifically: ； Among them, C(n) represents the one-dimensional ciphertext vector, P perm (n) represents the pixel value after scrambling the nth key component, k(n) represents the diffuse key value corresponding to the nth key component, and C(n-1) represents the n-1th ciphertext pixel value.

10. An image chaos encryption system based on magnetic controlled memristor, characterized in that: include: processor and memory; The memory stores a program or instruction that can be run on the processor, and when the program or instruction is executed by the processor, the steps of the image chaos encryption method based on magnetic controlled memristor are implemented as described in any one of claims 1 to 9.

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