Multi-image encryption algorithm based on hyperchaotic system and computer-generated holography

Abstract

The invention relates to the technical field of chaotic cryptography, image encryption and information security, in particular to a multi-image encryption algorithm based on a hyper-chaotic system and computer-generated holography, which comprises the following steps: S1, generating a pseudo-random sequence for encryption by using the hyper-chaotic system; s2, preprocessing the original image based on computer-generated holography; s3, combining the generated pseudo-random sequence with the preprocessed image to realize image encryption; s4, through decryption operation corresponding to the encryption process, the original image is restored after the correct secret key is input; and S5, the decryption operation comprises inverse transformation and reconstruction operation on the encrypted image. The algorithm comprises an image preprocessing module, a hyperchaotic system module, a compressed sensing coding module, a computer-generated holographic encryption module, a decryption module and a post-processing module, the security of sensitive image data in the transmission and storage process can be ensured, and efficient and reliable guarantee is provided for sensitive image encryption in various fields.

Description

Technical Field

[0001] The invention relates to the fields of chaos cryptography, image encryption and information security technology, and in particular to a multi-image encryption algorithm based on hyperchaotic system and computational holography. Background Art

[0002] With the rapid development of information technology, digital images, as an information-intensive and easy-to-understand carrier, have been widely used in the fields of medicine, finance, military, intelligent transportation, etc. However, with the continuous expansion of data scale and the advancement of transmission technology, the risks of privacy leakage and tampering faced by digital images are increasing. Especially in an open network environment, digital images are vulnerable to illegal access, interception and tampering during transmission, and data security faces severe challenges. Therefore, ensuring the confidentiality, integrity and security of digital images during transmission has become an important research direction in the field of information security.

[0003] Existing traditional security protection measures, such as virtual private networks (VPNs) and physical isolation, have enhanced the security of data transmission to a certain extent, but image data is still transmitted in plain text, which poses the risk of being illegally stolen or tampered with. In order to make up for the shortcomings of the underlying security protection mechanism, image encryption technology has been widely used and has become an important means to ensure data security.

[0004] With the development of high-performance computers and quantum computing technology, traditional encryption algorithms have gradually exposed their limitations, giving rise to the development of emerging technologies such as chaotic encryption and quantum encryption. These technologies have shown great potential in improving encryption strength, transmission efficiency and defending against complex attacks, bringing new opportunities and challenges to the field of image encryption. Chaotic encryption technology has been widely used in the field of image encryption because of its high sensitivity to initial conditions, pseudo-randomness and unpredictability, which can significantly enhance the randomness and complexity of encryption algorithms and meet strict data confidentiality requirements. In image encryption, chaotic encryption technology does not require external keys and can directly use the image itself as the key. By quantizing the generated random real number sequence into an integer sequence, the high correlation between pixels is effectively reduced, thereby further improving the encryption effect and security.

[0005] Aiming at the deficiencies of traditional image encryption algorithms in terms of security and efficiency, this paper proposes an image encryption scheme based on the combination of compressed sensing, hyperchaotic system and computer-generated holography. First, the chaotic sequence generated by the hyperchaotic system provides high randomness and complexity for the encryption process. Secondly, the computer-generated holography technology combining random phase encoding with Fourier transform is used to further enhance the encryption effect and improve the security of the algorithm. Finally, the compressed sensing technology is applied to compress and encrypt multiple images, which significantly reduces the amount of data transmission and key consumption, and improves the transmission efficiency of the encryption process. Summary of the invention

[0006] In view of the shortcomings of traditional encryption technology and existing image encryption schemes, the present invention combines a variety of advanced technologies to propose an efficient image encryption algorithm. The algorithm includes image preprocessing, hyperchaotic system, compressed sensing coding, computational holographic encryption, decryption and post-processing modules, which can ensure the security of sensitive image data during transmission and storage, and provide efficient and reliable protection for the encryption of sensitive images in various fields.

[0007] The technical implementation scheme of the present invention is: a multi-image encryption algorithm based on hyperchaotic system and computational holography, comprising the following steps: S1, using a hyperchaotic system to generate a pseudo-random sequence for encryption; S2, preprocessing the original image based on computational holography; S3, combining the generated pseudo-random sequence with the preprocessed image to achieve image encryption; S4, through a decryption operation corresponding to the encryption process, restoring the original image after inputting the correct key; S5, the decryption operation includes inverse transformation and reconstruction operations on the encrypted image.

[0008] Optionally, in the step S1, the generation process of the hyperchaotic system includes: applying the SHA-256 hash algorithm to the initial input value to obtain a 256-bit hash value, dividing it into 8 32-bit subsequences, converting each subsequence into a floating point number between 0 and 1 as the initial value of the chaotic system, and then driving the improved Logistic chaotic map and the six-dimensional cellular neural network chaotic system to generate a pseudo-random chaotic sequence; the improved Logistic chaotic map introduces a multiple initial value input mechanism, and its combination function is:

[0009]

[0010] Among them, α i is the weight coefficient, satisfying

[0011] Optionally, in step S2, the random phase encoding adopts the formula:

[0012] I(x,y)=I n exp(2iπ rand(M,N))

[0013] Encode the input image and perform inverse Fourier transform after encoding using the formula:

[0014] I freq =IFFT 2(IFFTShift(I(x,y)))

[0015] The frequency domain image is obtained, and then the iterative algorithm is used to restore the phase information by relying on the phase preservation and feedback mechanism. The formula is: Phase(I freq )=angle(I freq )

[0016] Calculate the phase information, and then use the formula: I unit =exp(1i·Phase(I freq ))

[0017] Processing is performed, and the iteration termination condition is: Corr(P, |I unit |)≥.9995After several iterations, we finally get a hologram with phase information: I holo =FFTShift(FFT2(I unit ))

[0018] Optionally, in the step of combining the generated pseudo-random sequence with the pre-processed image to realize image encryption, the image is first subjected to discrete cosine transform, and the formula is:

[0019]

[0020] This is the specific process of compressed sensing. The measured value y is calculated after discrete cosine transformation. Then the transformed image data is permuted with the permutation index chaotic sequence generated by the Logistic chaotic system, and then the permuted measured value is subjected to Sigmoid mapping. The formula used is:

[0021]

[0022] The data is mapped to the range of [0, 255] and normalized. Finally, the Sigmoid normalized measurement value is XORed with the generated chaotic sequence to complete the image encryption.

[0023] Optionally, in the decryption operation corresponding to the encryption process in step S4, after the correct key is input, the encrypted image is firstly subjected to Sigmoid inverse mapping, using the formula: Restore the sparse measurement value, then use the pseudo-random chaotic sequence and the key to construct the measurement matrix, and then use the SL0 reconstruction algorithm based on the sparsity assumption to solve the optimization problem. The sparse representation of the encrypted image is constructed, and then the inverse computational holographic operation is performed on the reconstructed sparse representation using the formula:

[0024] Restore the image spatial domain representation, where x′ is the reconstructed sparse representation. Finally, perform appropriate post-processing on the obtained decrypted image to output an approximate restored version of the original image.

[0025] Optionally, the dimensionless state equation of the six-dimensional cellular neural network chaotic system in the hyperchaotic system is:

[0026]

[0027] This formula is the equation for constructing chaos in a cellular neural network. The chaotic system is run by inputting the set system initial values ​​and parameters.

[0028] The attractor diagram is obtained by solving the equation based on the Runge-Kutta method, and the Jacobian matrix method is used to substitute relevant parameters to calculate the Lyapunov exponent method to study the system.

[0029] Optionally, in the discrete cosine transform step, Zigzag scanning prioritizes low-frequency coefficients, and the conversion process is to convert the DCT coefficients from a two-dimensional matrix to a one-dimensional vector in the Zigzag scanning order, which is helpful for subsequent compressed sensing processing.

[0030] Optionally, the measurement matrix adopts a Gaussian random matrix, and the compressed sensing measurement value is generated by multiplying the matrix with the sparse representation vector of the image, which plays a key transformation role in the encryption process.

[0031] Optionally, in the SL0 reconstruction algorithm, by continuous iterative optimization, the sparsest solution is found while satisfying the measurement value constraint condition to accurately reconstruct the sparse representation of the encrypted image, thereby ensuring the accuracy and efficiency of image decryption.

[0032] Optionally, in the inverse operation of the computational holography, the holographic code generated during the encryption process is removed by a combination of Fourier transform and its inverse transform, and the original spatial information of the image is restored, so that the decrypted image is close to the original image.

[0033] The present invention has the following advantages:

[0034] 1. The present invention adopts a method combining six-dimensional chaotic cellular neural network, SHA-256 and improved Logistic chaos, which greatly increases the space of the key and makes the algorithm more secure than the encryption scheme based on the low-dimensional chaotic system.

[0035] 2. The present invention simultaneously adopts compressed sensing technology and an improved lightweight Logistic chaos method, making the algorithm more suitable for processing multi-image encryption scenarios, reducing the computational burden, greatly shortening the encryption and decryption time, and improving transmission efficiency.

[0036] 3. The model uses chaotic systems, computational holography and cryptographic hash functions to effectively resist attacks such as brute force cracking, plaintext attacks and differential attacks, and has strong resistance to common attacks.

[0037] 4. The algorithm in this paper meets the requirements of information security systems, which require them to take into account confidentiality, integrity, availability, accuracy, reliability and other aspects at the same time, ensuring the security of sensitive image encryption and high efficiency of transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a framework diagram of the encryption scheme algorithm of the present invention;

[0039] Figure 2 This is a detailed encryption flow chart of the multi-image encryption algorithm based on hyperchaotic system and computational holography of the present invention;

[0040] Figure 3 This is a detailed decryption flow chart of the multi-image encryption algorithm based on hyperchaotic system and computational holography of the present invention;

[0041] Figure 4 A chaotic attractor generated by the hyperchaotic system of the present invention;

[0042] Figure 5 It is a simulation experiment result diagram of the present invention; DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. It is hereby stated that the directional terms such as up, down, left, right, front, back, inside, outside, etc. that appear or will appear in the text of the present invention are only based on the accompanying drawings of the present invention, and are not specific limitations of the present invention.

[0044] Example 1

[0045] A multi-image encryption algorithm based on hyperchaotic system and computational holography includes the following steps:

[0046] S1. Using hyperchaotic systems to generate pseudo-random sequences for encryption;

[0047] S2, preprocessing the original image based on computer holography;

[0048] S3, combining the generated pseudo-random sequence with the pre-processed image to achieve image encryption;

[0049] S4, through the decryption operation corresponding to the encryption process, the original image is restored after the correct key is input;

[0050] S5. The decryption operation includes inverse transformation and reconstruction operations on the encrypted image.

[0051] It should be noted that in the field of image encryption, traditional methods such as pixel position replacement or simple pixel value calculation have many limitations. These methods are easy to be analyzed and cracked, the key space is limited, and the efficiency is low when encrypting multiple images, and the key management is complex. The multi-image encryption algorithm based on hyperchaotic system and computational holography has obvious advantages. It uses the pseudo-random sequence generated by the hyperchaotic system, which is highly random and unpredictable. A small change in the parameters will make the sequence very different. The key space is large and can resist multiple attacks. The computational holographic preprocessing converts the image into a holographic form, increasing the dimension and complexity of the information, making it difficult for attackers to crack. In terms of multi-image encryption, the algorithm generates independent pseudo-random sequences for different images, combined with a unified framework, and is efficient and secure. Its decryption operation can perfectly restore the original image through the correct key to ensure image quality.

[0052] In order to restore the original image efficiently, safely and perfectly, this application adopts the following technical approach: encryption process:

[0053] Image preprocessing: Grayscale converts color images into black and white images, reducing color dimension information and simplifying subsequent processing. Normalization unifies pixel values ​​to the [0,1] interval, allowing different images to be subsequently operated at the same scale to ensure consistency and stability of calculations.

[0054] Computer-generated holography: Random phase encoding changes the image phase, causing the image information to change in the frequency domain, increasing the difficulty of cracking. Fourier transform can convert the image from the spatial domain to the frequency domain. The iterative algorithm combines phase retention and feedback mechanisms to continuously adjust and restore the phase information. The final hologram is a complex representation of the original image in the frequency domain and phase domain, which is difficult to crack directly.

[0055] Compressed sensing: DCT transform converts the image to the frequency domain, highlighting the frequency characteristics of the image. The low-frequency coefficients contain the main structural information of the image. Zigzag scanning prioritizes low-frequency coefficients for easy subsequent processing. The measurement values ​​are generated using a Gaussian random matrix. The measurement values ​​contain the original image information, but after chaotic sequence permutation, Sigmoid mapping and normalization, the information is disrupted and re-encoded. XOR with the chaotic sequence further increases the complexity and security of encryption, making it difficult for illegal acquirers to restore the original image.

[0056] Generation of chaotic sequences: The SHA-256 hash algorithm generates fixed-length hash values. The multiple initial value input mechanism is combined with the improved Logistic chaotic map and the six-dimensional cellular neural network chaotic system. A slight change in the initial value will cause a large difference in the chaotic sequence. The generated pseudo-random chaotic sequence is highly complex, unpredictable, and sensitive to initial values. It is used for permutation and scrambling in encryption, which greatly enhances the encryption effect.

[0057] Decryption process:

[0058] Input key: The key is the key to decryption and is used to generate the same pseudo-random chaotic sequence as that used for encryption, ensuring that the reverse calculation of each decryption step matches the encryption process. Only authorized users with the correct key can decrypt correctly. Sigmoid inverse mapping, through reverse Sigmoid mapping, restores the encrypted measurement value to the sparse measurement value state before encryption, preparing for the subsequent reconstruction of the original image information.

[0059] Construct measurement matrix and algorithm reconstruction: Use pseudo-random chaotic sequence and key to construct the measurement matrix corresponding to encryption, restore the original structure of encrypted data, so that subsequent reconstruction algorithm can correctly process data; SL0 reconstruction algorithm is based on sparsity assumption, recovers the sparsest signal from the measurement value, accurately reconstructs the sparse representation of the encrypted image, and ensures the accuracy and efficiency of image decryption.

[0060] Computational holographic inverse operation and output of decrypted image: Perform holographic inverse operation on the reconstructed sparse representation, remove the phase encoding during encryption, convert the image from the frequency domain and phase domain back to the spatial domain, and restore the image spatial information; perform post-processing such as normalization and de-grayscale on the decrypted image to restore the image to the original color and pixel value range, and output an image that is close to the original image.

[0061] Among them, the machine phase encoding performs random phase encoding on the input image, and uses the randomly generated phase information to keep the amplitude part of the image unchanged, while adjusting the phase part:

[0062] I(x, y) = I n exp(2iπ rand(M, N)) (1)

[0063] Wherein: I(x, y) represents a function with coordinates (x, y) in two-dimensional space, representing the distribution of physical quantities such as image intensity on a two-dimensional plane.

[0064] I n Represents a constant, which is the amplitude or reference value of a certain intensity.

[0065] exp represents the exponential function, "i" is the imaginary unit, and "rand(M,N)" is a function that generates an M×N random number matrix.

[0066] Perform inverse Fourier transform on the image with random phase to obtain the frequency domain image, and restore the phase information of the image through an iterative algorithm, mainly using the phase retention and feedback mechanism. Each iteration calculates the phase information and continuously approximates the original image through Fourier forward transform and inverse transform:

[0067] I freq=IFFT 2(IFFTShift(I(x,y))) (2)

[0068] Phase(I freq )=angle(I freq ) (3)

[0069] I unit =exp(1i·Phase(I freq )) (4)

[0070] Where: "I(x,y)": represents a function at the coordinate (x,y) in two-dimensional space, representing the intensity of the image at that position and other physical quantities.

[0071] "IFFT2": is the abbreviation of two-dimensional inverse fast Fourier transform (Inverse Fast-Fourier Transform), which is used to convert functions in the spatial domain to the frequency domain.

[0072] "IFFTShift" is the abbreviation of the inverse Fourier transform shift operation. In Fourier transform related operations, it can move the zero-frequency component to the center of the spectrum.

[0073] “I freq ”: It is the frequency domain signal obtained after performing “IFFTShift” operation and then “IFFT2” operation on “I(x,y)”.

[0074] "angle": is a function that obtains the phase of a complex number.

[0075] “Phase”: indicates the operation of obtaining the phase. “Phase(I_freq)” means obtaining the phase of “I_freq”, which has the same meaning as “angle(I_freq)”.

[0076] “1i”: represents the imaginary unit i, the square of i is equal to -1.

[0077] “I unit ”: It is a complex signal of unit amplitude obtained by multiplying “1i” by “Phase(I_freq)” and then performing an exponential operation (exp).

[0078] Calculate the correlation coefficient between the current amplitude and the original image, and determine the iteration termination condition. If the correlation coefficient meets the standard, then exit the iteration; otherwise, continue to iterate and adjust the phase and amplitude;

[0079] Corr(P,|I unit |)≥0.9995 (5)

[0080] Among them: "Corr": generally represents the correlation calculation function, which is used to calculate the correlation between two quantities;

[0081] "P": usually represents a signal or data set, "I unit ”: In the derivation of the above formula, it is a unit amplitude complex signal obtained by operating on the phase information of the frequency domain signal.

[0082] Finally, after several iterations, a hologram with phase information is obtained:

[0083] I holo =FFTShift(FFT 2(I unit )) (6)

[0084] Among them, "I holo ": Generally represents a signal, which is a signal related to the hologram after a specific transformation. "FFT2": is the abbreviation of "Two-dimensional Fast Fourier Transform", which is used to transform the function in the spatial domain (here refers to "I unit ”) to the frequency domain, “FFTShift”: is the abbreviation of “Fourier transform shift operation”, its function is to move the zero frequency component in the Fourier transform result to the center of the spectrum, which is convenient for observing and processing the spectrum information, “I unit ”: It is the unit amplitude complex signal obtained by operating the phase information of the frequency domain signal. The whole formula means that for “I unit "First, perform a two-dimensional fast Fourier transform, then perform a Fourier transform shift operation on the transformed result, and finally obtain "I holo ”.

[0085] Among them, for image I holo Perform discrete cosine transform (DCT) to obtain the two-dimensional representation of the image in the frequency domain. dct

[0086]

[0087] Formula (7) is the specific process of compressed sensing, and the measurement value y is calculated after discrete cosine transform.

[0088] Among them, "C(u,v)": is the calculation result of this formula, which is a binary function with u and v as independent variables, "α(u)" and "α(v)": are functions of u and v respectively, "∑(subscript x=0, superscript M-1)" and "∑(subscript y=0, superscript N-1)": represent double summation symbols. The former is to let x take values ​​from 0 to M-1 and perform summation operation, and the latter is to let y take values ​​from 0 to N-1 and perform summation operation, "I holo"(x,y)": is the previously mentioned function or signal related to holography. It is the key variable in the double summation operation and refers to the value at the coordinate (x,y) in the two-dimensional space. "cos((2x+1)uπ / 16)" and "cos((2y+1)vπ / 16)": two cosine functions, with independent variables related to x, u and y, v respectively. The denominator is the constant 16. They participate in the multiplication operation in the formula and are related to modulation or transformation in signal processing.

[0089] It should be noted that the DCT coefficients are converted from a two-dimensional matrix to a one-dimensional vector in Zigzag order. Zigzag scanning prioritizes low-frequency coefficients, which is beneficial to subsequent compressed sensing processing. sparse =I dct P zigzag .

[0090] Then, the measurement matrix Φ (the measurement matrix that appears in the compressed sensing part of the encryption process uses a Gaussian matrix) is used to generate the compressed sensing measurement value: y = Φ xsparse , the measured value Y is permuted by the permutation index chaotic sequence generated by the Logistic mapping:

[0091] y upset (i, j) = y(index(i, j)) (8)

[0092] Among them, the replaced value y upset (i, j) is equal to the value obtained by indexing the original measurement value y with the index value obtained by the index function index(i, j), where (i, j) is the coordinate, and y_upset(i, j) is the result after permutation at the coordinate (i, j).

[0093] Perform Sigmoid mapping on the permuted measurement values, map the data to the range of [0,255], and normalize the encrypted data:

[0094]

[0095] Among them, y sigmoid It is equal to 1 divided by (1 plus the natural constant e as the base, -y upeet is the exponential function value of the exponential), y sigmoid is the result value after the sigmoid function transformation. The sigmoid function is a commonly used nonlinear activation function. The output is usually between 0 and 1. exp is an exponential function that performs exponential operations based on the natural constant e. upeet is a variable, which is the intermediate value obtained by the previous operation.

[0096] Finally, the normalized Sigmoid measurement value is XORed with the generated chaotic sequence o1 to complete the image encryption:

[0097]

[0098] x reconstructed =SL 0(Φ,y,threshold,iterations) (11)

[0099] Among them, y encrypted (i, j) is the encrypted value at coordinate (i, j), which is equal to y sigmoid The result of the XOR operation of (i, j) and o1(i, j). Here “⊕” represents the logical operation of XOR, x reconstructed It is the result value after reconstruction, which is equal to the return value obtained by calling the SL0 function and passing Φ, y, threshold and number of iterations as parameters.

[0100] It should be noted that the measurement matrix Φ is a Gaussian random matrix.

[0101] Example 2

[0102] Logistic mapping is a common chaos mapping, which is widely used in chaos theory, nonlinear dynamic systems and their applications. Its system equation is as follows:

[0103] x i+1 =μx i (1-x i ) (12)

[0104] Among them, "x i+1 ” represents the value of the next moment (or the next iteration step) in the sequence, “μ” is a control parameter, usually a real number, whose value affects the dynamic behavior of the mapping, and “x i " represents the value at the current moment (or the current iteration step). The entire formula describes an iterative relationship. i " to calculate the next value "x i+1 ”.

[0105] On the basis of this chaotic mapping, a multiple initial value input mechanism is introduced. By introducing multiple initial conditions instead of relying on a single initial value, subtle changes in the initial state of the system can more significantly affect the chaotic sequence, thereby increasing the complexity, unpredictability and initial value sensitivity of the system, and improving the randomness and security of the sequence. The core of the multiple initial value input mechanism is to generate subsequent chaotic iterations based on the combination of multiple initial values, thereby forming a more complex sequence.

[0106] The above definition can be used to form a combination function, which is combined in a weighted average manner as follows:

[0107]

[0108]

[0109] Among them, α i is the weight coefficient, satisfying

[0110] Among them, f(x0(1),x0(2),…,x0(n)) is a function of n variables, ∑(i=1 to n)α i ·x n (i) Calculate the sum of the products of n variables and their corresponding weights, and then multiply it by 1 minus itself to get the function value, x n+1 is the next value of the sequence, obtained by multiplying the parameter r by the same two partial products as above, α i are weight coefficients, which sum to 1.

[0111] It should be noted that the design of introducing multiple initial value input mechanism based on Logistic mapping and adopting weighted average combination has significant advantages. It greatly improves the complexity of the system through the combination of multiple initial values ​​and their different weights, making the system dynamic behavior more diverse; the initial state space is greatly expanded, the unpredictability is enhanced, and it is difficult for attackers to predict the subsequent state of the system; the sensitivity of the initial value is further improved, and a small change in the initial value may make the chaotic sequence completely different. At the same time, this design optimizes the sequence performance, breaks the potential regularity of the traditional single initial value chaotic sequence, improves the randomness, and is closer to the real random sequence in statistical characteristics; in the fields of information security, it can greatly enhance security and build a solid defense line for encryption systems.

[0112] Example 3

[0113] A new type of six-dimensional chaotic cellular neural network, whose dimensionless state equation is:

[0114]

[0115] Among them, dy 1 / dt、dy 2 / dt、dy 3 / dt、dy 4 / dt、dy 5 / dt、dy 6 / dt: represents the variable y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y6 The rate of change of y with respect to time t 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 : are state variables in the system, their values ​​change over time, σ': is a coefficient used to measure y 2 -y 1 Tody 1 / dt influence, k1: is also a coefficient that determines y 1 2 -y 3 Tody 1 / dt contribution, ρ': coefficient, in dy 2 / dt expression, it determines y 1 (ρ'-y3) This term has an effect on y 2 The effect of the rate of change, ε': used to represent dy 2 The coefficient of the sine function term ε'sin(0.5y1) in / dt, β': 3 / dt and dy 6 / dt appears in the table and is used to measure y 3 and 6 The intensity of its own negative feedback on its rate of change, α': in dy 4 / dt is a measure of y 5 -y 4 For 4 The coefficient of the rate of change is related to the coupling and interaction strength between the two state variables in the system. The specific value of the dimensionless parameter is usually determined by analyzing the characteristic quantity of the system (such as characteristic time, characteristic length or characteristic speed), where the system parameters are set as σ = 16, ρ = 45, β = 4, α = 0.1, ∈ = 1.0.

[0116] Based on the Runge-Kutta method, the chaotic system is visualized, and the dimensionless state equation is solved to obtain its attractor diagram. The system is studied by substituting relevant parameters into the Lyapunov index method, and the six Lyapunov indexes are obtained:

[0117] λ 1 =3.1456,λ 2 =2.4718,λ 3 =-2.117,λ 4 =-0.0644,λ 5 =-0.36, λ 6 =2.1532;

[0118] Among them: there are three positive Lyapunov exponents, so the system is a hyperchaotic system with higher complexity and randomness. The calculation of the Lyapunov exponent is a direct method to prove whether it is a hyperchaotic system, and see whether the obtained exponent is >0.

[0119] In the six-dimensional chaotic cellular neural network system, the six Lyapunov exponents are obtained through the following steps:

[0120] Determine the system equation: The present invention constructs a new type of six-dimensional chaotic cellular neural network and obtains its dimensionless state equation (15), which describes the six variables (y 1 -y 6 ) The changing relationship with respect to time forms the basis of the dynamical system;

[0121] Setting parameter values: The specific values ​​of dimensionless parameters are determined by analyzing the characteristic quantities of the system (such as characteristic time, characteristic length or characteristic speed), and these parameters are substituted into the dimensionless state equation to make the equation a specific form that can be numerically calculated;

[0122] Numerical solution of equations: Based on the Runge-Kutta method, the dimensionless state equation is solved to obtain the evolution of the system state over time, and then its attractor diagram is obtained. This step provides the basic data of the system state for the subsequent calculation of the Lyapunov exponent;

[0123] Calculate the Lyapunov index: Use a suitable Lyapunov index calculation method (such as the definition method, Wolf algorithm, etc.) to calculate the solved system state data and finally obtain 6 Lyapunov index values.

[0124] In the above scheme, the decryption operation first requires the input of the correct key. The role of the key is to ensure that only authorized users can decrypt the image. The key is used to generate a pseudo-random chaotic sequence, construct a measurement matrix, and control all reverse calculation operations in the decryption process. After the encrypted image undergoes the Sigmoid mapping and encryption process, the data is converted into a compressed sensing measurement value. When decrypting, the encrypted image is first reversed by the key to perform a Sigmoid mapping to restore the sparse measurement value of the encrypted image. Assuming that the encrypted image measurement value is y, which is obtained in the compressed sensing encryption process, the inverse mapping operation can be performed using the following formula:

[0125]

[0126] Among them, y': generally represents the output value after transformation, 1+exp(-(yb) / a)": the denominator part, "exp" represents the exponential function with the natural constant e (approximately 2.71828) as the base, "y" is the original input variable, that is, the value before transformation, "b" is an adjustable parameter, and "a" is also an adjustable parameter.

[0127] The SL0 (Sparse L0 Norm) reconstruction algorithm is applied to process the measurement matrix Φ to reconstruct the sparse representation of the encrypted image. The SL0 algorithm solves the sparse representation by optimizing the problem, making the recovery process of the decrypted image more accurate and efficient.

[0128] In this encryption algorithm, the measurement matrix Φ adopts a Gaussian random matrix, which is used to generate compressed sensing measurement values ​​in the compressed sensing step. When implemented in a computer program, the random number generation function of the programming language can be used to generate random numbers that conform to the Gaussian distribution, thereby constructing the measurement matrix Φ.

[0129] The SL0 algorithm is based on the sparsity assumption, and its goal is to recover the sparsest signal from the measurement value y. The reconstruction process can be described by an optimization problem:

[0130]

[0131] Among them, x^: represents the estimated signal (vector) obtained by SL0 algorithm reconstruction, which is the approximate recovery result of the original signal x, arg min: means "the independent variable that makes... reach the minimum value", here it means finding the x that makes the following ||x||0 reach the minimum value;

[0132] ||x||0: represents the zero norm of vector x, which is used to measure the sparsity of vector x in fields such as signal processing, that is, the number of non-zero elements in vector x, subject to: used to describe constraints, y': represents the measurement value vector obtained after transformation, Φ': is the measurement matrix, which maps the original signal x to the measurement space to obtain the measurement value y', that is, y'=Φ'x, x: is the original sparse signal (vector) to be restored.

[0133] Once the sparse representation of the encrypted image is restored, a computational holographic inverse operation is required to restore the spatial information of the image. This process uses the holographic inverse transform algorithm to remove the phase encoding generated during the encryption process. Assuming that the reconstructed sparse representation is x′, the goal of the holographic inverse operation is to restore the spatial domain representation of the image through Fourier transform. The process of holographic inverse operation can be performed by the following formula:

[0134]

[0135] Among them, I recIt represents the image recovered by the holographic inverse operation, that is, the representation of the image that is ultimately to be reconstructed in the spatial domain; stands for Inverse Fourier Transform, which is used to convert frequency domain information back to the spatial domain and to restore the spatial domain form of the image from the intermediate results in the frequency domain in the inverse holographic operation; A is the coefficient matrix, which performs weighting and transformation operations on the Fourier transformed results in the inverse holographic operation; represents Fourier Transform, which converts the spatial domain signal (here is the sparse representation) into the frequency domain for subsequent processing in the frequency domain; x′ represents the reconstructed sparse representation, which is the intermediate result obtained after the previous processing (such as the SL0 algorithm, etc.), and contains the key information for restoring the original image.

[0136] Finally, the decrypted image Irec obtained after the holographic inverse operation is properly post-processed to complete the image restoration. The post-processing steps include normalizing and de-graying the image, and finally restoring it to an approximate version of the original image.

[0137] I final =Normalize(I rec ) (twenty one)

[0138] Among them, I final It represents the final restored image, which is the result obtained after a series of processing (including holographic inverse operation and post-processing), and is an approximate version of the original image; Normalize is a function that represents the normalization operation. Here, its function is to normalize the input image and adjust the pixel value of the image to a specific range to optimize the image display effect or meet the requirements of subsequent processing; I rec Represents the decrypted image obtained through the holographic inverse operation. It is the input image of the post-processing step. After post-processing operations such as normalization, it will be further close to the original image.

[0139] It should be noted that this new type of six-dimensional chaotic cellular neural network has significant advantages. It is a hyperchaotic system with three positive Lyapunov exponents. Compared with ordinary chaotic systems, it has higher complexity and randomness, which makes the encryption process based on it more difficult to crack, greatly improving the encryption security. In the encryption and decryption process, the use of keys strictly limits the image decryption authority, and only authorized users can operate it. Through Sigmoid mapping, SL0 reconstruction algorithm, and holographic inverse operation, the decryption process is accurate and efficient, and can accurately restore the image sparse representation and spatial information from the encrypted measurement value. Finally, after post-processing, an approximate original image is obtained, ensuring high-quality restoration of the image.

[0140] Simulation experiment

[0141] The present invention selects three 250×250 pixel images of “lena”, “Cameraman” and “boat” as test images, and the simulation software is MATLAB R2023a.

[0142] From the simulation results Figure 5 It can be seen that the size of the compressed and encrypted image is not equal to the size of the original image, and visually, there is no obvious difference between the decrypted image and the original image, which preliminarily shows that the encryption algorithm works well.

[0143] It should be noted that a histogram is a statistical chart that represents the grayscale distribution of an image. It counts the number of occurrences of each grayscale value and the corresponding number of pixels. In order to maintain a good histogram effect during the encryption process, it is usually necessary to ensure that the encrypted image or data is as uniform as possible in grayscale or color distribution to avoid obvious feature exposure, thereby improving security.

[0144] from Figure 5 It can be seen that the histogram analysis of the original image before encryption presents an uneven state, while the histogram distribution of the encrypted image is flat and uniform, making the distribution of image data in space and grayscale value more random, enhancing the contrast of the image and increasing security. Illegal attackers cannot restore the original image based on the statistical characteristics of the ciphertext image. Therefore, the algorithm in this paper has good anti-statistical attack capabilities.

[0145] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of those skilled in the art without departing from the spirit of the present invention.

Claims

1. A multi-image encryption algorithm based on hyperchaotic system and computational holography, characterized in that: It includes the following steps: S1. Using hyperchaotic systems to generate pseudo-random sequences for encryption; S2, preprocessing the original image based on computer holography; S3, combining the generated pseudo-random sequence with the pre-processed image to achieve image encryption; S4, through the decryption operation corresponding to the encryption process, the original image is restored after the correct key is input; S5. The decryption operation includes inverse transformation and reconstruction operations on the encrypted image.

2. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 1, characterized in that: In the step S1, the generation process of the hyperchaotic system includes: applying the SHA-256 hash algorithm to the initial input value to obtain a 256-bit hash value, dividing it into 8 32-bit subsequences, converting each subsequence into a floating point number between 0 and 1 as the initial value of the chaotic system, and then driving the improved Logistic chaotic map and the six-dimensional cellular neural network chaotic system to generate a pseudo-random chaotic sequence; The improved Logistic chaotic map introduces a multiple initial value input mechanism, and its combination function is: Among them, α i is the weight coefficient, satisfying 3. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 1, characterized in that: In the step S2, the random phase encoding adopts the formula: I(x,y)=I n ·exp(2iπ·rand(M,N)) (3) Encode the input image and perform inverse Fourier transform after encoding using the formula: I freq =IFFT 2(IFFTShift(I(x,y))) (4) The frequency domain image is obtained, and then the iterative algorithm is used to restore the phase information by relying on the phase preservation and feedback mechanism. The formula is: Phase(I freq )=angle(I freq ) (5) Calculate the phase information and then use the formula: unit =exp(1i·Phase(I freq )) (6) Processing is performed, and the iteration termination condition is: Corr(P, |I unit |)≥0.9995After several iterations, a hologram with phase information is obtained: I holo =FFTShift(FFT 2(I unit )) (7)。 4. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 1, characterized in that: In the step of combining the generated pseudo-random sequence with the pre-processed image to realize image encryption, the image is first subjected to discrete cosine transform, and the formula is: Then, the transformed image data is permuted with the permutation index chaotic sequence generated by the Logistic chaotic system, and then the permuted measurement values ​​are subjected to Sigmoid mapping, using the formula The data is mapped to the range of [0, 255] and normalized. Finally, the Sigmoid normalized measurement value is XORed with the generated chaotic sequence to complete the image encryption.

5. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 1, characterized in that: In the decryption operation corresponding to the encryption process in step S4, after the correct key is entered, the encrypted image is firstly subjected to Sigmoid inverse mapping using the formula: Recover the sparse measurement values, then use the pseudo-random chaotic sequence and the key to construct the measurement matrix, and then use the SL0 reconstruction algorithm based on the sparsity assumption to solve the optimization problem; The sparse representation of the encrypted image is constructed, and then the inverse computational holographic operation is performed on the reconstructed sparse representation using the formula: Restore the image spatial domain representation, where x′ is the reconstructed sparse representation. Finally, perform appropriate post-processing on the obtained decrypted image to output an approximate restored version of the original image.

6. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 1, characterized in that: The dimensionless state equation of the six-dimensional cellular neural network chaotic system in the hyperchaotic system is: The attractor diagram is obtained by solving the equation based on the Runge-Kutta method, and the Jacobian matrix method is used to substitute relevant parameters to calculate the Lyapunov exponent method to study the system.

7. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 4, characterized in that In the discrete cosine transform step, Zigzag scanning prioritizes low-frequency coefficients, and the conversion process is to convert the DCT coefficients from a two-dimensional matrix to a one-dimensional vector in the Zigzag scanning order, which is helpful for subsequent compressed sensing processing.

8. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 4, characterized in that: The measurement matrix adopts a Gaussian random matrix, and the compressed sensing measurement value is generated by multiplying the matrix with the sparse representation vector of the image, which plays a key transformation role in the encryption process.

9. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 5, characterized in that In the SL0 reconstruction algorithm, through continuous iterative optimization, the sparsest solution is found under the condition of satisfying the measurement value constraint to accurately reconstruct the sparse representation of the encrypted image, thereby ensuring the accuracy and efficiency of image decryption.

10. A multi-image encryption algorithm based on hyperchaotic system and computer generated holography according to claim 5, characterized in that In the inverse operation of the computational holography, the holographic code generated in the encryption process is removed through the combined operation of Fourier transform and its inverse transform, and the original spatial information of the image is restored, so that the decrypted image is close to the original image.

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