Chaotic mapping image holographic encryption method and system based on controllable Lyapunov index

Abstract

The invention relates to the technical field of information security and digital image processing, in particular to an image holographic encryption method and system based on controllable Lyapunov index chaotic mapping. In the encryption method, a plurality of original images are fused into a single digital hologram by using an improved Gerchberg-Saxton algorithm and a space division multiplexing technology; through a simulated annealing particle swarm optimization algorithm, adaptively searching an optimal initial parameter according to hologram features, and generating a dynamic key strongly associated with a plaintext; the method comprises the following steps: constructing an improved Logistic embedded sine and cosine mapping chaotic system with a controllable Lyapunov index, and generating a chaotic sequence by using a dynamic key; and performing block adaptive cross-channel scrambling and non-linear diffusion based on a semi-tensor product on the hologram by using the chaotic sequence to obtain a final ciphertext. According to the method, the problems of capacity limitation and key management in multi-image encryption are effectively solved, and the method has extremely high differential attack resistance, noise resistance and shearing attack resistance.

Description

Technical Field

[0001] This invention relates to the fields of information security and digital image processing technology, specifically to a method and system for image holographic encryption based on controllable Lyapunov exponential chaotic mapping. Background Technology

[0002] With the deep penetration of digital technology into various key technological fields, digital images have become a core carrier of information transmission and interaction. However, the security flaws of the open network environment have led to serious risks to image data, such as tampering, theft, and copyright infringement. Ensuring the confidentiality, integrity, and anti-interference capabilities of multiple images during transmission and storage has become a core need that urgently needs to be addressed in the field of information security.

[0003] While traditional text encryption algorithms are mature in the field of data encryption, the inherent characteristics of digital images—such as massive data volume, high redundancy, and strong correlation between adjacent pixels—often lead to inefficiencies and easy leakage of contour information when directly applied to image encryption, making it difficult to meet the requirements of real-time performance and high security. In contrast, image encryption technology based on chaos theory, due to its extreme sensitivity to initial conditions and control parameters, pseudo-randomness, ergodicity, and non-periodicity, naturally aligns with the confusion and diffusion principles of cryptography, thus becoming the mainstream direction of image encryption research in recent years.

[0004] Despite significant progress in chaotic image encryption technology, existing solutions still face numerous limitations in practical applications. First, regarding chaotic system models, low-dimensional chaotic systems (such as Logistic and Sine maps) have simple structures but narrow chaotic intervals, uneven trajectory distribution, and small key spaces, making them vulnerable to cracking methods like phase space reconstruction or parameter identification. While existing high-dimensional or coupled chaotic systems increase complexity, they often lack precise control over dynamic behavior (such as Lyapunov exponents), making it difficult to flexibly adjust the system's chaos strength according to security requirements. Second, in terms of encryption architecture, traditional "scramble-diffusion" structures often employ linear diffusion methods based on XOR operations, which are not only vulnerable to chosen-plaintext attacks but also lack sufficient avalanche effects against differential attacks. Furthermore, existing key generation mechanisms are mostly static or random, lacking strong correlation with plaintext image features; once the key is leaked, system security will be significantly compromised.

[0005] On the other hand, with the advent of the big data era, single-image encryption is no longer sufficient to meet the transmission needs of massive amounts of data. Optical holographic encryption technology, with its advantages of high parallelism, multi-dimensionality, and large capacity, provides a new solution for multi-image encryption. However, how to efficiently and losslessly fuse multiple images into a single hologram, solve the security risks caused by the linear characteristics of the optical system itself, and how to deeply and efficiently combine optical holographic technology with digital chaotic encryption to achieve both high capacity and high security remain current research challenges.

[0006] In summary, developing a novel multi-image holographic encryption method that integrates the high capacity advantage of holographic technology with the high security of controllable chaos, possesses a dynamic key mechanism with plaintext association, and can effectively resist various attacks such as differential, shearing, and noise, has significant theoretical and practical application value. Summary of the Invention

[0007] To address the technical problems of limited capacity, uncontrollable Lyapunov exponents in chaotic systems, weak correlation between keys and plaintext, incomplete scrambling diffusion, and insufficient resistance to attacks in existing multi-image encryption methods, this invention provides an image holographic encryption method based on controllable Lyapunov exponent chaotic mapping. Based on this encryption method, this invention also provides an image holographic encryption system based on controllable Lyapunov exponent chaotic mapping.

[0008] To achieve the above objectives, the present invention provides the following technical solution: The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping includes the following encryption steps: S1. The Gerchberg-Saxton algorithm is used to convert multiple images to be encrypted into downsampled pure phase holograms, which are then fused into a joint pure phase hologram. S2. Extract feature image blocks from the joint pure phase hologram, and use a particle swarm optimization algorithm combined with simulated annealing, with the evaluation index of the encrypted image as the fitness function, to adaptively search for the optimal chaotic system parameters as the dynamic key. S3. Input the dynamic key into the improved Logistic embedded sine and cosine map chaotic system to iteratively generate a chaotic sequence; the improved Logistic embedded sine and cosine map chaotic system achieves controllable adjustment of the Lyapunov exponent by introducing a dynamic exponent term; S4. Use chaotic sequences to perform block-adaptive cross-channel scrambling on the joint pure phase hologram to destroy the local, global and inter-channel correlations of the image; S5. Construct a key matrix using chaotic sequences, and perform a nonlinear diffusion operation based on half-tensor product on the scrambled image to generate a ciphertext image.

[0009] As a further improvement to the above scheme, the iterative rule for the improved Logistic embedding sine / cosine map chaotic system is as follows: When the number of iterations n is odd: ; When the number of iterations n is even: ; In the formula, x n y n z n Let x and x represent the dimensional state values ​​of the chaotic system at the nth iteration. n+1 y n+1 z n+1 denoted as c1, c2, and c3 respectively, representing the dimensional state values ​​of the chaotic system at the (n+1)th iteration; μ, c1, c2, and c3 are all system control parameters; k is the Lyapunov exponential master control parameter; sin(·) is the sine function; cos(·) is the cosine function; π is pi; e is the exponential function with the natural constant as the base; and mod(·) is the modulo function.

[0010] As a further improvement to the above scheme, the process for obtaining the joint pure phase hologram is as follows: S11. For each image to be encrypted, separate it into three independent color channel data layers: red, green, and blue. S12. For each color channel data layer, execute the Gerchberg-Saxton algorithm based on adaptive constraints to iteratively generate the corresponding single-channel downsampled pure phase hologram. S13. All single-channel downsampled pure phase holograms generated from all images to be encrypted are filled into the corresponding color channels and spatial quadrants of a joint hologram according to a preset mapping rule, thereby synthesizing a joint pure phase hologram. The mapping rule is as follows: each color channel plane of the joint hologram is pre-divided into a matrix region of P rows × Q columns, and downsampled pure phase holograms from different images to be encrypted but belonging to the same color channel are placed into the specified matrix region one by one.

[0011] As a further improvement to the above scheme, the adaptive constraint is expressed as follows: in each iteration, the amplitude of the object plane signal region is updated according to a dynamic constraint factor α that decreases linearly with the number of iterations. ; ; In the formula, α init is the initial constraint factor; e is an exponential function with the natural constant as the base; n represents the iteration number; A0 represents the amplitude of the target image; A x,nA represents the amplitude of the signal region in the object plane at the nth iteration; x,n-1 represents the amplitude of the signal region in the object plane at the (n-1)th iteration; |·| represents the absolute value.

[0012] As a further improvement to the above scheme, the process of obtaining the dynamic key is as follows: S21. Extract a feature block of a set size from the center of the joint pure phase hologram as input; S22. Taking the encryption effect of the feature block as the optimization goal, a particle swarm optimization algorithm combined with simulated annealing is adopted to search for a set of optimal chaotic system parameters in the parameter space of the chaotic system, and the optimal chaotic system parameters are used as the dynamic key of the joint pure phase hologram.

[0013] As a further improvement to the above scheme, the process of obtaining the chaotic sequence is as follows: S31. Input the dynamic key into the improved Logistic embedded sine and cosine map chaotic system to drive the chaotic system to iterate; S32. Based on the iterative rules of the chaotic system, the chaotic system is switched and iterated according to the parity of the number of iterations to generate a chaotic sequence of dynamic keys.

[0014] As a further improvement to the above scheme: the chaotic sequence is quantized and mapped into a row index sequence, column index sequence, and value parameter sequence that meet the requirements of subsequent encryption operations; ; In the formula, x i y i z i Let x, y, and z represent the i-th elements of the chaotic sequences respectively; P is the total number of rows in the target image; Q is the total number of columns in the target image; floor(·) is the floor function; row i ,col i val i They represent x respectively i y i z i The corresponding row index sequence, column index sequence, and value parameter sequence are divided into the row index sequence, column index sequence, and value parameter sequence.

[0015] As a further improvement to the above scheme, the specific steps of block-based adaptive cross-channel scrambling are as follows: S41. Divide the joint pure phase hologram into multiple non-overlapping image blocks; S42. For each image block, perform the following operations in sequence: a. Spatial scrambling: For the current image block, extract subsequences of corresponding length from the row index sequence and column index sequence obtained through chaotic sequence mapping, sort the subsequences in ascending order, obtain the row scrambling index and column scrambling index dedicated to the current image block, and use these two indices to rearrange the pixel positions of the red, green and blue color channels in the current image block simultaneously. b. Cross-channel scrambling: For the current image block, a shift number is generated based on the chaotic sequence, and the color channel order of the current image block after spatial scrambling is cyclically shifted according to the shift number; S43. Merge the data of all image blocks in the joint pure phase hologram that have undergone spatial scrambling and cross-channel scrambling into a one-dimensional vector. Rearrange the one-dimensional vector as a whole based on the global scrambling index generated by the chaotic sequence, and reshape it into a scrambled image with the same size as the joint pure phase hologram.

[0016] As a further improvement to the above scheme, the process of generating the encrypted image is as follows: S51. Extract values ​​from the value parameter sequence and reshape them into a square matrix R. Perform an invertibility test on the square matrix R. If it is not invertible, discard the current square matrix and extract values ​​again until an invertible key matrix is ​​generated. S52. Perform a semi-tensor product operation on each color channel data of the scrambled image with the invertible key matrix to obtain the quotient matrix and remainder matrix for each color channel; the formula for the semi-tensor product operation is as follows: ; ; in, Represents a semi-tensor product operation; P R P G P B These represent the red, green, and blue color channel data of the scrambled image, respectively; C R C G C B K represents the remainder matrices for the red, green, and blue color channels of the scrambled image, respectively; R K G K B These represent the quotient matrices of the red, green, and blue color channels of the scrambled image, respectively. S53. Retain the quotient matrix of each color channel as the decryption private key for the current encryption process; merge the remainder matrices of each color channel to generate the ciphertext image corresponding to the joint pure phase hologram.

[0017] This invention also provides a controllable Lyapunov exponential chaotic mapping-based image holographic encryption system for implementing the above-mentioned controllable Lyapunov exponential chaotic mapping-based image holographic encryption method, comprising: The image preprocessing and holographic fusion module is used to execute the Gerchberg-Saxton algorithm with adaptive constraints, convert multiple images to be encrypted into downsampled pure phase holograms, and fuse them into a joint pure phase hologram. An adaptive key generation module is used to extract feature blocks from the joint pure phase hologram, run a particle swarm optimization algorithm combined with simulated annealing, and obtain the optimal chaotic system parameters with the best encryption effect through iterative calculation. The optimal chaotic system parameters are then used as the dynamic key for the joint pure phase hologram. The chaotic sequence generation module has a built-in improved Logistic embedded sine and cosine map chaotic system, which is used to receive dynamic keys, generate multiple sets of chaotic sequences with controllable Lyapunov exponents through fractional or integer order iterative equations, and perform quantization processing. The encryption operation module includes a scrambling unit and a diffusion unit. The scrambling unit is configured to perform cross-channel scrambling, including intra-block row and column rearrangement, channel cyclic shift based on chaotic values, and global scrambling. The diffusion unit is configured to generate a reversible key matrix and perform a semi-tensor product nonlinear operation between the image matrix and the reversible key matrix. The control and output module is used to coordinate the data flow between modules, store the private key required for decryption, and output the final synthesized ciphertext image.

[0018] Compared with the prior art, the beneficial effects of the present invention are: This invention addresses the technical problems of existing multi-image encryption through a complete technical chain of "multi-image holographic fusion - plaintext-associated dynamic key - controllable chaotic sequence generation - cross-channel scrambling - nonlinear diffusion," specifically implemented as follows: First, addressing the "capacity limitation" problem, this invention utilizes the Gerchberg-Saxton algorithm to convert multiple images to be encrypted into downsampled pure phase holograms, which are then fused into a single joint pure phase hologram. By leveraging the high capacity of holographic technology and the efficient use of space in downsampling processing, batch encryption of multiple images is achieved, breaking through the efficiency bottleneck and capacity limitation of single-image encryption. It eliminates the need for simple stitching or channel multiplexing, significantly improving the storage and transmission efficiency of multi-image encryption.

[0019] Secondly, addressing the problem of "uncontrollable Lyapunov exponents in chaotic systems," this invention employs an improved Logistic embedded sine and cosine mapping chaotic system. By introducing a core design with dynamic exponent terms, the Lyapunov exponents of the system can be precisely adjusted. This overcomes the shortcomings of insufficient complexity in low-dimensional chaotic systems and solves the problem of uncontrollable dynamic characteristics in traditional high-dimensional chaotic systems. The chaos intensity can be flexibly adjusted according to security requirements, thereby improving the flexibility and security of the encryption system.

[0020] Furthermore, to address the issue of "weak correlation between key and plaintext," this invention constructs a dynamic key generation mechanism that correlates plaintext: feature image blocks are extracted from a joint pure phase hologram that fuses multiple plaintext images (images to be encrypted). Using the evaluation index of the encrypted image as the fitness function, the optimal chaotic system parameters are adaptively searched using a particle swarm optimization algorithm combined with simulated annealing as the dynamic key. This ensures that key generation is deeply bound to the features of the plaintext image, rather than being statically preset or randomly generated. This fundamentally improves the ability to resist chosen-plaintext attacks and avoids the risk of system failure due to key leakage.

[0021] Then, addressing the problem of "incomplete scrambling diffusion," this invention achieves a breakthrough through two core design steps: First, it utilizes chaotic sequences to perform block-based adaptive cross-channel scrambling, no longer limited to pixel rearrangement in a single spatial dimension, but simultaneously destroying the local, global, and inter-channel correlations of the image, resulting in a more thorough scrambling effect; Second, it constructs a key matrix based on chaotic sequences and employs a nonlinear diffusion operation of semi-tensor product to replace the traditional linear diffusion method, significantly enhancing the avalanche effect of the encryption process, ensuring that changes in a single pixel can trigger significant changes in the ciphertext, and completely breaking the pixel value correlation of the original image.

[0022] Finally, addressing the issue of "insufficient resistance to attacks," the aforementioned technical solutions form a synergistic protective effect: the controllable Lyapunov exponent chaotic system enhances the pseudo-randomness and complexity of chaotic sequences, resisting cracking methods such as phase space reconstruction; the plaintext-associative dynamic key enhances the resistance to chosen-plaintext attacks; block-adaptive cross-channel scrambling destroys the statistical characteristics of images, resisting statistical analysis attacks; and the semi-tensor product nonlinear diffusion strengthens the avalanche effect, resisting differential attacks. The synergy of multiple technologies significantly improves the overall anti-attack performance of the encryption system, ensuring the security of ciphertext during transmission and storage. Attached Figure Description

[0023] Figure 1 This is a general framework diagram of the encryption and decryption scheme in this invention.

[0024] Figure 2 This is the Lyapunov exponent spectrum of a chaotic system as a function of parameter k.

[0025] Figure 3 This is the Lyapunov exponent spectrum of a chaotic system as a function of parameter μ.

[0026] Figure 4 This is the Lyapunov exponent spectrum of the chaotic system as a function of parameter c1.

[0027] Figure 5 This is the Lyapunov exponent spectrum of the chaotic system as a function of parameter c2.

[0028] Figure 6This is the Lyapunov exponent spectrum of the chaotic system as a function of parameter c3.

[0029] Figure 7 Let be the sample entropy of the chaotic system as a function of two parameters.

[0030] Figure 8 These are the four images to be encrypted used in this embodiment of the invention.

[0031] Figure 9 This is a joint pure phase hologram generated in an embodiment of the present invention.

[0032] Figure 10 For example, when performing performance tests Figure 8 The pixel distribution map of the first image to be encrypted.

[0033] Figure 11 For performance testing of the example Figure 8 The pixel distribution map of the second image to be encrypted.

[0034] Figure 12 For example, when performing performance tests Figure 8 The pixel distribution of the third image to be encrypted.

[0035] Figure 13 For example, when performing performance tests Figure 8 The pixel distribution of the fourth image to be encrypted.

[0036] Figure 14 This is a pixel distribution diagram of the encrypted image during performance testing of an example.

[0037] Figure 15 This is a pixel correlation analysis diagram of a plaintext image in the horizontal direction during performance testing of an example.

[0038] Figure 16 This is a pixel correlation analysis diagram of a plaintext image in the vertical direction during performance testing as an example.

[0039] Figure 17 This is a pixel correlation analysis diagram of a plaintext image in the diagonal direction during performance testing as an example.

[0040] Figure 18 This is a pixel correlation analysis diagram of the encrypted image in the horizontal direction during performance testing of an example.

[0041] Figure 19 This is a pixel correlation analysis diagram of the encrypted image in the vertical direction during performance testing of an example.

[0042] Figure 20 This is a pixel correlation analysis diagram of the encrypted image in the diagonal direction during performance testing as an example.

[0043] Figure 21 These are encrypted images with different cropping ratios in the embodiments.

[0044] Figure 22 for Figure 21 The decrypted image generated after decryption.

[0045] Figure 23 This is a diagram showing the decryption result of a salt-and-pepper noise attack.

[0046] Figure 24 This is a diagram showing the decryption result of a Gaussian noise attack. Detailed Implementation

[0047] 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.

[0048] Please see Figure 1 This invention discloses a controllable Lyapunov exponential chaotic mapping image holographic encryption method. The core of this method is an integrated technical solution that addresses the problems of limited capacity, poor controllability of the chaotic system, weak key correlation, incomplete scrambling and diffusion, and insufficient anti-attack capability in existing multi-image encryption methods. This solution involves "multi-image holographic fusion - plaintext-associated dynamic key generation - controllable chaotic sequence driving - block-adaptive cross-channel scrambling - semi-tensor product nonlinear diffusion". First, the invention uses the Gerchberg-Saxton algorithm to convert multiple images to be encrypted into downsampled pure phase holograms and fuse them into a joint hologram. Then, feature blocks are extracted from the joint hologram. The optimal chaotic system parameters are adaptively searched using a particle swarm optimization algorithm combined with simulated annealing as the dynamic key. Subsequently, the dynamic key is input into an improved Logistic embedding sine and cosine mapping chaotic system (with Lyapunov exponent controllable through a dynamic exponential term) to generate a chaotic sequence. This chaotic sequence is then used to sequentially complete the block-adaptive cross-channel scrambling of the joint hologram and the nonlinear diffusion based on the semi-tensor product, ultimately generating a highly secure and robust encrypted image.

[0049] I. Improved Logistic Embedded Sine and Cosine Mapping Chaotic Systems

[0050] The range of the Lyapunov exponent and the range of chaotic sequence values ​​of the chaotic system can be adjusted by setting the parameters of the chaotic system, and the adjustment is made according to the parity of the iteration number n in the iteration rule.

[0051] The iterative rules for the improved Logistic embedding sine / cosine map chaotic system are as follows: When the number of iterations n is odd: ; When the number of iterations n is even: ; In the formula, x n y n z n Let x and x represent the dimensional state values ​​of the chaotic system at the nth iteration. n+1 y n+1 z n+1 Let sin(·) represent the dimensional state value of the chaotic system at the (n+1)th iteration. sin(·) is the sine function; cos(·) is the cosine function; π is pi; e is the exponential function with the natural constant as the base; and mod(·) is the modulo function.

[0052] μ, c1, c2, and c3 are all system control parameters that can be used to fine-tune and adjust the dynamic behavior of chaotic systems.

[0053] k is the master control parameter of the Lyapunov exponent, which is used to directly regulate the overall level of the Lyapunov exponent (LE) and achieve master control over the chaos intensity of the system.

[0054] The Lyapunov exponents are key indicators for measuring the sensitivity of a dynamical system to initial conditions and are also important criteria for determining whether a system has entered a chaotic state. A positive Lyapunov exponent means that the system trajectory separates exponentially with time in phase space, thus exhibiting chaotic characteristics. The three Lyapunov exponents of this chaotic system can be calculated as follows: ; In the formula, LE x LE y LE z These represent the Lyapunov exponents in the x, y, and z dimensions of a chaotic system, respectively, and are used to measure the degree of divergence / chaos in the three state dimensions of the chaotic system.

[0055] N is the total number of iterations of the chaotic system, and n is the iteration index (traversing each iteration). When N approaches infinity, the long-term chaotic intensity of the system is obtained by averaging the results of N iterations.

[0056] Here, s(n) is similar to a sign function, defined as s(n) = 1 when n is odd and -1 when n is even. This indicates that when k is sufficiently large, all three Lyapunov exponents of the chaotic system tend towards the value of parameter k. This means that by adjusting parameter k, the overall level of the system's Lyapunov exponents can be directly and effectively set.

[0057] xn y n z n These represent the state variables of the chaotic system at the nth iteration, corresponding to the values ​​of the chaotic system in the x, y, and z dimensions at the nth step. They are dynamic variables generated by the iteration of the chaotic system.

[0058] The initial value (x1,y1,z1)=(0.1,0.2,0.3) and the parameter (μ,c1,c2,c3)=(5,2,7,3) can be set. By adjusting the value of k, the overall level of the system LE can be controlled and its performance can be tested.

[0059] To verify the chaotic performance of the chaotic system, the following performance tests (Lyapunov exponent analysis and sample entropy analysis) were conducted, which verified the superior chaotic performance of the chaotic system developed in this invention.

[0060] Lyapunov exponent analysis: The Lyapunov exponent reflects the chaotic performance of a system; the larger the value, the better the chaotic performance. For example... Figures 2-6 The figure shows the Lyapunov exponent spectrum of the chaotic system developed in this invention as a function of parameters k, μ, c1, c2, and c3. Figures 2-6 It can be seen that after the value of k increases to a certain extent, the Lyapunov exponent of the chaotic system is almost the same as that of k. When k is constant, the other parameters have limited influence on the Lyapunov exponent of the chaotic system.

[0061] Sample entropy analysis: Sample entropy (SE) assesses the complexity of a time series by measuring the probability of new patterns emerging. Generally, a higher sample entropy indicates a more complex structure and greater unpredictability in the time series, corresponding to superior chaotic performance in the chaotic system. Figure 7 The figure shows the sample entropy of the chaotic system developed in this invention as a function of two parameters (k, μ). Figure 7 It can be seen that, within a large parameter range, the chaotic system developed in this invention has a large sample entropy.

[0062] II. Encryption Method

[0063] (a) Image preprocessing

[0064] The core of this section is the use of spatial segmentation multiplexing technology and the Gerchberg-Saxton algorithm with adaptive constraints. First, multiple images to be encrypted are converted into downsampled pure phase holograms. Then, these holograms are fused into a joint pure phase hologram through specific multiplexing logic, achieving efficient integration of multiple images and laying the foundation for subsequent encryption operations.

[0065] 1. Obtain the color channel data layer

[0066] For each image to be encrypted, it is first separated into three independent color channel data layers: red (R), green (G), and blue (B), so that the information of each color channel can become a basic data unit that can be processed independently, providing support for the subsequent generation of sub-channel holograms.

[0067] 2. Generate a single-channel downsampled pure phase hologram

[0068] Each independent color channel data layer in multiple original images to be encrypted is placed in the central signal region, with zeros filling the surrounding area as the background region, and the initial phase is set as a quadratic phase function approximated by discrete plane waves.

[0069] For each independent color channel data layer, the Gerchberg-Saxton algorithm based on adaptive constraints is executed. Through iterative optimization of Fourier transform and inverse transform operations, after iterating to a preset number of times, a 1 / 4 region of the phase center of the holographic plane is extracted to generate a single-channel downsampled pure phase hologram (POH) corresponding to that channel, ensuring that the image information of each channel can be efficiently encoded into holographic form.

[0070] In the nth iteration, the complex amplitude of the holographic plane is propagated to the object plane via inverse Fourier transform, preserving phase information. An adaptive constraint is applied to the object plane amplitude: in each iteration, the amplitude of the signal region on the object plane is updated according to a dynamic constraint factor α that decreases linearly with the iteration number. ; ; ; In the formula, α init is the initial constraint factor; e is an exponential function with the natural constant as the base; n represents the number of iterations; A0 represents the amplitude of the target image. x,n A represents the amplitude of the signal region in the object plane at the nth iteration; x,n-1 This represents the amplitude of the signal region in the object plane at the (n-1)th iteration. |·| represents the absolute value. A b,n A represents the amplitude of the background region on the object plane at the nth iteration; b,n-1 This represents the amplitude of the background region of the object plane during the (n-1)th iteration.

[0071] 3. Generate a joint pure phase hologram

[0072] The spatial segmentation multiplexing technique is used to achieve multi-image fusion. First, each color channel plane of the joint hologram is pre-divided into a matrix region of P rows × Q columns (2 rows × 2 columns in this embodiment). Then, according to the preset mapping rules, all single-channel downsampled pure phase holograms generated from all images to be encrypted are filled into the designated matrix region of the corresponding color channel of the joint hologram. Finally, a joint pure phase hologram integrating the information of each color channel of multiple images is synthesized, realizing efficient compression and unified carrying of multi-image information.

[0073] (ii) Obtaining the dynamic key

[0074] The core of this section is to construct a key mechanism strongly correlated with the plaintext, which is implemented as follows: A feature image patch of a set size is extracted from the center of a joint pure phase hologram integrating information from multiple images to be encrypted. A fitness function is constructed using the peak signal-to-noise ratio (PSNR) and information entropy of the encrypted image as evaluation metrics (the objective is to minimize PSNR and maximize information entropy). A particle swarm optimization algorithm combined with simulated annealing is used to map each particle to a set of chaotic system parameters. The particle velocity and position are iteratively updated, and the simulated annealing mechanism is used to accept inferior solutions to avoid local optima. Finally, the optimal parameter combination for encryption is adaptively searched in the chaotic system parameter space and used as a dynamic key to provide a secure initial input that is deeply bound to the plaintext for subsequent chaotic sequence generation.

[0075] 1. Obtain feature blocks

[0076] From the center of the joint pure phase hologram that integrates information from multiple images to be encrypted, a feature block of size 100×100 is extracted as the algorithm input. At the same time, the particle swarm population is initialized, and basic parameters such as population size and number of iterations are set.

[0077] 2. Define particle states

[0078] Each particle corresponds to a complete set of chaotic system parameters, specifically (x1, y1, z1, μ, k, c1, c2, c3), where x1, y1, and z1 are the initial state values ​​of the improved Logistic embedded sine and cosine map chaotic system, μ, c1, c2, and c3 are the system control parameters, and k is the Lyapunov exponential master control parameter.

[0079] 3. Construct the fitness function

[0080] Define the fitness function F(p) = ω1 PSNR(P)+ω2 H(P), where PSNR(P) is the peak signal-to-noise ratio of the feature block after encryption with the parameters corresponding to the current particle, H(P) is the information entropy of the encrypted feature block, and ω1 and ω2 are weight coefficients that satisfy ω1+ω2=1; the function optimization objective is to find the parameter combination that minimizes PSNR(P) and maximizes H(P) to ensure the optimal encryption effect.

[0081] 4. Update particle velocity and position

[0082] The particle state is updated iteratively according to the following formula: ; In the formula, v i x is the particle velocity of the i-th particle; i w represents the position of the i-th particle. i Let be the inertial weight of the i-th particle; , For learning factors; , pbest generates random numbers in the interval [0,1]. i is the historical best solution for the i-th particle, and gbest is the current global best solution for the entire population; the superscript t is the current iteration number.

[0083] 5. Introduce simulated annealing mechanism to optimize the search process.

[0084] Calculate the difference Δf between the fitness of the particle at its new position and its historical best fitness; if the difference Δf is greater than 0, the new surface parameter refinement effect is better, then update pbest. i The current new position is used; conversely, if the encryption effect of the new surface parameters is poor, the acceptance probability P is calculated. accept= exp(Δf / T cur If the random number in the interval [0,1] is less than P accept If so, then accept the inferior solution to avoid getting trapped in a local optimum; where T cur The current temperature is T, and the value increases with the number of iterations. cur =T start exp(-(t / iter) log(T start / T end )) Attenuation, T start Let T be the initial temperature. end The termination temperature is given by t, the current iteration number is given by iter, the total iteration number is given by exp, and exp represents an exponential function with the natural constant as the base.

[0085] 6. Iteration Termination and Key Determination

[0086] When the number of iterations reaches the preset total number or the fitness function value converges, the search stops, and the final global optimal solution (the optimal combination of chaotic system parameters corresponding to the optimal particle) is used as a dynamic key to provide initial input strongly correlated with the plaintext for the subsequent generation of chaotic sequences.

[0087] (III) Generation of Chaotic Series

[0088] The core of this section is the generation of controllable and highly complex chaotic sequences based on a dynamic key strongly correlated with the plaintext. Specifically, the dynamic key is input into an improved Logistic model embedded in a sine-cosine mapping chaotic system. The iteration rule is switched according to the parity of the iteration number n (state updates are achieved through sine / cosine functions, natural exponent terms, and modulo operations). The Lyapunov exponent is precisely controllable by designing the core parameter k and the dynamic exponent term. Finally, three sets of three-dimensional chaotic sequences are generated. These sequences are then quantized and mapped into row index sequences, column index sequences, and value parameter sequences that meet the requirements of subsequent encryption. This provides core parameter support with high pseudo-randomness for subsequent scrambling and diffusion operations.

[0089] 1. Enter the dynamic key

[0090] The obtained dynamic key is fully input into the improved Logistic embedded sine and cosine map chaotic system. The optimal parameters strongly correlated with the plaintext drive the chaotic system to start the iteration. The core parameter k is used as the main control parameter of the Lyapunov exponent. Combined with the built-in dynamic exponent term of the system, the intensity of chaos can be precisely and controllably adjusted.

[0091] 2. Iterative operation

[0092] Strictly adhering to the iteration rules of chaotic systems, the operational logic is dynamically switched based on the parity of the iteration number n: when n is odd, the operation is performed according to the condition containing... , , The exponential term and the corresponding sine / cosine function combination formula are used for calculation; when n is even, it is calculated according to the formula containing... , , The exponential term and the corresponding sine / cosine function combination formula are calculated. All iteration results are constrained in the interval [0,1) by mod(·) modulo operation. Finally, three sets of three-dimensional chaotic sequences (x sequence, y sequence, z sequence) with high pseudo-randomness and high complexity are generated, which provide core parameter support for subsequent scrambling and diffusion operations.

[0093] 3. Quantification

[0094] The chaotic sequence is quantized and mapped into a row index sequence, column index sequence, and value parameter sequence that meet the requirements of subsequent encryption operations; ; In the formula, x i y i z i Let x, y, and z represent the i-th elements of the chaotic sequences respectively; P is the total number of rows in the target image; Q is the total number of columns in the target image; floor(·) is the floor function; row i ,col i val i They represent x respectively i y i z i The corresponding row index sequence, column index sequence, and value parameter sequence are divided into the row index sequence, column index sequence, and value parameter sequence.

[0095] (iv) Disorder

[0096] The core of this section is to utilize the generated and quantized row index sequence, column index sequence, and value parameter sequence to thoroughly destroy the local, global, and inter-channel correlations of the joint pure phase hologram through multi-layer scrambling operations. Specifically, the joint pure phase hologram is first divided into multiple non-overlapping image blocks. For each image block, the corresponding subsequence is extracted from the row and column index sequences and sorted to obtain a dedicated scrambling index to rearrange the red, green, and blue channel pixels within the block (spatial scrambling). Then, a shift number is generated based on the value parameter sequence to cyclically shift the channel order (cross-channel scrambling). Finally, all processed image blocks are merged into a one-dimensional vector, which is then rearranged using a global scrambling index and reshaped into a scrambled image with the same size as the original joint pure phase hologram.

[0097] 1. Obtain the standard block

[0098] The joint pure phase hologram is divided into multiple non-overlapping standard blocks of size B×B. If the image size is not an integer multiple of B, zero padding is performed.

[0099] 2. To scramble

[0100] For each image block, perform the following operations in sequence: a. Spatial scrambling: For the current image block, extract subsequences of corresponding length from the row index sequence and column index sequence obtained through chaotic sequence mapping, sort the subsequences in ascending order, obtain the row scrambling index and column scrambling index dedicated to the current image block, and use these two indices to rearrange the pixel positions of the red (R), green (G), and blue (B) color channels in the current image block simultaneously.

[0101] b. Cross-channel scrambling: For the current image block, a shift number K is generated based on the chaotic sequence, and the color channel order of the spatially scrambled current image block is cyclically shifted according to this shift number. Specifically, if K=1, the channel order changes from (R,G,B) to (B,R,G); if K=2, the channel order changes to (G,B,R); if K=0, it remains unchanged.

[0102]

[0103] In the formula, Sshift(i) represents the i-th shift-related chaotic sequence element, which is obtained by quantization of the generated three-dimensional chaotic sequence. It is a decimal between 0 and 1 and serves as the parameter source data for the i-th scrambling unit.

[0104] 3. Generate a scrambled image

[0105] The data of all image blocks in the joint pure phase hologram that have undergone spatial scrambling and cross-channel scrambling are merged into a one-dimensional vector. The global scrambling index generated based on the chaotic sequence is used to rearrange the one-dimensional vector as a whole and reshape it into a scrambled image with the same size as the joint pure phase hologram.

[0106] (v) Generate ciphertext image

[0107] The core of this section is to enhance encryption security through nonlinear diffusion operations. Specifically, this is achieved by first extracting values ​​from the quantized parameter sequence and reshaping them into a square matrix, then determining the invertible key matrix R after a reversibility check (ensuring decryption feasibility); then... R ), green (P) G ), Blue (P) B The three channels of data are used to perform semi-tensor product operations with the invertible key matrix R. The quotient matrix (K) for each channel is obtained by floor((·) / 256) and mod(·,256). R K G K B ) and remainder matrix (C R C G C B Finally, the quotient matrix is ​​retained as the decryption private key, and all remainder matrices are merged to generate a ciphertext image that integrates multiple image encryption information and has high resistance to attacks.

[0108] 1. Generate an invertible key matrix

[0109] Extract values ​​from the parameter sequence and reshape them into a square matrix R. Then, check the invertibility of the square matrix R. If it is not invertible, discard the current square matrix and extract values ​​again until an invertible key matrix is ​​generated.

[0110] 2. Semi-tensor product operation

[0111] The scrambled image's color channel data is subjected to a semi-tensor product operation with the invertible key matrix to obtain the quotient matrix and remainder matrix for each color channel; the formula for the semi-tensor product operation is as follows: ; ; in, Represents a semi-tensor product operation; P R P G P B These represent the red, green, and blue color channel data of the scrambled image, respectively; C R C G C B K represents the remainder matrices for the red, green, and blue color channels of the scrambled image, respectively; R K G K B These represent the quotient matrices of the red, green, and blue color channels of the scrambled image, respectively.

[0112] The diffusion operation of semi-tensor product is a strongly nonlinear operation, which gives the ciphertext an excellent avalanche effect. Even when faced with 50% area occlusion or strong noise interference, it can still clearly reconstruct the original image information.

[0113] 3. Encrypted Image

[0114] The quotient matrix of each color channel is retained as the decryption private key for the current encryption process; the remainder matrices of each color channel are merged to generate the ciphertext image corresponding to the joint pure phase hologram.

[0115] III. Decryption Method

[0116] This section describes the inverse operation of the encryption process. The core principle is to rely on a dynamic key strongly associated with the plaintext and a decryption private key to gradually reverse the encryption process and recover the original image. Specifically, the following steps are implemented: First, the ciphertext image and the quotient matrix retained during encryption are obtained as the decryption private key. Combined with the same dynamic key used in the encryption stage (including the initial state and control parameters of the chaotic system), an improved Logistic embedding sine / cosine mapping chaotic system is driven to generate a three-dimensional chaotic sequence consistent with that used during encryption. Then, this chaotic sequence is used to reverse the block-adaptive cross-channel scrambling operation, sequentially completing the global... The process involves scrambling and reordering, cross-channel cyclic shifting and restoration, and intra-block pixel reordering to recover the joint pure phase hologram before scrambling. Then, through the inverse operation of the semi-tensor product, the remainder matrix and quotient matrix corresponding to the ciphertext are combined to restore the hologram data of each color channel. Finally, the joint pure phase hologram is split according to the preset spatial segmentation and reuse rules to obtain the single-channel downsampled pure phase hologram of each image to be encrypted. The original data of each channel is restored by the inverse iteration of the improved Gerchberg-Saxton algorithm. After merging the red, green and blue channels, multiple original images to be encrypted are output.

[0117] (I) Key Reconstruction and De-diffusion

[0118] Using the known dynamic key and system parameters, iteratively generate the same chaotic sequence using the improved Logistic embedding sine / cosine map chaotic system. Construct a key matrix R consistent with the encryption phase, combined with the decryption private key K. R K G K B Combine the ciphertext with the inverse half-tensor product operation to restore the pixel values ​​of each channel of the scrambled image.

[0119] (ii) Reverse block adaptive scrambling

[0120] The one-dimensional pixel vector is restored to a three-dimensional matrix by applying the inverse index of the global rearranged index. The color channel order of each image patch is restored using the negative operation of the shift bit K. The original pixel positions within each image patch are recovered using the inverse operation of the row and column scrambled indexes.

[0121] (III) Disassembly and Zero-filling of Joint Holograms

[0122] According to the spatial segmentation and multiplexing rules, each downsampled pure phase hologram is segmented from the restored joint hologram. Each downsampled pure phase hologram is then centrally padded with zeros to restore its size from 1 / 4 to the original holographic plane size.

[0123] (iv) Optical holographic reconstruction

[0124] Perform a Fourier transform (FT) on the zero-padded holographic phase distribution, extract the signal region intensity information from the transformed complex amplitude distribution, and obtain the final plaintext image.

[0125] IV. Experimental Analysis

[0126] To verify the performance of the image encryption and decryption method provided by this invention, the following performance test experiments were designed, and the performance advantages of the image encryption and decryption method provided by this invention were analyzed based on the experimental results.

[0127] (I) Analysis of Simulation Results

[0128] This invention first converts the image into a downsampled pure phase hologram, then stitches multiple downsampled pure phase holograms together into a joint pure phase hologram, and finally encrypts and decrypts the stitched joint pure phase hologram. For example... Figure 8 and Figure 9 As shown ( Figure 8 There are four images to be encrypted (plaintext images). Figure 9The chaotic sequence visualization distribution map generated for the chaotic system, after encryption, not only can extract relevant information from the plaintext image, but it can also correctly decrypt the plaintext image, verifying the effectiveness and integrity of the encryption method.

[0129] (II) Histogram Analysis

[0130] An image's histogram reflects the distribution of its pixel values ​​and is a key indicator for evaluating an algorithm's resistance to statistical analysis attacks. Typically, the histogram of a plaintext image is non-uniform and exhibits clear statistical regularities. A high-performance encryption algorithm must be able to flatten this distribution. Figures 10-13 It can be seen that (red represents the red channel, green represents the green channel, and blue represents the blue channel). Figure 8 The pixel distribution of the four images to be encrypted (plaintext images) is uneven, while Figure 14 The uniform pixel distribution of the encrypted image indicates that the algorithm has a good encryption effect.

[0131] (III) Correlation analysis of adjacent pixels

[0132] In plaintext images, due to the local continuity of content, adjacent pixels typically exhibit extremely high correlation, with correlation values ​​very close to 1. A secure encryption algorithm must be able to completely break this inherent correlation, making the values ​​of any adjacent pixels in the ciphertext image tend to be random and independent, with a correlation value close to zero. The correlation between plaintext and ciphertext images in the horizontal, vertical, and diagonal directions is shown below. Figures 15-20 As shown, adjacent pixels in the plaintext image exhibit strong correlation in the horizontal, vertical, and diagonal directions, and can be fitted into a straight line, displaying a linear distribution close to the diagonal on the image. In contrast, the correlation between adjacent pixels in the ciphertext image is close to 0. Therefore, the image encryption method provided in this embodiment can effectively mask the characteristics between adjacent pixels in an image and resist differential attacks.

[0133] Key space analysis.

[0134] A secure encryption algorithm should have a sufficiently large key space to resist any form of brute-force attack. In cryptography, it is generally considered that the key space needs to be greater than 2. 100 This ensures security within the current computing power. In this invention, the key is composed of the control parameters (μ, k, c1, c2, c3) and initial values ​​(x1, y1, z1) of the chaotic system. These parameters are all stored and calculated using double-precision floating-point numbers in a computer, with an effective precision on the order of approximately 10^- ... 16 Therefore, the theoretical key space of this invention can be calculated as follows:

[0135] Because of 2 425 >>2 100 This indicates that the key space of the encryption method of the present invention is large enough to effectively resist any brute-force attack.

[0136] By designing a dynamic exponent term, the Lyapunov exponent is made linearly variable with parameter k, overcoming the limitation of the limited parameter sensitivity range in traditional chaotic systems. This provides significant security flexibility and a key space of up to 2^k. 425 .

[0137] (iv) Robustness Analysis

[0138] During transmission, encrypted images are inevitably subject to channel noise and attacker interference, leading to partial data loss or corruption. A robust encryption system should be able to withstand a certain degree of external attacks and still recover some plaintext information after decryption. The robustness of the proposed encryption scheme will be analyzed below using occlusion attacks and noise attacks.

[0139] 1. Block attack

[0140] Occlusion attacks can simulate data loss that may occur during the transmission of encrypted images. To test the algorithm's resistance to data loss, such as... Figure 21 As shown in sub-images a, b, and c, the encrypted image underwent data cropping of 10%, 25%, and 50%, respectively. From... Figure 21 Corresponding Figure 22 As shown in sub-images a, b, and c, the decrypted image becomes increasingly blurry as the cropping ratio increases, but the main information of the original image can still be effectively identified and extracted. Therefore, this algorithm can effectively resist cropping attacks and has strong robustness.

[0141] 2. Noise attack

[0142] Noise is a common interference during image transmission, which can cause image distortion. To test the noise resistance of this encryption scheme, salt-and-pepper noise and Gaussian noise of different intensities were added to the encrypted image. Salt-and-pepper noise with attack strengths of 5%, 10%, and 15% was added to the encrypted image, and the decrypted image is shown below. Figure 23 Sub-figures a, b, and c are shown in the image. Gaussian noise with attack strengths of 5%, 10%, and 15% is added to the encrypted image, and the decrypted image is shown below. Figure 24 The subgraphs a, b, and c are shown in the diagram. Figure 23 and Figure 24 It can be seen that as the noise intensity increases, the distortion of the decrypted image also intensifies. However, even under high noise intensity, the outline and content of the original image can still be identified. Therefore, this scheme has strong resistance to noise attacks and is highly robust.

[0143] V. Encryption System

[0144] The encryption system is a multi-image security encryption system with "multi-image holographic fusion + plaintext-associated dynamic key + controllable chaotic sequence driving + block-based cross-channel scrambling + nonlinear diffusion" as its core links. Specifically, it achieves efficient and secure encryption through the following steps: First, multiple images to be encrypted are separated into color channels, and a single-channel downsampled pure phase hologram is generated using an adaptively constrained Gerchberg-Saxton algorithm. Then, a joint pure phase hologram is synthesized through spatial segmentation and multiplexing. Subsequently, feature blocks are extracted from this hologram, and a dynamic key strongly correlated with the plaintext is searched using a particle swarm optimization algorithm combined with simulated annealing, with the encryption effect as the goal. Next, this key is input into an improved Logistic embedding sine and cosine mapping chaotic system, and a controllable highly pseudo-random chaotic sequence is generated through parity iteration rules. Then, this sequence is used to perform block-based adaptive cross-channel scrambling on the joint hologram to destroy the correlation of each dimension of the image. Finally, ciphertext is generated through a semi-tensor product nonlinear diffusion operation, and the quotient matrix is ​​retained as the decryption private key. The encryption system specifically addresses the problems of limited capacity, poor controllability of chaotic systems, weak key correlation, incomplete scrambling and diffusion, and insufficient resistance to attacks in existing multi-image encryption. It is suitable for secure transmission and storage of images in key fields such as military communications and medical imaging.

[0145] (I) Image Preprocessing and Holographic Fusion Module

[0146] This algorithm, which incorporates adaptive constraints, is used to convert multiple images to be encrypted into downsampled pure phase holograms and fuse them into a single joint pure phase hologram.

[0147] (ii) Adaptive Key Generation Module

[0148] To extract feature blocks from the joint pure phase hologram, a particle swarm optimization algorithm combined with simulated annealing is run. The optimal chaotic system parameters with the best encryption effect are obtained through iterative calculation, and these optimal chaotic system parameters are used as the dynamic key of the joint pure phase hologram.

[0149] (III) Chaotic Sequence Generation Module

[0150] An improved Logistic embedding sine and cosine map chaotic system is built in, which receives a dynamic key, generates multiple sets of chaotic sequences with controllable Lyapunov exponents through fractional or integer iterative equations, and performs quantization processing.

[0151] (iv) Encryption Calculation Module

[0152] It includes a scrambling unit and a diffusion unit; the scrambling unit is configured to perform cross-channel scrambling, including intra-block row and column rearrangement, channel cyclic shift based on chaotic values, and global scrambling; the diffusion unit is configured to generate an invertible key matrix and perform a half-tensor product nonlinear operation between the image matrix and the invertible key matrix. (v) Control and Output Module It is used to coordinate the data flow of each module, store the private key required for decryption, and output the final synthesized ciphertext image.

[0153] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A holographic encryption method for images based on controllable Lyapunov exponential chaotic mapping, characterized in that, The encryption steps include the following: S1. The Gerchberg-Saxton algorithm is used to convert multiple images to be encrypted into downsampled pure phase holograms, which are then fused into a joint pure phase hologram. S2. Extract feature image blocks from the joint pure phase hologram, and use a particle swarm optimization algorithm combined with simulated annealing, with the evaluation index of the encrypted image as the fitness function, to adaptively search for the optimal chaotic system parameters as the dynamic key. S3. Input the dynamic key into the improved Logistic embedded sine and cosine map chaotic system to iteratively generate a chaotic sequence; the improved Logistic embedded sine and cosine map chaotic system achieves controllable adjustment of the Lyapunov exponent by introducing a dynamic exponent term; S4. Use chaotic sequences to perform block-adaptive cross-channel scrambling on the joint pure phase hologram to destroy the local, global and inter-channel correlations of the image; S5. Construct a key matrix using chaotic sequences, and perform a nonlinear diffusion operation based on half-tensor product on the scrambled image to generate a ciphertext image.

2. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 1, characterized in that, The iterative rules for the improved Logistic embedding sine / cosine map chaotic system are as follows: When the number of iterations n is odd: ； When the number of iterations n is even: ； In the formula, x n y n z n Let x and x represent the dimensional state values ​​of the chaotic system at the nth iteration. n+1 y n+1 z n+1 denoted as c1, c2, and c3 respectively, representing the dimensional state values ​​of the chaotic system at the (n+1)th iteration; μ, c1, c2, and c3 are all system control parameters; k is the Lyapunov exponential master control parameter; sin(·) is the sine function; cos(·) is the cosine function; π is pi; e is the exponential function with the natural constant as the base; and mod(·) is the modulo function.

3. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 2, characterized in that, The specific process for obtaining the joint pure phase hologram is as follows: S11. For each image to be encrypted, separate it into three independent color channel data layers: red, green, and blue. S12. For each color channel data layer, execute the Gerchberg-Saxton algorithm based on adaptive constraints to iteratively generate the corresponding single-channel downsampled pure phase hologram. S13. All single-channel downsampled pure phase holograms generated from all images to be encrypted are filled into the corresponding color channels and spatial quadrants of a joint hologram according to a preset mapping rule, thereby synthesizing a joint pure phase hologram. The mapping rule is as follows: each color channel plane of the joint hologram is pre-divided into a matrix region of P rows × Q columns, and downsampled pure phase holograms from different images to be encrypted but belonging to the same color channel are placed into the specified matrix region one by one.

4. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 3, characterized in that, The adaptive constraint is expressed as follows: in each iteration, the amplitude of the object plane signal region is updated according to a dynamic constraint factor α that decreases linearly with the number of iterations. ； ； In the formula, α init is the initial constraint factor; e is an exponential function with the natural constant as the base; n represents the iteration number; A0 represents the amplitude of the target image; A x,n A represents the amplitude of the signal region in the object plane at the nth iteration; x,n-1 represents the amplitude of the signal region in the object plane at the (n-1)th iteration; |·| represents the absolute value.

5. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 2, characterized in that, The process of obtaining a dynamic key is as follows: S21. Extract a feature block of a set size from the center of the joint pure phase hologram as input; S22. Taking the encryption effect of the feature block as the optimization goal, a particle swarm optimization algorithm combined with simulated annealing is adopted to search for a set of optimal chaotic system parameters in the parameter space of the chaotic system, and the optimal chaotic system parameters are used as the dynamic key of the joint pure phase hologram.

6. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 2, characterized in that, The process of obtaining the chaotic sequence is as follows: S31. Input the dynamic key into the improved Logistic embedded sine and cosine map chaotic system to drive the chaotic system to iterate; S32. Based on the iterative rules of the chaotic system, the chaotic system is switched and iterated according to the parity of the number of iterations to generate a chaotic sequence of dynamic keys.

7. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 6, characterized in that, The chaotic sequence is quantized and mapped into a row index sequence, column index sequence, and value parameter sequence that meet the requirements of subsequent encryption operations; ； In the formula, x i y i z i Let x, y, and z represent the i-th elements of the chaotic sequences respectively; P is the total number of rows in the target image; Q is the total number of columns in the target image; floor(·) is the floor function; row i ,col i val i They represent x respectively i y i z i The corresponding row index sequence, column index sequence, and value parameter sequence are divided into the row index sequence, column index sequence, and value parameter sequence.

8. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 7, characterized in that, The specific steps for block-based adaptive cross-channel scrambling are as follows: S41. Divide the joint pure phase hologram into multiple non-overlapping image blocks; S42. For each image block, perform the following operations in sequence: a. Spatial scrambling: For the current image block, extract subsequences of corresponding length from the row index sequence and column index sequence obtained through chaotic sequence mapping, sort the subsequences in ascending order, obtain the row scrambling index and column scrambling index dedicated to the current image block, and use these two indices to rearrange the pixel positions of the red, green and blue color channels in the current image block simultaneously. b. Cross-channel scrambling: For the current image block, a shift number is generated based on the chaotic sequence, and the color channel order of the current image block after spatial scrambling is cyclically shifted according to the shift number; S43. Merge the data of all image blocks in the joint pure phase hologram that have undergone spatial scrambling and cross-channel scrambling into a one-dimensional vector. Rearrange the one-dimensional vector as a whole based on the global scrambling index generated by the chaotic sequence, and reshape it into a scrambled image with the same size as the joint pure phase hologram.

9. The image holographic encryption method based on controllable Lyapunov exponential chaotic mapping according to claim 8, characterized in that, The process of generating the encrypted image is as follows: S51. Extract values ​​from the value parameter sequence and reshape them into a square matrix R. Perform an invertibility test on the square matrix R. If it is not invertible, discard the current square matrix and extract values ​​again until an invertible key matrix is ​​generated. S52. Perform a semi-tensor product operation on each color channel data of the scrambled image with the invertible key matrix to obtain the quotient matrix and remainder matrix for each color channel; the formula for the semi-tensor product operation is as follows: ； ； in, Represents a semi-tensor product operation; P R P G P B These represent the red, green, and blue color channel data of the scrambled image, respectively; C R C G C B K represents the remainder matrix for the red, green, and blue color channels of the scrambled image, respectively; R K G K B These represent the quotient matrices of the red, green, and blue color channels of the scrambled image, respectively. S53. Retain the quotient matrix of each color channel as the decryption private key for the current encryption process; merge the remainder matrices of each color channel to generate the ciphertext image corresponding to the joint pure phase hologram.

10. A controllable Lyapunov exponential chaotic mapping-based image holographic encryption system, used to implement the controllable Lyapunov exponential chaotic mapping-based image holographic encryption method as described in any one of claims 1-9, characterized in that, include: The image preprocessing and holographic fusion module is used to execute the Gerchberg-Saxton algorithm with adaptive constraints, convert multiple images to be encrypted into downsampled pure phase holograms, and fuse them into a joint pure phase hologram. An adaptive key generation module is used to extract feature blocks from the joint pure phase hologram, run a particle swarm optimization algorithm combined with simulated annealing, and obtain the optimal chaotic system parameters with the best encryption effect through iterative calculation. The optimal chaotic system parameters are then used as the dynamic key for the joint pure phase hologram. The chaotic sequence generation module has a built-in improved Logistic embedded sine and cosine map chaotic system, which is used to receive dynamic keys, generate multiple sets of chaotic sequences with controllable Lyapunov exponents through fractional or integer order iterative equations, and perform quantization processing. The encryption operation module includes a scrambling unit and a diffusion unit; the scrambling unit is configured to perform cross-channel scrambling, including intra-block row and column rearrangement, channel cyclic shift based on chaotic values, and global scrambling; The diffusion unit is configured to generate an invertible key matrix and perform a nonlinear operation of the half-tensor product of the image matrix and the invertible key matrix; The control and output module is used to coordinate the data flow between modules, store the private key required for decryption, and output the final synthesized ciphertext image.

Images