Optical key and high-dimensional chaotic dynamics combined image encryption method and device

Abstract

The invention relates to the technical field of image processing, in particular to an optical key and high-dimensional chaos dynamics combined image encryption method and device, and the method comprises the following steps: obtaining a CIE color coordinate pair, generating RGB vectors, laying the RGB vectors into a key matrix, executing the pixel-by-pixel XOR fusion operation, and obtaining a fused optical key image; extracting an initial vector and a Hash fingerprint, constructing a high-dimensional chaotic power system, and performing Lyapunov spectrum adaptive optimization to obtain an optimal parameter group; dynamically generating one or more pairs of chaotic sequences, dividing the chaotic sequences into scrambling sequences and diffusion sequences, and dynamically constructing an S-box lookup table; performing global scrambling, forward depth nonlinear diffusion and backward global avalanche diffusion to obtain a final ciphertext block; and performing final chaos mask whitening to obtain a ciphertext image. According to the method and the device provided by the invention, the key system driven by the physical parameters can be quantified, the safety and the replaceability are improved, and the randomness and the anti-prediction capability are improved.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an image encryption method and apparatus that combines optical keys with high-dimensional chaotic dynamics. Background Technology

[0002] Existing image encryption schemes mostly rely on pure digital keys or low-dimensional chaotic mappings (such as Logistic, Tent, Henon, etc.) to generate pseudo-random key streams. These methods have the following drawbacks: 1. Insufficient physical uniqueness of keys: Pure digital keys can be copied, backed up, or exhaustively searched, lacking physical unclonability and failing to provide traceable physical binding for critical data.

[0003] 2. Limited complexity of chaotic space and orbit: Low-dimensional chaotic systems are prone to problems such as periodic windows, orbital degradation or insufficient parameter sensitivity, which makes the unpredictability of key sequences weaker and easier to analyze and reconstruct.

[0004] 3. Weak coupling between diffusion and scrambling: Existing solutions often separate scrambling and diffusion, lacking dynamic S-box or inter-round coupling mechanisms, thus limiting their ability to resist differential and linear attacks. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an image encryption method and device that combines optical keys with high-dimensional chaotic dynamics, a key system driven by quantifiable physical parameters, which improves security and substitutability, and enhances randomness and anti-prediction ability.

[0006] This invention is achieved through the following technical solution: An image encryption method combining optical keys and high-dimensional chaotic dynamics includes the following steps: S1: Obtain CIE color coordinate pairs from multiple fluorescent material samples, generate RGB vectors through quantization mapping, flatten each set of RGB vectors into a key matrix with the same size as the image to be encrypted, and perform pixel-by-pixel XOR fusion operation on the key matrix to obtain a fused optical key image; S2: Extracting the initial vector and hash fingerprint from the self-fused optical key image; S3: Construct a high-dimensional chaotic dynamic system based on the extracted initial vector and hash fingerprint, and perform Lyapunov spectral adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set; S4: Drive a high-dimensional chaotic dynamic system with initial vectors and optimal parameter sets to dynamically generate one or more pairs of chaotic sequences. Map each pair of chaotic sequences to byte sequences through amplification and modulo operation. Divide the byte sequences into scrambled sequences and diffused sequences, and dynamically construct an S-box lookup table. S5: Generate a scrambling index based on the scrambling sequence, and globally scramble the image to be encrypted. Then, perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image based on a dynamically constructed S-box lookup table to obtain the final ciphertext block. S6: Perform final chaotic masking whitening on the final ciphertext block to obtain the ciphertext image.

[0007] Furthermore, the method for generating the RGB vector in step S1 is shown in equation (1): (1); in: This represents the mapped and quantized red channel value. This represents the mapped and quantized green channel value. This indicates that the value within the parentheses will be rounded to the nearest integer. This indicates that the mapped value does not exceed the range within the parentheses. This represents the coordinates of CIE color coordinate pairs obtained from multiple fluorescent material samples. This represents the mapped and quantized blue channel value. This indicates element-wise addition. This represents the maximum value of a color space channel.

[0008] Furthermore, the mathematical form of the high-dimensional chaotic dynamical system constructed in step S3 is Equation (2), and the iterative form is Equation (3): (2); (3); in: Represents state variables and The linear relationship strength coefficient between them Represents the state vector. This represents the state variables in the state vector used to generate the scrambling key. This represents the state variables in the state vector used to generate the diffusion key. This represents the state variables in the state vector used to introduce the nonlinearity and complex folding characteristics of the system. This represents the state variables in the state vector used to enhance chaotic properties. Indicates the first The state vector of the next iteration. Indicates the first The state vector of the next iteration. Represents state variables right The driving strength coefficient, Represents state variables The attenuation rate coefficient, Represents state variables right Influence intensity coefficient Indicates the iteration step size. This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in the middle, This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in.

[0009] The optimized step S3, which performs Lyapunov spectrum adaptive optimization of the control parameters of the high-dimensional chaotic dynamic system, includes two stages: coarse search and fine search. The coarse search refers to the process of extracting the hash features of the image to be encrypted and using the hash features as seeds to make a certain micro-perturbation to the parameter search grid. The fine search refers to the process of using the Lyapunov spectrum as a fitness function to perform high-precision search and evaluation within the determined region.

[0010] Furthermore, the method for obtaining the scrambled sequence and the diffusion sequence in step S4 is as follows: After multiplying and amplifying the chaotic sequence, take the modulus and trim it to the range of 0–255. Then, uniformly map the floating-point chaotic sequence to 256 gray levels to form a byte sequence. Finally, divide the byte sequence into a scrambled sequence and a diffused sequence according to equation (4): (4); in: Indicates the first The scrambled sequence of the next iteration. Indicates the first The diffusion sequence of the next iteration, Represents a modulo mapping. Indicates rounding down. Indicates the first The state variables used to generate the scrambling key in the next iteration state vector. Indicates the first The state variables used to generate the diffusion key in the next iteration state vector.

[0011] Furthermore, the method for global scrambling in step S5 is as follows: First, a scrambling index with the same size as the image to be encrypted is generated using the chaotic key stream of the scrambling sequence. Then, the pixel positions of the image to be encrypted are globally scrambled according to the scrambling index to obtain the globally scrambled image.

[0012] Furthermore, the method for obtaining the final ciphertext block in step S5 is as follows: S51: Flatten the globally scrambled image pixel by pixel into a one-dimensional byte stream according to equation (5): (5); in: Represents a one-dimensional byte stream. Indicates the first bytes, Indicates the total number of bytes; S52: For each byte of the one-dimensional byte stream, internal iteration is performed according to the diffusion sequence based on equation (6) in byte order to achieve forward deep nonlinear diffusion, obtain the intermediate ciphertext of a single round operation, and finally output the ciphertext stream; (6); in: This represents the intermediate ciphertext output from a single round of operations. This represents a bijective nonlinear mapping provided by a dynamic S-box. This indicates the intermediate value of the byte currently being processed before entering a single round of operations. This represents a subkey derived from an internal round. Represents a modulo mapping. This indicates element-wise addition. This indicates that the input byte value will be shifted to the left by a specified number of bits. This indicates the ciphertext output obtained after processing the previous pixel byte; S53: Iterate backward from the end of the ciphertext stream to the beginning, perform backward global avalanche diffusion, and generate the current final ciphertext block based on the intermediate ciphertext block and the calculated next final ciphertext block according to equation (7): (7); in: This indicates the final ciphertext block currently being processed. This represents an invertible transformation consisting of modulo and bitwise operations. The first term represents the final output of the forward deep nonlinear diffusion. bytes, express, This indicates the next final ciphertext block.

[0013] Furthermore, in step S6, the final chaotic mask whitening is performed on the final ciphertext block to obtain the ciphertext image, as follows: The output ciphertext of the backward global avalanche diffusion is XORed with an independent chaotic key stream byte by byte according to Equation (8) to obtain the final encryption result. The final encryption result is reorganized into a matrix according to the size and channel information of the image to be encrypted to obtain the ciphertext image. (8); in: This indicates the final encryption result. This indicates element-wise addition. Represents an independent chaotic key stream.

[0014] An image encryption device combining optical keys and high-dimensional chaotic dynamics is used to execute an image encryption method combining optical keys and high-dimensional chaotic dynamics as described in any of the above, comprising an optical key generation module, an enhanced four-dimensional chaotic key stream module, a phase space uniform mapping and discretization module, and a multi-round encryption and bidirectional diffusion module. The optical key generation module is used to generate RGB vectors by quantization mapping using the CIE color coordinates of multiple sets of fluorescent materials as primitives, and then tile and XOR them to form a fused optical key image. The enhanced four-dimensional chaotic keystream module is used to construct a high-dimensional chaotic dynamic system and to perform Lyapunov spectrum adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set. The phase space uniform mapping and discretization module is used to map each pair of chaotic sequences into byte sequences through amplification and modulo, and to divide the byte sequences into scrambled sequences and diffused sequences. The multi-round encryption and bidirectional diffusion module is used to globally scramble the image to be encrypted, and then perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image in byte order based on the diffusion sequence to obtain the diffused image. Finally, the diffused image is whitened by a chaotic mask to obtain the ciphertext image.

[0015] Beneficial effects of the invention: The image encryption method and apparatus combining optical keys and high-dimensional chaotic dynamics provided by this invention have the following advantages: 1. A key system driven by quantifiable physical parameters improves security and substitutability.

[0016] 2. Adaptive parameter selection using Lyapunov spectra ensures strong chaotic characteristics and improves randomness and anti-prediction ability.

[0017] 3. A preheating mechanism is added to the perturbation term to eliminate transient effects and improve the stability and cycle length of the key stream.

[0018] 4. The phase space uniform mapping strategy eliminates floating-point quantization bias and ensures byte-level uniformity.

[0019] 5. Dynamic S-box and inter-wheel binding significantly increase nonlinear entropy and differential complexity.

[0020] 6. The multi-round bidirectional diffusion architecture ensures a complete avalanche effect, and statistical whitening further smooths out residual patterns, improving resistance to statistical attacks. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the process of this invention.

[0022] Figure 2 This is a schematic diagram of the bifurcation of the present invention.

[0023] Figure 3 This is the histogram of the original image to be encrypted in this invention.

[0024] Figure 4 This is the encrypted image histogram of the present invention. Detailed Implementation

[0025] An image encryption method combining optical keys and high-dimensional chaotic dynamics, the flowchart of which is as follows: Figure 1 As shown, the specific steps include the following: S1: Obtain CIE color coordinate pairs from multiple fluorescent material samples, generate RGB vectors through quantization mapping, flatten each set of RGB vectors into a key matrix with the same size as the image to be encrypted, and perform pixel-by-pixel XOR fusion operation on the key matrix to obtain a fused optical key image; Specifically, the method for generating RGB vectors is shown in equation (1): (1); in: This represents the mapped and quantized red channel value. This represents the mapped and quantized green channel value. This indicates that the value within the parentheses will be rounded to the nearest integer. This indicates that the mapped value does not exceed the range within the parentheses. This represents the coordinates of CIE color coordinate pairs obtained from multiple fluorescent material samples. This represents the mapped and quantized blue channel value. This indicates element-wise addition. This represents the maximum value of a color space channel.

[0026] S2: Extract the initial vector and hash fingerprint from the self-fused optical key image.

[0027] The overall framework of this invention consists of three collaborative units, including a physical entropy source layer, a dynamic key layer, and a spatiotemporal encryption layer.

[0028] Steps S1 and S2 belong to the physical entropy source layer, which is a multimodal optical key generation mechanism based on multi-wavelength fluorescence response. The color coordinate differences of different fluorescent materials under multi-wavelength excitation are quantized and encoded as key primitives. By utilizing the color coordinates of fluorescent materials at specific wavelengths, these color coordinates directly reflect their quantum chemical properties in the physical world. This breaks through the traditional image encryption algorithm, which usually relies on pure digital keys and whose security is limited by key length and generation method.

[0029] Furthermore, a channel-wise XOR operation is performed on multiple sets of fluorescent color coordinates, quantizing each set of coordinates into unique RGB values. A key matrix matching the image size is then generated through a tile operation. This key matrix is ​​then XORed pixel-wise, ultimately producing a unique and highly complex fused optical key pattern. This process is physically equivalent to introducing a physically unclonable function (PUF). The key depends not only on pixel information but also on the microstructure and spectral characteristics of the sample material, making the key physically unique and resistant to copying. Any attempt to reconstruct the pattern through reverse engineering or physical replication is computationally infeasible, thus providing a verifiable physical entropy source for digital encryption systems.

[0030] By extracting the initial vector and hash fingerprint from the self-fused optical key image, the physical key is seamlessly bound to the subsequent digital encryption process, ensuring the integrity and tamper-proof nature of the key.

[0031] This invention treats the CIE chromatic coordinates of fluorescent materials as a type of quantifiable, inputtable physical key parameter, rather than a fixed hardware dependency. Users can independently change the chromatic coordinate values ​​and generate new fusion optical key patterns according to different materials, measurement conditions, or experimental requirements. Since these parameters are essentially derived from the spectral response of the real world, and optical measurement results are affected by multiple microscopic factors such as material doping ratio, lattice state, local morphology, excitation wavelength, and temperature, even if the values ​​can be replaced by the user, their origin is inherently highly complex and unpredictable, making them difficult to reproduce through software simulation or numerical calculation.

[0032] At the algorithm level, the fusion optical key mechanism of this invention binds these physical quantization parameters with pixel-level random perturbations and initial chaotic states, generating a unique fusion optical key through requantization, encoding, and XOR superposition. Even if an attacker fully understands the algorithm logic, they cannot reverse engineer the exact key input used to drive the system without knowing the source of the real parameters. Simultaneously, the SHA-256 digital digest of this key input serves as a robust integrity identifier, establishing a unique mapping between each set of physical parameters, key pattern, and chaotic initialization. This supports verifiable key replacement, key auditing, and long-term traceability management. The key system driven by quantifiable physical parameters improves security and substitutability.

[0033] S3: Construct a high-dimensional chaotic dynamic system based on the extracted initial vector and hash fingerprint, and perform Lyapunov spectral adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set; Specifically, the mathematical form of the constructed high-dimensional chaotic dynamical system is Equation (2), and the iterative form is Equation (3): (2); (3); in: Represents state variables and The linear relationship strength coefficient between them Represents the state vector. This represents the state variables in the state vector used to generate the scrambling key. This represents the state variables in the state vector used to generate the diffusion key. This represents the state variables in the state vector used to introduce the nonlinearity and complex folding characteristics of the system. This represents the state variables in the state vector used to enhance chaotic properties. Indicates the first The state vector of the next iteration. Indicates the first The state vector of the next iteration. Represents state variables right The driving strength coefficient, Represents state variables The attenuation rate coefficient, Represents state variables right Influence intensity coefficient Indicates the iteration step size. This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in the middle, This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in.

[0034] The optimized Lyapunov spectrum adaptive optimization of control parameters for high-dimensional chaotic dynamical systems includes two stages: coarse search and fine search. The coarse search refers to the process of extracting hash features from the image to be encrypted and using the hash features as seeds to make a defined micro-perturbation to the parameter search grid. The fine search refers to the process of using the Lyapunov spectrum as a fitness function to perform high-precision search and evaluation within the defined region.

[0035] S4: Drive a high-dimensional chaotic dynamic system with initial vectors and optimal parameter sets to dynamically generate one or more pairs of chaotic sequences. Map each pair of chaotic sequences to byte sequences through amplification and modulo operation. Divide the byte sequences into scrambled sequences and diffused sequences, and dynamically construct an S-box lookup table. Steps S3 and S4 belong to the dynamic key layer, proposing an adaptive parameter optimization enhanced high-dimensional chaotic dynamical system to generate a high-entropy, time-varying keystream. Unlike chaotic mapping with fixed parameters, this invention introduces a two-stage adaptive search based on the Lyapunov spectrum, associated with the content of the image to be encrypted. This search process first extracts the hash features of the original image to be encrypted, and then uses these features as seeds to perform deterministic micro-perturbations on the parameter search space. This mechanism ensures that for different input images, the system can adaptively explore different parameter sets, thereby automatically selecting parameter sets that are in a stable chaotic attraction domain and have good spectral spacing. This allows the system to adaptively select the optimal parameter set, ensuring that the system always operates in a stable, high-entropy chaotic region. This maximizes the complexity of the keystream at the continuous dynamics level and avoids trajectory degradation, enabling the system to operate within a parameter domain with a definite chaotic index (maximum Lyapunov exponent). Compared to static manual parameter setting, this method can effectively avoid parameters falling into periodic windows or weakly chaotic regions near the boundaries, significantly improving the trajectory complexity and long-term unpredictability of the key stream, thereby enhancing its resistance to linear and statistical prediction methods.

[0036] Meanwhile, by introducing bounded non-polynomial perturbations in the numerical solution and setting sufficient preheating steps, as shown in Equation (3), orbital degradation and short-period behavior can be suppressed, ensuring that the generated chaotic sequence is statistically closer to white noise and improving the entropy and autocorrelation uniformity of the key stream. The generated chaotic sequence is used to dynamically construct the S-box and scrambling and diffusion control flow, which can realize time-dependent nonlinear mapping and key-driven transformation with wheel change.

[0037] Furthermore, the method for obtaining the scrambled sequence and the diffusion sequence in step S4 is as follows: After multiplying and amplifying the chaotic sequence, take the modulus and trim it to the range of 0–255. Then, uniformly map the floating-point chaotic sequence to 256 gray levels to form a byte sequence. Finally, divide the byte sequence into a scrambled sequence and a diffused sequence according to equation (4): (4); in: Indicates the first The scrambled sequence of the next iteration. Indicates the first The diffusion sequence of the next iteration, Represents a modulo mapping. Indicates rounding down. Indicates the first The state variables used to generate the scrambling key in the next iteration state vector. Indicates the first The state variables used to generate the diffusion key in the next iteration state vector.

[0038] When obtaining the scrambled and diffused sequences, the floating-point chaotic sequence is multiplied by an amplification factor and mapped modulo 256. Combined with pruning and resampling, the mapped byte sequence is evenly distributed in histogram and autocorrelation statistics, avoiding the peak and hole problems caused by direct quantization, thereby reducing the effectiveness of statistical analysis attacks.

[0039] S5: Generate a scrambling index based on the scrambling sequence, and globally scramble the image to be encrypted. Then, perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image based on a dynamically constructed S-box lookup table to obtain the final ciphertext block. Specifically, the method for performing a global scramble is as follows: First, a scrambling index with the same size as the image to be encrypted is generated using the chaotic key stream of the scrambling sequence. Then, the pixel positions of the image to be encrypted are globally scrambled according to the scrambling index to obtain the globally scrambled image.

[0040] The final ciphertext block is obtained by performing forward depth-linear diffusion and backward global avalanche diffusion on the globally scrambled image in byte order based on the diffusion sequence, as follows: S51: Flatten the globally scrambled image pixel by pixel into a one-dimensional byte stream according to equation (5): (5); in: Represents a one-dimensional byte stream. Indicates the first bytes, Indicates the total number of bytes; S52: For each byte of the one-dimensional byte stream, internal iteration is performed according to the diffusion sequence based on equation (6) in byte order to achieve forward deep nonlinear diffusion, obtain the intermediate ciphertext of a single round operation, and finally output the ciphertext stream; (6); in: This represents the intermediate ciphertext output from a single round of operations. This represents a bijective nonlinear mapping provided by a dynamic S-box. This indicates the intermediate value of the byte currently being processed before entering a single round of operations. This represents a subkey derived from an internal round. Represents a modulo mapping. This indicates element-wise addition. This indicates that the input byte value will be shifted to the left by a specified number of bits. This indicates the ciphertext output obtained after processing the previous pixel byte; S53: Iterate backward from the end of the ciphertext stream to the beginning, perform backward global avalanche diffusion, and generate the current final ciphertext block based on the intermediate ciphertext block and the calculated next final ciphertext block according to equation (7): (7); in: This indicates the final ciphertext block currently being processed. This represents an invertible transformation consisting of modulo and bitwise operations. The first term represents the final output of the forward deep nonlinear diffusion. bytes, express, This indicates the next final ciphertext block.

[0041] function This is a computationally lightweight yet diffusion-efficient reversible transformation, typically composed of modulo and bitwise operations. Its key function is to ensure that a bit flip at any position in the intermediate data stream propagates in a cascading manner, ultimately affecting the final ciphertext block. This guarantees a complete avalanche effect throughout the entire ciphertext, providing a fundamental safeguard against differential attacks.

[0042] The globally scrambled image undergoes forward deep nonlinear diffusion and backward global avalanche diffusion based on a dynamically constructed S-box lookup table. The dynamically constructed S-box lookup table is primarily used for forward deep nonlinear diffusion. In each round of encryption, a portion of the chaotic output is used to generate the scrambling index (perm), and another portion serves as the S-box construction seed (_build_sbox). The S-box is not a static lookup table but is dynamically generated from a real-time chaotic sequence. This design couples the nonlinear transformation and scrambling to the specific keystream for each encryption, significantly increasing resilience to differential and linear attacks. Attackers not only need to guess the round key but also must reconstruct the dynamic S-box mapping for each round, significantly increasing nonlinear entropy and differential complexity. The S-box lookup table can preferably be 256 bytes.

[0043] Step S5 is the spatiotemporal encryption layer, employing a multi-round iterative bidirectional diffusion coupling structure. Each round of encryption is driven by a round IV derived from a unique wavelength sequence, and each round efficiently integrates global chaotic scrambling and enhanced bidirectional diffusion mechanisms. Scrambling dismantles the spatial correlation of pixels; while the core bidirectional diffusion, through a cascaded design of forward coupling and backward feedback, ensures that pixel perturbations are thoroughly globally coupled in the spatiotemporal dimension. Finally, a chaotic mask is used for statistical whitening. This architecture significantly amplifies the impact of minute plaintext modifications, making its differential sensitivity approach an ideal avalanche effect.

[0044] S6: Perform final chaotic masking whitening on the final ciphertext block to obtain the ciphertext image.

[0045] Specifically, the method for performing final chaotic masking whitening on the final ciphertext block to obtain the ciphertext image is as follows: The output ciphertext of the backward global avalanche diffusion is XORed with an independent chaotic key stream byte by byte according to Equation (8) to obtain the final encryption result. The final encryption result is reorganized into a matrix according to the size and channel information of the image to be encrypted to obtain the ciphertext image. (8); in: This indicates the final encryption result. This indicates element-wise addition. Represents an independent chaotic key stream.

[0046] Performing final chaotic masking whitening on the final ciphertext block significantly amplifies the impact of minor modifications, making its differential sensitivity approach the ideal avalanche effect. This eliminates any weak statistical biases or linear relationships that may still exist after complex diffusion processes, significantly improving the algorithm's resistance to various statistical analyses and known plaintext attacks. It ensures that the final output ciphertext is computationally indistinguishable from a true random number sequence. Theoretically, it achieves cross-layer integration of physical security and algorithm security; in engineering, it ensures the stability and reproducibility of chaotic key streams through adaptive parameter selection and bifurcation, and spectral visualization, providing a systematic and engineeringable solution for high-security image encryption based on physical random sources.

[0047] To comprehensively evaluate the performance of this method, an in-depth analysis of the key security and statistical properties of encrypted images is conducted to fully assess the robustness and resistance to attacks of the algorithm.

[0048] The results of the key sensitivity analysis are shown in Table 1: Table 1 Key Sensitivity Analysis ; As shown in Table 1, when using the correct key and wavelength order, the peak signal-to-noise ratio (PSNR) approaches infinity, and the structural similarity index (SSIM) reaches 1.0000, indicating perfect image reconstruction. However, when only the wavelength order is changed or an incorrect set of fluorescence images is used, the ciphertext image in Table 1 is subjected to 20% shearing and 10 standard deviations of random noise. The PSNR value plummets to around 8.33 dB, and the SSIM value is close to 0. This proves that even a small error in the key or its order will lead to decryption failure, and the output will be entirely random noise.

[0049] The image encryption method provided by this invention was verified by examining its nonlinear dynamic characteristics and parameter sensitivity. Its bifurcation diagram is shown below. Figure 2 As shown, from Figure 2As can be seen, when the value of parameter c exceeds the critical point, the system rapidly transitions from a periodic state to a chaotic state. Within the interval [32.5, 36], the system exhibits broad and continuous chaotic attractor properties. This figure strongly demonstrates that the image encryption method provided by this invention has a broad chaotic operating region. Therefore, regardless of the parameter fine-tuning value calculated by the adaptive algorithm based on the input image, as long as it is within this broad chaotic region (usually further verified by Lyapunov spectral analysis), the chaotic system can be ensured to possess high complexity and high pseudo-randomness. This mechanism provides technical flexibility and sensitivity to input images for the encryption scheme of this invention, and ensures high security performance of the key stream.

[0050] In addition, two internationally recognized sensitivity evaluation metrics, the Number of Pixels Change Rate (NPCR) and the Unified Average Changing Intensity (UACI), are used to evaluate the robustness of the image encryption method provided by this invention in the face of differential attacks. These two metrics measure the degree of change coverage and intensity of the encryption result at the pixel level, respectively, and are important criteria for judging whether the encryption method has an avalanche effect.

[0051] First, the original image matrix to be encrypted is read, with a pixel range of [0, 255]. Then, at fixed random positions... The perturbation is applied to a single pixel, i.e., at random locations in the image. By adding or subtracting a unit value and cropping it to a legal range, a perturbed image is obtained. Both images are then processed by the same optical key generation module, enhanced four-dimensional chaotic keystream module, phase space uniform mapping and discretization module, and multi-round encryption and bidirectional diffusion module to obtain the corresponding ciphertext images. and The D array is directly generated based on the pixel-by-pixel comparison operation of the following formula: . The formula for calculating NPCR is given by the following equation: ; This metric reflects the percentage of pixels where the perturbation actually diffuses within the encrypted image. This value is based on the statistical assumption that in an ideal 8-bit encryption system, the probability of unequal grayscale values ​​at any pixel location is 255 / 256 (i.e., 1 - 1 / 256). Therefore, the expected value of NPCR is... It is approximately equal to 99.6094%.

[0052] On the other hand, UACI focuses on the average difference in the grayscale levels of the encrypted data, and the code uses... The element-wise absolute difference is calculated and normalized to a pixel value range of 255, as shown in the following formula: ; This value is based on a statistical assumption: when and When the pixel values ​​are considered as random variables that are independently and uniformly distributed in the interval [0, 255], the theoretical ideal value of UACI is calculated by probability integration. Its value is approximately 33.4635%.

[0053] Where F represents the number of gray levels of an image pixel.

[0054] In the experiments conducted using this method, applying a perturbation of only one pixel to the original image to be encrypted resulted in a significant avalanche effect in the encryption results, with an NPCR of 99.61% and a UACI of 33.47%, both highly close to the theoretical ideal values. This indicates that the encryption algorithm exhibits a significant avalanche effect in the diffusion mechanism, keystream coupling perturbation, and fluorescence mapping encoding stages. The results also verify that the algorithm has excellent resistance to differential attacks; that is, any extremely small input change will trigger global randomization and strong diffusion of the ciphertext image, effectively preventing attackers from inferring the key or recovering the original content through small input perturbations.

[0055] Furthermore, information entropy is an important indicator for measuring the randomness and uniformity of the distribution of pixel values ​​in an image, and it also represents the amount of information contained in the image. For a standard 8-bit image with a grayscale level L=256, the formula for calculating its information entropy is as follows: ,in: Represents grayscale value The probability of appearing in an image.

[0056] Its theoretical calculated value is .

[0057] The horizontal correlation index measures the degree of linear dependence between adjacent pixel values ​​in an image. This index typically uses the Pearson linear correlation coefficient. The calculation formula is as follows: ; in and These represent the values ​​of a pair of adjacent pixels (in the horizontal direction). and They are and The average of two pixel sequences, and It represents the total number of selected pixel pairs.

[0058] The histogram of the original image to be encrypted is as follows: Figure 3 As shown, the histogram of the encrypted image of the present invention is as follows: Figure 4 As shown in the figure, the horizontal axis represents pixel value, and the vertical axis represents frequency.

[0059] The statistical analysis results are shown in Table 2: Table 2 ; As shown in Table 2, the information entropy of the original image to be encrypted is 7.7131, which is lower than the ideal entropy value of 8, indicating that its grayscale distribution exhibits obvious structural regularity and predictable statistical characteristics. Combined with... Figure 3 As can be seen, the R, G, and B channel curves fluctuate violently, with obvious peaks and troughs, further confirming the non-uniformity of pixel distribution.

[0060] In comparison, the entropy value of the encrypted image obtained by this method increases to 7.9997, almost reaching the theoretical limit of 8. Meanwhile, from... Figure 4 The histogram of the encrypted image shows that the pixel frequency distribution of the three channels tends to be a completely flat random perturbation, with all gray values ​​appearing at approximately the same frequency. This indicates that the encryption operation completely destroys the statistical structure of the original image, and the pixel distribution tends to be a completely uniform random model.

[0061] Furthermore, adjacent pixels in the original image to be encrypted typically have similar grayscale values, resulting in a horizontal correlation close to 1, indicating strong correlation. As shown in Table 1, the horizontal correlation of the original image to be encrypted is as high as 0.9887, reflecting a high degree of predictability between adjacent pixels. In contrast, the correlation of the encrypted image drops significantly to -0.0001, almost zero. This demonstrates that the encryption algorithm effectively achieves local decoupling and information diffusion among pixels, completely eliminating linear dependence and predictability between adjacent pixels.

[0062] The statistical analysis results above fully verify the global uniformity and local decoupling of the proposed encryption algorithm at the pixel level. The grayscale distribution of the encrypted image conforms to an ideal random model, and its correlation index indicates that information has been completely diffused in space. This means that even if an attacker possesses a large number of ciphertext samples, it will be difficult to recover any usable information through statistical or histogram analysis, thus ensuring the high security and irreversibility of the system from an information theory perspective.

[0063] An image encryption device combining optical keys and high-dimensional chaotic dynamics is used to execute an image encryption method combining optical keys and high-dimensional chaotic dynamics as described in any of the above, comprising an optical key generation module, an enhanced four-dimensional chaotic key stream module, a phase space uniform mapping and discretization module, and a multi-round encryption and bidirectional diffusion module. The optical key generation module is used to generate RGB vectors by quantization mapping using the CIE color coordinates of multiple sets of fluorescent materials as primitives, and then tile and XOR them to form a fused optical key image. The enhanced four-dimensional chaotic keystream module is used to construct a high-dimensional chaotic dynamic system and to perform Lyapunov spectrum adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set. The phase space uniform mapping and discretization module is used to map each pair of chaotic sequences into byte sequences through amplification and modulo, and to divide the byte sequences into scrambled sequences and diffused sequences. The multi-round encryption and bidirectional diffusion module is used to globally scramble the image to be encrypted, and then perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image in byte order based on the diffusion sequence to obtain the diffused image. Finally, the diffused image is whitened by a chaotic mask to obtain the ciphertext image.

[0064] Each functional module of this invention can be implemented in software or mapped to a hardware acceleration module, facilitating flexible deployment on edge devices, embedded nodes, or the cloud. The design allows for replacement of the PUF source (speckle optics, nano PUF, etc.) or the chaotic model, providing a good pathway for technological evolution.

[0065] In summary, the image encryption method and apparatus combining optical keys and high-dimensional chaotic dynamics provided by this invention tightly binds the physical layer's unclonable optical key with a Lyapunov-optimized high-dimensional chaotic keystream, and employs a dynamic S-box and bidirectional multi-round diffusion architecture, forming an image encryption scheme that combines physical uncopyability, strong dynamic randomness, strict reversibility, and engineering feasibility. This scheme significantly improves resistance to differential, statistical, linear, and exhaustive attacks both theoretically and experimentally, while meeting the requirements of high-precision applications for lossless restoration, possessing good industrialization and patent protection value.

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An image encryption method combining optical keys and high-dimensional chaotic dynamics, characterized in that: Includes the following steps: S1: Obtain CIE color coordinate pairs from multiple fluorescent material samples, generate RGB vectors through quantization mapping, flatten each set of RGB vectors into a key matrix with the same size as the image to be encrypted, and perform pixel-by-pixel XOR fusion operation on the key matrix to obtain a fused optical key image; S2: Extracting the initial vector and hash fingerprint from the self-fused optical key image; S3: Construct a high-dimensional chaotic dynamic system based on the extracted initial vector and hash fingerprint, and perform Lyapunov spectral adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set; S4: Drive a high-dimensional chaotic dynamic system with initial vectors and optimal parameter sets to dynamically generate one or more pairs of chaotic sequences. Map each pair of chaotic sequences to byte sequences through amplification and modulo operation. Divide the byte sequences into scrambled sequences and diffused sequences, and dynamically construct an S-box lookup table. S5: Generate a scrambling index based on the scrambling sequence, and globally scramble the image to be encrypted. Then, perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image based on a dynamically constructed S-box lookup table to obtain the final ciphertext block. S6: Perform final chaotic masking whitening on the final ciphertext block to obtain the ciphertext image.

2. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: The method for generating the RGB vector in step S1 is shown in equation (1): （1）； in: This represents the mapped and quantized red channel value. This represents the mapped and quantized green channel value. This indicates that the value within the parentheses will be rounded to the nearest integer. This indicates that the mapped value does not exceed the range within the parentheses. This represents the coordinates of CIE color coordinate pairs obtained from multiple fluorescent material samples. This represents the mapped and quantized blue channel value. This indicates element-wise addition. This represents the maximum value of a color space channel.

3. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: The mathematical form of the high-dimensional chaotic dynamical system constructed in step S3 is Equation (2), and the iterative form is Equation (3): （2）； （3）； in: Represents state variables and The linear relationship strength coefficient between them Represents the state vector. This represents the state variables in the state vector used to generate the scrambling key. This represents the state variables in the state vector used to generate the diffusion key. This represents the state variables in the state vector used to introduce the nonlinearity and complex folding characteristics of the system. This represents the state variables in the state vector used to enhance chaotic properties. Indicates the first The state vector of the next iteration. Indicates the first The state vector of the next iteration. Represents state variables right The driving strength coefficient, Represents state variables The attenuation rate coefficient, Represents state variables right Influence intensity coefficient Indicates the iteration step size. This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in the middle, This indicates the introduction of a state variable. The periodic nonlinear disturbance intensity coefficient in.

4. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: Step S3 involves Lyapunov spectral adaptive optimization of the control parameters of the high-dimensional chaotic dynamical system, which includes two stages: coarse search and fine search. The coarse search refers to the process of extracting the hash features of the image to be encrypted and using the hash features as seeds to make a certain micro-perturbation to the parameter search grid. The fine search refers to the process of using the Lyapunov spectrum as a fitness function to perform high-precision search and evaluation within the determined region.

5. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: The method for obtaining the scrambled sequence and the diffusion sequence in step S4 is as follows: After multiplying and amplifying the chaotic sequence, take the modulus and trim it to the range of 0–255. Then, uniformly map the floating-point chaotic sequence to 256 gray levels to form a byte sequence. Finally, divide the byte sequence into a scrambled sequence and a diffused sequence according to equation (4): （4）； in: Indicates the first The scrambled sequence of the next iteration. Indicates the first The diffusion sequence of the next iteration, Represents a modulo mapping. This indicates rounding down. Indicates the first The state variables used to generate the scrambling key in the next iteration state vector. Indicates the first The state variables used to generate the diffusion key in the next iteration state vector.

6. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: The method for global scrambling in step S5 is as follows: First, a scrambling index with the same size as the image to be encrypted is generated using the chaotic key stream of the scrambling sequence. Then, the pixel positions of the image to be encrypted are globally scrambled according to the scrambling index to obtain the globally scrambled image.

7. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 1, characterized in that: The method for obtaining the final ciphertext block in step S5 is as follows: S51: Flatten the globally scrambled image pixel by pixel into a one-dimensional byte stream according to equation (5): （5）； in: Represents a one-dimensional byte stream. Indicates the first bytes, Indicates the total number of bytes; S52: For each byte of the one-dimensional byte stream, internal iteration is performed according to the diffusion sequence based on equation (6) in byte order to achieve forward deep nonlinear diffusion, obtain the intermediate ciphertext of a single round operation, and finally output the ciphertext stream; （6）； in: This represents the intermediate ciphertext output from a single round of operations. This represents a bijective nonlinear mapping provided by a dynamic S-box. This indicates the intermediate value of the byte currently being processed before entering a single round of operations. This represents a subkey derived from an internal round. Represents a modulo mapping. This indicates element-wise addition. This indicates that the input byte value will be shifted to the left in a circular fashion by the specified number of bits. This indicates the ciphertext output obtained after processing the previous pixel byte; S53: Iterate backward from the end of the ciphertext stream to the beginning, perform backward global avalanche diffusion, and generate the current final ciphertext block based on the intermediate ciphertext block and the calculated next final ciphertext block according to equation (7): （7）； in: This indicates the final ciphertext block currently being processed. This represents an invertible transformation consisting of modulo and bitwise operations. The first term represents the final output of the forward deep nonlinear diffusion. bytes, express, This indicates the next final ciphertext block.

8. The image encryption method combining optical keys and high-dimensional chaotic dynamics according to claim 7, characterized in that: The method for performing final chaotic masking whitening on the final ciphertext block in step S6 to obtain the ciphertext image is as follows: The output ciphertext of the backward global avalanche diffusion is XORed with an independent chaotic key stream byte by byte according to Equation (8) to obtain the final encryption result. The final encryption result is reorganized into a matrix according to the size and channel information of the image to be encrypted to obtain the ciphertext image. （8）； in: This indicates the final encryption result. This indicates element-wise addition. Represents an independent chaotic key stream.

9. An image encryption device combining optical keys and high-dimensional chaotic dynamics, characterized in that: Used to perform an image encryption method combining optical keys and high-dimensional chaotic dynamics as described in any one of claims 1 to 8. It includes an optical key generation module, an enhanced four-dimensional chaotic key stream module, a phase space uniform mapping and discretization module, and a multi-round encryption and bidirectional diffusion module; The optical key generation module is used to generate RGB vectors by quantization mapping using the CIE color coordinates of multiple sets of fluorescent materials as primitives, and then tile and XOR them to form a fused optical key image. The enhanced four-dimensional chaotic keystream module is used to construct a high-dimensional chaotic dynamic system and to perform Lyapunov spectrum adaptive optimization on the control parameters of the high-dimensional chaotic dynamic system to obtain the optimal parameter set. The phase space uniform mapping and discretization module is used to map each pair of chaotic sequences into byte sequences through amplification and modulo, and to divide the byte sequences into scrambled sequences and diffused sequences. The multi-round encryption and bidirectional diffusion module is used to globally scramble the image to be encrypted, and then perform forward depth nonlinear diffusion and backward global avalanche diffusion on the globally scrambled image in byte order based on the diffusion sequence to obtain the diffused image. Finally, the diffused image is whitened by a chaotic mask to obtain the ciphertext image.

Images