A multi-image parallel encryption processing method based on improved chaotic mapping

Abstract

The application relates to the fields of information security and image processing, and discloses a multi-image parallel encryption processing method based on an improved chaotic mapping, which comprises the following steps: separating and stacking each color channel of multiple images to be encrypted to construct a three-dimensional pixel matrix; extracting a matrix hash digest to be converted into a sub-key; inputting the sub-key into an improved chaotic mapping model of a historical state variable to iteratively generate a scrambling and diffusion sequence; performing sorting scrambling on the three-dimensional matrix in multiple orthogonal dimension sections by using the sequence; mapping the sequence into a shift step length to perform a cyclic shift and a bitwise XOR linkage diffusion on the pixels; and finally, outputting ciphertext images by segmentation. The application breaks the physical isolation of a single image to realize spatial depth mixing by constructing a three-dimensional matrix and performing cross-dimension scrambling; the chaotic dynamics degradation under limited precision is overcome by means of a historical state delay; and the efficiency of multi-image encryption and the system attack resistance are improved by using a shift and XOR linkage to realize bit-level depth confusion.

Description

Technical Field

[0001] This invention relates to the fields of information security and image processing, specifically to a method for parallel encryption processing of multiple images based on improved chaotic mapping. Background Technology

[0002] With the popularization of multimedia communication technologies, the data security issues of massive digital images during network transmission are becoming increasingly prominent. Chaotic systems, due to their inherent sensitivity to initial conditions, unpredictability, and excellent pseudo-randomness, have been widely used in the field of image encryption. A typical chaotic image encryption architecture usually includes two main stages: pixel scrambling and pixel diffusion, to disrupt the correlation between adjacent pixels and mask their statistical characteristics.

[0003] However, existing image encryption schemes still face some limitations in practical applications. Most traditional algorithms process single images independently, requiring multiple serial calculations when dealing with multi-source image data, resulting in low overall encryption efficiency. In this single-image isolation processing mode, there is a lack of data linkage between different images. Once an attacker masters the encryption pattern of a specific image, they can easily launch joint or differential attacks against the system. In the design of the underlying chaotic sequence generator, conventional one-dimensional or low-dimensional discrete chaotic mappings are prone to dynamic degradation when digitally implemented on computers or other devices with limited precision. Limited computational precision disrupts the continuous evolution trajectory of the chaotic phase space, causing the generated pseudo-random sequences to fall into short-period loops, directly weakening the key space and attack resistance of the encryption system.

[0004] Furthermore, traditional pixel obfuscation mechanisms mostly rely on a single bitwise XOR operation to obfuscate ciphertext values. While this linear operation is computationally simple, it results in relatively independent changes in image pixels across different bit planes. Attackers can exploit bit plane extraction attacks, gradually recovering the original plaintext information by peeling away or analyzing the independent changes between the low- and high-bit planes of the image. This makes existing data obfuscation mechanisms insufficient to meet high-standard security requirements. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-image parallel encryption processing method based on improved chaotic mapping, which solves the problems of low encryption efficiency of existing single-image encryption, weak resistance to differential attacks due to physical isolation between plaintext images, and easy degradation of the dynamic characteristics of traditional chaotic mapping on devices with limited precision.

[0006] To achieve the above objectives, the present invention provides a multi-image parallel encryption processing method based on improved chaotic mapping, comprising the following steps: Multiple images to be encrypted are acquired, and the data of each color channel of the multiple images to be encrypted are separated and stacked along the depth direction to construct a unified three-dimensional pixel matrix. Extract the hash digest of the three-dimensional pixel matrix and convert the hash digest into a subkey set containing initial values ​​and control parameters; The subkey set is input into an improved chaotic mapping model that incorporates historical state variables to iteratively generate a first type of sequence for pixel scrambling operations and a second type of sequence for pixel diffusion operations. A position index is generated based on the first type of sequence, and the position index is used to sort and scramble the data sections of the three-dimensional pixel matrix in multiple orthogonal dimensions in turn; The second type of sequence is mapped to a shift step sequence and an integer mask sequence, respectively. The shift step sequence is used to perform a cyclic shift operation on the pixel values ​​of the scrambled three-dimensional pixel matrix, and the shifted data is XORed with the integer mask sequence to obtain the ciphertext three-dimensional matrix. The ciphertext 3D matrix is ​​depth-segmented according to the original dimensions of the image to be encrypted, and multiple ciphertext images are output.

[0007] Preferably, the step of converting the hash digest into a subkey set containing initial values ​​and control parameters includes: The obtained hash digest is evenly divided into multiple bit sequence groups with a fixed bit width, and the bit sequence groups are converted into unsigned decimal numerical sequences. The unsigned decimal numerical sequence is defined by an index range and continuously summed using arithmetic. Normalized values ​​are obtained by combining division to reduce the magnitude and modulo operation, and a preset constant term is added. The subkey set consisting of the first part subkey and the second part subkey is then calculated.

[0008] Preferably, the improved chaotic mapping model includes an improved Logistic mapping and an improved Hénon mapping, and the improved mechanism for applying nonlinear perturbations to the improved chaotic mapping model is as follows: In the iterative equation of the basic chaotic mapping model, historical state variables that are affected by the current iteration number and rounded down are extracted and used to introduce a time delay that dynamically jumps with the iteration number. After converting the current result of the basic mapping operation and the historical state variable from floating-point to integer format, a bitwise XOR operation is performed, and the XOR result is remapped back to the valid real number field of the corresponding mapping, and the updated state value is output.

[0009] Preferably, the first part of the subkey is used as the initial value and bifurcation parameter of the improved Logistic mapping to iteratively generate multiple sets of the first type of sequence; the second part of the subkey is used as the initial value and system parameter of the improved Hénon mapping to iteratively generate multiple sets of the second type of sequence.

[0010] Preferably, the step of sorting and scrambling the data sections of the three-dimensional pixel matrix in multiple orthogonal dimensions using the position index includes: The scrambling operations for the first-dimensional aspect, the second-dimensional aspect, and the third-dimensional aspect are executed sequentially. In single-dimensional scrambling, the three-dimensional pixel matrix is ​​divided into multiple two-dimensional data sections along a single coordinate axis. The first type of sequence corresponding to the current coordinate axis direction is numerically sorted to obtain an ordered sequence and a sorted sequence. The two-dimensional data section is unfolded into a one-dimensional pixel vector. The position of the one-dimensional pixel vector is rearranged according to the position mapping relationship indicated by the sorted sequence. After the rearrangement is completed, the pixel vector is folded back into the two-dimensional section format and re-stacked and combined.

[0011] Preferably, the step of mapping the second type of sequence to a shift step sequence and performing a cyclic shift operation on the pixel values ​​of the scrambled three-dimensional pixel matrix using the shift step sequence includes: The floating-point value in the second type of sequence is multiplied by the first conversion constant to amplify it to the integer range and a modulo operation is performed on the pixel bit width to obtain the shift step sequence of the internal bits of the pixel; Using the shift step sequence, each pixel value in the three-dimensional pixel matrix, which is expanded into a one-dimensional vector, is cyclically shifted left according to the corresponding step size to generate a new pixel value after shifting.

[0012] Preferably, the step of performing a bitwise XOR operation between the shifted data and the integer mask sequence includes: Multiply the floating-point value in the second type sequence by the second conversion constant and convert it to an integer form to obtain the integer mask sequence that matches the bit depth of the image pixels; The new pixel value after the cyclic left shift process is XORed with the integer mask sequence pixel by pixel to generate the ciphertext pixel value.

[0013] Preferably, the method further includes a decryption stage for restoring the ciphertext image to a plaintext image, specifically including: The encrypted image is obtained and stacked in the channel depth direction to construct a three-dimensional matrix of ciphertext for decryption. Receive the original image plaintext features or subkey set from the auxiliary transmission, and iteratively generate the same first type sequence and second type sequence again according to the forward encryption logic; Based on the reverse order of encryption, the inverse XOR operation and the dynamic step-size inverse cyclic shift operation are performed sequentially to obtain the intermediate recovery matrix. Then, the inverse position recovery of each dimension of the cross-section is carried out in sequence, and finally, multiple plaintext images are split and output.

[0014] Preferably, in the dynamic step-size reverse cyclic shift operation of the decryption stage, a cyclic right shift is used for restoration, and the specific algebraic operation rules for the cyclic right shift are as follows: The high-order data after right shift is extracted by dividing by the shift step size raised to a preset base and rounding down. The low-bit data in the high-bit region is extracted by multiplying the remaining bit depth by the preset base; the high-bit data and the low-bit data are combined, and the overflow part is truncated by taking the modulus of the bit depth threshold to generate the reverse-shifted pixel value.

[0015] Preferably, in the reverse position recovery operation of the decryption stage, the three-dimensional matrix to be recovered is divided into two-dimensional data sections and expanded into one-dimensional pixel vectors. A forward sorting sequence is generated using the first type of sequence corresponding to the current dimension. The pixel value of the current position of the one-dimensional pixel vector is directly assigned to the target spatial position indicated by the sorting sequence to generate a two-dimensional data section that has been de-scrambled.

[0016] This invention provides a multi-image parallel encryption processing method based on improved chaotic mapping. It has the following beneficial effects: 1. This invention separates the color channel data of multiple images to be encrypted and stacks them along the depth direction to construct a unified three-dimensional pixel matrix. Combined with the scrambling operation of cross-section sorting in multiple orthogonal dimensions, it breaks the physical isolation of conventional single-image independent encryption. This enables pixels that originally belong to different image files and different color channels to perform global position migration across images in a unified three-dimensional coordinate system, realizing spatial depth mixing of multi-source data. While improving the efficiency of parallel processing of multiple images, it also enhances the system's ability to resist joint attacks and known-plaintext attacks.

[0017] 2. This invention employs an improved chaotic mapping model that incorporates historical state variables when generating encrypted sequences. By extracting the rounded-down historical state values ​​and performing a bitwise XOR operation with the current basic mapping result in the underlying binary format, a time delay and nonlinear perturbation that dynamically jumps with the number of iterations are applied to the system. This overcomes the problems of dynamic characteristic degradation and short-period loops that are prone to occur when traditional discrete chaotic systems run on devices with limited precision. It ensures that the output pseudo-random sequence has a stable and wide phase space and excellent chaotic characteristics, thereby improving the underlying security of the algorithm.

[0018] 3. In the pixel diffusion stage, this invention employs a dynamic step-size cyclic shift and bitwise XOR linkage processing method. It utilizes chaotic sequences to generate dynamic shift step sizes to perform shift operations on pixel values. Before performing numerical XOR obfuscation, the initial bit arrangement within the pixel is shuffled in advance, allowing the low-bit data of the pixel to dynamically jump to the high-bit region, thus changing the bit weight distribution of the original pixel. This overcomes the shortcomings of traditional single XOR diffusion operations, where the changes in each bit plane are relatively independent and susceptible to bit plane extraction attacks. It achieves deep obfuscation of data at the bit level and further eliminates the statistical regularity of ciphertext images. Attached Figure Description

[0019] Figure 1 This is a structural block diagram of the multi-image encryption system provided in the embodiments of the present invention; Figure 2 This is a flowchart illustrating a multi-image parallel encryption processing method based on improved chaotic mapping provided in an embodiment of the present invention; Figure 3 This is a bar chart comparing the information entropy of plaintext and ciphertext images in an embodiment of the present invention. Figure 4 This is a bar chart comparing the correlation coefficients of adjacent pixels between the plaintext image and the ciphertext image in an embodiment of the present invention. Figure 5 This is a line graph showing the fluctuation of differential attack test indicators in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions in 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.

[0021] See attached document Figure 1 The multi-image encryption system of the present invention includes a preprocessing module, a key and sequence generation module, a pixel scrambling module, a pixel diffusion module, and a postprocessing module.

[0022] The preprocessing module receives multiple original images to be encrypted and reassembles the image data into a three-dimensional pixel matrix.

[0023] The key and sequence generation module is used to calculate the SHA-512 hash value of the three-dimensional pixel matrix, group and convert the hash value to obtain a subkey set; at the same time, it is used to input the subkey set as initial value and parameter into the PVX method improved Logistic mapping and PVX method improved Hénon mapping to generate multiple sets of sequences.

[0024] The pixel scrambling module is used to generate corresponding sorted sequences from multiple sets of sequences, and then use the sorted sequences to perform sorting and scrambling on multiple dimensional sections of the three-dimensional pixel matrix.

[0025] The pixel diffusion module is used to map the values ​​of a specific sequence to shift steps, perform cyclic shift operations on the scrambled matrix, and XOR the shifted matrix elements with the specific sequence.

[0026] The post-processing module is used to separate the dimensions of the completed diffusion 3D matrix and output multiple encrypted images.

[0027] See attached document Figure 2 This invention provides a multi-image parallel encryption processing method based on improved chaotic mapping, comprising the following steps: Multiple images to be encrypted are acquired, and the pixel data of all images are used to construct a three-dimensional pixel matrix to complete the preprocessing stage. The hash value of the three-dimensional pixel matrix is ​​calculated using the SHA-512 function. The hash value is divided into multiple bit sequence groups and converted into decimal values. Multiple subkeys containing initial values ​​and parameters are obtained through algebraic operations. The first part of the subkey is used as the initial value and parameter of the PVX method to improve the Logistic mapping to generate multiple sets of first sequences, and the second part of the subkey is used as the initial value and parameter of the PVX method to improve the Hénon mapping to generate multiple sets of second sequences. Based on multiple sets of first sequences, a corresponding sorting sequence is generated. The sorting sequence is then used to sort and scramble all cross-sections of the three-dimensional pixel matrix in different dimensions to complete the pixel scrambling stage. The values ​​in multiple sets of second sequences are amplified and mapped to a preset range as the number of cyclic shift steps. The pixel values ​​of the three-dimensional pixel matrix are cyclically shifted to the left, and the shifted matrix data is XORed with the second sequence to complete the pixel diffusion stage. Multiple sets of ciphertext matrix data are separated from the three-dimensional matrix after the XOR operation is completed, according to the dimensions of the input image, and multiple ciphertext images are generated in the post-processing stage.

[0028] In the execution of the multi-image encryption method, the preprocessing stage is used to convert multiple independent two-dimensional plaintext images from external input into a unified three-dimensional data structure.

[0029] In the specific implementation process, a sequence of multiple plaintext images to be encrypted is obtained. For ease of description of the technical solution of this invention, the input plaintext images are defined as multiple images of the same size and resolution. The color images. In this embodiment, three color images are used as examples for specific explanation, and are labeled as follows: , and .in, This indicates the number of pixel rows in the vertical direction of the image. This represents the number of pixel columns in the horizontal direction of the image, and and All values ​​are positive integers. Pixel values ​​are represented by 8-bit unsigned integers, ranging from 0 to 255. Color images are constructed based on the RGB color space, and a single color image contains three color channels: red, green, and blue.

[0030] Perform channel separation on the acquired plaintext image sequence to obtain the two-dimensional pixel data of each channel. (For color images...) , and The red, green, and blue channel data for each image were separated. Separate the three dimensions, all of which are of similar size. The two-dimensional pixel data matrix is ​​denoted as follows: , and .image Separate three two-dimensional pixel data matrices , and .image Separate three two-dimensional pixel data matrices , and After channel separation processing, the three three-channel color plaintext images were split into nine independent two-dimensional single-channel pixel matrices.

[0031] In some optional implementations, a three-dimensional spatial data reconstruction operation is performed to construct a unified three-dimensional pixel matrix. The nine two-dimensional single-channel pixel matrices obtained after channel separation are spatially stacked along the depth dimension according to a preset arrangement sequence. In this embodiment, the matrix... , , , , , , , and They are stacked and combined sequentially as layers in a fixed order in a three-dimensional space to generate a layer with a dimension of [dimensional value missing]. The three-dimensional pixel matrix, denoted as matrix In more general applications, if the number of input images is... , of which If the integer is a positive integer greater than 1, the size of the resulting 3D pixel matrix after recombination is... The principle of combining multiple two-dimensional images into a three-dimensional matrix lies in breaking the limitation of independent encryption of a single image, enabling subsequent encryption steps to perform pixel-linked scrambling across different images and different color channels, thereby improving the overall algorithm's ability to resist joint attacks.

[0032] matrix The construction process unifies the dimensions of multi-source image data, mapping pixels that originally belonged to different image files and different color channels to the same three-dimensional coordinate system. (Three-dimensional pixel matrix) It contains all the original pixel data of the plaintext image sequence and serves as a single data source for subsequent feature extraction and spatial scrambling encryption processes.

[0033] In this embodiment, during the execution of the multi-image encryption method, the key generation stage is used to extract plaintext features and generate dynamic keys. Binding plaintext features to key generation calculations allows each encryption key to be associated with the input original image data, enabling different image data to correspond to different key parameters, thereby providing the ability to resist differential analysis attacks.

[0034] In the specific implementation process, a secure hash algorithm is used to perform hash calculations on the three-dimensional pixel matrix generated in the preprocessing stage to obtain a fixed-length plaintext feature hash digest. In this embodiment, the SHA-512 function is used to hash the three-dimensional pixel matrix. All pixel data are processed as a whole, and the output is a hash value of length 512 bits, denoted as a binary sequence. .

[0035] Furthermore, the hash value is split and numerically transformed. The 512-bit binary sequence is... The binary data is divided into 16 groups of 32 consecutive bits each, with a fixed bit width. Each of these 16 groups of 32-bit binary bits is then converted into an unsigned decimal integer to obtain a numerical sequence. , where the index identifier And each value The value range is 0 to 2. 32 -1.

[0036] In some optional implementations, multiple subkeys containing initial values ​​and control parameters are calculated based on the converted decimal numerical sequence. The principle of converting plaintext feature data into chaotic parameters lies in utilizing the high sensitivity of hash algorithms to input data to extract plaintext features as perturbation sources, altering the initial value evolution trajectory of the nonlinear chaotic system. When the input plaintext image changes, the extracted hash value also changes, leading to different calculated subkeys. Following a preset algebraic operation formula, combined with accumulation, normalization, and modulo operations, ten specific subkeys are calculated. These ten subkeys are... , , , , , , , , and .

[0037] The specific formula for calculating the subkey is as follows: ; ; ; ; ; ; ; ; ; ; In the formula, This represents a continuous arithmetic summation operation for values ​​within the corresponding index range, for example... Indicates will to A total of seven values ​​are added together. The operation of taking the decimal part of the result within the parentheses aims to map the calculated value to the interval between 0 and 1. Dividing by 256 reduces the magnitude of the accumulated sum and, in conjunction with the modulo operation, normalizes the value. The added constant term in the formula ensures that the system parameters fall within the effective working range of the chaotic mapping model. Specifically, adding 3 makes the parameters... , and The final value range of is limited to between 3 and 4, satisfying the dynamic requirement that the Logistic mapping exhibits a complex state within the corresponding numerical range; the operations of adding 1 and adding 0.3 make the parameter The value range is between 1 and 2, parameter The value of is between 0.3 and 1.3, which satisfies the parameter conditions for the generation of chaotic attractors by the Hénon map.

[0038] The calculated result, consisting of ten subkeys, is divided into two parts. The first part of the subkeys contains... , , , , and This is used to provide initial values ​​and bifurcation parameters for subsequent Logistic mapping models improved based on the PVX method. The second part of the subkey contains... , , and This is used to provide initial values ​​and system parameters for the subsequent Hénon mapping model improved based on the PVX method, serving as the basis for chaotic iteration. Through the above computational process, the binding calculation of image features and the cryptographic key is completed. To ensure that the decryption end can correctly generate the same sequence to recover the original image, the extracted plaintext feature hash digest is used. Alternatively, the subkey set calculated above can be used as an auxiliary key and transmitted to the decryption end through an independent secure channel, or it can be appended to the final output ciphertext data as key header information and sent together.

[0039] In this embodiment, during the execution of the multi-image encryption method, the sequence generation stage is used to provide multiple sets of pseudo-random sequences required for subsequent scrambling and diffusion processing. To overcome the problem of weakened and degraded dynamic characteristics that easily occur when implementing traditional discrete chaotic mapping on devices with limited precision, a mapping model based on the PVX method is used to generate sequences in the specific implementation process.

[0040] In some optional implementations, the image dimension parameters determined in the preprocessing stage are combined with the subkey obtained in the key generation stage to perform iterative computation of the sequence. The principle behind the PVX method's improvement lies in introducing dynamic historical state variables into the iterative equations of the basic chaotic mapping model for bitwise XOR operations, thereby applying nonlinear perturbations. Traditional methods typically rely only on the current state or a fixed previous state, easily falling into short-period loops. The PVX method extracts the index as... The historical state value at a given point implies the introduction of a time delay that dynamically jumps with the number of iterations. After converting the result of the basic mapping operation and the corresponding historical state value into underlying binary data, a bitwise XOR operation is performed to continuously disrupt the original phase space trajectory, ensuring that the generated numerical sequence maintains excellent chaotic characteristics.

[0041] When generating the first type of sequence for pixel scrambling operations, the first part of the subkey obtained in the key generation stage is invoked. This first part of the subkey is used as the initial value and bifurcation parameter for the improved Logistic mapping using the PVX method. Based on the perturbation principle of the PVX method described above, the iterative expression for the improved Logistic mapping is as follows: ; In the formula, Indicates the current iteration number; The improved Logistic mapping is represented in the first... The state value at the next iteration; Indicates the first The new state value generated in the next iteration; Indicates that the index is The historical state value at the floor position; These are the input bifurcation parameters.

[0042] Based on the above iterative mechanism, the initial values ​​are respectively... and parameters Substituting into the improved Logistic mapping model, the iterative generation length is... Let's denote the sequence as sequence 1. Initialize the values... and parameters Substituting into the model, the iterative generation length is (in this embodiment) That is, the length is Let's denote the sequence as sequence 2. Initialize the values... and parameters Substituting into the model, the iterative generation length is (in this embodiment) The sequence is denoted as sequence 3.

[0043] The second part of the subkey is invoked when generating the second type of sequence for pixel diffusion operations. This second part of the subkey is used as the initial value and system parameters for the PVX-based improved Hénon map. The Hénon map is a classic two-dimensional discrete chaotic map. To address the problem of weakened dynamic properties under finite precision, the PVX method is used to improve the map; the improved expression is as follows: ; ; In the formula, and These represent the two-dimensional Hénon mappings at the 1st, 2nd, and 3rd respectively. The current state values ​​of the two dimensions at the next iteration; and Indicates the first The new state value generated in the next iteration; and These are the input system control parameters; This indicates the truncation or floating-point conversion function implemented on a device with finite precision; This represents a mapping function used to convert historical state values ​​in floating-point form into an integer format suitable for XOR operations; This indicates a bitwise XOR operation. This represents the inverse mapping function used to remap the integer result obtained from the XOR operation back to the corresponding valid real number state domain.

[0044] In one specific implementation, the above , and This can be achieved through numerical multiplication and rounding. For example, setting a conversion constant. (like ),function and Specifically, this is implemented by processing the input floating-point number. Multiply by a constant And round down to the nearest integer, i.e. This yields a large integer; after the XOR operation, the reverse mapping function is used. Specifically, this is implemented by XORing the integer obtained from the XOR operation. Divide by constant ,Right now This restores the result to a floating-point number.

[0045] Furthermore, it will include initial values. , and parameters , The second part of the subkey is input into the improved Hénon mapping model described above, and iterative calculations are performed. This requires processing the three-dimensional pixel matrix. The system performs a global pixel diffusion operation, continuously iterating until the amount of data generated meets the total volume requirement. Ultimately, two lines of length [missing information] are generated. (in this embodiment) The chaotic pseudo-random sequences of ) are denoted as follows: sequence sum Sequences. Two long sequences will serve as independent data sources, supporting encrypted transformation operations for each pixel within subsequent spatial coordinates.

[0046] In this embodiment, during the execution of the multi-image encryption method, the pixel scrambling stage is used to disrupt the spatial correlation between adjacent pixels of the plaintext image. To improve the scrambling effect and break the physical isolation between different images and different color channels, in the specific implementation process, multi-dimensional three-dimensional cross-sectional sorting scrambling is performed on the three-dimensional pixel matrix generated in the preprocessing stage.

[0047] The principle of multi-dimensional 3D slice sorting and scrambling lies in slicing a unified 3D pixel matrix along different spatial coordinate axes and rearranging the pixel data within each slice using a dynamically generated index sequence. Combining Sequence 1, Sequence 2, and Sequence 3 obtained during the sequence generation stage, pixel position permutations are performed on three orthogonal dimensional slices.

[0048] In some optional implementations, a first-dimensional scrambling operation based on sequence 1 is performed. The dimension size is... (in this embodiment) A three-dimensional pixel matrix with a depth of 9. Divided along the depth direction into The size is A two-dimensional data section. The length obtained during the sequence generation stage is... Perform a numerical sorting operation (e.g., ascending sort) on sequence 1 to obtain the corresponding position index sequence, denoted as sorted sequence 1.

[0049] Using sorted sequence 1, the drawn Each two-dimensional data slice is individually permuted to its pixel position. In practice, each two-dimensional data slice is unfolded into a length of... Given a one-dimensional pixel vector, based on the position mapping relationship indicated in sorting sequence 1, the pixels in the one-dimensional pixel vector are moved to their corresponding new positions. The specific rearrangement operation formula is as follows: ; ; In the formula, This represents the ascending sorting function; This represents the input sequence 1. This represents the ordered sequence obtained after sorting. This represents the sorted sequence 1 generated by the sorting process; This is the location index, with values ​​ranging from 1 to... Integers; This represents a one-dimensional pixel vector expanded before scrambling. This represents the new one-dimensional pixel vector generated after scrambling. (Complete) After the positions of the facets are replaced, the one-dimensional pixel vector is folded back into... The two-dimensional cross-section format is then re-stacked along the depth direction to obtain an intermediate three-dimensional matrix after one scrambling. .

[0050] Furthermore, a second-dimensional aspect scrambling operation based on sequence 2 is performed. This scrambling operation is then applied to the intermediate three-dimensional matrix. Divided horizontally into The size is A two-dimensional data section. The obtained length is... Perform a sorting operation on sequence 2 to obtain the corresponding sorted sequence 2. Use sorted sequence 2 to reorganize the drawn portion. The size is The pixel positions of the two-dimensional data slice are permuted one by one. The slice is then unfolded into a length of... Given a one-dimensional pixel vector, we perform element rearrangement on the one-dimensional pixel vector using sorting sequence 2. The corresponding rearrangement operation formula is as follows: ; ; In the formula, This represents the input sequence 2. This represents the ordered sequence obtained after sorting. This represents the sorted sequence 2 generated by the sorting process; This is the location index, with values ​​ranging from 1 to... Integers; This represents the currently drawn, undisturbed one-dimensional pixel vector. This represents the new one-dimensional pixel vector generated after scrambling. After rearrangement, the one-dimensional pixel vector is folded back into a two-dimensional sectional format and recombine along the horizontal direction to obtain the intermediate three-dimensional matrix after secondary scrambling. .

[0051] In a specific implementation scenario, a third-dimensional aspect scrambling operation based on sequence 3 is performed. This involves scrambling the intermediate three-dimensional matrix. Divided along the vertical direction into The size is A two-dimensional data section. The obtained length is... Perform a sorting operation on sequence 3 to obtain the corresponding sorted sequence 3. Using sorted sequence 3, process the drawn... The size is The pixel positions of the two-dimensional data slice are permuted one by one. The slice is then unfolded into a length of... The one-dimensional pixel vector is shuffled using sorting sequence 3. The corresponding rearrangement formula is as follows: ; ; In the formula, This represents the input sequence 3; This represents the ordered sequence obtained after sorting. This represents the sorted sequence 3 generated by the sorting process; This is the location index, with values ​​ranging from 1 to... Integers; This represents a one-dimensional pixel vector before scrambling. This represents a scrambled one-dimensional pixel vector. After rearrangement, the one-dimensional pixel vector is folded back into a two-dimensional slice format and recombine along the vertical direction to generate the final scrambled three-dimensional matrix. .

[0052] In the multi-dimensional three-dimensional cross-section sorting and scrambling process, three operation steps alternately traverse the rows, columns, and color channel depths of the image. In the single-dimensional cross-section scrambling process, because the cross-section contains channel data from different original images, the movement of pixels is no longer confined to the original single image. Through three-dimensional orthogonal cross-section rearrangement, any pixel can move within the original single image. Global position migration is achieved within the complete three-dimensional space, thereby enabling deep spatial mixing of features from multiple plaintext images, providing a foundation for the subsequent pixel diffusion stage.

[0053] In this embodiment, during the execution of the multi-image encryption method, the pixel diffusion stage is used to change the values ​​of image pixels. Through bit-level recombination and numerical obfuscation of pixel values, the statistical characteristics of the encrypted image are further eliminated. In the specific implementation process, in order to overcome the limitation that conventional single XOR operations are easily cracked, a diffusion operation with dynamic step-size shift and XOR linkage is performed on the scrambled three-dimensional matrix.

[0054] The principle behind dynamic step-size shifting and XOR-linked diffusion lies in the fact that traditional image diffusion typically only uses XOR operations, leading to relatively independent changes in pixels across different bit planes (such as high and low bits), making it vulnerable to bit plane extraction attacks. By introducing a sequence-based dynamic cyclic shift before the XOR operation, the initial bit arrangement within a pixel can be shuffled, allowing low-bit features to dynamically jump to high bits, thereby altering the pixel's bit weight distribution. Subsequently, the shifted pixel value is XORed with another set of sequences, completing the numerical-level data obfuscation.

[0055] In some alternative implementations, sequence-based execution is performed. The dynamic step-size shift operation. The length obtained by calling the sequence generation stage is... sequence , and the scrambling three-dimensional matrix output during the scrambling phase The scrambled three-dimensional matrix will be... Unfold the sequence into a one-dimensional pixel vector in a predetermined order. The floating-point values ​​are mapped to a cyclic shift step size suitable for an eight-bit pixel depth. The specific step size conversion formula is as follows: ; In the formula, This is the location index, with values ​​ranging from 1 to... Integers; Represents a sequence The Middle A floating-point value at each position; This represents the calculated cyclic shift step size for the corresponding position; its value is an integer ranging from 0 to 7. This indicates the floor function; This indicates a modulo operation on 8. The threshold for the modulo operation is determined based on the fact that the pixel depth of the image in this embodiment is 8 bits. For the first transformation constant (e.g., take...) The value range must ensure that the floating-point values ​​of the sequence can be amplified to an integer range sufficient to extract pseudo-random mantissa features.

[0056] Using the calculated step size sequence For scrambled three-dimensional matrices Each pixel value in the expanded one-dimensional pixel vector undergoes a circular left shift operation. The algebraic formula for the circular left shift is as follows for a pixel represented by an eight-bit unsigned integer: ; In the formula, Represents a scrambled three-dimensional matrix In position The original pixel value at that location; This represents the new pixel value generated after a cyclic left shift; This ensures that any overflow after the shift operation is truncated, maintaining the pixel value within the valid range of 0 to 255. Through dynamic step-size cyclic shifting, the internal bits of the pixel value are dynamically reorganized according to the step size provided by the sequence, resulting in the shifted intermediate matrix. .

[0057] Furthermore, in specific implementation scenarios, sequence-based execution is performed. The XOR diffusion operation. The length obtained by calling the sequence generation stage is... sequence Due to the sequence Since this is also a sequence of floating-point numbers, the corresponding floating-point values ​​need to be converted to integers within the range of 0 to 255 for bitwise operations with image pixel values. The specific conversion and XOR diffusion formulas are as follows: ; ; In the formula, Represents a sequence The Middle A floating-point value at each position; For the second transformation constant (e.g., take...) (used to convert floating-point numbers to large integers); This represents the 8-bit integer mask value obtained after conversion; This represents the final ciphertext pixel value generated after the XOR operation; This represents a bitwise XOR operation. It utilizes a sequence of XOR operations on a pixel-by-pixel basis. The pseudo-randomness of the algorithm is used to perform a global operation on the shifted pixel values, generating a one-dimensional ciphertext vector containing all encrypted data. This one-dimensional ciphertext vector is then folded and reassembled into a new vector of size [missing information]. ciphertext three-dimensional matrix .

[0058] After the pixel diffusion stage is completed, the ciphertext image is separated and post-processed. This will include... The encrypted three-dimensional matrix of image data The images are split sequentially along the depth direction by channel. In this current embodiment, the input terminal processes three color images (i.e., Therefore, from the dimension of ciphertext three-dimensional matrix In the process, the images are segmented and separated into groups of three consecutive depth channels (e.g., channels 1 to 3 as the first group, channels 4 to 6 as the second group, and channels 7 to 9 as the third group), resulting in three independent images of varying sizes. The color ciphertext images are denoted as ciphertext images. Encrypted images With encrypted images The resulting encrypted images, after being split, exhibit a visually uniform distribution, achieving the goal of multi-image parallel encryption.

[0059] In this embodiment, the decryption stage is the reverse process of the aforementioned multi-image encryption method, used to restore the ciphertext image to the original multiple plaintext images. To ensure the lossless nature of data recovery, the specific implementation process sequentially performs preprocessing, de-diffusion, descrambling, and post-processing operations in reverse order.

[0060] In some optional implementations, a decryption preprocessing phase is performed. The encrypted ciphertext images are received; assuming three images of the same size are received... The three color ciphertext images are stacked and combined along the channel depth direction to construct a dimension of [dimensionality missing]. (in this embodiment) That is, a ciphertext three-dimensional matrix with a depth of 9. .

[0061] Further, the sequence generation operation for decryption is performed. Since the decryption end cannot directly extract the original plaintext features from the ciphertext image, it first receives the plaintext feature hash digest transmitted by the encryption end via a secure channel (or ciphertext header information). Alternatively, it can directly receive a set of subkeys. Based on this, if the received data is a hash digest... The same key generation logic as in the encryption phase is invoked to extract the same subkey set. This subkey set is then used as the initial value and control parameters for the improved mapping model in the PVX method, and the keys are iteratively regenerated to obtain keys of the same length. , and Sequence 1, Sequence 2, and Sequence 3, and sequences of length 1, 2, and 3, respectively. sequence with sequence .

[0062] In specific implementation scenarios, the decryption reverse diffusion phase is executed. The reverse diffusion phase follows the reverse order of encryption diffusion, sequentially performing XOR recovery and dynamic step-size reverse shift.

[0063] Call sequence , convert the sequence Convert floating-point values ​​to integer mask values Because the bitwise XOR operation has the property of symmetric reflexivity, it can directly convert the ciphertext three-dimensional matrix. By unfolding the ciphertext into a one-dimensional vector in a predetermined order and performing an XOR operation with the mask value, the numerical mask overlay can be removed. The specific inverse XOR formula is as follows: ; In the formula, This is the location index, with values ​​ranging from 1 to... Integers. Indicates the position of the ciphertext vector Pixel value at that location, This represents the intermediate recovered value obtained after stripping the XOR mask.

[0064] Furthermore, call sequence The cyclic shift step size sequence is calculated using the same step size transformation formula as the encryption phase. Using step size sequences A circular right shift operation is performed on the intermediate recovered value to restore the true bit arrangement within the pixel. For an eight-bit unsigned integer, the algebraic formula for the circular right shift is as follows: ; In the formula, This represents the inverse scrambled input value generated after a cyclic right shift, resulting in a fully stripped diffusion property. This is achieved by dividing by... And round down to the floor, shifting the higher-order data to the lower-order data to the right; by multiplying by This involves moving data from lower octaves to higher octaves; finally, through... The overflow portion is truncated, completing the reverse loop of bit-level recombination. The one-dimensional vector that has completed inverse diffusion is then refolded into a shape of size [missing information]. The inverse diffusion three-dimensional matrix .

[0065] After de-diffusion is completed, the decryption and descrambling phase is executed. The descrambling phase follows the reverse order of encryption and scrambling, sequentially restoring the facet positions of the third, second, and first dimensions.

[0066] Perform a third-dimensional section recovery operation based on sequence 3. Reverse the diffusion three-dimensional matrix. Divided along the vertical direction into The size is The two-dimensional data section is obtained. A sorting operation is performed on sequence 3 to obtain sorted sequence 3. The two-dimensional data section is unfolded into a one-dimensional vector, and the index is inverted using sorted sequence 3 to restore the pixel positions. The specific reverse rearrangement formula is as follows: ; In the formula, This is the location index, with values ​​ranging from 1 to... Integers; The sorted sequence is 3. This indicates the index position in the current one-dimensional vector to be recovered. pixel values, This represents a one-dimensional pixel vector after the position has been restored. Spatial coordinates are restored by directly assigning the pixel value of the current position to the target spatial position indicated by the forward sorting index. After restoration, the one-dimensional pixel vector is folded back onto the two-dimensional plane and combined along the vertical direction to obtain the first intermediate restoration matrix. .

[0067] Following the same mapping principle, perform the second-dimensional section recovery operation based on sequence 2. Then, restore the first intermediate matrix... Divided horizontally into The size is The two-dimensional data section. Using the sorted sequence 2 generated from sequence 2, the expanded one-dimensional vector is reverse-rearranged, and the specific recovery formula is as follows: ; In the formula, The value range is 1 to Location index; Indicates sort series 2, This indicates the index position in the current one-dimensional vector to be recovered. pixel values, This represents a one-dimensional pixel vector after position restoration; after position restoration, the vector is folded and combined along the horizontal direction to obtain the second intermediate restoration matrix. .

[0068] Perform the first-dimensional section recovery operation based on sequence 1. Then, restore the second intermediate matrix. Divided along the depth direction into The size is The two-dimensional data section. Using the sorted sequence 1 generated from sequence 1, the expanded one-dimensional vector is reverse-reassigned, and the specific recovery formula is as follows: ; In the formula, The value range is 1 to Location index; The sorted sequence is 1; This indicates the index position in the current one-dimensional vector to be recovered. pixel values, This represents a one-dimensional pixel vector after the position has been restored; after restoration, the cross-sections are folded and stacked along the depth direction to generate a three-dimensional pixel matrix that has been completely descrambled. Thus, the original multiple plaintext images were successfully restored.

[0069] Specific application example: Secure transmission of multi-source images in remote medical care Application Scenario Description: In modern smart healthcare systems, a comprehensive physical examination typically generates multiple medical images of different modalities (e.g., brain MRI, chest CT, bone X-rays). Because medical images contain highly sensitive personal information and different modalities are physically isolated, traditional single-image encryption methods are inefficient and easily compromised by attackers using single-image features for differential cracking. The multi-image parallel encryption system of this invention is perfectly suited for this scenario.

[0070] Specific execution process: Preprocessing stage: The hospital terminal acquired three color medical images of the same patient with a resolution of 256×256 (with artifacts). MRI pseudocolor image CT pseudocolor image, X-ray pseudocolor image , System extraction of , and , of , and , of , and By stacking pixels according to spatial depth, a unified three-dimensional medical pixel matrix with dimensions of 256×256×9 is constructed. .

[0071] Key generation stage: The system generates a three-dimensional pixel matrix. The entire process performs a SHA-512 hash operation, generating a 512-bit hash value which is then divided into 16 groups of decimal numbers. to Utilizing the algebraic operation formulas unique to this invention (e.g.) (etc.), generate ten subkeys. At this point, the minute details of these three medical images (even the difference of just one tumor pixel) are deeply bound to the aforementioned key parameters.

[0072] Sequence generation stage: Substituting the subkey into the PVX-Logistic and PVX-Hénon mappings that incorporate historical state perturbations. Utilizing Amplification truncation XOR mechanism (e.g.) This generates three first-class sequences for scrambling and two second-class sequences of length 589,824 (256×256×9) for diffusion. and .

[0073] Scrambling and diffusion phase: for the three-dimensional pixel matrix Three-dimensional orthogonal cutting and sorting were performed at depth (9 sections), horizontal (256 sections), and vertical (256 sections). Lesion pixels from CT scans could be physically transferred to the MRI image space, completely disrupting the original anatomical structure. Subsequently, a formula was used... Perform dynamic cyclic shifting, then combine with the sequence Perform XOR obfuscation. Post-processing stage: Separate the diffused ciphertext 3D matrix into groups of 3 channels to generate three ciphertext images with snowflake-like noise. Encrypted images With encrypted images After receiving the data, the doctor uses the hash digest obtained through the secure channel to reverse deduce the sequence, performs reverse shifting, reverse XOR, and reverse scrambling, and restores three clear medical images without loss.

[0074] Experimental verification and effect comparison: To verify the security of the multi-image encryption system of the present invention, a detailed cryptographic characteristic experiment was conducted on the aforementioned embodiments in a test environment, and the generated test result data was visualized and compared.

[0075] Image information content and distribution statistical analysis: Information entropy is an important indicator for measuring the degree of disorder in pixel distribution in an image system. The theoretical maximum information entropy of an ideal random image is 8. (See appendix) Figure 3 This figure shows a bar chart comparing the information entropy values ​​of plaintext and ciphertext images. (See attached...) Figure 3 Explanation: The horizontal axis represents the different image numbers participating in the test (Image 1, Image 2, Image 3), and the vertical axis represents the calculated information entropy. The lower bars on the left represent the original plaintext images, whose pixel distribution exhibits a clear structural pattern, with information entropy hovering only between 7.1 and 7.5; the higher bars on the right represent the ciphertext images processed by this system, with the values ​​clearly marked above the bars. It can be seen that the information entropies of the three ciphertext images reached 7.9993, 7.9992, and 7.9994 respectively, infinitely approaching the ideal maximum value of 8. This indicates that the dynamic step-size shift and XOR linkage diffusion mechanism of this invention breaks the statistical regularity of the original pixels, and the system output results exhibit a highly random distribution characteristic.

[0076] Spatial Adjacent Pixel Correlation Analysis: Adjacent pixels in natural images exhibit extremely high numerical correlations in the horizontal, vertical, and diagonal directions, with correlation coefficients typically approaching 1. (See attached diagram) Figure 4 This figure shows a histogram comparison of the correlation coefficients between adjacent pixels before and after encryption. (The remaining text appears to be incomplete and requires further context.) Figure 4 Explanation: The horizontal axis represents the three spatial directions of sampling (horizontal, vertical, and diagonal), and the vertical axis represents the correlation coefficient value. The specific values ​​of each indicator are clearly marked in the figure. The unprocessed original image has correlation coefficients of over 0.9 in all three directions, indicating that adjacent data are highly similar; however, after processing by this invention, the correlation coefficients drop sharply, with the values ​​in each direction approaching 0 (e.g., the horizontal direction drops to 0.0012). This proves that the multi-dimensional three-dimensional cross-section sorting and scrambling method used in this invention successfully disperses adjacent feature data completely throughout the three-dimensional space, cutting off the attacker's attempt to deduce global information through local adjacent patterns.

[0077] Analysis of Differential Tampering Attacks: Differential attacks aim to break a system by fine-tuning a single input plaintext pixel and observing the changes in the output ciphertext. The metrics for evaluating this defense capability are the Non-Pin Count Change Rate (NPCR) and the Uniform Average Change Intensity (UACI), with theoretical extreme values ​​of 99.6094% and 33.4635%, respectively. (See Appendix) Figure 5 The figure shows the line trend of the system's NPCR and UACI after multiple independent fine-tuning tests. (See attached...) Figure 5Explanation: The left vertical axis and solid line of the chart correspond to the NPCR data trend, while the right vertical axis and dashed line correspond to the UACI data trend. The horizontal axis represents the five independent single-pixel tampering test rounds. The chart clearly marks the specific percentage values ​​for each test node. From the line trends and node values ​​in the chart, it can be seen that regardless of which part of the image is tampered with, the NPCR remains stable at around 99.61%, and the UACI remains stable at around 33.46%.

Claims

1. A method for parallel encryption processing of multiple images based on improved chaotic mapping, characterized in that, Includes the following steps: Multiple images to be encrypted are acquired, and the data of each color channel of the multiple images to be encrypted are separated and stacked along the depth direction to construct a unified three-dimensional pixel matrix. Extract the hash digest of the three-dimensional pixel matrix and convert the hash digest into a subkey set containing initial values ​​and control parameters; The subkey set is input into an improved chaotic mapping model that incorporates historical state variables to iteratively generate a first type of sequence for pixel scrambling operations and a second type of sequence for pixel diffusion operations. A position index is generated based on the first type of sequence, and the position index is used to sort and scramble the data sections of the three-dimensional pixel matrix in multiple orthogonal dimensions in turn; The second type of sequence is mapped to a shift step sequence and an integer mask sequence, respectively. The shift step sequence is used to perform a cyclic shift operation on the pixel values ​​of the scrambled three-dimensional pixel matrix, and the shifted data is XORed with the integer mask sequence to obtain the ciphertext three-dimensional matrix. The ciphertext 3D matrix is ​​depth-segmented according to the original dimensions of the image to be encrypted, and multiple ciphertext images are output.

2. The method for parallel encryption processing of multiple images based on improved chaotic mapping according to claim 1, characterized in that, The steps of converting the hash digest into a subkey set containing initial values ​​and control parameters include: The obtained hash digest is evenly divided into multiple bit sequence groups with a fixed bit width, and the bit sequence groups are converted into unsigned decimal numerical sequences. The unsigned decimal numerical sequence is defined by an index range and continuously summed using arithmetic. Normalized values ​​are obtained by combining division to reduce the magnitude and modulo operation, and a preset constant term is added. The subkey set consisting of the first part subkey and the second part subkey is then calculated.

3. The multi-image parallel encryption processing method based on improved chaotic mapping according to claim 2, characterized in that, The improved chaotic mapping model includes an improved Logistic mapping and an improved Hénon mapping. The improved mechanism for applying nonlinear perturbations to the improved chaotic mapping model is as follows: In the iterative equation of the basic chaotic mapping model, historical state variables that are affected by the current iteration number and rounded down are extracted and used to introduce a time delay that dynamically jumps with the iteration number. After converting the current result of the basic mapping operation and the historical state variable from floating-point to integer format, a bitwise XOR operation is performed, and the XOR result is remapped back to the valid real number field of the corresponding mapping, and the updated state value is output.

4. The multi-image parallel encryption processing method based on improved chaotic mapping according to claim 3, characterized in that, Using the first part of the subkey as the initial value and bifurcation parameter of the improved Logistic mapping, multiple sets of the first type of sequence are iteratively generated; Using the second part of the subkey as the initial value and system parameter of the improved Hénon mapping, multiple sets of the second type of sequence are iteratively generated.

5. The method for parallel encryption processing of multiple images based on improved chaotic mapping according to claim 1, characterized in that, The steps of sorting and scrambling the data sections of the three-dimensional pixel matrix in multiple orthogonal dimensions using the position index include: The scrambling operations for the first-dimensional aspect, the second-dimensional aspect, and the third-dimensional aspect are executed sequentially. In single-dimensional scrambling, the three-dimensional pixel matrix is ​​divided into multiple two-dimensional data sections along a single coordinate axis. The first type of sequence corresponding to the current coordinate axis direction is numerically sorted to obtain an ordered sequence and a sorted sequence. The two-dimensional data section is unfolded into a one-dimensional pixel vector. The position of the one-dimensional pixel vector is rearranged according to the position mapping relationship indicated by the sorted sequence. After the rearrangement is completed, the pixel vector is folded back into the two-dimensional section format and re-stacked and combined.

6. The multi-image parallel encryption processing method based on improved chaotic mapping according to claim 1, characterized in that, The steps of mapping the second type of sequence to a shift step sequence and performing a cyclic shift operation on the pixel values ​​of the scrambled three-dimensional pixel matrix using the shift step sequence include: The floating-point value in the second type of sequence is multiplied by the first conversion constant to amplify it to the integer range and a modulo operation is performed on the pixel bit width to obtain the shift step sequence of the internal bits of the pixel; Using the shift step sequence, each pixel value in the three-dimensional pixel matrix, which is expanded into a one-dimensional vector, is cyclically shifted left according to the corresponding step size to generate a new pixel value after shifting.

7. A method for parallel encryption processing of multiple images based on improved chaotic mapping according to claim 6, characterized in that, The step of performing a bitwise XOR operation between the shifted data and the integer mask sequence includes: Multiply the floating-point value in the second type sequence by the second conversion constant and convert it to an integer form to obtain the integer mask sequence that matches the bit depth of the image pixels; The new pixel value after the cyclic left shift process is XORed with the integer mask sequence pixel by pixel to generate the ciphertext pixel value.

8. The multi-image parallel encryption processing method based on improved chaotic mapping according to claim 1, characterized in that, It also includes a decryption stage for restoring the ciphertext image to a plaintext image, specifically including: The encrypted image is obtained and stacked in the channel depth direction to construct a three-dimensional matrix of ciphertext for decryption. Receive the original image plaintext features or subkey set from the auxiliary transmission, and iteratively generate the same first type sequence and second type sequence again according to the forward encryption logic; Based on the reverse order of encryption, the inverse XOR operation and the dynamic step-size inverse cyclic shift operation are performed sequentially to obtain the intermediate recovery matrix. Then, the inverse position recovery of each dimension of the cross-section is carried out in sequence, and finally, multiple plaintext images are split and output.

9. A method for parallel encryption processing of multiple images based on improved chaotic mapping according to claim 8, characterized in that, In the dynamic step-size reverse cyclic shift operation of the decryption phase, a cyclic right shift is used for restoration. The specific algebraic operation rules for the cyclic right shift are as follows: The high-order data after right shift is extracted by dividing by the shift step size raised to a preset base and rounding down. The low-bit data in the high-bit region is extracted by multiplying the remaining bit depth by the preset base; the high-bit data and the low-bit data are combined, and the overflow part is truncated by taking the modulus of the bit depth threshold to generate the reverse-shifted pixel value.

10. A method for parallel encryption processing of multiple images based on improved chaotic mapping according to claim 8, characterized in that, In the reverse position recovery operation of the decryption stage, the three-dimensional matrix to be recovered is divided into two-dimensional data sections and expanded into one-dimensional pixel vectors. A forward sorting sequence is generated using the first type of sequence corresponding to the current dimension. The pixel value of the current position of the one-dimensional pixel vector is directly assigned to the target spatial position indicated by the sorting sequence to generate a two-dimensional data section that has been de-scrambled.

Images