A Multi-Medical Image Encryption Method Based on a 3D Hyperchaotic System

Abstract

The present invention relates to a multi-medical image encryption method based on a three-dimensional hyperchaotic system, belonging to the technical field of medical image encryption. In the image preprocessing stage, this method generates a matrix to be encrypted by fusing two medical images through the Alpha channel, generates a key sequence by using the SHA-512 function in combination with the RGB and Alpha channel matrices, and generates a double-key matrix and a chaotic sequence through the three-dimensional hyperchaotic Logistic-Sine (3D-HCLSM) system; in the encryption stage, triple encryption operations are implemented: a primary ciphertext is generated by adopting a parameter-randomized dynamic Joseph scrambling strategy, and through an improved zigzag bidirectional cross-permutation strategy, while pixel diffusion is performed with the key matrix to obtain a secondary ciphertext, and finally a new bit-level scrambling strategy is carried out, and bitwise exclusive OR operation is performed with the key matrix to complete the final encryption. The present invention proposes a dynamic Joseph traversal mechanism with random parameters, combines an optimized zigzag permutation strategy and a new bit-level processing technology, and through the cooperative action of multi-level chaotic keys, significantly improves the anti-attack performance and security of medical image encryption.

Description

Technical Field

[0001] The present invention relates to a multi-medical image encryption method based on a three-dimensional hyperchaotic system, belonging to the technical field of medical image encryption, and applicable to the synchronous secure transmission and storage of multi-source medical images such as CT (Computed Tomography), MRI (Magnetic Resonance Imaging), and PET (Positron Emission Tomography). Background Art

[0002] The large-scale deployment of medical information systems and the normal operation of telemedicine have accelerated the digital process of the medical image data chain (transmission - storage - invocation). However, the data interaction in multiple links and the cloud hosting mode have significantly amplified the potential risks of privacy leakage and unauthorized access. Therefore, ensuring the security and privacy of medical image data is crucial for safeguarding the rights and interests of patients, complying with laws and regulations, and enhancing the credibility of medical institutions.

[0003] In this context, it is particularly urgent to develop a reliable and efficient medical image encryption technology. Existing medical image encryption methods usually only support the encryption of single images, while methods that can process multiple images are often inefficient and difficult to meet the actual application requirements. Therefore, there is an urgent need for a technology that can support the encryption of multiple medical images while ensuring high efficiency. This technology should not only be able to resist various potential security threats but also be able to quickly encrypt and decrypt medical images without sacrificing image quality, thereby effectively ensuring the security of medical images during transmission and storage and fully protecting patient privacy.

[0004] In recent years, due to its complex dynamic behavior and high randomness, the chaotic system has received extensive attention in the field of image encryption. The sequence generated by the chaotic system has unpredictability and initial value sensitivity, which can provide a strong randomness basis for encryption algorithms. Based on the chaotic theory and the above requirements, the present invention proposes a multi-medical image encryption method based on a three-dimensional hyperchaotic system, aiming to improve the security and privacy of medical images through innovative encryption technology. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-medical image encryption method based on a three-dimensional hyperchaotic system, aiming to solve the technical problem that existing medical image encryption methods are difficult to support the encryption of multiple medical images while ensuring high efficiency.

[0006] To achieve the above purpose, the technical solution of the present invention is as follows: A multi-medical image encryption method based on a three-dimensional hyperchaotic system, specifically including the following steps:

[0007] Step 1: Perform dual-image fusion preprocessing, and synthesize two original medical images into a four-channel matrix to be encrypted through the Alpha channel;

[0008] Step 2: Construct a chaotic key system. Based on the preprocessed fused image data, extract the four-channel matrix to be encrypted as the input of the hash function, and combine the obtained result with the chaotic sequence generated by the 3D-HCLSM system to construct a key sequence;

[0009] Step 3: Perform iterative operations on the chaotic system. Input two sets of preset initial parameters and the constructed key sequence into the 3D-HCLSM system, and iteratively generate two key matrices key_matrix1 and key_matrix2, and an auxiliary chaotic sequence chaos_sequence;

[0010] Step 4: Perform pixel-level dynamic scrambling. Use the parameter-randomized dynamic Joseph scrambling strategy to scramble the fused image for L rounds to generate a primary ciphertext image;

[0011] Step 5: Implement spatial-numerical joint encryption on the primary ciphertext image. Reconstruct the pixel distribution through the improved zigzag bidirectional cross-permutation strategy, and perform non-linear diffusion calculation based on the key matrix key_matrix1 to generate a secondary ciphertext image;

[0012] Step 6: Complete bit-level ultimate encryption. Generate Joseph scrambling rules through the parameter-randomized dynamic Joseph scrambling strategy, and chaos sequence scrambling rules generated based on the auxiliary chaotic sequence chaos_sequence. After performing a new type of bit-level decomposition scrambling operation on the secondary ciphertext image, recombine it, and then perform bitwise XOR operation with the key matrix key_matrix2 to generate the final encrypted image.

[0013] The specific content of Step 1 is as follows:

[0014] Step 1.1: Perform size normalization on the original medical images image1 and image2, and uniformly convert them to the RGBA four-channel mode to generate standardized image data containing the RGB three channels and the Alpha transparency channel;

[0015] Step 1.2: Perform weighted mixing calculation on the RGB channels of the two original medical images, and retain the transparency information of the Alpha channel to ensure the reversibility and integrity of the mixed data;

[0016] Step 1.3: Perform multi-dimensional data reconstruction on the fused RGB channel and the Alpha channel to form a structured image array, and convert its data format to output a dataset before encryption containing the fused image, the RGB channel matrix, and the Alpha channel matrix.

[0017] The specific content of Step 2 is as follows:

[0018] Step 2.1: Take the RGB channel matrix and the Alpha channel matrix to be encrypted as inputs, use a hash function to generate a 512-bit binary hash value, and then group every 8 bits and convert them to decimal to obtain a hash sequence of length 64, denoted as: ;

[0019] Step 2.2: Save the preset system variable and the control parameter as the initial key, and bring the initial key into the 3D-HCLSM system for iteration. The number of iterations is 3 times the size of the image pixel points, and 3 chaotic sequences are obtained, denoted as where represents the size of the image;

[0020] Step 2.3: Select the chaotic sequence and perform an operation on it with the hash sequence to obtain the key sequence . The specific operation formula is:

[0021]

[0022] where represents the exclusive OR operation, represents the modulo operation, and is to ensure that the value does not overflow the range from 0 to 255.

[0023] The specific content of step 3 is as follows:

[0024] Step 3.1: Input the preset initial value and the generated key sequence into the 3D-HCLSM system in sequence for iteration. The number of iterations is 3 times the size of the number of pixels. Each iteration generates 3 chaotic sequences, and a total of two groups of chaotic sequences are generated, denoted as Chaotic_sequences1 and Chaotic_sequences2 respectively, with each group consisting of 3 chaotic sequences;

[0025] Step 3.2: Respectively intercept the second half of the 3 chaotic sequences in the Chaotic_sequences1 and the Chaotic_sequences2, and splice them into a sequence of the image size. After rounding up, two key matrices key_matrix1 and key_matrix2 are constructed;

[0026] Step 3.3: Splice the second half of the obtained chaotic sequence into a one-dimensional chaotic sequence chaos_sequence of the total number of image pixels, which is used to construct the chaotic sequence scrambling rule.

[0027] The specific content of step 4 is as follows:

[0028] Step 4.1: Flatten the obtained fused image into a one-dimensional array, denoted as mixted_image_array, and simultaneously create an index array of the same size as it.

[0029] Step 4.2: According to the chaotic sequence generated by the 3D-HCLSM system, randomly determine the starting position start and the interval step from the key sequence keys.

[0030] Step 4.3: Based on the total number of pixels, the determined starting position and interval, perform a parameter-randomized dynamic Josephus scrambling operation using the index array to generate a permuted index list.

[0031] Step 4.4: According to the permuted index list, rearrange the flattened pixel array mixted_image_array to obtain a scrambled pixel array.

[0032] Step 4.5: Rearrange the scrambled pixel array back into a shape the same as the fused image to generate a scrambled image.

[0033] Step 4.6: Replace the fused image with the generated scrambled image, and repeat steps 4.1 - 4.5 for a preset number of rounds L to obtain a primary ciphertext image.

[0034] The specific steps of step 5 are as follows:

[0035] Step 5.1: Divide the obtained primary ciphertext image into several pixel blocks, each block having a size of ;

[0036] Step 5.2: Perform an improved zigzag bidirectional cross-scrambling operation on the pixel blocks to obtain a scrambled matrix corresponding to each block.

[0037] Step 5.3: If all pixel blocks have been scrambled, proceed to step 5.4; otherwise, execute step 5.2.

[0038] Step 5.4: Combine the scrambled matrices of all pixel blocks to form an intermediate image.

[0039] Step 5.5: Perform a non-linear diffusion calculation on the intermediate image and the key matrix key_matrix1 to generate a secondary ciphertext image.

[0040] The specific steps of step 5.2 are as follows:

[0041] Step 5.2.1: Select two different center points within the pixel block, and define a diffusion direction for each center point, and the two directions do not overlap.

[0042] Step 5.2.2: Along the two directions, generate two independent subsequences respectively: the first subsequence starts from the first center point and spreads along the first direction; the second subsequence starts from the second center point and spreads along the second direction; each subsequence contains pixel values selected along its respective direction starting from its respective center point;

[0043] Step 5.2.3: Cross - merge the two subsequences generated in 5.2.2 to obtain the long sequence of this pixel block;

[0044] Step 5.2.4: Adjust the long sequence into a matrix with the same size as the pixel block before scrambling to obtain the scrambled matrix of this pixel block.

[0045] The specific content of step 6 is as follows:

[0046] Step 6.1: Divide the obtained secondary ciphertext image into several pixel blocks of size D F;

[0047] Step 6.2: Convert each pixel block into a binary matrix and decompose it into 8 bit - planes based on the principle of bit - plane decomposition, and perform a new bit - level scrambling operation to generate a scrambled pixel block;

[0048] Step 6.3: After all pixel blocks are scrambled, splice all the scrambled pixel blocks into a pixel matrix with the same size as the secondary ciphertext image, and perform an exclusive - OR operation with the key matrix key_matrix2 to generate the final encrypted image.

[0049] The specific content of step 6.2 is as follows:

[0050] Step 6.2.1: Denote the 8 bit - planes of each pixel block as ;

[0051] Step 6.2.2: Group the 8 bit - planes. The first group of planes is , and the second group of planes is ;

[0052] Step 6.2.3: Spread the generated chaos sequence chaos_sequence to all the numbers included in to generate a chaos - sequence scrambling rule. The specific generation formula is as follows:

[0053]

[0054] In the formula, is the generated chaos - sequence scrambling rule, represents the chaos sequence chaos_sequence, is the a chaotic sequence value, is the size of the pixel block, and respectively represent the maximum and minimum values of, indicating a rounding operation;

[0055] Step 6.2.4: The first group of planes applies the parameter - randomized dynamic Joseph scrambling strategy to obtain the scrambled plane ; The second group of planes uses the generated chaotic sequence scrambling rule to obtain the scrambled plane ;

[0056] Step 6.2.5: Re - combine the scrambled plane and construct each pixel value according to the bit order to generate the scrambled pixel block.

[0057] The 3D - HCLSM is specifically as follows:

[0058]

[0059] Among them, is the iterative value of the system variable , is the control parameter, n is the modulo coefficient,

[0060] ensuring that the chaotic system is globally bounded in the phase space. The 3D - HCLSM system is developed on the basis of the existing one - dimensional logical maps (Logistic map) and sine maps (Sine map). Compared with the one - dimensional chaotic maps Logistic and Sine, the improved 3D - HCLSM system has a wider parameter space, a larger Lyapunov exponent, and more complex dynamic behaviors, providing good randomness and security for the encryption algorithm of the present invention.

[0061] The beneficial effects of the present invention are as follows: First, the present invention constructs a three-dimensional Logistic-Sine mapping, which is developed on the basis of the existing one-dimensional Logistic mapping and Sine mapping. Second, for image preprocessing and key generation, two target medical images are synthesized into a four-channel matrix to be encrypted through the Alpha channel, and then the RGB channels and Alpha channels of the fused medical image are used as inputs. Combined with the SHA-512 hash function, a key sequence is generated, and the key sequence is used in the parameter-randomized dynamic Joseph scrambling process, thus significantly enhancing the randomness of pixel scrambling. Then, the present invention improves the traditional zigzag scrambling method, allowing random selection of the center point for two-way scrambling and adopting an alternating merging strategy when merging sequences, further enhancing the degree of pixel chaos. Finally, the present invention proposes a new type of bit-level scrambling technology, which combines the parameter-randomized dynamic Joseph scrambling rule and the scrambling rule based on the chaotic sequence, achieving deep chaos of pixels, thereby greatly improving the security of encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is the flowchart of the multi-medical image encryption method based on a three-dimensional hyperchaotic system of the present invention;

[0063] Figure 2 is the bifurcation diagram of the 3D-HCLSM system of the present invention, where Figure 2 (a) is the bifurcation diagram of the system variable xi, Figure 2 (b) is the bifurcation diagram of the system variable yi, Figure 2 (c) is the bifurcation diagram of the system variable zi;

[0064] Figure 3 is the three-dimensional phase space trajectory diagram of the 3D-HCLSM system of the present invention, where Figure 3 (a) is the trajectory diagram of xi, Figure 3 (b) is the trajectory diagram of yi, Figure 3 (c) is the trajectory diagram of zi, Figure 3 (d) is the trajectory diagram of xi-yi-zi;

[0065] Figure 4 is the Lyapunov exponent diagram of the three-dimensional hyperchaotic system 3D-HCLSM system of the present invention;

[0066] Figure 5 is the improved zigzag scrambling operation diagram of the present invention;

[0067] Figure 6 is the new type of bit-level scrambling operation diagram of the present invention;

[0068] Figure 7 is the flowchart of the parameter-randomized dynamic Joseph scrambling stage of the present invention;

[0069] Figure 8 is the flow chart of the improved zigzag scrambling and diffusion stage of the present invention;

[0070] Figure 9 is the flow chart of the novel bit-level scrambling and diffusion stage of the present invention;

[0071] Figure 10 is the experimental result diagram of image encryption and decryption of the present invention, where Figure 10 (a), Figure 10 (b) are the original images, Figure 10 (c) is the image after mixing two original images, Figure 10 (d) is the encrypted image, Figure 10 (e), Figure 10 (f) are the decrypted images;

[0072] Figure 11 is the comparison diagram of the histograms of the plaintext and ciphertext, where Figure 11 (a), Figure 11 is (b) the histograms of the plaintext and the plaintext, Figure 11 (c), Figure 11 (d) are the histograms of the ciphertext and the ciphertext;

[0073] Figure 12 is the pixel correlation diagram of the plaintext and ciphertext. Among them, Figure 12 (a) is the original image, Figure 12 (b) is the pixel correlation of the original image, Figure 12 (c) is the encrypted image, Figure 12 (d) is the pixel correlation of the encrypted image;

[0074] Figure 13 is the test diagram of the anti-noise ability. Among them Figure 13 (a), Figure 13 (e) are the original medical images, Figure 13 (b), Figure 13 (c), Figure 13 (d) are the decrypted images after being attacked by Gaussian noise of different intensities, Figure 13 (f), Figure 13 (g), Figure 13 (h) are the decrypted images under the attack of salt-and-pepper noise of different intensities. Specific embodiments

[0075] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0076] Example 1: As Figure 1 shown, a multi-medical image encryption method based on a three-dimensional hyperchaotic system, the specific operation is as follows:

[0077] Image preprocessing stage:

[0078] Perform dual-image fusion preprocessing. Synthesize the two original medical images into a four-channel matrix to be encrypted through the Alpha channel, generate the original image Mixed_image before encryption, and record its size as .

[0079] Key generation stage:

[0080] Take the RGB channel matrix and the Alpha channel matrix of the image Mixed_image obtained in the preprocessing stage as inputs, use the SHA-512 hash function to generate a 512-bit binary sequence, and then convert every 8 bits of it into a decimal number to generate a hash sequence of length 64, denoted as: ;

[0081] Bring the initial key into the 3D-HCLSM system for iteration. The number of iterations is , which is three times the size of the original image pixel points, to obtain three chaotic sequences, denoted as ;

[0082] Select the chaotic sequence , and perform an exclusive OR operation on it with the hash sequence to obtain the key sequence , and the specific operation formula is:

[0083]

[0084] Among them, represents the exclusive OR operation, represents the modulo operation, is to prevent the value from overflowing the range of 0 to 255.

[0085] Generate two key matrices for the pixel diffusion stage and a chaotic sequence for the new bit-level scrambling. The specific operation steps are as follows:

[0086] Input the preset initial value and the generated key sequence into the 3D-HCLSM system in sequence for iteration. The number of iterations is 3 times the size of the number of pixels. Each iteration generates 3 chaotic sequences, and every 3 form a group, generating two groups of chaotic sequences, denoted as Chaotic_sequences1 and Chaotic_sequences2 respectively;

[0087] Respectively intercept the second half of the 3 chaotic sequences in the Chaotic_sequences1 and the Chaotic_sequences2, and splice them into sequences of the image size. After rounding up, construct two key matrices key_matrix1 and key_matrix2;

[0088] The second half of the obtained chaotic sequence is spliced into a one-dimensional chaotic sequence chaos_sequence with the size of the total number of image pixels, which is used to generate the chaotic sequence scrambling rule in the new bit-level scrambling stage. The specific generation formula is as follows:

[0089]

[0090] In the formula, is the generated chaotic sequence scrambling rule, represents the chaotic sequence chaos_sequence, is the th chaotic sequence value in is the size of the pixel block, and respectively represent the maximum and minimum values of represents the rounding operation;

[0091] The 3D-HCLSM system is specifically as follows:

[0092]

[0093] Among them, is the iterative value of the system variable , is the control parameter, and n is the modulo coefficient.

[0094] As Figure 2 shown, when , , within the entire range of values, it shows a high degree of irregularity and complexity, indicating that the system has entered the chaotic state. Figure 3 The three-dimensional phase space trajectory diagram of the system is plotted. The entire trajectory in the diagram fills the phase space, indicating that the chaotic system has complex dynamic behaviors and a continuous parameter range.

[0095] As Figure 4 shown, all Lyapunov exponent values within the parameter range are positive, further indicating that the 3D-HCLSM system is chaotic and is a hyperchaotic system.

[0096] Through the analysis of the bifurcation diagram, phase space trajectory diagram, and Lyapunov exponents of the chaotic system, the chaotic system proposed by the present invention has complex dynamic behaviors and a high degree of randomness, and the generated sequence has unpredictability and initial value sensitivity, which can provide a strong randomness basis for medical image encryption algorithms.

[0097] Based on the traditional zigzag scrambling operation, the present invention proposes an improved zigzag bidirectional cross-scrambling operation. Taking a pixel block of size as an example for illustration, as shown in Figure 5 , the specific operation steps are as follows:

[0098] Select two different center points within the pixel block, and define a diffusion direction for each center point, and randomly perform scrambling along the two directions. In the figure, the center points are selected as 28 and 37, and bidirectional diffusion is performed along the upper left and lower right respectively to obtain two sequences, denoted as sub_sequence1 and sub_sequence2;

[0099] Cross-combine sub_sequence1 and sub_sequence2 to obtain the scrambled sequence List1 of this pixel block;

[0100] Reshape the sequence List1 back to a block of size to obtain the scrambled image matrix.

[0101] Based on the ordinary bit-level scrambling operation, the present invention proposes a new bit-level scrambling method. Taking a pixel block of size as an example for illustration, as shown in Figure 6 , the specific operation steps are as follows:

[0102] First, convert the pixel matrix of the original image original_image into a corresponding binary matrix; then, according to the principle of bit-plane decomposition of the image, put the bits of the pixel values into the corresponding bit planes respectively. In the figure, respectively represent the 8 bit planes obtained after image decomposition;

[0103] Use the parameter randomization dynamic Joseph scrambling strategy proposed by the present invention to generate scrambling rule 1. Then, use the chaos sequence chaos_sequence generated in the key generation stage to construct a sequence with the length of the pixel block size, while retaining the randomness of the chaos sequence, and generate the chaos sequence scrambling rule, denoted as scrambling rule 2;

[0104] Group the obtained 8 bit planes. The first group of planes is , apply Joseph scrambling of scrambling rule 1, and obtain the corresponding scrambled plane ; The second group of planes is , apply scrambling rule 2 for scrambling, and obtain the scrambled bit plane ;

[0105] Recombine the scrambled plane , and construct each pixel value according to the order of bits to obtain the scrambled image;

[0106] The obtained scrambled image is XOR - operated with the key matrix generated by the 3D - HCLSM system, and finally an image with bit - level scrambling and diffusion, that is, an encrypted image, is generated.

[0107] Scrambling stage:

[0108] Based on the rules of the Josephus problem, a key sequence is randomly selected as the starting position start and the interval step, and the Mixed_image is dynamically and randomly scrambled by the Josephus scrambling to obtain a primary ciphertext image.

[0109] As Figure 7 shown, the specific operation in the dynamic random Josephus scrambling stage is as follows:

[0110] Flatten the fused image into a one - dimensional array, and at the same time create an index array of the same size as it;

[0111] According to the chaotic sequence generated by the 3D - HCLSM system, randomly determine the starting position start and the interval step from the key sequence keys;

[0112] According to the total number of pixels, the determined starting position and interval, use the index array to perform parameter - randomized dynamic Josephus scrambling operation to generate a permuted index list;

[0113] According to the permuted index list, rearrange the flattened pixel array to obtain a scrambled pixel array;

[0114] Readjust the scrambled pixel array to the same shape as the fused image to generate a scrambled image;

[0115] Replace the fused image with the generated scrambled image, and repeat the above steps L rounds to obtain a primary ciphertext image. In the present invention, L = 2.

[0116] The first stage of scrambling and diffusion:

[0117] First, divide the primary ciphertext image into several pixel blocks, each block with a size of ; then, perform improved zigzag bidirectional cross - scrambling on each block respectively; then perform a non - linear diffusion operation on the obtained scrambled sequence and the key matrix key_matrix1 generated by the chaotic system to generate an image in the first stage of scrambling and diffusion, that is, a secondary ciphertext image. The operation process of the improved zigzag bidirectional cross - scrambling diffusion proposed in the present invention is as Figure 8 shown.

[0118] The second stage of scrambling and diffusion:

[0119] First, divide the secondary ciphertext image with The size is divided into several pixel blocks; then, each block is decomposed into 8 bit planes, corresponding to each bit of the pixel value. Then, using the scrambling rule of the chaotic sequence generated in the key generation stage , combined with the dynamic Joseph scrambling algorithm, perform alternating improved bit-level scrambling operations on the 8 bit planes of each block. After completing the bit-level scrambling, reassemble the bit planes to form an intermediate image. Finally, perform a pixel-by-pixel exclusive OR operation on this intermediate image and the key matrix key_matrix2 generated by the chaotic system to obtain the image in the second stage of scrambling diffusion, that is, the final encrypted image. As Figure 9 shown, the specific operation process of this stage is described as follows:

[0120] Divide the secondary encrypted image into several blocks of size , as labeled in the figure , where block represents a pixel block;

[0121] Convert each pixel block into a corresponding binary matrix;

[0122] Decompose the binary matrix of each pixel block into corresponding 8 bit planes;

[0123] Introduce the generated chaotic sequence scrambling rule and dynamic randomized Joseph scrambling rule, perform alternating bit-level scrambling on the 8 bit planes of each pixel block to generate a scrambled matrix;

[0124] Perform a bitwise exclusive OR operation on the obtained scrambled matrix and the key matrix key_matrix2 generated based on the 3D-HCLSM system to obtain the image in the second stage of scrambling diffusion, that is, the final encrypted image encrypted_image.

[0125] Figure 10 Figure [] is the experimental simulation result of image encryption and decryption of the present invention, which verifies the effectiveness and feasibility of this encryption method. Further, Figure 11 、 Figure 12 、 Figure 13 and Table 1 respectively analyze aspects such as the histograms of plaintext and ciphertext, pixel correlation, resistance to noise attacks, and resistance to differential attacks. The experimental results show the security of this multi-medical image encryption algorithm.

[0126] Table 1 Results of pixel change rate NPCR and unified average change intensity UACI

[0127]

[0128] The specific embodiments of the present invention have been described in detail with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A multi-medical image encryption method based on a three-dimensional hyperchaotic system, characterized in that, The specific implementation steps are as follows: Step 1: Perform dual-image fusion preprocessing, and synthesize the two original medical images into a four-channel matrix to be encrypted through the Alpha channel; Step 2: Construct a chaotic key system. Based on the preprocessed fused image data, extract the four-channel matrix to be encrypted as the input of the hash function, and combine the obtained result with the chaotic sequence generated by the 3D-HCLSM system to construct a key sequence; Step 3: Perform iterative operations of the chaotic system. Input two groups of preset initial parameters and the constructed key sequence into the 3D-HCLSM system, and iteratively generate two key matrices key_matrix1 and key_matrix2, and an auxiliary chaotic sequence chaos_sequence; Step 4: Perform pixel-level dynamic scrambling. Use the parameter-randomized dynamic Joseph scrambling strategy to scramble the fused image for L rounds to generate a primary ciphertext image; Step 5: Implement spatial-numerical joint encryption on the primary ciphertext image. Reconstruct the pixel distribution through the improved zigzag bidirectional cross-permutation strategy, and perform non-linear diffusion calculation based on the key matrix key_matrix1 to generate a secondary ciphertext image; Step 6: Complete bit-level ultimate encryption. Generate a Joseph scrambling rule through the parameter-randomized dynamic Joseph scrambling strategy and a chaotic sequence scrambling rule generated based on the auxiliary chaotic sequence chaos_sequence. After performing a new type of bit-level decomposition scrambling operation on the secondary ciphertext image, recombine it, and then perform a bitwise XOR operation with the key matrix key_matrix2 to generate the final encrypted image.

2. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, wherein, The specific content of Step 1 is as follows: Step 1.1: Perform size normalization processing on the original medical images image1 and image2, and uniformly convert them to the RGBA four-channel mode to generate standardized image data containing the RGB three channels and the Alpha transparency channel; Step 1.2: Perform weighted mixing calculation on the RGB channels of the two original medical images, and retain the transparency information of the Alpha channel; Step 1.3: Reconstruct the multi-dimensional data of the fused RGB channel and the Alpha channel to form a structured image array, and convert its data format to output a dataset before encryption containing the fused image, the RGB channel matrix, and the Alpha channel matrix.

3. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, characterized in that The specific content of Step 2 is as follows: Step 2.1: Take the RGB channel matrix and the Alpha channel matrix to be encrypted as inputs, use a hash function to generate a 512-bit binary hash value, and then group every 8 bits and convert them to decimal to obtain a hash sequence of length 64, denoted as: ; Step 2.2: Save the preset system variables and control parameters as the initial key, and bring the initial key into the 3D-HCLSM system for iteration. The number of iterations is 3 times the size of the image pixel points, and 3 chaotic sequences are obtained, denoted as , where represents the size of the image; Step 2.3: Select the chaotic sequence , perform an operation on it with the hash sequence to obtain the key sequence . The specific operation formula is as follows: ； Among them, represents an exclusive OR operation, represents a modulo operation, which is to prevent the value from overflowing the range of 0 to 255.

4. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, wherein The specific content of Step 3 is as follows: Step 3.1: The preset initial value and the generated key sequence are sequentially input into the 3D-HCLSM system for iteration respectively. The number of iterations is 3 times the number of pixels. Each iteration generates 3 chaotic sequences, which are grouped into two groups of 3 each, generating two chaotic sequences denoted as Chaotic_sequences1 and Chaotic_sequences2 respectively; Step 3.2: Respectively intercept the second half of 3 chaotic sequences in the Chaotic_sequences1 and the Chaotic_sequences2, and splice them into sequences of the image size. After rounding up, construct two key matrices key_matrix1 and key_matrix2; Step 3.3: Concatenate the second half of the obtained chaotic sequence into a one-dimensional chaotic sequence chaos_sequence of the size of the total number of image pixels, which is used to construct the chaotic sequence scrambling rule.

5. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, characterized in that, The specific content of Step 4 is as follows: Step 4.1: Flatten the obtained fused image into a one-dimensional array, denoted as mixted_image_array, and simultaneously create an index array of the same size as it; Step 4.2: According to the chaotic sequence generated by the 3D-HCLSM system, randomly determine the starting position start and the interval step from the key sequence keys; Step 4.3: Based on the total number of pixels, the determined starting position, and the interval, perform parameter randomization dynamic Josephus scrambling operation using the index array to generate a permuted index list; Step 4.4: Rearrange the flattened pixel array mixted_image_array according to the permuted index list to obtain a scrambled pixel array; Step 4.5: Readjust the scrambled pixel array to the same shape as the fused image to generate a scrambled image; Step 4.6: Replace the fused image with the generated scrambled image, and repeat steps 4.1 - 4.5 for a preset number of rounds L to obtain a primary ciphertext image.

6. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, characterized in that, The specific content of step 5 is as follows: Step 5.1: Divide the obtained primary ciphertext image into several pixel blocks, each block having a size of ; Step 5.2: Perform an improved zigzag bidirectional cross-scrambling operation on the pixel blocks to obtain a scrambled matrix corresponding to each block; Step 5.3: If all pixel blocks have been scrambled, proceed to step 5.4; otherwise, execute step 5.2; Step 5.4: Combine the scrambled matrices of all pixel blocks to form an intermediate image; Step 5.5: Perform a non-linear diffusion calculation on the intermediate image and the key matrix key_matrix1 to generate a secondary ciphertext image.

7. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 6, characterized in that, The specific content of step 5.2 is as follows: Step 5.2.1: Select two different center points within the pixel block, and define a diffusion direction for each center point, with the two directions not overlapping; Step 5.2.2: Along the two directions, generate two independent subsequences respectively: the first subsequence starts from the first center point and diffuses along the first direction; the second subsequence starts from the second center point and diffuses along the second direction; each subsequence contains the pixel values selected along its respective direction starting from its respective center point; Step 5.2.3: Cross-combine the two subsequences generated in 5.2.2 to obtain a long sequence of this pixel block; Step 5.2.4: Adjust the long sequence to a matrix of the same size as the pixel block before scrambling to obtain the scrambled matrix of this pixel block.

8. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, characterized in that, The specific content of step 6 is as follows: Step 6.1: Divide the obtained secondary ciphertext image into a number of pixel blocks of size D F; Step 6.2: Convert each pixel block into a binary matrix, and decompose it into 8 bit planes based on the principle of bit-plane decomposition, and perform a new bit-level scrambling operation to generate a scrambled pixel block; Step 6.3: After all pixel blocks have been scrambled, splice all the scrambled pixel blocks into a pixel matrix of the same size as the secondary ciphertext image, and perform a bitwise XOR operation with the key matrix key_matrix2 to generate the final encrypted image.

9. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 8, characterized in that, The specific content of step 6.2 is as follows: Step 6.2.1: Denote the 8 bit-planes of each pixel block as ; Step 6.2.2: Group the 8 bit planes. The first group of planes is , and the second group of planes is ; Step 6.2.3: Diffuse the generated chaos sequence chaos_sequence to all the numbers included in to generate a chaos sequence scrambling rule. The specific generation formula is as follows: ； In the formula, is the scrambling rule of the generated chaotic sequence, represents the chaotic sequence chaos_sequence, is the th chaotic sequence value in is the size of the pixel block, and respectively represent the maximum and minimum values of represents the rounding operation; Step 6.2.4: Apply the randomization dynamic Joseph scrambling strategy to the first group of planes to obtain the scrambled planes ; Use the generated chaotic sequence scrambling rule for the second group of planes to obtain the scrambled planes ; Step 6.2.5: Recombine the scrambled plane and construct each pixel value according to the bit order to generate a scrambled pixel block.

10. The multi-medical image encryption method based on a three-dimensional hyperchaotic system according to claim 1, characterized in that, The specific content of 3D-HCLSM is as follows: ； Among them, is the iterative value of the system variable , is the control parameter, and n is the modulo coefficient.

Images