Medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping

Abstract

A medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, the method is based on traditional Logistic mapping and Gaussian mapping, a 2D Logistic-Gaussian hyperchaotic mapping with complex dynamic characteristics is constructed, the random sequence generated is further used to replace pixels and change pixel positions, the invention effectively breaks the correlation between adjacent pixels and completely changes the global pixel value of the image; through testing of various medical images, the results show that the scheme has high robustness and effectiveness, and can resist different attacks. The present invention has good security and efficiency, and can be applied to medical images of different forms.

Description

Technical Field

[0001] The invention relates to a medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, belonging to the technical field of information security. Background Art

[0002] Medical imaging technologies, including computed tomography (CT), magnetic resonance imaging (MRI), X-rays, and ultrasound, play a vital role in medical diagnosis, which has also caused many researchers to worry about the confidentiality of medical image transmission. Medical images contain various private information of patients. Unauthorized access to patient information will cause serious information security risks. Especially with the continuous maturity of emerging medical technologies such as Internet-based cloud services, remote consultations, and remote surgery, there are extremely high requirements for the real-time and robustness of medical image transmission. Therefore, it is very necessary to protect the security of confidential transmission of medical images.

[0003] Traditional image encryption methods are mainly based on the Data Encryption Standard (DES) and the Advanced Encryption Standard (AES). However, the security and efficiency of traditional methods face unprecedented challenges due to the rapid improvement of computer arithmetic capabilities.

[0004] In order to improve the security level and practical value of image encryption, some researchers have introduced chaos theory into encryption schemes. The characteristics of chaotic systems, such as high sensitivity to initial conditions and long-term unpredictable iterative trajectories, are similar to the requirements of cryptography in many aspects. Therefore, encryption schemes based on chaos theory have begun to be widely used in the field of digital image encryption. Classic image encryption schemes based on chaotic mapping often require increasing the number of encryption and decryption rounds or other pixel scrambling links because of the weak randomness and small chaotic range of chaotic sequences, which makes the algorithm time longer, the efficiency lower, and the practicality insufficient. Therefore, constructing a chaotic system with a large chaotic interval, strong randomness of chaotic sequences, and sensitivity to initial conditions will greatly improve the performance of the algorithm. Based on this chaotic system, further designing an encryption scheme that can fully and effectively conceal the overall pixel information of the image has great research value. Summary of the invention

[0005] The technical problem to be solved by the present invention is to propose a medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping in view of the shortcomings of the classical medical image encryption scheme based on chaotic mapping and the need for improvement.

[0006] The technical solution implemented by the present invention is as follows: a medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, the method steps are as follows:

[0007] S1. By introducing cosine variables and exponential variables to construct chaotic mapping, the shortcomings of small chaotic range and multiple period windows are overcome. The chaotic input and output are nested with each other to build a hyperchaotic system with excellent performance.

[0008] The hyperchaotic system is constructed as follows:

[0009] According to the one-dimensional Logistic mapping:

[0010] x n+1 =ux n (1-x n )

[0011] Where u is the control parameter, n is the number of iterations, x is the iterative output value, and when u∈[3.57,4], the mapping is a chaotic state; x n is the value obtained at the nth iteration;

[0012] One-dimensional Gaussian mapping:

[0013]

[0014] Among them, α and β are control parameters, and when α=-8, β∈[0.26,0.80], the mapping is in a chaotic state;

[0015] Combining the above two mappings and nesting the input and output, we get a two-dimensional hyperchaotic mapping:

[0016]

[0017] Among them, x n ,y n is the value obtained at the nth iteration, where a, b, k1, k2 are control parameters, and when a=1, b=1, k2=25, k1∈[-25,25], the two-dimensional mapping is in a chaotic state and has two large Lyapunov exponents.

[0018] S2. The key is calculated bit by bit and the modulo-rounding operation is performed to obtain the initial control parameters of the chaotic system. The hyperchaotic system and the initial control parameters are iterated multiple times to generate a strong random sequence with the same number of image pixels, and the sequence is constrained to be a pseudo-random number matrix with the same size as the image. This matrix is ​​used in pixel diffusion and scrambling operations.

[0019] The method for generating the initial control parameters of the chaotic system is as follows:

[0020] A 256-bit key is randomly generated. To increase the randomness of the initial state value, the key is further processed. The 256-bit binary key is calculated to obtain (x0, y0, r0, d, A1, A2);

[0021] Among them, x0, y0 are the initial values ​​of each chaotic sequence; r0 is the initial value of the chaotic sequence control parameter; d is the disturbance parameter; A1 is the proportional coefficient of x0; A2 is the proportional coefficient of y0;

[0022] How to get integer (x0, y0, r0, d):

[0023]

[0024] Among them, Bin is the key binary sequence, FN is the floating point number obtained according to the binary, and the floating point number (A1, A2) is obtained as follows:

[0025]

[0026] Where IN is an integer obtained according to binary; based on this, the initial control parameter can be obtained as follows:

[0027]

[0028] The iterated initial control parameters are used to generate chaotic sequences; mod is a remainder operation, and each group generates the same number of random numbers (mn) as the image pixels, and is constrained to be a pseudo-random number matrix of size m×n.

[0029] S3. Perform pixel multidirectional diffusion operation based on pseudo-random number matrix to replace the original image pixel value. The pixel value of each point in the diffused image is obtained by the interaction of the previous pixel value, pseudo-random number matrix and plaintext image and the remainder rounding. That is, the pixel values ​​of the diffused image are replaced by random numbers.

[0030] The pixel multi-directional diffusion operation method comprises:

[0031] The diffusion process is performed by the initial image and the random number matrix together and the remainder is calculated. The ciphertext image can be obtained by the following formula:

[0032]

[0033] Among them, C is the diffused image, T is the initial image, R is the pseudo-random number matrix, and F is the maximum pixel value allowed by the image. C is the rounding operation; i,j is the pixel value of the ciphertext in row i and column j; R i,j is the pixel value of the i-th row and j-th column of the random number matrix; T i,j is the pixel value of the i-th row and j-th column of the initial image;

[0034] At the same time, the decryption operation of medical image diffusion is provided as follows:

[0035]

[0036] Among them, C' is the image after the inverse diffusion operation, T' is the image after diffusion, R is the pseudo-random number matrix, F is the maximum pixel value allowed by the image, is the rounding operation; C′ i,j is the pixel value of the i-th row and j-th column of the image after the inverse diffusion operation; T′ i,j is the pixel value of the i-th row and j-th column of the diffused image.

[0037] After two rounds of diffusion operations, the pixel values ​​of the original image are globally replaced.

[0038] S4. Each random number matrix obtains a sorting matrix and a bit-selecting matrix according to the row and column indices respectively, and the corresponding pixels are selected in the diffused image according to the bit-selecting matrix. The selected pixels are rearranged by the sorting matrix, thereby completing the efficient pixel scrambling operation; after the diffusion and scrambling operations, the ciphertext image is finally obtained.

[0039] The efficient scrambling operation method comprises:

[0040] Two matrices, a row index matrix and a column index matrix, are obtained from the pseudo-random number matrix through row and column indexes respectively; each value in the row index matrix is ​​recombined with the value of its row into coordinates, and the row index matrix becomes a coordinate set matrix. The composed coordinates are used to select positions in the original image, and the selected positions are reordered based on the column index matrix, and the order is performed by column, starting from the first column, and the corresponding pixels are selected in the original image according to the coordinate set of the first column, and the selected pixels are sorted according to the column index matrix, and this is performed in sequence until the last column.

[0041] At the same time, each value in the column index matrix is ​​recombined with the value of its column into coordinates, and the column index matrix becomes a coordinate set matrix. The composed coordinates are used to select positions in the original image. The selected positions are reordered based on the row index matrix. The order is row by row, starting from the first row. According to the coordinate set of the first row, the corresponding pixels are selected in the original image. The selected pixels are sorted according to the row index matrix, and this is done in sequence until the last row.

[0042] After the rows and columns are reordered, the original pixel positions are completely disrupted, and the scrambling operation of the encryption process is completed; conversely, the decryption process only needs to perform the inverse operation on the scrambled image based on the pseudo-random number matrix.

[0043] The beneficial effect of the present invention lies in that the medical image encryption method based on the two-dimensional Logistic-Gaussian hyperchaotic mapping of the present invention constructs a two-dimensional Logistic-Gaussian hyperchaotic mapping with two large Lyapunov exponents by improving the shortcomings of the existing chaotic system, which overcomes the shortcomings of the traditional mapping, such as small chaotic range and many periodic windows. The initial parameters of the chaotic mapping are randomly processed, and the control parameters of each iteration have been changed. The generated chaotic sequence has good randomness and can be effectively applied to medical image encryption.

[0044] The medical image encryption method of the present invention is based on two-dimensional Logistic-Gaussian hyperchaotic mapping. A pseudo-random number matrix constrained by a chaotic sequence is indexed into a row index matrix and a column index matrix, and a scrambling is further completed according to the interaction of the index matrix with the initial image. Therefore, only one chaotic sequence is needed to scramble the pixel position once. This operation can improve the efficiency of the algorithm and effectively scramble the global pixel position.

[0045] The invention is a medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, which nests pseudo-random number matrices, image pixels before diffusion, and image pixels after diffusion, replaces pixel values ​​from point to surface, fully changes global pixel values, and increases the confidentiality strength of the image. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flowchart of a medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping;

[0047] Figure 2 It is the Lyapunov index LE1 diagram of 2D Logistic-Gaussian chaotic mapping;

[0048] Figure 3 It is the Lyapunov index LE2 graph of 2D Logistic-Gaussian chaotic mapping;

[0049] Figure 4 For input medical images (chest radiographs);

[0050] Figure 5 To output the ciphertext image (decrypted image of chest X-ray image);

[0051] FIG6(a) is a heart MRI image; FIG6(b) is a brain MRI image; FIG6(c) is a pixel histogram of FIG6(a); FIG6(d) is a pixel histogram of FIG6(b);

[0052] FIG7(a) is an encrypted image of a heart MRI image; FIG7(b) is an encrypted image of a brain MRI image; FIG7(c) is a pixel histogram of FIG7(a); FIG7(d) is a pixel histogram of FIG7(b);

[0053] FIG8(a) is a retinal image; FIG8(b) is a ciphertext image of FIG8(a); FIG8(c) is a correlation image of adjacent pixels in the horizontal, vertical and oblique directions of FIG8(a); FIG8(d) is a correlation image of adjacent pixels in the horizontal, vertical and oblique directions of FIG8(b);

[0054] Figure 9(a) is an encrypted image of the elbow joint without disturbance; Figure 9(b) is a ciphertext image with 0.5% disturbance added to Figure 9(a); Figure 9(c) is a decrypted image of Figure 9(a); Figure 9(d) is a decrypted image of Figure 9(b);

[0055] Figure 10(a) is a ciphertext image of the elbow joint image that is cropped by 50% after encryption; Figure 10(b) is a ciphertext image of the elbow joint image that is cropped by 55% after encryption; Figure 10(c) is the decrypted image of Figure 10(a); and Figure 10(d) is the decrypted image of Figure 10(b). DETAILED DESCRIPTION

[0056] like Figure 1 As shown, this embodiment is a medical image efficient encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, and the specific steps are as follows:

[0057] S1. By introducing cosine variables and exponential variables to construct chaotic mapping, the shortcomings of small chaotic range and multiple period windows are overcome. The chaotic input and output are nested with each other to construct a hyperchaotic system with excellent performance.

[0058] S2. The key is calculated bit by bit and the remainder operation is performed to obtain the initial control parameters of the chaotic system. The hyperchaotic system and the initial control parameters are iterated multiple times to generate a strong random sequence with the same number of image pixels, and the sequence is constrained to be a pseudo-random number matrix with the same size as the image. This matrix is ​​used in pixel diffusion and scrambling operations.

[0059] S3. The original image pixel values ​​are replaced based on a pseudo-random number matrix. The pixel value of each point in the diffused image is obtained by the interaction of the previous pixel value, the pseudo-random number matrix and the plaintext image and the remainder is rounded. That is, the pixel values ​​of the diffused image are replaced by random numbers.

[0060] S4. Each random number matrix obtains a sorting matrix and a bit matrix according to the row and column indexes, and selects the corresponding pixels in the diffused image according to the bit matrix. The selected pixels are rearranged by the sorting matrix to complete the efficient pixel scrambling operation. After the diffusion and scrambling operations, the ciphertext image is finally obtained, and the encryption algorithm is analyzed for performance.

[0061] In this embodiment, the steps of constructing the hyperchaotic map are as follows:

[0062] According to the one-dimensional Logistic mapping:

[0063] x n+1 =ux n (1-x n )

[0064] Where u is the control parameter, n is the number of iterations, x is the iterative output value, and when u∈[3.57,4], the mapping is a chaotic state.

[0065] One-dimensional Gaussian mapping:

[0066]

[0067] Among them, α and β are control parameters, and when α=-8, β∈[0.26,0.80], the mapping is in a chaotic state. Considering that the above two one-dimensional chaotic mappings have a small chaotic range but a simple structure, the above two mappings are combined, and the input and output are nested to obtain a two-dimensional hyperchaotic mapping (2D Logistic-Gaussian):

[0068]

[0069] Among them, x n ,y n is the value obtained at the nth iteration, where a, b, k1, k2 are control parameters, and when a=1, b=1, k2=25, k1∈[-25,25], the two-dimensional mapping is in a chaotic state and has two large Lyapunov exponents. Figure 2 and Figure 3 The Lyapunov index diagram of the chaotic mapping is shown. It can be seen from the figure that the 2D Logistic-Gaussian mapping has the advantages of hyperchaotic properties and a large chaotic range, which provides a preliminary foundation for encryption.

[0070] In this embodiment, the method for generating the initial control parameters of the chaotic system is as follows:

[0071] This embodiment randomly generates a 256-bit key. To increase the randomness of the initial state value, the key is preprocessed before generating the initial control parameters. The 256-bit binary key is calculated to obtain (x0, y0, r0, d, A1, A2), where the integer (x0, y0, r0, d) is obtained as follows:

[0072]

[0073] Where Bin is the key binary sequence, FN is the floating point number obtained according to the binary, and the floating point number (A1, A2) is obtained as follows:

[0074]

[0075] Where IN is an integer obtained according to binary. Based on this, the initial control parameter can be obtained by the following formula:

[0076]

[0077] The iterated initial parameters are used to generate chaotic sequences, where mod is the remainder operation. Each group generates a random number sequence seq with the same number (mn) as the image pixels, and is constrained to be a pseudo-random number matrix R of size m×n:

[0078] R = reshape(m,n,seq)

[0079] In this embodiment, the pixel multi-directional diffusion operation steps are as follows:

[0080] The diffusion process is calculated by the initial image and the random number matrix, and the ciphertext image can be obtained by the following formula:

[0081]

[0082] Where C is the diffused image, T is the initial image, R is the pseudo-random number matrix, and F is the maximum pixel value allowed by the image. This is a rounding operation.

[0083] After two rounds of diffusion operations, the pixel values ​​of the original image are globally replaced. Another aspect of the present invention also provides a decryption operation for medical image diffusion, as shown below:

[0084]

[0085] Where C is the image after the inverse diffusion operation, T is the image after diffusion, R is the pseudo-random number matrix, and F is the maximum pixel value allowed by the image. For the rounding operation, after the decryption operation, the image can be restored to the image before diffusion.

[0086] The specific steps of efficient scrambling operation in this embodiment are as follows:

[0087] Two matrices (row index matrix and column index matrix) are obtained from the pseudo-random number matrix through row and column indexes respectively. Each value in the row index matrix is ​​recombined with the value of its row into coordinates. The row index matrix becomes a coordinate set matrix. The composed coordinates are used to select positions in the original image. The selected positions are reordered based on the column index matrix. The order is column by column, starting from the first column. The corresponding pixels are selected in the original image according to the coordinate set of the first column. The selected pixels are sorted according to the column index matrix, and this is done in sequence until the last column.

[0088] At the same time, each value in the column index matrix is ​​recombined with the value of its column into coordinates, and the column index matrix becomes a coordinate set matrix. The composed coordinates are used to select positions in the original image. The selected positions are reordered based on the row index matrix. The order is row by row, starting from the first row. According to the coordinate set of the first row, the corresponding pixels are selected in the original image. The selected pixels are sorted according to the row index matrix, and this is done in sequence until the last row.

[0089] After the rows and columns are reordered, the original pixel positions are all disrupted, and the scrambling operation of the encryption process is completed. Conversely, the decryption process only needs to perform the inverse operation on the scrambled image based on the pseudo-random number matrix.

[0090] The intuitive images before and after encryption are as follows Figure 4 and Figure 5 As shown in the figure, it can be seen that the encrypted image no longer contains any valuable information.

[0091] Next, the performance of the algorithm is analyzed through image encryption indicators such as histogram, adjacent pixel correlation, key space, and robustness.

[0092] (1) Histogram analysis

[0093] Figures 6 and 7 show the pixel distribution of the original image and the encrypted image.

[0094] FIG6(a) is a heart MRI image; FIG6(b) is a brain MRI image; FIG6(c) is a pixel histogram of FIG6(a); and FIG6(d) is a pixel histogram of FIG6(b).

[0095] Figure 7(a) is an encrypted image of a cardiac MRI image; Figure 7(b) is an encrypted image of a brain MRI image; Figure 7(c) is a pixel histogram of Figure 7(a); and Figure 7(d) is a pixel histogram of Figure 7(b).

[0096] As can be seen from the figure, the frequency of occurrence of each pixel in the original image is extremely different, and the feature distribution is distinct. It is easy for an attacker to obtain the general information of the image from the features of the pixel distribution. However, the histogram of the encrypted image is evenly distributed, and the feature information of the original image has been masked. The frequency of occurrence of each pixel is close to the same, which has good security and can resist some attacks.

[0097] (2) Correlation analysis of adjacent pixels

[0098] There is a strong correlation between adjacent pixels in medical images. The distribution of other pixels can often be deduced based on partial pixel information. Therefore, destroying the correlation between adjacent pixels is very important for encryption. The solution proposed in the present invention can effectively reduce the correlation between adjacent pixels.

[0099] Figure 8(a) is a retinal image; Figure 8(b) is the ciphertext image of Figure 8(a); Figure 8(c) is the correlation image of adjacent pixels in Figure 8(a) in horizontal, vertical and oblique directions; Figure 8(d) is the correlation image of adjacent pixels in Figure 8(b) in horizontal, vertical and oblique directions

[0100] As can be seen from Figure 8, the correlation between adjacent pixels in all directions of the original medical image is greatly reduced after encryption.

[0101] (3) Key Analysis

[0102] The key is very important in the encryption algorithm. A high-security algorithm has very high requirements for the key. The key designed in this embodiment has 256 bits and the key space is 2 256 , much larger than 2 100 , can effectively resist key exhaustive attacks and has good security performance.

[0103] (4) Robustness analysis

[0104] During the transmission of ciphertext, there are varying degrees of signal interference or information loss, and even intentional perturbation attacks by attackers. Therefore, the algorithm needs to have a certain degree of anti-interference when decrypting the ciphertext image, that is, it can still be successfully decrypted even if part of the ciphertext information is lost or changed.

[0105] As shown in Figure 9, the decryption of this embodiment without disturbance and under 0.5% salt and pepper noise is demonstrated. Figure 9(a) is the encrypted image of the elbow joint without disturbance; Figure 9(b) is the ciphertext image with 0.5% disturbance added on the basis of Figure 9(a); Figure 9(c) is the decrypted image of Figure 9(a); Figure 9(d) is the decrypted image of Figure 9(b).

[0106] As shown in FIG10 , the decryption of the present invention under the conditions of 50% and 55% cropping is shown. FIG10(a) is a ciphertext image of the elbow joint image after being encrypted and cropped by 50%; FIG10(b) is a ciphertext image of the elbow joint image after being encrypted and cropped by 55%; FIG10(c) is the decrypted image of FIG10(a); and FIG10(d) is the decrypted image of FIG10(b). It can be seen from the figure that when the information is partially lost or changed, the image can still be restored to a visible level, so the present invention has strong robustness.

Claims

1. A medical image encryption method based on two-dimensional Logistic-Gaussian hyperchaotic mapping, characterized in that: The method steps are as follows: S1. By introducing cosine variables and exponential variables to construct chaotic mapping, the chaotic input and output are nested with each other to build a hyperchaotic system; The hyperchaotic system is constructed as follows: According to the one-dimensional Logistic mapping: x n+1 =ux n (1-x n ) Where u is the control parameter, n is the number of iterations, x is the iterative output value, and when u∈[3.57,4], the mapping is a chaotic state; x n is the value obtained at the nth iteration; One-dimensional Gaussian mapping: Among them, α and β are control parameters, and when α=-8, β∈[0.26,0.80], the mapping is in a chaotic state; Combining the above two mappings and nesting the input and output, we get a two-dimensional hyperchaotic mapping: Among them, x n ,y n is the value obtained at the nth iteration, where a, b, k1, k2 are control parameters, and when a=1, b=1, k2=25, k1∈[-25,25], the two-dimensional mapping is in a chaotic state and has two large Lyapunov exponents; S2, the key is calculated bit by bit and the modulo rounding operation is performed to obtain the initial control parameters of the hyperchaotic system; the hyperchaotic system and the initial control parameters are iterated multiple times to generate a strong random sequence with the same number of image pixels, and the sequence is constrained to be a pseudo-random number matrix with the same size as the image, and the matrix is ​​used in pixel diffusion and scrambling operations; The initial control parameters of the hyperchaotic system are generated as follows: A 256-bit key is randomly generated. To increase the randomness of the initial state value, the key is further processed. The 256-bit binary key is calculated to obtain (x0, y0, r0, d, A1, A2); Among them, x0, y0 are the initial values ​​of each chaotic sequence; r0 is the initial value of the chaotic sequence control parameter; d is the disturbance parameter; A1 is the proportional coefficient of x0; A2 is the proportional coefficient of y0; How to get integer (x0, y0, r0, d): Among them, Bin is the key binary sequence, FN is the floating point number obtained according to the binary, and the floating point number (A1, A2) is obtained as follows: Where IN is an integer obtained according to binary; based on this, the initial control parameter is obtained by the following formula: The iterated initial control parameters are applied to generate chaotic sequences; mod is a remainder operation, and each group generates random numbers with the same number mm as the image pixels, and is constrained to be a pseudo-random number matrix of size m×n; S3, performing a pixel multi-directional diffusion operation based on a pseudo-random number matrix to replace the original image pixel value, wherein the pixel value of each point of the diffused image is obtained by the interaction of the previous pixel value, the pseudo-random number matrix and the plaintext image and the remainder rounding, that is, the pixel values ​​of the diffused image are all replaced by random numbers; The pixel multi-directional diffusion operation includes: The diffusion process is a combination of the initial image and the pseudo-random number matrix, and the remainder calculation is performed. The image after diffusion is obtained by the following formula: Among them, C is the diffused image, T is the initial image, R is the pseudo-random number matrix, and F is the maximum pixel value allowed by the image. C is the rounding operation; i,j is the pixel value of the i-th row and j-th column of the diffused image; R i,j is the pixel value of the i-th row and j-th column of the pseudo-random number matrix; T i,j is the pixel value of the i-th row and j-th column of the initial image; At the same time, the decryption operation of image diffusion is provided as follows: Among them, C' is the image after the inverse diffusion operation, T' is the image after diffusion, R is the pseudo-random number matrix, F is the maximum pixel value allowed by the image, C is the rounding operation; i ' ,j is the pixel value of the i-th row and j-th column of the image after the inverse diffusion operation; T i, ' j is the pixel value of the i-th row and j-th column of the diffused image; After two rounds of diffusion operations, the pixel values ​​of the original image are replaced globally; S4, each random number matrix obtains a sorting matrix and a bit matrix according to the row and column indexes, selects the corresponding pixels in the diffused image according to the bit matrix, and the selected pixels are rearranged by the sorting matrix, thereby completing the efficient pixel scrambling operation; after the diffusion and scrambling operations, the ciphertext image is finally obtained; The efficient scrambling operation includes: Two matrices, a row index matrix and a column index matrix, are obtained from the pseudo-random number matrix through row and column indexes respectively; each value in the row index matrix is ​​recombined into coordinates with the value of the row in which it is located, and the row index matrix becomes a coordinate set matrix, and the composed coordinates are used to select positions in the original image, and the selected positions are reordered based on the column index matrix, and the order is performed by column, starting from the first column, and the corresponding pixels are selected in the original image according to the coordinate set of the first column, and the selected pixels are sorted according to the column index matrix, and this is performed in sequence until the last column; At the same time, each value in the column index matrix is ​​recombined with the value of its column into coordinates, and the column index matrix becomes a coordinate set matrix. The composed coordinates are used to select positions in the original image. The selected positions are reordered based on the row index matrix. The order is row by row. Starting from the first row, the corresponding pixels are selected in the original image according to the coordinate set of the first row. The selected pixels are sorted according to the row index matrix, and this is done in sequence until the last row. After the rows and columns are reordered, the original pixel positions are all disrupted, and the scrambling operation of the encryption process is completed; Conversely, the decryption process is to perform the inverse operation on the scrambled image based on the pseudo-random number matrix.

Images