A Remote Sensing Image Encryption Method Based on Two-Dimensional Discrete Memristor Hyperchaotic Mapping

Abstract

A remote sensing image encryption method based on two-dimensional discrete memristor hyperchaotic mapping includes (1) chaotic sequence generation; (2) main diagonal row-column diffusion; (3) pixel position scrambling operation; and (4) sub-diagonal row-column diffusion. This method employs a diffusion-scrambling-diffusion structure, using the obtained chaotic matrix to perform main diagonal row-column diffusion, pixel position scrambling, and sub-diagonal row-column diffusion operations on the plaintext image to obtain the ciphertext image. Experimental results show that this invention can resist differential attacks and brute-force attacks, making it difficult for attackers to obtain effective information from the ciphertext image. It not only has fast and efficient encryption capabilities but also high security performance, successfully ensuring the secure transmission of remote sensing images in the network.

Description

Technical Field

[0001] This invention relates to an image encryption method, and more particularly to a remote sensing image encryption method based on two-dimensional discrete memristor hyperchaotic mapping. Background Technology

[0002] Remote sensing technology plays a crucial role in military reconnaissance, resource surveys, environmental monitoring, and global research. Remote sensing images contain a wealth of information about remotely sensed targets and are the primary means by which satellites acquire remote sensing information. They are characterized by large data volumes, multiple targets, and strong confidentiality requirements. Therefore, researchers both domestically and internationally have placed great emphasis on the secure transmission of remote sensing images. Researchers have proposed many image encryption methods. Some of these algorithms are computationally simple but lack complexity and are easily deciphered, while others are highly complex but have low computational efficiency, making them unsatisfactory.

[0003] Color images are common in daily life, characterized by high redundancy, large data volume, multiple dimensions, and strong correlation. These characteristics lead to low efficiency and unsatisfactory encryption effects of traditional cryptographic methods, resulting in weak security. To improve the encryption efficiency and security performance of algorithms, it is necessary to design a remote sensing image encryption method based on two-dimensional discrete memristor hyperchaotic mapping by establishing a memristor hyperchaotic model using a chaotic system coupled with a memristor. This method can securely and efficiently protect image data transmitted over networks. Summary of the Invention

[0004] The technical problem to be solved by this invention is to improve the encryption efficiency and security performance of remote sensing image encryption algorithms by proposing a remote sensing image encryption method based on two-dimensional discrete memristor hyperchaotic mapping.

[0005] The technical solution for implementing this invention is as follows: a remote sensing image encryption method based on two-dimensional discrete memristor hyperchaotic mapping, comprising the following steps:

[0006] Step 1: Chaotic Sequence Generation: Let the size of the original image (or plaintext image) P be m×n, and generate a chaotic sequence by using a key space of 2... 256 The binary external key K is processed as follows:

[0007]

[0008] Where λ1, λ2, λ3, λ4, and λ5 are five initial system parameters obtained from the decompression key, and K i Let be the value of the i-th bit in the key K. Then, further processing of the parameters yields the initial values ​​x1 and y1 of the two-dimensional discrete memristor hyperchaos (2D-LMHM) and the algorithm control parameter α. The processing method can be expressed as follows:

[0009]

[0010] This yields the initial values ​​x1 and y1 of the two-dimensional discrete memristor hyperchaotic (2D-LMHM) system, as well as the algorithm control parameter α. The system is then iterated m×n times according to the following formula to obtain two chaotic sequences X={x i} m×n and Y = {y i} m×n ;

[0011]

[0012] Where, x i and y i It is the result of the i-th iteration, x i+1 and y i+1 This is the result of the (i+1)th iteration, where u is the control parameter of the improved Logistic mapping, k is the coupling strength between the improved Logistic mapping and the memristor, a and b are the memristor parameters, and q is the result of the (i+1)th iteration. i Let be the charge amount at the i-th iteration.

[0013] In this invention, k = 1.77, u = -0.1, a = -1, b = 0.1, and the initial values ​​x1 and y1 are limited to the interval [0.5, 1]. The resulting chaotic sequences X and Y are then transformed into chaotic matrices S1 and S2 of size m × n.

[0014] Step 2: Main diagonal row and column diffusion: Using the chaotic matrix S1, perform row and column diffusion operation on P along the main diagonal direction (from the upper left to the lower right) to obtain the diffusion image matrix C1.

[0015] Its specific diffusion method is as follows:

[0016] (1) Use the elements of the m-th row and 1-th column of the plaintext image P and the elements of the 1-th row and n-th column to perform diffusion processing on the elements of the 1-th row and 1-th column.

[0017] (2) Use the elements in the m-th row and the elements in the first row and first column of the plaintext image P to iteratively spread the elements in the first row to the right.

[0018] (3) Use the elements in the nth column of the plaintext image P and the elements in the first row and first column to iteratively spread the elements in the first column downwards.

[0019] (4) Using the elements in the first row and first column after diffusion, the image matrix C1 is obtained by diffusing along the main diagonal.

[0020] The detailed process can be represented as follows:

[0021]

[0022] Where P represents the plaintext image, which is the image matrix before diffusion; C1 represents the image matrix after diffusion; P (m,j) Let P be the pixel value in the m-th row and j-th column of the plaintext image P; (i,n) P represents the pixel value in the i-th row and n-th column of the plaintext image; (i,j) S is the pixel value in the i-th row and j-th column of the plaintext image; 1(i,j) C is the element in the i-th row and j-th column of the chaotic matrix S1; 1(i,j) Let be the pixel value in the i-th row and j-th column of the diffused image matrix; in the expression, floor means rounding down, and mod means modulo.

[0023] Step 3: Pixel position scrambling: Extract the t column from the chaotic matrix S1 to form matrix S. t Where t is the value obtained by processing the external key K, and its calculation method is as follows:

[0024] t=floor(mod(∑S(:,floor(mod(α,m)+1))×α),m)+1

[0025] Where S is the chaos matrix; m is the number of rows in the image; and α is the algorithm control parameter.

[0026] The specific method for scrambling pixel positions is described as follows: For the chaotic matrix S1 and matrix S... t Sort the columns in ascending order to obtain index matrices U and V. Combine the index matrix U with the corresponding columns and further process to construct a position matrix O1.

[0027] The position matrix O1 can be represented as: [(U (1,1) ,1),(U (1,2) ,2),...,(U (i,j) ,j)], where, U (i,j) Let be the element in the i-th row and j-th column of the index matrix U;

[0028] The pixel values ​​in the position matrix O1 are then sorted in ascending order by row to obtain the index matrix H. The index matrix H and the index matrix V are then further processed to construct a position matrix O2.

[0029] The position matrix O2 can be represented as: [(V1,H (1,1) ),(V1,H (1,2) ),...,(V i H (i,j) )], where V i H is the i-th element of the index matrix V; (i,j) The element in the i-th row and j-th column of the index matrix H;

[0030] The scrambled image matrix C2 is obtained by swapping the pixels at the corresponding positions of position matrices O1 and O2, row by row and column by column.

[0031] Step 4: Diagonal Row and Column Diffusion: Using the chaotic matrix S2, perform row and column diffusion operations on the scrambled image matrix C2 along the diagonal direction (from the upper right to the lower left) to obtain the diffused image matrix C3, which is the final encrypted image.

[0032] The specific diffusion method for the secondary diagonal rows and columns is as follows:

[0033] (1) Use the elements of the m-th row and 1-th column of the scrambled image matrix C2 and the elements of the 1-th row and 1-th column to perform diffusion processing on the elements of the 1-th row and n-th column.

[0034] (2) Use the elements in the m-th row and the elements in the n-th column of the scrambled image matrix C2 to iteratively spread the elements in the first row to the left.

[0035] (3) Use the elements in the first column of the scrambled image matrix C2 and the elements in the first row and nth column to iteratively spread the elements in the nth column downwards.

[0036] (4) Using the elements in the first row and nth column after diffusion, perform row and column diffusion along the secondary diagonal to obtain the diffused image matrix C3; the process can be represented as follows:

[0037]

[0038] Where C2 represents the scrambled image matrix, and C3 represents the diffused image matrix; C 2(m,n) S represents the pixel value in the m-th row and n-th column of the scrambled image C2; 2(i,j) Let C be the element value in the i-th row and j-th column of the chaotic matrix S2; 3(i,j) Let be the pixel value in the i-th row and j-th column of the diffused image matrix C3.

[0039] During the decryption process, the same chaotic sequence can be obtained using the same key K, and then the same chaotic matrix can be used to decrypt the encrypted image C3 to obtain the original image (or plaintext image) P; that is, the decryption process is the reverse process of the encryption process.

[0040] The working principle of this invention is based on a two-dimensional discrete memristor hyperchaotic map (2D-LMHM) coupled with an improved Logistic map and a discrete memristor. This map has a wide chaotic interval and a large hyperchaotic range, making it highly suitable for image encryption. Based on this, this invention proposes an algorithm, RS-IEA, suitable for remote sensing image encryption. This algorithm employs a diffusion-scrambling-diffusion structure, using the obtained chaotic matrix to perform diagonal diffusion, pixel position scrambling, and sub-diagonal diffusion on the plaintext image to obtain the ciphertext image.

[0041] The beneficial effects of this invention lie in its construction of a two-dimensional discrete memristor hyperchaotic map, which improves the complexity and initial value sensitivity of the hyperchaotic map, effectively expands the key space, and greatly enhances the security and encryption efficiency of image encryption. Based on this, an image encryption method based on two-dimensional discrete memristor hyperchaos is proposed. This method employs a structure of main diagonal diffusion-pixel position scrambling-secondary diagonal diffusion. This encryption method significantly improves the encryption efficiency of the algorithm and enhances its resistance to differential attacks, while also effectively resisting brute-force attacks. Therefore, the image encryption method proposed in this invention is secure and efficient, effectively ensuring the security of images during transmission.

[0042] Experimental results show that the present invention can resist differential attacks and brute-force attacks. It is difficult for attackers to obtain effective information from the encrypted image. It not only has fast and efficient encryption capabilities, but also has high security performance, and can successfully ensure the secure transmission of remote sensing images in the network. Attached Figure Description

[0043] Figure 1 This is a flowchart of the encryption process of the present invention;

[0044] Figure 2 This is a schematic diagram of the 4×4 actual position index matrix constructed by the present invention;

[0045] Figure 3 This is a schematic diagram illustrating the scrambling of a 4×4 actual image matrix according to the present invention;

[0046] Figure 4 shows the plaintext image and its corresponding ciphertext image of the present invention.

[0047] Figure 4(a) is a 512×512 remote sensing image.

[0048] Figure 4(b) is a histogram of the plaintext image.

[0049] Figure 4(c) is the encrypted image.

[0050] Figure 4(d) is a histogram of the ciphertext image.

[0051] Figure 4(e) is the decrypted image of the ciphertext image;

[0052] Figure 5 illustrates the key sensitivity of the encryption and decryption processes of this invention.

[0053] Figure 5(a) shows the key sensitivity of the encryption process.

[0054] Figure 5(b) shows the key sensitivity of the decryption process;

[0055] Figure 6 shows the pixel correlation between the plaintext image and its corresponding ciphertext image of the present invention.

[0056] Figure 6(a) shows the correlation between plaintext and images.

[0057] Figure 6(b) shows the correlation of the ciphertext image;

[0058] Figure 7 These are the encrypted and decrypted images of this invention after being subjected to noise attacks;

[0059] Figure 8 These are the encrypted and decrypted images after being cropped according to the present invention. Detailed Implementation

[0060] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0061] like Figure 1 As shown in the figure, this embodiment of a remote sensing image encryption method based on two-dimensional memristor hyperchaotic mapping includes: First, main diagonal row and column diffusion: using an external key K as the initial state, the chaotic sequence generated by the two-dimensional memristor hyperchaotic 2D-LMHM is used to diffuse the plaintext image in rows and columns from the upper left to the lower right along the main diagonal direction; Second, pixel position scrambling: using the index matrix generated by the chaotic sequence to obtain the position matrix, and then using the position matrix to obtain the index matrix to achieve pixel position scrambling; Finally, the chaotic sequence generated by the 2D-LMHM mapping is used to diffuse the scrambled image in rows and columns from the upper right to the lower left along the secondary diagonal direction.

[0062] The specific steps are as follows:

[0063] Step 1: Chaotic Sequence Generation: Let the original image P be m×n in size, and generate a chaotic sequence by using a key space of 2... 256 The binary external key K is processed as follows:

[0064]

[0065] Where λ1, λ2, λ3, λ4, and λ5 are five initial system parameters obtained from the decompression key; K i Let be the value of the i-th bit in key K.

[0066] Then, the parameters are further processed to obtain the initial values ​​x1 and y1 of 2D-LMHM and the algorithm control parameter α. The processing method can be expressed as follows:

[0067]

[0068] Thus, the initial values ​​x1 and y1 of the two-dimensional discrete memristor hyperchaotic system 2D-LMHM and the algorithm control parameter α are obtained, and the system is iterated m×n times according to the following formula to obtain two chaotic sequences X={x i} m×n and Y = {y i} m×n ;

[0069]

[0070] Where, x i and y i It is the result of the i-th iteration, x i+1 and y i+1 This is the result of the (i+1)th iteration, where u is the control parameter of the improved Logistic mapping, k is the coupling strength between the improved Logistic mapping and the memristor, a and b are the memristor parameters, and q is the result of the (i+1)th iteration. i Let be the charge amount at the i-th iteration.

[0071] In this embodiment, k = 1.77, u = -0.1, a = -1, b = 0.1, and the initial values ​​x1 and y1 are limited to the interval [0.5, 1].

[0072] The obtained chaotic sequences X and Y are transformed into chaotic matrices S1 and S2 of size m×n.

[0073] Step 2: Main diagonal row and column diffusion: Using the chaotic matrix S1, perform row and column diffusion operations on the plaintext image P along the main diagonal direction (from the top left to the bottom right) to obtain the diffused image matrix C1.

[0074] Its specific diffusion method is as follows:

[0075] (1) Use the elements of the m-th row and 1-th column of the plaintext image P and the elements of the 1-th row and n-th column to perform diffusion processing on the elements of the 1-th row and 1-th column.

[0076] (2) Use the elements in the m-th row and the elements in the first row and first column of the plaintext image P to iteratively spread the elements in the first row to the right.

[0077] (3) Use the elements in the nth column of the plaintext image P and the elements in the first row and first column to iteratively spread the elements in the first column downwards.

[0078] (4) Using the elements in the first row and first column after diffusion, the image matrix C1 is obtained by diffusing along the main diagonal.

[0079] The detailed process can be represented as follows:

[0080]

[0081] Where P represents the image matrix before diffusion, and C1 represents the image matrix after diffusion; P (m,j) Let P be the pixel value in the m-th row and j-th column of the plaintext image P; (i,n) P represents the pixel value in the i-th row and n-th column of the plaintext image; (i,j) S is the pixel value in the i-th row and j-th column of the plaintext image; 1(i,j) C is the element in the i-th row and j-th column of the chaotic matrix S1; 1(i,j) Let be the pixel value in the i-th row and j-th column of the diffused image matrix.

[0082] Step 3: Pixel position scrambling: Extract the t column from the chaotic matrix S1 to form matrix S. t Where t is the value obtained by processing the external key K, and its calculation method is as follows:

[0083] t=floor(mod(∑S(:,floor(mod(α,m)+1))×α),m)+1

[0084] Where S is the chaos matrix; m is the number of rows in the image; and α is the algorithm control parameter.

[0085] The specific method for scrambling pixel positions is described as follows: For chaotic matrix S1 and matrix S... t Sort the columns in ascending order to obtain index matrices U and V. Combine index matrix U with the corresponding columns and further process them to construct a position matrix O1.

[0086] The position matrix O1 can be represented as: [(U (1,1) ,1),(U (1,2) ,2),...,(U (i,j) ,j)], where, U (i,j) Let be the element in the i-th row and j-th column of the index matrix U;

[0087] The pixel values ​​in the position matrix O1 are then sorted in ascending order by row to obtain the index matrix H. The index matrix H and the index matrix V are then further processed to construct a position matrix O2.

[0088] The position matrix O2 can be represented as: [(V1,H (1,1) ),(V1,H (1,2) ),...,(V i H (i,j))], where V i H is the i-th element of the index matrix V; (i,j) The element in the i-th row and j-th column of the index matrix H;

[0089] The diffused image matrix C1 is swapped row by row and column by pixel at the corresponding positions of position matrices O1 and O2 to obtain the scrambled image matrix C2.

[0090] Combination Figure 2 C in the image matrix after diagonal diffusion 1(4,1) pixels and C 1(3,4) Pixel swapping, C 1(3,2) pixels and C 1(3,1) Pixel swapping, ...,C 1(2,4) pixels and C 1(2,3) The pixels are swapped, and finally the scrambled image matrix C2 is obtained.

[0091] An example of complete scrambling is as follows Figure 3 As shown.

[0092] Step 4: Diagonal Row and Column Diffusion: Using the chaotic matrix S2, perform row and column diffusion operations on the scrambled image matrix C2 along the diagonal direction (from the upper right to the lower left) to obtain the diffused image matrix C3, which is the final encrypted image.

[0093] The specific diffusion methods are as follows:

[0094] (1) Use the elements of the m-th row and 1-th column of the scrambled image matrix C2 and the elements of the 1-th row and 1-th column to perform diffusion processing on the elements of the 1-th row and n-th column;

[0095] (2) Use the elements in the m-th row of the scrambled image matrix C2 and the elements in the n-th column of the 1st row to spread the elements in the 1st row to the left iteratively;

[0096] (3) Use the elements in the first column of the scrambled image matrix C2 and the elements in the first row and nth column to iteratively spread the elements in the nth column downwards;

[0097] (4) Using the elements in the first row and nth column after diffusion, the row and column are diffused along the secondary diagonal to obtain the diffused image matrix C3, which is the ciphertext image.

[0098] The detailed process of the diffused image matrix C3 can be represented as follows:

[0099]

[0100] Where C2 represents the scrambled image matrix; C3 represents the diffused image matrix; C 2(m,n) S represents the pixel value in the m-th row and n-th column of the scrambled image C2; 2(i,j)Let C be the element value in the i-th row and j-th column of the chaotic matrix S2; 3(i,j) Let be the pixel value in the i-th row and j-th column of the diffused image matrix C3.

[0101] To verify the feasibility of this embodiment, an experimental simulation was conducted on a computer configured with Windows 10, 8GB RAM, and an Intel(R) Core(TM) i7-6700HQ CPU@2.60GHz using MATLAB 2018b software.

[0102] This embodiment uses a simulation experiment on a 512×512 color remote sensing image as shown in Figure 4(a). The histogram represents the distribution of all pixels in the image. Figure 4(b) shows the histogram of the plaintext image, and the encryption result is shown in Figure 4(c). Figure 4(d) shows the histogram of the ciphertext image, and the decryption result is shown in Figure 4(e). The experimental results show that the ciphertext image can completely hide the valid information contained in the plaintext image. The histogram of the encrypted image resembles a noise distribution, approaching an ideal uniform distribution. No valid data related to the plaintext image can be obtained from the ciphertext image, indicating that the image encryption algorithm is effective.

[0103] This embodiment will then conduct a comprehensive analysis of the algorithm's security performance using key space, key sensitivity, resistance to differential attacks, correlation between adjacent pixels, information entropy, and robustness.

[0104] 1. Key Space

[0105] Key space is an important indicator of the security of a cryptographic system. A larger key space provides stronger resistance to brute-force attacks, effectively resisting brute-force attacks and resulting in higher security performance. However, if the key space is too large, the encryption speed will decrease, leading to lower image encryption efficiency. Therefore, while ensuring key space security, the encryption speed should be maximized. In this embodiment, a 256-bit key space is used for the binary key K.

[0106] 2. Key sensitivity

[0107] Taking remote sensing images as an example, to test the key sensitivity of this embodiment, only one bit of the key was slightly modified each time, while the other keys remained unchanged. The test used two keys, K1 and K2, which differed by only one bit.

[0108] The key sensitivity during encryption in this embodiment is shown in Figure 5(a). The remote sensing image is encrypted using keys K1 and K2 to obtain encrypted images E1 and E2. By comparing the pixel values ​​in encrypted images E1 and E2, it can be found that encrypted images E1 and E2 are completely different.

[0109] The key sensitivity during decryption in this embodiment is shown in Figure 5(b). After encrypting the remote sensing image with key K1, an encrypted image E1 is obtained. Then, the encrypted image is decrypted using keys K2 and K3 to obtain D2 and D3. It can be observed that using keys K2 and K3 cannot correctly decrypt the image encrypted with key K1. Furthermore, comparing the pixel values ​​in the decrypted images D2 and D3 reveals that different decrypted images D2 and D3 are completely different. Therefore, the experimental results show that even a slight modification to the key will prevent the generation of identical ciphertext or decrypted images during either the encryption or decryption process. This embodiment exhibits strong key sensitivity.

[0110] 3. Resistance to differential attacks

[0111] The commonly used metrics for measuring the differences between encrypted images are Non-Positive PCR (NPCR) and UACI (Uniform Difference Index). NPCR compares the pixel values ​​at corresponding positions in two images, recording the proportion of different pixels to all pixels. UACI compares the pixel values ​​at corresponding positions in two images, calculating the average of the ratios of all differences at corresponding positions to the maximum difference. The formulas for NPCR and UACI are as follows:

[0112]

[0113] Here, P1 and P2 represent two images to be compared, and Sign() is the sign function. For two random images, the ideal NPCR value is 99.6094%, and the ideal UACI value is 33.4635%.

[0114] The specific test results for resistance to differential attacks in this embodiment are shown in the table below:

[0115]

[0116]

[0117] Based on the above experimental results, the NPCR and UACI test results for different images are very close to the ideal values, indicating that the present invention has a strong ability to resist differential attacks.

[0118] 4. Correlation between adjacent pixels

[0119] The correlation between adjacent pixels indicates the degree of pixel diffusion in an image. A correlation coefficient closer to 0 indicates a lower correlation, meaning less effective information can be obtained from adjacent pixels; a correlation coefficient closer to 1 indicates a stronger correlation. The correlation between adjacent pixels in plaintext images is usually very high. Pixel correlation can be expressed as:

[0120]

[0121] Where x and y represent the values ​​of two adjacent pixels, and x and y represent the mean values ​​of x and y. This embodiment analyzes the correlation coefficients of five images (Lena, Baboon, Pepper, Boat, and Plane) before and after encryption in the horizontal, vertical, and diagonal directions. Figure 6(a) shows the correlation of the five images in these three directions before encryption; Figure 6(b) shows the correlation diagram of the five images in these three directions after encryption.

[0122] The correlation coefficients in each direction for the plaintext and ciphertext images of the five images in this embodiment are shown in the table below:

[0123]

[0124]

[0125] The results above show that the correlation coefficients of the encrypted images are all very close to 0, indicating that the information between adjacent pixels in the encrypted images of this invention is well hidden.

[0126] 5. Information entropy

[0127] Information entropy represents the degree of uncertainty in image information. The higher the information entropy, the more uniform the pixel distribution, and the higher the security performance; the lower the information entropy, the more concentrated the pixel distribution, and the more information can be obtained. The formula for information entropy is defined as follows:

[0128]

[0129] Where n represents the pixel depth of the image, and the pixel depth for 256 gray levels is 8, p(x i ) is the grayscale value x i The probability of occurrence. For an image of 256, the theoretical value of information entropy is 8. This means that the closer the result is to 8, the lower the possibility of information leakage, indicating a higher level of security for the proposed encryption scheme. The information entropy of the five images Lena, Baboon, Pepper, Boat, and Plane before and after encryption is analyzed in this invention on the R, G, and B channels, respectively. The information entropy calculation results are shown in the table below:

[0130]

[0131] As can be seen from the table above, the information entropy of the encrypted image is very close to 8, indicating that the uncertainty of the encrypted image information of this invention is very high and the security performance is very high.

[0132] 6. Robustness

[0133] During network transmission, images inevitably suffer from noise attacks and data loss. Therefore, image encryption algorithms should have a certain degree of immunity to noise attacks and data loss. Taking remote sensing images as an example, firstly, the ciphertext image is interfered with using Gaussian noise of 0.001, salt-and-pepper noise of 0.01, Poisson noise, and multiplicative noise of 0.01 respectively. Then, the interfered ciphertext image is decrypted, and the decrypted image is as follows. Figure 7 As shown.

[0134] Even after the encrypted image is subjected to a noise attack, this embodiment can still recover most of the valid plaintext image information; therefore, the present invention can effectively resist noise attacks. Next, the encrypted image is cropped by 1 / 16 and 1 / 8 respectively, and then the cropped encrypted image is decrypted; the cropped encrypted image and the decrypted image are as follows. Figure 8 As shown, this embodiment can still recover most of the valid plaintext image information, so the present invention can effectively resist data loss.

Claims

1. A remote sensing image encryption method based on a two-dimensional discrete memristive hyperchaotic mapping, characterized in that, The method steps are as follows: Step 1, chaotic sequence generation: let the size of the plaintext image P be m x n, and the initial value x1 and y1 of the two-dimensional discrete memristive hyperchaotic system 2D-LMHM and the algorithm control parameter a are calculated by processing the binary external key K with a key space of 2 256 ​ Iterate m x n times according to the following formula to obtain two chaotic sequences X = {x i} m×n and Y = {y i} m×n ; where x i and y i are the results of the i-th iteration; x i+1 and y i+1 are the results of the i+1-th iteration; u is the control parameter of the improved Logistic map; k is the coupling strength between the improved Logistic map and the memristor; a, b are the parameters of the memristor; q i is the charge amount at the i-th iteration; Let k=1.77, u=-0.1, a=-1, b=0.1, and the initial values x1 and y1 are limited in the interval [0.5, 1]; the obtained chaotic sequences X and Y are converted into chaotic matrices S1 and S2 with the size of m*n; Step 2, main diagonal row-column diffusion: using the chaotic matrix S1, the plaintext image P is subjected to row-column diffusion operation in the main diagonal direction from the top left to the bottom right to obtain a diffusion image matrix C1; Step 3, pixel position scrambling: extract the t column in the chaotic matrix S1 as matrix S t , wherein t is a value obtained by processing the external key K; then the chaotic matrix S1 and the matrix S t are sorted in ascending order by column to obtain index matrices U and V, and a position matrix O1 is obtained by combining the index matrix U and its corresponding column; the values in the position matrix O1 are further sorted in ascending order by row to obtain an index matrix H, and the index matrix H and the index matrix V are further processed to obtain a position matrix O2; the pixel values in the corresponding positions of the position matrix O1 and the position matrix O2 in the diffusion image matrix C1 are exchanged by row and column to obtain a scrambled image matrix C2; Step 4, sub-diagonal row-column diffusion: using the chaotic matrix S2, the diffusion image matrix C2 is subjected to row-column diffusion operation in the sub-diagonal direction from the top right to the bottom left to obtain a diffusion image matrix C3, which is the final encrypted image.

2. The remote sensing image encryption method based on two-dimensional discrete memristive hyperchaotic mapping according to claim 1, characterized in that, The processing mode of the external key K is: wherein λ1, λ2, λ3, λ4, λ5 are five system initial value parameters obtained from the decompression key; K i is the value of the i-th bit in the key K; Then the parameters are further processed to obtain the initial values x1 and y1 of the 2D-LMHM and the algorithm control parameter a, and the processing mode is represented as:

3. The remote sensing image encryption method based on two-dimensional discrete memristive hyperchaotic mapping according to claim 1, characterized in that, The main diagonal row-column diffusion operation method is as follows: (1) the elements in the first row and the first column of the plaintext image P are subjected to diffusion processing; (2) the elements in the first row of the plaintext image P are subjected to iterative diffusion to the right using the elements in the first column and the first row; (3) the elements in the first column of the plaintext image P are subjected to iterative diffusion downward using the elements in the first row and the first column; (4) the elements in the first row and the first column after diffusion are subjected to row-column diffusion in the main diagonal direction to obtain a diffusion image matrix C1; The image matrix C1 is expressed as: wherein C1 represents the image matrix after diffusion; P (m,j) is the pixel value of the mth row and jth column of the plaintext image P; P (i,n) is the pixel value of the ith row and nth column of the plaintext image; P (i,j) is the pixel value of the i-th row and j-th column of the plaintext image; S 1(i,j) is the element of the i-th row and j-th column of the chaotic matrix S1; C 1(i,j) is the pixel value of the i-th row and j-th column of the diffused image matrix.

4. The remote sensing image encryption method based on two-dimensional discrete memristive hyperchaotic mapping according to claim 1, characterized in that, The calculation method of the value t obtained by processing the external key K is as follows: t=floor(mod(∑S(:,floor(mod(α,m)+1))×α),m)+1 Wherein, S is a chaotic matrix; m is the number of rows of the image; and a is an algorithm control parameter.

5. The remote sensing image encryption method based on two-dimensional discrete memristive hyperchaotic mapping according to claim 1, characterized in that, The pixel position scrambling method is as follows: The chaotic matrix S1 and the matrix S t The index matrix U and V are obtained by ascending sorting by column. The index matrix U is combined with the corresponding column to further process and construct a position matrix O1. The position matrix O1 is expressed as: [(U (1,1) ,1),(U (1,2) ,2),...,(U (i,j) ,j)], where U (i,j) is the element of the i-th row and j-th column of the index matrix U. The pixel values in the position matrix O1 are further sorted in ascending order by row to obtain an index matrix H, and the index matrix H and the index matrix V are further processed to construct a position matrix O2; The position matrix O2 is expressed as: [(V1,H (1,1) ),(V1,H (1,2) ),...,(V i ,H (i,j) )] where V i is the i-th element of the index matrix V; H (i,j) is the i-th row and j-th column element of the index matrix H. The diffusion image matrix C1 is exchanged according to the pixel positions in the position matrix O1 and the position matrix O2 to obtain a scrambled image matrix C2.

6. The remote sensing image encryption method based on two-dimensional discrete memristive hyperchaotic mapping according to claim 1, characterized in that, The sub-diagonal row-column diffusion operation method is as follows: The scrambled image matrix C2 is subjected to diffusion processing in the sub-diagonal direction using the chaotic matrix S2, and the specific diffusion method is as follows: (1) the elements in the first row and the first column of the scrambled image matrix C2 are subjected to diffusion processing; (2) the elements in the first row of the scrambled image matrix C2 are subjected to iterative diffusion to the left using the elements in the first column and the first row; (3) the elements in the first column of the scrambled image matrix C2 are subjected to iterative diffusion downward using the elements in the first row and the first column; (4) the elements in the first row and the first column after diffusion are subjected to row-column diffusion in the sub-diagonal direction to obtain a diffusion image matrix C3; The process is represented as: Where C2 represents the scrambled image matrix, and C3 represents the diffused image matrix; C 2(m,n) S represents the pixel value in the m-th row and n-th column of the scrambled image C2; 2(i,j) Let C be the element value in the i-th row and j-th column of the chaotic matrix S2; 3(i,j) Let be the pixel value in the i-th row and j-th column of the diffused image matrix C3.

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