A remote sensing image encryption method based on four-dimensional hyperchaotic mapping

Abstract

The present invention relates to a remote sensing image encryption method based on a four-dimensional hyperchaotic map, belonging to the field of information security technology. The method comprises: constructing a four-dimensional hyperchaotic system based on improved Henon and Quadratic maps; generating an initial value of the four-dimensional hyperchaotic system by combining the chi-square test value and hash value of the remote sensing image to be encrypted, and iteratively generating a pseudo-random sequence; dividing the remote sensing image to be encrypted into blocks, using a pseudo-random sequence to generate a three-dimensional random matrix to perform pixel scrambling on the block image, then using the pseudo-random sequence to generate four one-dimensional random matrices and combining them with a dynamic mask interleaving method to obtain four new S-boxes for pixel replacement; combining a Gaussian function and a sine function to generate a waveform curve, and performing XOR with the value of the pseudo-random sequence to achieve pixel scrambling and diffusion, ultimately forming a ciphertext image. The present invention aims to solve the technical problem that traditional chaotic maps are difficult to ensure security when encrypting images due to their relatively simple phase space structure and obvious periodic characteristics.

Description

Technical Field

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

[0002] Remote sensing images are images obtained through remote sensing technology, which can observe and collect information about Earth's surface features from a distance. With the rapid development of aerospace technology and the growing demand for geographic information, remote sensing technology is also advancing rapidly. Therefore, due to their unique advantages, remote sensing images have demonstrated significant value in a number of key areas, such as environmental monitoring and disaster warning. However, the widespread use of remote sensing images also poses significant information security challenges. Because they contain a wealth of sensitive information, they are vulnerable to attacks and theft during transmission and storage. Once illegally obtained or tampered with, they can pose a threat to social stability. Therefore, ensuring the security of remote sensing images during transmission and storage has become a pressing issue.

[0003] In the field of information security, image encryption technology is a key means of protecting image information from unauthorized access and tampering. This technology utilizes a series of complex transformations to process the original image, converting the raw data into a difficult-to-crack ciphertext, thereby preventing attackers from obtaining the image information. Chaotic systems, as highly complex and unpredictable nonlinear dynamic systems, offer a new approach to remote sensing image encryption. However, in this field, traditional chaotic mappings are susceptible to cracking due to their relatively simple phase space structure and pronounced periodicity, failing to fully meet the stringent security requirements of this field.

[0004] In recent years, many scholars have focused on remote sensing image security research, primarily on small images. While proposed remote sensing image encryption methods can meet certain security requirements, there is still much room for improvement in key space and security performance. To further enhance the randomness and complexity of chaotic systems and improve the security of remote sensing image encryption, this paper proposes a remote sensing image encryption method based on a four-dimensional hyperchaotic map. Summary of the Invention

[0005] The purpose of the present invention is to provide a remote sensing image encryption method based on four-dimensional hyperchaotic mapping, aiming to solve the technical problem that traditional chaotic mapping is difficult to ensure security when encrypting images due to its relatively simple phase space structure and obvious periodic characteristics.

[0006] To achieve the above-mentioned purpose, the technical solution of the present invention is: a remote sensing image encryption method based on four-dimensional hyperchaotic mapping to enhance the randomness and complexity of the chaotic system and improve the key space and security performance of the remote sensing image encryption algorithm. First, a new type of hyperchaotic system is constructed. Compared with the traditional chaotic system, the system has stronger randomness and complexity and is more evenly distributed; then, based on the pseudo-random sequence generated by the chaotic system, a three-dimensional random matrix is ​​generated to perform pixel scrambling on the block image; then, four one-dimensional random matrices are generated and combined with the dynamic mask interleaving method to construct four new s-boxes to achieve pixel value replacement; finally, the Gaussian function is combined with the sine function to generate a waveform curve for scrambling, and then the pixel value is XORed with the pseudo-random sequence value to achieve pixel diffusion, thereby forming a ciphertext image. The specific implementation steps are as follows:

[0007] Step 1: Combining the Henon map and the Quadratic map, new state variables and high-order nonlinear terms of state variables and nonlinear coupling terms are introduced to complete the construction of the four-dimensional hyperchaotic system;

[0008] Step 2: generating an initial value of the four-dimensional hyperchaotic system based on the chi-square test value and the hash value of the remote sensing image to be encrypted, and iterating the initial value of the four-dimensional hyperchaotic system to generate a pseudo-random sequence;

[0009] Step 3: Generate a three-dimensional random matrix and four one-dimensional random matrices based on the pseudo-random sequence;

[0010] Step 4: Divide the remote sensing image to be encrypted into blocks to obtain a plurality of image blocks, perform pixel scrambling on all image blocks based on the three-dimensional random matrix, and then recombine all the image blocks after pixel scrambling to obtain a preliminary encrypted image;

[0011] Step 5: Generate four new S-boxes based on the four one-dimensional random matrices in combination with the dynamic mask interleaving method;

[0012] Step 6: Replace the pixel values ​​of the preliminary encrypted image based on the four new S-boxes to obtain a second encrypted image;

[0013] Step 7: Generate a waveform curve based on the Gaussian function and the sine function, perform pixel replacement on the pixel values ​​of the second encrypted image and the waveform curve, and then perform an XOR operation with the value of the pseudo-random sequence to obtain the encrypted pixel value, thereby obtaining the final ciphertext image.

[0014] Optionally, the four-dimensional hyperchaotic system is constructed as follows:

[0015] Merge the Henon map and the Quadratic map, and introduce new state variables based on this and The four-dimensional hyperchaotic system is obtained by combining the high-order nonlinear terms of the state variables and the nonlinear coupling terms. The mathematical model is as follows:

[0016]

[0017] in, 、 、 、 is the state variable of the four-dimensional hyperchaotic system, 、 、 、 are the iterated values ​​of each state variable, 、 、 is the high-order nonlinear term of the introduced state variable, is the nonlinear coupling term, is a multiplication operation, a, b, c, and d are control parameters. By adjusting the values ​​of the control parameters, the constructed four-dimensional hyperchaotic system is placed in a hyperchaotic state to expand the key space.

[0018] Optionally, the step 2 is specifically as follows:

[0019] Step 2.1: Decompose the remote sensing image P to be encrypted with a size of MxN into three components: R, G, and B. Each component is represented by a two-dimensional matrix, which are 、 、 , calculate the chi-square test value of each component, denoted as ch R 、ch G 、ch B , the calculation formula is:

[0020]

[0021] in, ;

[0022] Step 2.2: Use the SHA-512 algorithm to calculate the hash value of the remote sensing image to be encrypted. Split the generated 512-bit hash value into four segments, each with a length of 128 bits, denoted as h1, h2, h3, and h4 respectively;

[0023] Step 2.3: Combine the chi-square test value and the hash value to generate the initial values ​​x0, y0, z0, and w0 of the four-dimensional hyperchaotic system. The specific formula is:

[0024]

[0025] Among them, scale factoris the scaling factor, and the pseudo-random sequences X, Y, Z, and W are generated by iterating the initial values ​​of the four-dimensional hyperchaotic system.

[0026] Optionally, the step 3 is specifically as follows:

[0027] Step 3.1: Arrange a series of consecutive integers in order and reassemble them into a three-dimensional structure with a specific dimension to generate a three-dimensional sequential matrix; start from 0 and increase the number of consecutive integers to generate a one-dimensional sequential matrix containing 256 consecutive integers, and generate a total of four one-dimensional sequential matrices;

[0028] Step 3.2: Convert the pseudo-random sequences X, Y, Z, and W into integer sequences respectively, and sort them in ascending order of the pseudo-random sequence values ​​to obtain the sequences 、 、 、 According to the sequence 、 、 、 , generate four index arrays, where the values ​​in each index array correspond to the positions of the sorted data in the original sequence X, Y, Z, and W respectively. Based on the four index arrays, extract the corresponding elements in the one-dimensional sequential matrix according to the values ​​in the index array and store them in sequence to obtain a one-dimensional random matrix, and finally obtain four one-dimensional random matrices C, D, E, and F, each of which contains 256 elements;

[0029] Step 3.3: For the sequence , divide the corresponding index array into three index arrays, corresponding to the one-dimensional, two-dimensional and three-dimensional of the three-dimensional sequential matrix respectively, extract elements from the three-dimensional sequential matrix in turn, and then store them according to the values ​​in the three divided index arrays to obtain a three-dimensional random matrix A.

[0030] Optionally, step 4 is specifically as follows:

[0031] Step 4.1: Flatten the generated three-dimensional random matrix A and image block H into a one-dimensional array to obtain random data A flattern and the image pixel array P flattern , the formula is as follows:

[0032]

[0033] in, Is a flattening function used to flatten a multidimensional array into a one-dimensional array;

[0034] Step 4.2: Random data A flatternSort in ascending order to generate an index array I. Each element in the index array corresponds to the position of the sorted data in the original data. Use the index to rearrange the pixel data of the remote sensing image to be encrypted, complete the pixel scrambling, and obtain the scrambled image pixel array. The formula is as follows:

[0035]

[0036] Where, is the scrambled image pixel array;

[0037] Step 4.3: Reshape the original remote sensing image block to be encrypted, merge all image blocks, and obtain the preliminary encrypted image .

[0038] Optionally, the generation of four new S-boxes in combination with the dynamic mask interleaving method is specifically as follows:

[0039] Step 5.1: Divide the one-dimensional random matrix into 16 blocks, each containing 16 elements;

[0040] Step 5.2: Circularly shift the elements in the block, and then combine all the blocks after the circular shift to obtain a new random matrix O. The circular shift amount shift is determined by the following formula:

[0041]

[0042] Among them, block[0] is the first element in the block;

[0043] Step 5.3: Generate Mask , the length of the mask is half the length of the new random matrix O, and the formula is as follows:

[0044]

[0045] Where i∈{0,1,2……,127}, is the i-th mask value, is the element with index i in the random matrix O, is the element with index [255-i] in the random matrix O, Indicates an exclusive OR operation;

[0046] Step 5.4: XOR the elements in the mask list modulo the length with the elements in the new random matrix O to generate the transformation matrix :

[0047]

[0048] Where i∈{0,1,2……,255}, is the value in the i-th transformation matrix;

[0049] Step 5.5: Determine whether the elements in the transformation matrix are 0;

[0050] If it is 0, it is directly stored in the S-box list;

[0051] If it is not 0, it is input into the GF256 domain for polynomial transformation, and then the power operator is used to calculate the multiplication inverse element and stored in the S-box list;

[0052] Step 5.6: Sort the S-box list in ascending order and obtain the corresponding index array. Each element in the index array corresponds to the position of the sorted data in the original list. Enter the values ​​in order according to the index, sort them, and fill the values ​​corresponding to the index into the S-box list in turn to ensure the bijectivity of the generated S-box, and finally generate a new S-box;

[0053] Step 5.7: Repeat steps 5.1 to 5.6, and use four one-dimensional random matrices C, D, E, and F in sequence to generate four new S-boxes, and store the four new S-boxes in a new list S1.

[0054] Optionally, step 6 is specifically as follows:

[0055] Step 6.1: From the preliminary encrypted image Get the pixel value pixel step by step, the formula is as follows:

[0056]

[0057] Among them, j, k, and l represent the coordinates of the pixel values;

[0058] Step 6.2: Select the new S-box to be used from the new list S1 based on the pixel value and its coordinates, and store the selected new S-box index s_index in the list S2 for subsequent decryption. The formula is as follows:

[0059]

[0060]

[0061] Among them, Sbox is the new S box selected from the new list S1;

[0062] Step 6.3: Use the linear mapping formula to map the pseudo-random sequence Z to a new uniformly distributed interval to obtain the mapping sequence , the specific formula is as follows:

[0063]

[0064] Among them, i∈{0,1,2……,m}, Represents the i-th mapping sequence value, represents the i-th pseudo-random sequence value, , , represents the original range of the pseudo-random sequence Z, , , represents the target range of the mapping;

[0065] Step 6.4: Based on pixel values ​​and mapping sequence The value in is selected to replace the value in the new S box. The formula is as follows:

[0066]

[0067] Among them, encrypted_pixel is the pixel value after replacement, is the pseudo-random sequence value obtained for the i-th pixel, and after completing the pixel value replacement, the second encrypted image is obtained. .

[0068] Optionally, the specific process of step 7 includes:

[0069] Step 7.1: The second encrypted image after S-box pixel replacement The pixel data in is copied to obtain the copied encrypted image, which is recorded as P1;

[0070] Step 7.2: Get pixel value coordinates step by step and ;

[0071] Step 7.3: Starting from 0 and ending at the image height minus 1, generate the same number of values ​​as the image height in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ;

[0072] Step 7.4: Starting from 0 and ending with the image width minus 1, generate the same number of values ​​as the image width in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ;

[0073] Step 7.5: Multiply the pseudorandom sequence Y by 255 and convert it to an unsigned 8-bit integer to generate a sequence, denoted as chaos.

[0074] Step 7.6: Combine the pseudo-random sequence Y and the sequence chaos to dynamically adjust the amplitude Am, frequency Fr, and phase when generating the curve , so that the curve generated each time is inconsistent, as shown in the formula:

[0075]

[0076] Among them, rotation speed Indicates the phase change rate, which is used to control the speed at which the phase changes with the coordinates, thereby affecting the periodicity of the curve. Width is the width of the image. and Represent the generated curves and Phase;

[0077] Step 7.7: Sequence the array The coordinate origin is moved to the center;

[0078]

[0079] in, Indicates the last data in the array sequence. Represents the first data in the array sequence;

[0080] Step 7.8: Generate the Gaussian function array gauss, the formula is as follows:

[0081]

[0082] Among them, σ represents the standard deviation of the Gaussian function, which determines the decay rate of the function value from the center to the edge;

[0083] Step 7.9: Multiply the Gaussian function array and the sine function to generate a modulated signal wave(x) with a Gaussian shape. The signal gradually weakens as the distance from the center increases. The formula is:

[0084]

[0085] Step 7.10: Bring in the array sequence and , generating two curves , ;

[0086] Step 7.11: Select the perturbation value perturb from the pseudo-random sequence Y according to the following formula:

[0087]

[0088] in, To convert the data into integers;

[0089] Step 7.12: Select the coordinates of the corresponding curve according to the current pixel value position coordinates. When the coordinate selected from the curve is (0,0), the new coordinates ( , ) is calculated as follows:

[0090]

[0091] Among them, height is the height of the image, Indicates that from the sequence chaos according to The selected value; Indicates that from the sequence chaos according to The selected value;

[0092] When the selected coordinate is not (0,0), the new coordinate ( , ) is calculated as follows:

[0093]

[0094] in, Indicates that the waveform Based on The selected value; Indicates that the waveform Based on The selected value;

[0095] Step 7.13: Randomly select a value from the sequence chaos:

[0096]

[0097] Step 7.14: Select pixel values ​​from P1 and perform XOR operation with value to obtain the encrypted pixel value, and pass the encrypted pixel value to the new coordinate calculated in step 7.12 ( , ), perform the above processing on all pixel values ​​in P1 to obtain the final ciphertext image .

[0098] The beneficial effects of the present invention are as follows: the present invention constructs a four-dimensional hyperchaotic map, which significantly enhances the complexity of the chaotic map and the randomness and initial value sensitivity of the pseudo-random sequence, effectively expands the secret key space, and greatly improves the security of image encryption. On this basis, a remote sensing image encryption method based on a four-dimensional hyperchaotic map is proposed. The method uses a random matrix to scramble the block image - construct a new S-box to achieve pixel replacement - a waveform curve to achieve pixel scrambling and diffusion structure. The encryption method effectively destroys the correlation between pixels through an efficient pixel perturbation mechanism, making the pixel values ​​extremely random and difficult to predict. In addition, the method also demonstrates strong anti-attack capabilities and is extremely sensitive to initial conditions and keys, further enhancing the security of image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 is a flow chart of the steps of the present invention;

[0100] Figure 2 is the phase diagram of the four-dimensional hyperchaotic system of the present invention, wherein, Figure 2 (a) is the xyz phase diagram of the four-dimensional hyperchaotic system, Figure 2 (b) is the xyw phase diagram of the four-dimensional hyperchaotic system, Figure 2 (c) is the xzw phase diagram of the four-dimensional hyperchaotic system;

[0101] Figure 3 Lyapunov exponent diagram of the four-dimensional hyperchaotic system of the present invention;

[0102] Figure 4 is the encryption and decryption diagram of the present invention, wherein, Figure 4 (a) is the original remote sensing image used. Figure 4 (b) is the encrypted remote sensing image ciphertext, Figure 4 (c) is the decrypted remote sensing image;

[0103] Figure 5 is the histogram of the remote sensing image and the ciphertext image of the present invention, wherein, Figure 5 (a) is the histogram of the remote sensing image, Figure 5 (b) is the histogram of the ciphertext image;

[0104] Figure 6 is the adjacent pixel correlation map of the remote sensing image used in the present invention, where: Figure 6 (a)- Figure 6 (c) is the R channel of the remote sensing image and the correlation map of adjacent pixels in three directions. Figure 6 (d)- Figure 6 (f) is the G channel of the remote sensing image and the correlation map of adjacent pixels in three directions. Figure 6 (g)- Figure 6 (i) is the B channel of the remote sensing image and the correlation map of adjacent pixels in three directions;

[0105] Figure 7 is the adjacent pixel correlation diagram of the ciphertext image of the present invention, Figure 7 (a)- Figure 7 (c) is the R channel of the ciphertext image and the correlation diagram of adjacent pixels in three directions. Figure 7 (d)- Figure 7 (f) is the G channel of the ciphertext image and the correlation graph of adjacent pixels in three directions. Figure 7 (g)- Figure 7 (i) is the B channel of the ciphertext image and the adjacent pixel correlation map in three directions;

[0106] Figure 8 The noise attack test diagram of the present invention is as follows: Figure 8 (a) is an image with a noise level of 0.005 added to the encrypted image. Figure 8 (b) is an image with a noise level of 0.01 added to the encrypted image. Figure 8 (c) is an image with a noise level of 0.1 added to the encrypted image. Figure 8 (d)- Figure 8 (f) is the decrypted image with added noise. DETAILED DESCRIPTION

[0107] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0108] Example 1: Figure 1 The figure shows a flowchart of the steps of a remote sensing image encryption method based on four-dimensional hyperchaotic mapping of the present invention. First, the chi-square test value and hash value of the remote sensing image to be encrypted are combined to generate the initial value of the four-dimensional hyperchaotic system, and the four-dimensional hyperchaotic system is iterated to generate a pseudo-random sequence. Second, a random matrix is ​​generated using the pseudo-random sequence to scramble the block image. Then, the pseudo-random matrix is ​​combined with the dynamic mask interleaving method to generate a new substitution box (S-box) to achieve pixel replacement. Finally, a Gaussian function and a sine function are combined to generate a waveform curve, which is combined with the pseudo-random sequence to achieve pixel displacement and diffusion, forming the final ciphertext image. The specific steps are as follows:

[0109] Step 1: Combine the Henon map and Quadratic map, introduce new state variables and high-order nonlinear terms of state variables and nonlinear coupling terms to complete the construction of the four-dimensional hyperchaotic system.

[0110] Specifically, the Henon map is a two-dimensional discrete chaotic map, and its mathematical model is as follows:

[0111]

[0112] in, 、 are the iterated values ​​of each state variable, 、 is the state variable, a and b are the control parameters, and the control parameters of the Henon map in this embodiment are , b=0.3.

[0113] Specifically, the Quadratic map is a typical nonlinear discrete-time dynamical system, which is expressed as follows:

[0114]

[0115] in, For the control parameters, in this embodiment .

[0116] Furthermore, based on the above Henon mapping and Quadratic mapping, the Henon mapping and Quadratic mapping are merged, and a new state variable is introduced on this basis and The four-dimensional hyperchaotic system is obtained by combining the high-order nonlinear terms of the state variables and the nonlinear coupling terms. The mathematical model is as follows:

[0117]

[0118] in, 、 、 、 is the state variable of the four-dimensional hyperchaotic system, 、 、 、 are the iterated values ​​of each state variable, 、 、 is the high-order nonlinear term of the introduced state variable, is the nonlinear coupling term, is a multiplication operation, a, b, c, and d are control parameters. By adjusting the values ​​of the control parameters, the constructed four-dimensional hyperchaotic system is placed in a hyperchaotic state to expand the key space.

[0119] Furthermore, in this embodiment, the control parameters are a=1.4, b=0.3, c=12, d=1, and the system initial values ​​(x0, y0, z0, w0) are (1, 1, 1, 1). At this time, the constructed four-dimensional hyperchaotic system is in a hyperchaotic state. Figure 2 As shown, Figure 2 (a), (b) and (c) are the xyz phase diagram, xyw phase diagram and xzw phase diagram of the four-dimensional hyperchaotic mapping in this embodiment. It can be seen from the figures that the system is evenly distributed and covers the entire phase space.

[0120] Furthermore, the chaotic characteristics of the system are analyzed by calculating the Lyapunov exponent (LE) of the chaotic system. Specifically, if there is a positive LE, it means that the system exhibits chaotic behavior. If there are two or more positive LEs, it means that the system is a hyperchaotic system. Figure 3This is the Lyapunov index diagram of the four-dimensional hyperchaotic system of the present invention. The diagram shows the changes in the four LEs as the control parameter a changes. It can be seen from the diagram that the Lyapunov exponents 1, 2, and 3 are all positive. Therefore, the chaotic system belongs to hyperchaos, and the pseudo-random sequence it generates has stronger randomness.

[0121] Step 2: Generate the initial value of the four-dimensional hyperchaotic system based on the chi-square test value and the hash value of the remote sensing image to be encrypted, and iterate the initial value of the four-dimensional hyperchaotic system to generate a pseudo-random sequence.

[0122] Step 2.1: Decompose the remote sensing image P to be encrypted with a size of MxN into three components: R, G, and B. Each component is represented by a two-dimensional matrix, which are 、 、 , calculate the chi-square test value of each component, denoted as ch R 、ch G 、ch B , the calculation formula is:

[0123]

[0124] in, ;

[0125] Step 2.2: Since the hash algorithm has high security and collision resistance, this embodiment uses the SHA-512 algorithm to calculate the hash value of the remote sensing image to be encrypted. The generated 512-bit hash value is divided into four segments, each with a length of 128 bits, denoted as h1, h2, h3, and h4 respectively;

[0126] Step 2.3: Combine the chi-square test value and the hash value to generate the initial values ​​x0, y0, z0, and w0 of the four-dimensional hyperchaotic system. The specific formula is:

[0127]

[0128] Among them, scale factor is the scaling factor, and the pseudo-random sequence X, Y, Z, and W is generated by iterating the initial value of the four-dimensional hyperchaotic system. In this embodiment, scale factor Take 0.5.

[0129] Step 3: Generate a three-dimensional random matrix and four one-dimensional random matrices based on the pseudo-random sequence.

[0130] Step 3.1: Arrange a series of consecutive integers in order and reassemble them into a three-dimensional structure with a specific dimension to generate a three-dimensional sequential matrix; start from 0 and increase the number of consecutive integers to generate a one-dimensional sequential matrix containing 256 consecutive integers, and generate a total of four one-dimensional sequential matrices;

[0131] Step 3.2: Convert the pseudo-random sequences X, Y, Z, and W into integer sequences respectively, and sort them in ascending order of the pseudo-random sequence values ​​to obtain the sequences 、 、 、 According to the sequence 、 、 、 , generate four index arrays, where the values ​​in each index array correspond to the positions of the sorted data in the original sequence X, Y, Z, and W respectively. Based on the four index arrays, extract the corresponding elements in the one-dimensional sequential matrix according to the values ​​in the index array and store them in sequence to obtain a one-dimensional random matrix, and finally obtain four one-dimensional random matrices C, D, E, and F, each of which contains 256 elements;

[0132] Step 3.3: For the sequence , divide the corresponding index array into three index arrays, corresponding to the one-dimensional, two-dimensional and three-dimensional of the three-dimensional sequential matrix respectively, extract elements from the three-dimensional sequential matrix in turn, and then store them according to the values ​​in the three divided index arrays to obtain a three-dimensional random matrix A.

[0133] Step 4: Divide the remote sensing image to be encrypted into blocks to obtain several image blocks, perform pixel scrambling on all image blocks based on the three-dimensional random matrix, and then recombine all the image blocks after pixel scrambling to obtain a preliminary encrypted image.

[0134] Step 4.1: Divide the remote sensing image P to be encrypted into blocks of size size x block size The image block H of size is obtained, and the generated three-dimensional random matrix A and the image block H are flattened into a one-dimensional array to obtain random data A flattern and the image pixel array P flattern , the formula is as follows:

[0135]

[0136] in, Is a flattening function used to flatten a multidimensional array into a one-dimensional array;

[0137] Step 4.2: Random data A flatternSort in ascending order to generate an index array I. Each element in the index array corresponds to the position of the sorted data in the original data. Use the index to rearrange the pixel data of the remote sensing image to be encrypted, complete the pixel scrambling, and obtain the scrambled image pixel array. The formula is as follows:

[0138]

[0139] Where, is the scrambled image pixel array;

[0140] Step 4.3: Reshape the original remote sensing image block to be encrypted, merge all image blocks, and obtain the preliminary encrypted image .

[0141] Step 5: Based on the four one-dimensional random matrices, four new S-boxes are generated in combination with the dynamic mask interleaving method.

[0142] Specifically, the dynamic mask interleaving method is a technique used to construct S-boxes in cryptography. Its core concept is to introduce dynamic changes and interleaving structures during the generation process to enhance the security of the S-boxes. This method combines randomization, masking, data diffusion, and interleaving operations to construct S-boxes that meet cryptographic strength requirements. The overall process involves a series of steps that combine dynamic operations with structure to enhance the nonlinearity, anti-differential, and obfuscation properties of the generated S-boxes, thereby strengthening the security of the cryptographic system.

[0143] Specifically, in this embodiment, the specific steps of generating four new S-boxes in combination with the dynamic mask interleaving method are as follows:

[0144] Step 5.1: Divide the one-dimensional random matrix into 16 blocks, each containing 16 elements;

[0145] Step 5.2: Circularly shift the elements in the block, and then combine all the blocks after the circular shift to obtain a new random matrix O. The circular shift amount shift is determined by the following formula:

[0146]

[0147] Among them, block[0] is the first element in the block;

[0148] Step 5.3: Generate Mask , the length of the mask is half the length of the new random matrix O, and the formula is as follows:

[0149]

[0150] Where i∈{0,1,2……,127}, is the i-th mask value, is the element with index i in the random matrix O, is the element with index [255-i] in the random matrix O, Indicates an exclusive OR operation;

[0151] Step 5.4: XOR the elements in the mask list modulo the length with the elements in the new random matrix O to generate the transformation matrix :

[0152]

[0153] Where i∈{0,1,2……,255}, is the value in the i-th transformation matrix;

[0154] Step 5.5: Determine whether the elements in the transformation matrix are 0;

[0155] If it is 0, it is directly stored in the S-box list;

[0156] If it is not 0, it is input into the GF256 domain for polynomial transformation, and then the power operator is used to calculate the multiplication inverse, which is stored in the S-box list to ensure that the S-box has good cryptographic properties;

[0157] Step 5.6: Sort the S-box list in ascending order and obtain the corresponding index array. Each element in the index array corresponds to the position of the sorted data in the original list. Enter the values ​​in order according to the index, sort them, and fill the values ​​corresponding to the index into the S-box list in turn to ensure the bijectivity of the generated S-box, and finally generate a new S-box;

[0158] Step 5.7: Repeat steps 5.1 to 5.6, and use four one-dimensional random matrices C, D, E, and F in sequence to generate four new S-boxes, and store the four new S-boxes in a new list S1.

[0159] The four new S-boxes obtained are then used in the subsequent pixel value replacement process. The four new S-boxes are stored in the S1 list. Then, based on the index, the required new S-box is found from the S1 list, and the pixel replacement value is finally selected from the new S-box. This process is repeated, and each new S-box selected from the S1 list is different, so the pixel replacement value is selected from a different new S-box each time, thus achieving encryption.

[0160] Step 6: Replace the pixel values ​​of the preliminary encrypted image based on the four new S-boxes to obtain a second encrypted image.

[0161] Step 6.1: From the preliminary encrypted image Get the pixel value pixel step by step, the formula is as follows:

[0162]

[0163] Among them, j, k, and l represent the coordinates of the pixel values;

[0164] Step 6.2: Select the new S-box to be used from the new list S1 based on the pixel value and its coordinates, and store the selected new S-box index s_index in the list S2 for subsequent decryption. The formula is as follows:

[0165]

[0166]

[0167] Among them, Sbox is the new S box selected from the new list S1;

[0168] Step 6.3: Use the linear mapping formula to map the pseudo-random sequence Z to a new uniformly distributed interval to obtain the mapping sequence , the specific formula is as follows:

[0169]

[0170] Among them, i∈{0,1,2……,m}, Represents the i-th mapping sequence value, represents the i-th pseudo-random sequence value, , , represents the original range of the pseudo-random sequence Z, , , represents the target range of the mapping;

[0171] Step 6.4: Based on pixel values ​​and mapping sequence The value in is selected to replace the value in the new S box. The formula is as follows:

[0172]

[0173] Among them, encrypted_pixel is the pixel value after replacement, is the pseudo-random sequence value obtained for the i-th pixel, and after completing the pixel value replacement, the second encrypted image is obtained. .

[0174] Step 7: Generate a waveform curve based on the Gaussian function and the sine function, perform pixel replacement on the pixel values ​​of the second encrypted image and the waveform curve, and then perform an XOR operation with the value of the pseudo-random sequence to obtain the encrypted pixel value, thereby obtaining the final ciphertext image.

[0175] Step 7.1: The second encrypted image after S-box pixel replacement The pixel data in is copied to obtain the copied encrypted image, which is recorded as P1;

[0176] Step 7.2: Get pixel value coordinates step by step and ;

[0177] Step 7.3: Starting from 0 and ending at the image height minus 1, generate the same number of values ​​as the image height in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ;

[0178] Step 7.4: Starting from 0 and ending with the image width minus 1, generate the same number of values ​​as the image width in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ;

[0179] Step 7.5: Multiply the pseudorandom sequence Y by 255 and convert it to an unsigned 8-bit integer to generate a sequence, denoted as chaos.

[0180] Step 7.6: Combine the pseudo-random sequence Y and the sequence chaos to dynamically adjust the amplitude Am, frequency Fr, and phase when generating the curve , so that the curve generated each time is inconsistent, as shown in the formula:

[0181]

[0182] Among them, rotation speed Indicates the phase change rate, which is used to control the speed at which the phase changes with the coordinates, thereby affecting the periodicity of the curve. Width is the width of the image. and Represent the generated curves and Phase, in this embodiment, rotation speed Take 0.0001;

[0183] Step 7.7: Sequence the array The coordinate origin is moved to the center;

[0184]

[0185] in, Indicates the last data in the array sequence. Represents the first data in the array sequence;

[0186] Step 7.8: Generate the Gaussian function array gauss, the formula is as follows:

[0187]

[0188] Among them, σ represents the standard deviation of the Gaussian function, which determines the width of the Gaussian function, that is, the decay rate of the function value from the center to the edge;

[0189] Step 7.9: Multiply the Gaussian function array and the sine function to generate a modulated signal wave(x) with a Gaussian shape. The signal is strong at the center and gradually weakens as the distance from the center increases. The formula is:

[0190]

[0191] Step 7.10: Bring in the array sequence and , generating two curves , ;

[0192] Step 7.11: Select the perturbation value perturb from the pseudo-random sequence Y according to the following formula:

[0193]

[0194] in, To convert the data into integers;

[0195] Step 7.12: Select the coordinates of the corresponding curve according to the current pixel value position coordinates. When the coordinate selected from the curve is (0,0), the new coordinates ( , ) is calculated as follows:

[0196]

[0197] Among them, height is the height of the image, Indicates that from the sequence chaos according to The selected value; Indicates that from the sequence chaos according to The selected value;

[0198] When the selected coordinate is not (0,0), the new coordinate ( , ) is calculated as follows:

[0199]

[0200] in, Indicates that the waveform Based on The selected value; Indicates that the waveform Based on The selected value;

[0201] Step 7.13: Randomly select a value from the sequence chaos:

[0202]

[0203] Step 7.14: Select pixel values ​​from P1 and perform XOR operation with value to obtain the encrypted pixel value, and pass the encrypted pixel value to the new coordinate calculated in step 7.12 ( , ), perform the above processing on all pixel values ​​in P1 to obtain the final ciphertext image .

[0204] Furthermore, to fully verify the effectiveness of the encryption method of the present invention, this embodiment also decrypts the final ciphertext image. The specific steps are as follows:

[0205] Step 1: The final ciphertext image Use the waveform curve to perform pixel inverse permutation, and then perform XOR diffusion with the value of the pseudo-random sequence Y to obtain the first decrypted image;

[0206] Step 2: Get the pixel values ​​in the first encrypted image step by step through a loop;

[0207] Step 3: Construct the corresponding inverse S-boxes based on the four constructed S-boxes, and store the obtained four inverse S-boxes in list S3. The formula for constructing the inverse S-box is as follows:

[0208]

[0209] in, is the inverse S-box, is the i-th value selected from the S-box;

[0210] Step 4: Use the index in list S2 to select the inverse S box from list S3, and select the corresponding replacement value from the selected inverse S box according to the pixel value selected in Step 2 ;

[0211] Step 5: Obtain the decrypted pixel value according to the following formula and store it in memory to obtain the second decrypted image:

[0212]

[0213] in, represents the decrypted pixel value obtained by the i-th pixel, Represents the i-th slave mapping sequence The selected value;

[0214] Step 6: Divide the second decrypted image into image blocks of size MxN, and then use the three-dimensional random matrix A to perform pixel inverse scrambling on the image blocks to obtain an image block list;

[0215] Step 7: Reorganize the image block list to obtain the final decrypted image.

[0216] The present invention will be further described below through specific experiments.

[0217] Since the key (i.e., pseudo-random sequence) of the present invention is related to the remote sensing image to be encrypted, and different remote sensing images have different keys, this embodiment uniformly selects the San Francisco and Oakland images from the USC-SIPI image database maintained by the Signal and Image Processing Institute of the University of Southern California. The remote sensing image size is 1024x1024x3, and the encryption and decryption methods of the present invention are used to encrypt and decrypt the remote sensing images. Figure 4 (a), (b) and (c) are the remote sensing image before encryption, the ciphertext image and the decrypted image of the present invention, respectively.

[0218] Furthermore, a histogram analysis is performed on the encryption method proposed in the present invention. Figure 5 (a) is the histogram of the remote sensing image, Figure 5 (b) is the histogram of the ciphertext image. From the figure, we can see that the histogram of the remote sensing image is unevenly distributed and fluctuates, while the histogram of the ciphertext image is evenly distributed in each channel, indicating that the encryption algorithm has a better encryption effect.

[0219] Furthermore, the correlation analysis of adjacent pixels of the remote sensing image was performed, and the correlation of adjacent pixel values ​​was calculated according to the following formula. The calculated value is recorded as The larger the calculated correlation coefficient value is, the stronger the correlation is. The closer the correlation coefficient value is to 0, the better the encryption algorithm breaks the association between pixel values, indicating that the encryption effect is better.

[0220]

[0221] Among them, n is the number of selected pixel pairs, t is the pixel pair index, is the current pixel value, are the adjacent pixel values, is the pixel average value, is the average value of adjacent pixels.

[0222] Furthermore, Table 1 shows the comparison of correlation coefficients between remote sensing images and ciphertext images;

[0223] Table 1 Comparison of correlation coefficients between remote sensing images and ciphertext images

[0224]

[0225] As can be seen from the table, the correlation of remote sensing images is high, and the correlation coefficient of ciphertext images is close to 0, which shows that the encryption method proposed in the present invention can effectively break the pixel correlation. Figure 6 (a)-(i) are the adjacent pixel correlation diagrams of the three RGB channels and three directions of the remote sensing image of the present invention. It can be seen from the diagram that there is a linear correlation between the adjacent pixel values. Figure 7 (a)-(i) are the correlation diagrams of adjacent pixels in the three RGB channels and three directions of the ciphertext image. It can be seen from the figure that the correlation coefficients between adjacent pixels in different directions are small, indicating that the encryption method has effectively disrupted the association between pixels, indicating that the encryption effect is good.

[0226] Furthermore, this embodiment also verifies the effectiveness of the present invention by introducing a noise attack. Noise attacks are a common threat that often occur during image transmission. They attempt to destroy the information of the encrypted image by introducing random noise. This embodiment uses salt and pepper noise and adds different levels of salt and pepper noise to the San Francisco and Oakland images. Figure 8 (a)-(c) show the images after adding salt and pepper noise with intensities of 0.005, 0.01, and 0.1 to the ciphertext image. Figure 8 (d)-(f) show the corresponding decrypted images. It can be seen from the figures that although the decrypted images will be distorted as the noise level increases, the images can still be clearly identified, which also verifies the effectiveness of the present invention.

[0227] The above describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A remote sensing image encryption method based on four-dimensional hyperchaotic mapping, characterized in that: The method comprises the following steps: Step 1: Combining the Henon map and the Quadratic map, new state variables and high-order nonlinear terms of state variables and nonlinear coupling terms are introduced to complete the construction of the four-dimensional hyperchaotic system; Step 2: generating an initial value of the four-dimensional hyperchaotic system based on the chi-square test value and the hash value of the remote sensing image to be encrypted, and iterating the initial value of the four-dimensional hyperchaotic system to generate a pseudo-random sequence; Step 3: Generate a three-dimensional random matrix and four one-dimensional random matrices based on the pseudo-random sequence; Step 4: Divide the remote sensing image to be encrypted into blocks to obtain a plurality of image blocks, perform pixel scrambling on all image blocks based on the three-dimensional random matrix, and then recombine all the image blocks after pixel scrambling to obtain a preliminary encrypted image; Step 5: Generate four new S-boxes based on the four one-dimensional random matrices in combination with the dynamic mask interleaving method; Step 6: Replace the pixel values ​​of the preliminary encrypted image based on the four new S-boxes to obtain a second encrypted image; Step 7: Generate a waveform curve based on the Gaussian function and the sine function, perform pixel replacement on the pixel values ​​of the second encrypted image and the waveform curve, and then perform an XOR operation with the value of the pseudo-random sequence to obtain the encrypted pixel value, thereby obtaining the final ciphertext image.

2. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1, characterized in that: The four-dimensional hyperchaotic system is constructed as follows: Merge the Henon map and the Quadratic map, and introduce new state variables based on this and The four-dimensional hyperchaotic system is obtained by combining the high-order nonlinear terms of the state variables and the nonlinear coupling terms. The mathematical model is: ； in, 、 、 、 is the state variable of the four-dimensional hyperchaotic system, 、 、 、 are the iterated values ​​of each state variable, 、 、 is the high-order nonlinear term of the introduced state variable, is the nonlinear coupling term, is a multiplication operation, a, b, c, and d are control parameters. By adjusting the values ​​of the control parameters, the constructed four-dimensional hyperchaotic system is placed in a hyperchaotic state to expand the key space.

3. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: Decompose the remote sensing image P to be encrypted with a size of MxN into three components: R, G, and B. Each component is represented by a two-dimensional matrix, which are 、 、 , calculate the chi-square test value of each component, denoted as ch R 、ch G 、ch B , the calculation formula is: ； in, ; Step 2.2: Use the SHA-512 algorithm to calculate the hash value of the remote sensing image to be encrypted. Split the generated 512-bit hash value into four segments, each with a length of 128 bits, denoted as h1, h2, h3, and h4 respectively; Step 2.3: Combine the chi-square test value and the hash value to generate the initial values ​​x0, y0, z0, and w0 of the four-dimensional hyperchaotic system. The specific formula is: ； Among them, scale factor is the scaling factor, and the pseudo-random sequences X, Y, Z, and W are generated by iterating the initial values ​​of the four-dimensional hyperchaotic system.

4. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1, characterized in that: The step 3 is specifically as follows: Step 3.1: Arrange a series of consecutive integers in order and reassemble them into a three-dimensional structure to generate a three-dimensional sequential matrix; start from 0 and generate a one-dimensional sequential matrix containing 256 consecutive integers in sequence, and generate a total of four one-dimensional sequential matrices; Step 3.2: Convert the pseudo-random sequences X, Y, Z, and W into integer sequences respectively, and sort them in ascending order of the pseudo-random sequence values ​​to obtain the sequences 、 、 、 According to the sequence 、 、 、 , generate four index arrays, where the values ​​in each index array correspond to the positions of the sorted data in the original sequence X, Y, Z, and W respectively. Based on the four index arrays, extract the corresponding elements in the one-dimensional sequential matrix according to the values ​​in the index array and store them in sequence to obtain a one-dimensional random matrix, and finally obtain four one-dimensional random matrices C, D, E, and F, each of which contains 256 elements; Step 3.3: For the sequence , divide the corresponding index array into three index arrays, corresponding to the one-dimensional, two-dimensional and three-dimensional of the three-dimensional sequential matrix respectively, extract elements from the three-dimensional sequential matrix in turn, and then store them according to the values ​​in the three divided index arrays to obtain a three-dimensional random matrix A.

5. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1 is characterized in that: The step 4 is specifically as follows: Step 4.1: Flatten the generated three-dimensional random matrix A and image block H into a one-dimensional array to obtain random data A flattern and the image pixel array P flattern , the formula is: ； in, Is a flattening function used to flatten a multidimensional array into a one-dimensional array; Step 4.2: Random data A flattern Sort in ascending order to generate an index array I. Each element in the index array I corresponds to the position of the sorted data in the original data. Use the index array I to rearrange the pixel data of the remote sensing image to be encrypted, complete pixel scrambling, and obtain the scrambled image pixel array. The formula is: ； Where, is the scrambled image pixel array; Step 4.3: Reshape the original remote sensing image block to be encrypted, merge all image blocks, and obtain the preliminary encrypted image .

6. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1, characterized in that: The method of generating four new S-boxes by combining the dynamic mask interleaving method is as follows: Step 5.1: Divide the one-dimensional random matrix into 16 blocks, each containing 16 elements; Step 5.2: Circularly shift the elements in the block, and then combine all the blocks after the circular shift to obtain a new random matrix O. The circular shift amount shift is determined by the following formula: ； Among them, block[0] is the first element in the block; Step 5.3: Generate Mask , the length of the mask is half the length of the new random matrix O, and the formula is: ； Where i∈{0,1,2……,127}, is the i-th mask value, is the element with index i in the random matrix O, is the element with index [255-i] in the random matrix O, Indicates an exclusive OR operation; Step 5.4: XOR the elements in the mask list modulo the length with the elements in the new random matrix O to generate the transformation matrix : ； Where i∈{0,1,2……,255}, is the value in the i-th transformation matrix; Step 5.5: Determine whether the elements in the transformation matrix are 0; If it is 0, it is directly stored in the S-box list; If it is not 0, it is input into the GF256 domain for polynomial transformation, and then the power operator is used to calculate the multiplication inverse element and stored in the S-box list; Step 5.6: Sort the S-box list in ascending order and obtain the corresponding index array. Each element in the index array corresponds to the position of the sorted data in the original list. Enter the values ​​in order according to the index array, sort them, and fill the values ​​corresponding to the indexes into the S-box list in turn to ensure the bijectivity of the generated S-box, and finally generate a new S-box. Step 5.7: Repeat steps 5.1 to 5.6, and use four one-dimensional random matrices C, D, E, and F in sequence to generate four new S-boxes, and store the four new S-boxes in a new list S1.

7. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1, characterized in that: The step 6 is specifically as follows: Step 6.1: From the preliminary encrypted image Get the pixel value pixel step by step, the formula is: ； Among them, j, k, and l represent the coordinates of pixel values; Step 6.2: Select the new S-box to be used from the new list S1 based on the pixel value and its coordinates, and store the selected new S-box index s_index in the list S2 for subsequent decryption. The formula is: ； ； Among them, Sbox is the new S box selected from the new list S1; Step 6.3: Use the linear mapping formula to map the pseudo-random sequence Z to a new uniformly distributed interval to obtain the mapping sequence , the specific formula is: ； Among them, i∈{0,1,2……,m}, Represents the i-th mapping sequence value, represents the i-th pseudo-random sequence value, , , represents the original range of the pseudo-random sequence Z, , , represents the target range of the mapping; Step 6.4: Based on pixel values ​​and mapping sequence The value in is selected to replace the value in the new S box. The formula is: ； Among them, encrypted_pixel is the pixel value after replacement, is the pseudo-random sequence value obtained for the i-th pixel, and after completing the pixel value replacement, the second encrypted image is obtained. .

8. The remote sensing image encryption method based on four-dimensional hyperchaotic mapping according to claim 1 is characterized in that: The specific process of step 7 includes: Step 7.1: The second encrypted image after S-box pixel replacement The pixel data in is copied to obtain the copied encrypted image, which is recorded as P1; Step 7.2: Get pixel value coordinates step by step and ; Step 7.3: Starting from 0 and ending at the image height minus 1, generate the same number of values ​​as the image height in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ; Step 7.4: Starting from 0 and ending with the image width minus 1, generate the same number of values ​​as the image width in an evenly spaced manner. The values ​​are consecutive integers with an interval of 1. The generated array sequence is recorded as ; Step 7.5: Multiply the pseudorandom sequence Y by 255 and convert it to an unsigned 8-bit integer to generate a sequence, denoted as chaos. Step 7.6: Combine the pseudo-random sequence Y and the sequence chaos to dynamically adjust the amplitude Am, frequency Fr, and phase when generating the curve , so that the curve generated each time is inconsistent, the formula is: ； Among them, rotation speed Indicates the phase change rate, which is used to control the speed at which the phase changes with the coordinates, thereby affecting the periodicity of the curve. Width is the width of the image. and Represents the generated curves and Phase; Step 7.7: Sequence the array The coordinate origin is moved to the center; ； in, Indicates the last data in the array sequence. Represents the first data in the array sequence; Step 7.8: Generate the Gaussian function array gauss, the formula is as follows: ； in, Represents the standard deviation of the Gaussian function, which determines the decay rate of the function value from the center to the edge; Step 7.9: Multiply the Gaussian function array and the sine function to generate a modulated signal wave(x) with a Gaussian shape. The signal gradually weakens as the distance from the center increases. The formula is: ； Step 7.10: Bring in the array sequence and , generating two curves , ; Step 7.11: Select the perturbation value perturb from the pseudo-random sequence Y according to the formula: ； in, To convert the data into integers; Step 7.12: Select the coordinates of the corresponding curve according to the current pixel value position coordinates. When the coordinate selected from the curve is (0,0), the new coordinates ( , ) is calculated as: ； Among them, height is the height of the image, Indicates that from the sequence chaos according to The selected value; Indicates that from the sequence chaos according to The selected value; When the selected coordinate is not (0,0), the new coordinate ( , ) is calculated as: ； in, Indicates that the waveform Based on The selected value; Indicates that the waveform Based on The selected value; Step 7.13: Randomly select a value from the sequence chaos: ； Step 7.14: Select pixel values ​​from P1 and perform XOR operation with value to obtain the encrypted pixel value, and pass the encrypted pixel value to the new coordinate calculated in step 7.12 ( , ), perform the above processing on all pixel values ​​in P1 to obtain the final ciphertext image .

Images