Remote sensing image encryption algorithm based on novel spatiotemporal chaotic system

Abstract

The invention relates to the technical field of image processing and secret communication, in particular to a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system. Comprising the following steps: constructing a spatiotemporal chaotic system based on a coupling mapping lattice CML model, scrambling a plaintext by using a point-taking blocking Arnold periodic scrambling algorithm, eliminating a boundary generated by a blocking effect by using a bit-level arrangement algorithm, and designing a diffusion algorithm based on the spatiotemporal chaotic system and a Hash index chain. The method has the advantages that more complex behaviors of the spatiotemporal chaotic system can be described, and the spatiotemporal chaotic system not only has a larger parameter range, but also has more chaotic sequences; from the perspective of anti-decoding capability of an encryption algorithm, the dynamic characteristic of the spatio-temporal chaotic system is very suitable for image encryption; on the basis of a spatiotemporal chaotic system, the remote sensing image encryption algorithm is designed in combination with a point-taking partitioning algorithm, so that the spatial features of the remote sensing image can be processed more comprehensively, and the encryption algorithm has relatively high capability of resisting cracking.

Description

Technical Field

[0001] The invention relates to the technical field of image processing and secure communication, and in particular to a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system. Background Art

[0002] With the rapid development of information technology, information sharing has brought great convenience to people. However, in the process of sharing, the protection of key information has become increasingly important. Remote sensing images usually contain sensitive geographic, military or commercial information. If unencrypted remote sensing data is obtained by criminals, it may lead to information leakage and even security threats. In recent years, some studies have shown that traditional image encryption algorithms may be difficult to meet the requirements of high confidentiality when processing satellite remote sensing image data. Therefore, it is particularly important to improve the performance of remote sensing image encryption algorithms, including reducing the correlation between pixels and enhancing the ability of encryption algorithms to resist attacks. At present, the use of chaotic systems for information encryption has become one of the most popular research directions. Due to the sensitivity of chaotic systems to initial values ​​and the randomness they exhibit, encryption schemes based on chaos have unique advantages in processing large data such as remote sensing images. Image encryption techniques based on chaotic systems include chaotic mapping scrambling and chaotic sequence diffusion. Chaotic mapping can generate pseudo-random sequences as the keys of encryption algorithms. Chaotic sequences have pseudo-random characteristics and can diffuse images through XOR operations with image pixels to improve encryption strength. However, due to the limited number of chaotic systems discovered so far, there are only a handful of chaotic models that can be used for remote sensing image encryption, which makes it increasingly difficult to crack ciphertext. Therefore, there is an urgent need to design a more efficient remote sensing image encryption algorithm based on a new type of chaotic system.

[0003] In the prior art, when a chaotic system is selected for application in an encryption algorithm, the commonly used chaotic system is a low-dimensional static system, whose chaotic behavior is relatively simple, and the chaotic sequence has strong periodicity and regularity, and is easy to retain certain statistical characteristics. Therefore, in recent years, spatiotemporal chaos encryption has become one of the hot research topics in the fields of information security and image encryption. However, due to the limited number of existing spatiotemporal chaos models, the difficulty of parameter adjustment, the high implementation complexity and the lack of good integration into the algorithm design. At present, in the encryption algorithm design part, the commonly used design scheme is to use one algorithm for the complete image, and its encryption architecture is relatively simple, and there is a lack of encryption schemes that combine different algorithms to improve the anti-cracking ability. Summary of the invention

[0004] The purpose of the present invention is to provide a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system to solve the problems of the existing chaotic system structure used for remote sensing image encryption being too simple, low in complexity, poor in encryption efficiency, and insufficient in security of ciphertext remote sensing images.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A remote sensing image encryption algorithm based on a new spatiotemporal chaotic system, including:

[0007] S1. Construct a spatiotemporal chaotic system based on the coupled mapping lattice CML model;

[0008] S2, using the point-based block Arnold periodic scrambling algorithm to scramble the plaintext;

[0009] S3, using a bit-level permutation algorithm to eliminate the boundaries created by the blocking effect;

[0010] S4. Design a diffusion algorithm based on spatiotemporal chaotic system and hash index chain.

[0011] In S1, a spatiotemporal chaotic system based on the coupled mapping lattice CML model is constructed, and the formula is as follows:

[0012] x n+1 (i) = (1-ε)f[x n (i)]+(ε / 2)(f[x n (i+1)]+f[x n (i-1)]) ①

[0013] In formula ①, ε is the coupling coefficient, and its value range is (0≤ε≤1); i+1 and i-1 are two adjacent grids, and the coupling mode of the CML model is affected by the adjacent grids. f(x) is a Logistic chaotic system, and the formula of the Logistic chaotic system is as follows:

[0014] x n+1 =μx n (1-x n ), (μ∈(0,4],ε∈[0,1]) ②

[0015] In formula ②, μ is the control parameter of f(x), and its value range is (0,4];

[0016] When 3.57≤μ≤4, f(x) enters a completely chaotic state. The Arnold cat mapping is used to change the coupling mode of the CML model. The formula is as follows:

[0017] x n+1 (i) = (1-ε)f[x n (i)]+(ε / 2)(f[x n (j)]+f[x n (k)]) ③

[0018] In formula ③, i, j and k are spatial grid points and are determined by the Arnold cat mapping, as follows:

[0019]

[0020] In formula ④, i ≥ 1 and j, k ≤ L; p and q are integer parameters, p is used to control the transformation characteristics of the mapping in the horizontal direction, and q is used to control the transformation characteristics of the mapping in the vertical direction;

[0021] Map the hash index chain to the i, j values ​​of the Arnold cat map using the following formula:

[0022]

[0023] In formula ⑤, H(i) is a hash index array generated by the conflict resolution method.

[0024] In S2, the point-by-point block Arnold periodic scrambling algorithm is used, including:

[0025] S21, dividing the remote sensing image into multiple square areas and non-square areas by taking points and dividing them into blocks, and using Arnold scrambling of different periods for each area;

[0026] S22, stitching together regions with different scrambling periods to obtain a ciphertext image;

[0027] S23. Decrypt the ciphertext using the inverse transformation equation of Arnold scrambling.

[0028] In S21, each square area is scrambled with equal distance Arnold, and the formula is as follows:

[0029]

[0030] In formula ⑥, (x0, y0) is the coordinate of the upper left corner pixel of each square area, whose value is (0, 0), and (x∈X, y∈Y), the scrambled coordinates are (X-x0, Y-y0);

[0031] The non-equidistant Arnold cat scrambling of each non-square region is as follows:

[0032]

[0033] In formulas ⑦ and ⑧, a is the main expansion ratio in the x direction, b is the coupling degree between the x and y directions, c is the coupling degree between the y and x directions, and d is the main expansion ratio in the y direction; a=1=b=c, d=2, and n is the side length.

[0034] In S3, the bit-level permutation algorithm is as follows:

[0035] 1) Taking five pixels as a whole, the first and second columns follow the (1-3-2-4-5) path loop pattern. When the loop reaches the maximum number of rows, it jumps out of this loop and then follows the (1-3-4-2) path loop pattern;

[0036] The third and fourth columns follow the (3-1-4-2-5) path loop pattern, and when the loop reaches the first row, a full forward and reverse loop is completed; the connection between two complete arrangements follows the (3-1-2-4) loop pattern;

[0037] Path 4-5 is to check the coordinate value (x, y) at 4. When x is an even number and y is an even number, follow path 4-5. When x reaches the maximum number of rows N and y is an even number, this loop stops.

[0038] In path 3-4, add 1 to the value of y;

[0039] 2) In the reverse circular arrangement, path 2-5 is to check the coordinate value (x, y) at 2;

[0040] When x is an odd number and y is an even number, the loop follows path 2-5;

[0041] When x reaches the first row and y is an even number, the loop from the first to the fourth column ends;

[0042] Treat the four columns as a whole and perform N / 4 cycles on the complete image.

[0043] In S4, the diffusion algorithm based on spatiotemporal chaotic system and hash index chain is as follows:

[0044] S41. Use hash index chain H1 to perform pixel diffusion. The formula is as follows:

[0045] F e (H(i)) = mod(F o (H(i))+f(F e (H(i-2)))+F e (H(i-1)), 256) ⑨

[0046] In formula 9, Fe and Fo are the one-dimensional sequence of the encrypted frame and the one-dimensional sequence after block scrambling respectively; i-1 is the previous value of the hash index chain H1, and i-2 represents the previous two values;

[0047] f(x) is defined as follows:

[0048]

[0049] In formula ⑩, i-2 is the first two values ​​of the hash index chain H1;

[0050] Use the hash index chain H2 to perform pixel diffusion. The formula is as follows:

[0051] F′ e (H′(i))=mod(F e (H′(i))+f(F′ e (H′(i-2)))+F′ e (H′(i-1)), 256)

[0052] formula In , i-1 is the previous value of the hash index chain H2, i-2 is the previous two values; Fe' is the pixel value of the encrypted frame obtained after the last diffusion operation;

[0053] In the designed XOR diffusion algorithm, each pixel value is determined by the previous two pixel values ​​and the chaotic sequence cs generated by the spatiotemporal chaotic system, and undergoes two XOR diffusion operations. The formula is as follows:

[0054]

[0055] formula In the figure, the initial value LL(i) is the chaotic sequence generated by the spatiotemporal chaotic system, D(i) is the sequence after hash diffusion, the value of SS(i+2) depends on the values ​​of SS(i), SS(i+1), D(i) and LL(i); ssk(i+2) is calculated from the values ​​of ssk(i), ssk(i+1), LL(i) and sk(i), and sssk(i+1) is the pixel value after applying the diffusion algorithm.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The spatiotemporal chaotic system takes into account the complexity of space and time, and can describe the more complex behavior of the spatiotemporal chaotic system. The spatiotemporal chaotic system not only has a larger parameter range, but also has more chaotic sequences. From the perspective of the anti-decryption ability of the encryption algorithm, the dynamic characteristics of the spatiotemporal chaotic system are very suitable for image encryption. Based on the spatiotemporal chaotic system, the design of the remote sensing image encryption algorithm combined with the point-taking block algorithm can not only process the spatial characteristics of the remote sensing image more comprehensively, but also has a stronger encryption algorithm to resist cracking. This is of great significance for the research in related fields such as information confidentiality communication.

[0058] 2. The spatiotemporal chaotic system effectively combines the hash index chain with the original model of the spatiotemporal chaotic system to improve the performance of the chaotic system;

[0059] 3. Design an Arnold periodic scrambling algorithm based on point-based block partitioning, and use a bit-level permutation algorithm to eliminate the boundaries caused by the block periodic effect;

[0060] 4. Design a new diffusion algorithm based on the constructed spatiotemporal chaotic system and hash index chain, which can further encrypt pixel values ​​and improve the security of the encryption algorithm;

[0061] 5. The image encryption algorithm has high security performance by utilizing the partition encryption mechanism, and provides theoretical guidance and experimental verification for the fields of military information security, confidential communications, and remote sensing image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a schematic diagram of the generation principle of the hash index chain H1.

[0063] Figure 2 It is a schematic diagram of the bit level arrangement.

[0064] Figure 3 It is a diagram of the behavior of a spatiotemporal chaotic system in the time and space dimensions.

[0065] Figure 4 This is a schematic diagram of the generation principle of the hash index chain H2.

[0066] Figure 5 It is the encryption and decryption diagram of the remote sensing image after the encryption algorithm proposed by the present invention.

[0067] Figure 6 It is the histogram test result of the encryption algorithm.

[0068] Figure 7 It is a robustness test of the encryption algorithm. DETAILED DESCRIPTION

[0069] The present invention is described in detail below in conjunction with the accompanying drawings, but it should be noted that the implementation of the present invention is not limited to the following embodiments.

[0070] The following examples are implemented on the premise of the technical solution of the present invention, and provide detailed implementation methods and specific operation processes, but the protection scope of the present invention is not limited to the following examples. The methods used in the following examples are conventional methods unless otherwise specified.

[0071] Example 1

[0072] A remote sensing image encryption algorithm based on a new spatiotemporal chaotic system, including:

[0073] S1. Construct a spatiotemporal chaotic system based on the coupled mapping lattice CML model. The formula is as follows:

[0074] x n+1 (i) = (1-ε)f[x n (i)]+(ε / 2)(f[x n (i+1)]+f[xn (i-1)]) ①

[0075] In formula ①, ε is the coupling coefficient, and its value range is (0≤ε≤1); i+1 and i-1 are two adjacent grids, and the coupling mode of the CML model is affected by the adjacent grids. f(x) is the Logistic chaotic system, and the Logistic chaotic system formula is as follows:

[0076] x n+1 =μx n (1-x n ), (μ∈(0,4],ε∈[0,1]) ②

[0077] In formula ②, μ is the control parameter of f(x), and its value range is (0,4];

[0078] When 3.57≤μ≤4, f(x) enters a completely chaotic state. The Arnold cat mapping is used to change the coupling mode of the CML model. The formula is as follows:

[0079] x n+1 (i) = (1-ε)f[x n (i)]+(ε / 2)(f[x n (j)]+f[x n (k)]) ③

[0080] In formula ③, i, j and k are spatial grid points and are determined by the Arnold cat mapping, as follows:

[0081]

[0082] In formula ④, i ≥ 1 and j, k ≤ L; p and q are integer parameters, p is used to control the transformation characteristics of the mapping in the horizontal direction, and q is used to control the transformation characteristics of the mapping in the vertical direction;

[0083] The introduction of Arnold cat mapping changes the coupling mode between grids, changing the interaction between adjacent grids to the interaction between non-adjacent grids, making the energy diffusion between grids more uniform, effectively improving the chaotic differences between grids, and making the system produce better chaotic behavior;

[0084] Map the hash index chain to the i, j values ​​of the Arnold cat map using the following formula:

[0085]

[0086] In formula ⑤, H(i) is the hash index array, which is Figure 1 The conflict handling method shown generates,constant changes in the values ​​of i and j, which increases the complexity of the,algorithm and reduces the differences in chaotic characteristics between different,grids.

[0087] S2, use the point-based block Arnold periodic scrambling algorithm to scramble the plaintext

[0088] When encrypting remote sensing satellite images, due to the particularity of security, the encryption algorithm has a high requirement for anti-cracking ability. Therefore, a point-based block encryption algorithm is designed by utilizing the reversibility and periodicity of Arnold scrambling.

[0089] The point-by-point Arnold periodic scrambling algorithm includes:

[0090] S21. The remote sensing image is divided into four square areas and four square areas by taking points and blocks, and the block areas are allowed to overlap each other. Each area uses Arnold scrambling of different periods. The formula is as follows:

[0091]

[0092] In formula ⑥, (x0, y0) is the coordinate of the upper left corner pixel of each square area, whose value is (0, 0), and (x∈X, y∈Y), the scrambled coordinates are (X-x0, Y-y0);

[0093] The non-equidistant Arnold cat scrambling of each non-square region is as follows:

[0094]

[0095] In formulas ⑦ and ⑧, a represents the main expansion ratio in the x direction, b represents the coupling degree between the x and y directions, and c represents the coupling degree between the y and x directions. d represents the main expansion ratio in the y direction. a=1=b=c, d=2. n is the side length; using different Arnold scrambling cycles in the same remote sensing image not only improves the anti-cracking ability, but also increases the complexity of the encryption algorithm.

[0096] S22, stitching together regions with different scrambling periods to obtain a ciphertext image;

[0097] S23. Considering the reversibility of Arnold scrambling, the inverse transformation equation of Arnold scrambling is used to decrypt the ciphertext;

[0098] The above encryption algorithm can not only enhance the complexity of the algorithm, but also improve the anti-cracking ability of the ciphertext; the traditional block segmentation algorithm divides the original image into blocks of equal size and uniform distribution; in the point-taking block algorithm proposed in the present invention, the larger the value of the initial block, the more basic blocks are obtained; in order to simplify the subsequent encryption and decryption algorithms, the initial block is set to 2.

[0099] S3. Use a bit-level arrangement algorithm to eliminate the boundary line caused by the blocking effect. The bit-level arrangement algorithm is as follows:

[0100] In the result of point-by-point block scrambling, there are some obvious boundaries between the eight regions. This is due to the block effect. The scrambling period of each region is different. The boundaries appear after splicing. The attacker can use the boundaries to try to segment and decrypt the image. To solve this problem, we propose a bit-level permutation algorithm. The proposed bit-level permutation is shown in Figure 2 , take the 8*8 grid as an example; first, consider the five pixels as a whole, the first and second columns follow the (1-3-2-4-5) path cycle mode, when the cycle reaches the maximum number of rows, jump out of this cycle, and then follow the (1-3-4-2) path cycle mode; after the cycle path mode conversion, the third and fourth columns follow the (3-1-4-2-5) path cycle mode, when the cycle reaches the first row, a complete forward and reverse cycle is achieved; the 8*8 grid needs to be arranged into two complete cycle paths; therefore, the connection between the two complete arrangements is Then follow the (3-1-2-4) loop pattern; where path 4-5 is by checking the coordinate value (x, y) at 4, when x is an even number and y is an even number, follow path 4-5, when x reaches the maximum number of rows N, y is an even number, this loop stops; in path 3-4, add 1 to the value of y, then, in the reverse loop arrangement, path 2-5 is to check the coordinate value (x, y) at 2, when x is an odd number and y is an even number, the loop follows path 2-5, when x reaches the first row and y is an even number, the loop from the first column to the fourth column ends. Take the four columns as a whole and loop N / 4 times for the complete image.

[0101] S4. Design a diffusion algorithm based on spatiotemporal chaotic system and hash index chain

[0102] Using hash index chains to diffuse pixel values ​​is a common technique in cryptography. A chaotic sequence cs is obtained through the spatiotemporal chaotic system of the present invention, and the sequence X1 is cs. Figure 1 According to the designed conflict handling method, the hash index chain H1 can be inverted to obtain the hash index inverse chain NH1; see Figure 4 , using the same conflict handling method to calculate the data in the reverse chain NH1, the second hash index chain H2 can be obtained; the use of the second hash index chain increases the complexity of the algorithm and also makes it difficult for attackers to crack; the specific content is as follows:

[0103] S41. Use hash index chain H1 to perform pixel diffusion. The formula is as follows:

[0104] F e (H(i)) = mod(F o (H(i))+f(F e(H(i-2)))+F e (H(i-1)), 256) ⑨

[0105] In formula 9, Fe and Fo are the one-dimensional sequence of the encrypted frame and the one-dimensional sequence after block scrambling respectively; i-1 is the previous value of the hash index chain H1, and i-2 represents the previous two values;

[0106] f(x) is defined as follows:

[0107]

[0108] In formula ⑩, i-2 is the first two values ​​of the hash index chain H1;

[0109] Use the hash index chain H2 to perform pixel diffusion. The formula is as follows:

[0110] F′ e (H′(i))=mod(F e (H′(i))+f(F′ e (H′(i-2)))+F′ e (H′(i-1)), 256)

[0111] formula In , i-1 is the previous value of the hash index chain H2, i-2 is the previous two values; Fe′ is the pixel value of the encrypted frame obtained after the last diffusion operation;

[0112] In the designed XOR diffusion algorithm, each pixel value is determined by the previous two pixel values ​​and the chaotic sequence cs generated by the spatiotemporal chaotic system. After two XOR diffusion operations, the correlation between adjacent pixels is greatly reduced, and the encryption effect of pixels is significantly enhanced. The formula is as follows:

[0113]

[0114] formula In the above, the initial value LL(i) is the chaotic sequence generated by the spatiotemporal chaotic system, D(i) is the sequence after hash diffusion, and the value of SS(i+2) depends on the values ​​of SS(i), SS(i+1), D(i) and LL(i). In the XOR algorithm, we introduce two disturbance parameters s1 and s6 to enhance the anti-cracking ability of the algorithm. ssk(i+2) is calculated by the values ​​of ssk(i), ssk(i+1), LL(i) and sk(i). sssk(i+1) represents the pixel value after the diffusion algorithm is applied. The complex diffusion algorithm structure design effectively reduces the correlation between the pixel values ​​of remote sensing images.

[0115] Example 2

[0116] Figure 3 is the spatiotemporal behavior diagram of the HACLML system. When μ∈[3.6,3.7), the HACLML system will exhibit two chaotic bands regardless of the ε value. When μ∈[3.7,3.8), the system behavior becomes unstable. With the increase of ε value, the HACLML system exhibits random patterns of different shapes in a larger spatial area. The system intermittently enters a chaotic state of mode competition. When μ=3.8 and ε>0.5, or when μ∈(3.8,4.0], it is difficult to observe stable behavior. This is because the introduction of the hash index chain enhances the diffusion effect of the spatiotemporal chaotic system. When most of the spatial grid points exhibit periodic behavior, coupling the Arnold cat mapping with the hash index chain will lead to rapid dissipation of energy in the spatial grid. Therefore, when most of the spatial grid points are in a chaotic state, the diffusion effect not only fails to suppress the system from moving towards stability, but enhances the chaotic nature of the system.

[0117] Figure 5 To test the effectiveness of the encryption process, we conducted encryption and decryption tests on two remote sensing images with a resolution of 512*512. According to the test results, we found that the encryption algorithm we proposed effectively encrypts the remote sensing images; in the figure, (a) is a remote sensing image of farmland, (b) is a scrambled image of farmland blocks, (c) is an encrypted remote sensing image of farmland, (d) is a decrypted remote sensing image of farmland, (e) is a remote sensing image of the coastal area, (f) is a scrambled image of the coastal area blocks, (g) is an encrypted remote sensing image of the coastal area, and (h) is a decrypted remote sensing image of the coastal area.

[0118] Figure 6 A histogram test is performed on the plaintext image and the ciphertext. The histogram test can be used to check whether the pixel distribution of the encrypted image is uniform. A good encryption algorithm should introduce enough randomness to make it difficult for attackers to infer the characteristics of the image. The results show that the proposed encryption algorithm uniformly changes the pixel intensity, the ciphertext pixel intensity distribution is relatively symmetrical, and there is an obvious difference between the ciphertext and the plaintext. In the figure, (a) is a plaintext farmland remote sensing image, (b) is a ciphertext farmland remote sensing image, (c) is a decrypted farmland remote sensing image, (d) is a plaintext coastal area remote sensing image, (e) is a ciphertext coastal area remote sensing image, and (f) is a decrypted coastal area remote sensing image.

[0119] Figure 7It is a test of the ability to resist noise attacks and shearing attacks; there are several types of attacks that can affect image encryption during transmission; occlusion and salt and pepper noise attacks are two common noise sources; salt and pepper noise attacks usually randomly select several pixels in the image and set their values ​​to the maximum or minimum value (white or black), and the attack strength depends on the proportion of noise; in order to verify the anti-noise attack ability of the proposed algorithm, 5% density of salt and pepper noise was added to the remote sensing ciphertext image; the experimental results show that the designed encryption algorithm has a strong ability to resist noise attacks; at the same time, we carried out a 25% letter occlusion attack on the remote sensing ciphertext image, and the original remote sensing images were clearly restored after decryption. The experimental results show that the designed encryption algorithm has a good ability to resist occlusion attacks; in the figure, (a) shows a 5% salt and pepper attack, (b) shows a remote sensing image of the coastal area under the salt and pepper attack, (c) shows a 25% shearing attack, and (d) shows a remote sensing image of the farmland under the shearing attack.

[0120] Example 3

[0121] The security performance of the encryption algorithm proposed in the present invention is compared and analyzed, and the average variation intensity (UACI) and the number of pixels changing rate (NPCR) of the encryption algorithm are tested.

[0122] The closer the values ​​of NPCR and UACI are to the ideal values ​​(99.6094070% and 33.4635070%), the better the security of the algorithm. As shown in Table 1, compared with the five encrypted pictures in other algorithms, the values ​​of NPCR and UACI of the proposed encryption algorithm are closer to the ideal values, that is, the encryption algorithm based on spatiotemporal chaotic system proposed in the present invention has better security and stronger anti-decryption ability.

[0123] Table 1 shows the comparative analysis of UACI and NPCR.

[0124]

[0125] Information entropy is often used as a quantitative indicator of image information content. For a 256-grayscale image, 8 usually represents the maximum uncertainty and the maximum amount of information. If the value is closer to 8, the randomness of the ciphertext data is higher and the encryption effect is better. As shown in Table 2, the information entropy of the five plaintext images is relatively low, but after being encrypted by the algorithm proposed in the present invention, the information entropy is close to the ideal value.

[0126] Table 2 shows the information entropy.

[0127]

[0128] The spatiotemporal chaotic system of the present invention takes into account the complexity of space and time, and can describe more complex behaviors of the spatiotemporal chaotic system. The spatiotemporal chaotic system not only has a larger parameter range, but also has more chaotic sequences. From the perspective of the anti-decryption ability of the encryption algorithm, the dynamic characteristics of the spatiotemporal chaotic system are very suitable for image encryption. Based on the spatiotemporal chaotic system, the remote sensing image encryption algorithm is designed in combination with the point-taking block algorithm, which can not only process the spatial characteristics of the remote sensing image more comprehensively, but also has a stronger encryption algorithm resistance to cracking. This is of great significance for research in related fields such as information confidentiality communication. The spatiotemporal chaotic system effectively combines the hash index chain with the original model of the spatiotemporal chaotic system to improve the performance of the chaotic system. An Arnold periodic scrambling algorithm based on point-taking block is designed, and a bit-level arrangement algorithm is used to eliminate the dividing line generated by the block period effect. A new diffusion algorithm is designed according to the constructed spatiotemporal chaotic system and the hash index chain, which can further encrypt the pixel value and improve the security of the encryption algorithm. The image encryption algorithm has high security performance by utilizing the partition encryption mechanism, and provides theoretical guidance and experimental verification for the fields of military information security, confidential communication, remote sensing image encryption, etc.

Claims

1. A remote sensing image encryption algorithm based on a new spatiotemporal chaotic system, characterized in that: include: S1. Construct a spatiotemporal chaotic system based on the coupled mapping lattice CML model; S2, using the point-based block Arnold periodic scrambling algorithm to scramble the plaintext; S3, using a bit-level permutation algorithm to eliminate the boundaries created by the blocking effect; S4. Design a diffusion algorithm based on spatiotemporal chaotic system and hash index chain.

2. According to claim 1, a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system is characterized in that: In S1, the construction is based on the spatiotemporal chaotic system of the coupled mapping lattice CML model, and the formula is as follows: x n+1 (i)=(1-ε)f[x n (i)]+(ε / 2)(f[x n (i+1)]+f[x n (i-1)]) ① In formula ①, ε is the coupling coefficient, and its value range is (0≤ε≤1); i+1 and i-1 are two adjacent grids, and the coupling mode of the CML model is affected by the adjacent grids. f(x) is a Logistic chaotic system, and the formula of the Logistic chaotic system is as follows: x n+1 =μx n (1-x n ),(μ∈(0,4],ε∈[0,1] ② In formula ②, μ is the control parameter of f(x), and its value range is (0,4]; When 3.57≤μ≤4, f(x) enters a completely chaotic state. The Arnold cat mapping is used to change the coupling mode of the CML model. The formula is as follows: x n+1 (i)=(1-ε)f[x n (i)]+(ε / 2)(f[x n (j)]+f[x n (k)]) ③ In formula ③, i, j and k are spatial grid points and are determined by the Arnold cat mapping, as follows: In formula ④, i ≥ 1 and j, k ≤ L; p and q are integer parameters, p is used to control the transformation characteristics of the mapping in the horizontal direction, and q is used to control the transformation characteristics of the mapping in the vertical direction; Map the hash index chain to the i, j values ​​of the Arnold cat map using the following formula: In formula ⑤, H(i) is a hash index array generated by the conflict resolution method.

3. According to claim 1, a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system is characterized in that: In S2, the point-taking block Arnold periodic scrambling algorithm includes: S21, dividing the remote sensing image into multiple square areas and non-square areas by taking points and dividing them into blocks, and using Arnold scrambling of different periods for each area; S22, stitching together regions with different scrambling periods to obtain a ciphertext image; S23. Decrypt the ciphertext using the inverse transformation equation of Arnold scrambling.

4. According to claim 3, a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system is characterized in that: In S21, each square area is scrambled with equal distance Arnold, and the formula is as follows: In formula ⑥, (x0, y0) is the coordinate of the upper left corner pixel of each square area, whose value is (0, 0), and (x∈X, y∈Y), the scrambled coordinates are (X-x0, Y-y0); The non-equidistant Arnold cat scrambling of each non-square region is as follows: In formulas ⑦ and ⑧, a is the main expansion ratio in the x direction, b is the coupling degree between the x and y directions, c is the coupling degree between the y and x directions, and d is the main expansion ratio in the y direction; a=1=b=c, d=2, and n is the side length.

5. According to claim 1, a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system is characterized in that: In S3, the bit-level arrangement algorithm is as follows: 1) Taking five pixels as a whole, the first and second columns follow the (1-3-2-4-5) path loop pattern. When the loop reaches the maximum number of rows, it jumps out of this loop and then follows the (1-3-4-2) path loop pattern; The third and fourth columns follow the (3-1-4-2-5) path loop pattern, and when the loop reaches the first row, a full forward and reverse loop is completed; The connection between two complete arrangements follows a (3-1-2-4) cyclic pattern; Path 4-5 is to check the coordinate value (x, y) at 4. When x is an even number and y is an even number, follow path 4-5. When x reaches the maximum number of rows N and y is an even number, this loop stops. In path 3-4, add 1 to the value of y; 2) In the reverse circular arrangement, path 2-5 is to check the coordinate value (x, y) at 2; When x is an odd number and y is an even number, the loop follows path 2-5; When x reaches the first row and y is an even number, the loop from the first to the fourth column ends; Treat the four columns as a whole and perform N / 4 cycles on the complete image.

6. According to claim 1, a remote sensing image encryption algorithm based on a novel spatiotemporal chaotic system is characterized in that: In S4, the diffusion algorithm based on spatiotemporal chaotic system and hash index chain is as follows: S41. Use hash index chain H1 to perform pixel diffusion. The formula is as follows: F e (H(i))=mod(F o (H(i))+f(F e (H(i-2)))+F e (H(i-1)),256 ⑨ In formula 9, Fe and Fo are the one-dimensional sequence of the encrypted frame and the one-dimensional sequence after block scrambling respectively; i-1 is the previous value of the hash index chain H1, and i-2 represents the previous two values; f(x) is defined as follows: In formula ⑩, i-2 is the first two values ​​of the hash index chain H1; Use the hash index chain H2 to perform pixel diffusion. The formula is as follows: F′ e (H′(i))=mod(F e (H′(i))+f(F′ e (H′(i-2)))+F′ e (H′(i-1)),256) formula In , i-1 is the previous value of the hash index chain H2, i-2 is the previous two values; Fe′ is the pixel value of the encrypted frame obtained after the last diffusion operation; In the designed XOR diffusion algorithm, each pixel value is determined by the previous two pixel values ​​and the chaotic sequence cs generated by the spatiotemporal chaotic system, and undergoes two XOR diffusion operations. The formula is as follows: formula In the above equation, the initial value LL(i) is the chaotic sequence generated by the spatiotemporal chaotic system, D(i) is the sequence after hash diffusion, and the value of SS(i+2) depends on the values ​​of SS(i), SS(i+1), D(i) and LL(i); ssk(i+2) is calculated from the values ​​of ssk(i), ssk(i+1), LL(i), and sk(i), where sssk(i+1) is the pixel value after the diffusion algorithm is applied.

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