Image encryption method based on two-dimensional discrete hyperchaotic system

Abstract

This invention provides an image encryption method based on a two-dimensional discrete hyperchaotic system, comprising: constructing a two-dimensional discrete hyperchaotic system; generating pseudo-random numbers using the two-dimensional discrete hyperchaotic system; performing diffusion processing on the chaotic sequence and the RGB channels of the image respectively to enhance the correlation between pixel information and the pseudo-random number stream, effectively hiding the original image information; converting the image into a binary bit stream, and scrambling the information stream based on the chaotic sequence to further break the spatial structure of the plaintext image. The scrambling and obfuscation operations implemented at the bit level significantly improve the security of the encrypted image. This invention not only destroys the spatial structure of the plaintext image but also weakens the correlation between pixels, effectively improving the anti-attack capability of the encrypted image.

Description

Technical Field

[0001] This invention belongs to the field of image encryption technology and relates to an image encryption method based on a two-dimensional discrete hyperchaotic system. Background Technology

[0002] In modern digital communication, cryptography is typically represented by randomly distributed 0s and 1s. The generation of a high-quality random number sequence is crucial for ensuring the security of a cryptographic system. Nonlinear dynamic systems, due to their inherent randomness, have become an important research subject in random number generation. Among them, chaotic systems, which combine dynamics and randomness, exhibit stronger adaptability and application potential. As an important branch of nonlinear science, chaos theory has received widespread attention and in-depth research in recent years.

[0003] Image encryption technology is a crucial technology in the field of information network security. Its primary goal is to protect privacy information from leakage during image transmission. Currently, image encryption technology still has some shortcomings in terms of key security and stability, making it vulnerable to various cracking methods. Hyperchaotic systems, as a class of dynamic systems with highly nonlinear, initial value sensitive, ergodic, and aperiodic characteristics, possess inherent chaos and pseudo-randomness, enabling them to generate complex and unpredictable sequences. This makes them particularly suitable for key generation and encryption process enhancement in encryption algorithms. Therefore, applying the theory and methods of hyperchaotic systems to image encryption technology can provide a more secure solution for the field of information security.

[0004] Currently, some classic chaotic systems have been incorporated into the design of image encryption algorithms, such as the Logistic, Circle, and Tent systems. However, these systems suffer from limitations in terms of chaotic range, low entropy, and overly simple structure, significantly restricting their application potential in the encryption field. In contrast, hyperchaotic systems, with their more complex nonlinear dynamic behavior, can generate more unpredictable chaotic characteristics, significantly enhancing the security of encryption systems. In particular, their multiple positive Lyapunov exponents ensure the system's high sensitivity to initial conditions, making it impossible for attackers to predict their dynamic behavior even if they possess partial system information. Although some discrete hyperchaotic systems, such as 2D-LASM, 2D-SIMM, SCM, and LSMCL, have been used for image encryption, their performance in terms of hyperchaotic activity and randomness remains insufficient, limiting their further application.

[0005] To address the aforementioned technical deficiencies, this invention proposes an image encryption method based on a two-dimensional discrete hyperchaotic system. This method utilizes a two-dimensional discrete hyperchaotic system to generate a high-quality pseudo-random number sequence, and performs pixel-level diffusion and bit-level scrambling operations on the plaintext image to generate a pixel-independent high-entropy ciphertext image.

[0006] A search revealed a Chinese patent that also uses a hyperchaotic system in an image encryption system, titled "An Image Processing Method Based on Discrete Hyperchaotic System and Diffusion-Based Dynamic DNA Encoding," application number "202210478909.2." This patent is used as a prior art document. The following describes the technical features that distinguish this invention from the prior art document:

[0007] (1) Different chaotic systems: The mathematical models of chaotic systems in the comparison documents are more complex, while the chaotic system proposed in this invention is more concise in expression. The range of chaotic control parameters in this invention is wider, which helps to enhance the flexibility of the encryption algorithm and expand the key space, thereby improving the security of the encryption system.

[0008] (2) Different encryption processes: The comparison file uses DNA encoding theory to enhance the security of the ciphertext image. However, the introduction of DNA encoding theory increases computational complexity and brings certain limitations. For example, the encryption process of the comparison file includes: converting each pixel in the image into 4 binary characters, recombining pixels according to DNA encoding rules, and performing element-wise scrambling and diffusion operations. Compared with the comparison file, this invention significantly reduces the computational complexity of the encryption process and optimizes the encryption process while ensuring the security of the ciphertext image. Specifically, this invention can complete the entire encryption process by simply performing pixel-wise diffusion and bit-wise scrambling operations. At the same time, this invention omits the DNA encoding step and adopts a novel diffusion and scrambling mechanism. In addition, the generation of random numbers in this invention is based on the proposed hyperchaotic system, and the pseudo-random sequence generated by this system has passed the NIST test suite, thus proving that this invention can further improve the security and randomness of encryption.

[0009] (3) Different security: In the pixel correlation test analysis of the encrypted image, the pixel correlation coefficient of the encrypted image obtained by the present invention can reach as low as 0.0001, while that of the comparison file is only 0.01. Since the pixel correlation coefficient is closer to 0, it means that the security is higher. Therefore, the encrypted security of the present invention is better than that of the comparison file. In addition, in the information entropy test, the average information entropy of the encrypted image of the present invention reaches 7.99973, while that of the comparison file is only 7.9990. Since the average information entropy of the image is closer to 8, the security is higher. Therefore, the present invention has significant advantages in reducing pixel correlation and increasing information entropy, thus enhancing the security of the encrypted image.

[0010] In summary, compared with the comparison document, the present invention can not only effectively improve the security of encryption, but also reduce the computational complexity of the algorithm and the encryption operation process. Summary of the Invention

[0011] The purpose of this invention is to address the problems existing in the prior art by providing an image encryption method based on a two-dimensional discrete hyperchaotic system, which solves the following problems: 1. Traditional discrete chaotic systems have low complexity, many periodic windows, and poor pseudo-randomness of the generated chaotic sequences; 2. The key stream used in traditional encryption algorithms has poor randomness quality; 3. Traditional image encryption algorithms have low security.

[0012] Therefore, the present invention adopts the following technical solution:

[0013] An image encryption method based on a two-dimensional discrete hyperchaotic system includes: performing diffusion processing on the chaotic sequence and the RGB channels of the image respectively to enhance the correlation between pixel information and pseudo-random number stream, thereby effectively hiding the information of the original image; converting the image into a binary bit stream, and scrambling the information stream based on the chaotic sequence to further break the spatial structure of the plaintext image. The scrambling and obfuscation operations implemented at the bit level significantly improve the security of the ciphertext image; the specific steps are as follows:

[0014] Step 1: To generate random chaotic sequences, a two-dimensional discrete hyperchaotic system is constructed based on the coupling and modulo operation of logistic mapping and quadratic equations.

[0015] The expression for a two-dimensional discrete hyperchaotic system is as follows:

[0016]

[0017] The logistic mapping equation and the quadratic equation used in the two-dimensional discrete hyperchaotic system are shown below:

[0018] x t =μx t-1 ·(1-x t-1 )

[0019]

[0020] In the formula, x t Let y be the output state of the first system state variable x in the hyperchaotic system at the current moment; t The output of the second system's state variable y at the current moment in the hyperchaotic system; x t-1 Let y be the output state of the first system state variable x in the hyperchaotic system at the previous moment; t-1 The output of the second system state variable y in the previous moment in the hyperchaotic system; μ, a, b∈(-∞,0)U(0,+∞) are all control parameters; mod1 is the modulo operation performed according to 1.

[0021] The two-dimensional discrete hyperchaotic system proposed in this invention significantly improves upon existing discrete chaotic systems in terms of complexity, nonlinearity, and pseudo-randomness. The system also possesses better parameter adaptability, spatial ergodicity, pseudo-randomness, and sensitivity to initial conditions.

[0022] To more accurately verify the randomness of the time series generated by the two-dimensional discrete hyperchaotic system proposed in this invention, the NIST SP800-22 randomness test suite was used to evaluate the binary sequence of the two-dimensional discrete hyperchaotic system. The NIST SP800-22 randomness test suite contains 15 tests to detect possible non-random patterns in binary sequences and is widely used to evaluate the randomness of binary sequences. During the test, each decimal number in the two-dimensional discrete hyperchaotic system was converted into a 32-bit binary number and output cyclically in xy order. Thus, each iteration of the two-dimensional discrete hyperchaotic system can generate a 64-bit binary sequence, thereby forming a complete cryptographic stream.

[0023] In this test, the significance level is set to 0.01, requiring a p-value of at least 0.01 for each test to pass the corresponding NIST test item. Only when all tests in the NIST suite are passed will the chaotic sequence be considered to meet the randomness criteria.

[0024] The NIST test results of the two-dimensional discrete hyperchaotic system proposed in this invention are shown in Table 1, where "*" indicates the average value of the test. Under the conditions of a single sample sequence length of 1.0176 Mb, a significance level of 0.01, and a sample size of 100, the minimum number of passes for each statistical test should be 98. As can be seen from Table 1, the pseudo-random sequences generated by the two-dimensional discrete hyperchaotic system proposed in this invention successfully passed all NIST SP800-22 randomness statistical tests, fully verifying the high randomness of the sequences generated by the proposed two-dimensional discrete hyperchaotic system, indicating its excellent applicability in image encryption system design.

[0025] Table 1. NIST test results of the two-dimensional discrete hyperchaotic system proposed in this invention.

[0026]

[0027]

[0028] Step 2: Randomly select the initial control parameters μ0, a0, b0 and the initial state parameters x0, y0 in the two-dimensional discrete hyperchaotic system.

[0029] Step 3: Input an RGB color plaintext image P with a matrix size of M×N×3. Use the SHA-256 algorithm to generate a 256-bit key K for the plaintext image, and divide it into 16 blocks. The expression for key K is:

[0030] K = {k1, k2, k3, 3, k} 16}

[0031] In the formula, k i This represents the i-th key.

[0032] Step 4: This invention uses the SHA-256 hash function to obtain a 256-bit binary key, thereby creating a key space exceeding 2... 256 Obviously, based on the current computing power in this field, a 256-bit binary key is sufficient to resist brute-force attacks and can guarantee the reliability of the encryption scheme.

[0033] Step 5: To enhance the correlation between keys K, calculate the intermediate parameter h. i ;

[0034] intermediate parameter h i The formula for calculating (i = 1, 2, 3, 4) is as follows:

[0035]

[0036] In the formula, This indicates the XOR operation.

[0037] Step 6: Utilize the intermediate parameter h i The iterative values ​​of the state parameters x0', y0' and the iterative values ​​of the control parameters μ0', a0', b0' of a two-dimensional discrete hyperchaotic system are calculated using the following formulas:

[0038]

[0039] In the formula, mod represents the modulo operation.

[0040] Step 7: Using the key K, randomly generate a first chaotic sequence A1 and a second chaotic sequence A2 with a total length of 3×M×N for the RGB color plaintext image P.

[0041] Step 8: Perform an XOR operation between the plaintext image P and the first chaotic sequence A1 to generate the correlation matrix Q1; specifically:

[0042] The first chaotic sequence A1 is reorganized into three R-channel chaotic matrices A1 of size M×N. M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B These three correspond to the R, G, and B color channels, respectively.

[0043] The chaotic matrix A of channel R M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B The plaintext matrices P corresponding to the R, G, and B channels of the plaintext image P are respectively... G and the plaintext matrix P of channel B B Performing a pixel-level XOR operation yields the correlation matrix Q1, whose expression is as follows:

[0044]

[0045] Pixel-level XOR operation refers to performing a binary XOR operation on each pixel value in two images. This is a technique known to those skilled in the art, so its operation process will not be described in detail here.

[0046] Step 9: Convert all elements of the correlation matrix Q1 into an 8-bit binary data stream. Use the second chaotic sequence A2 to perform bit-level scrambling on the 8-bit binary data stream to obtain a one-dimensional binary data stream Q2. Reassemble the one-dimensional binary data stream Q2 to obtain a ciphertext matrix Q3 of size M×N×3, thereby obtaining the ciphertext image.

[0047] The beneficial effects of this invention are as follows:

[0048] 1. This invention proposes a two-dimensional discrete hyperchaotic system, which has significant improvements in complexity, nonlinearity and pseudo-randomness compared with existing discrete chaotic systems. The two-dimensional discrete hyperchaotic system has good parameter adaptability, spatial ergodicity, pseudo-randomness and sensitivity to initial conditions.

[0049] 2. The pseudo-random sequence generated by the two-dimensional discrete hyperchaotic system proposed in this invention has been verified by the NISTSP800-22 test suite, proving that the time series it generates has sufficiently high complexity and unpredictability, exhibiting good randomness, thereby ensuring that the key stream has excellent randomness and robustness, and can effectively resist malicious attacks such as differential attacks and statistical attacks, providing a guarantee for the design of image encryption algorithms.

[0050] 3. This invention proposes a color image encryption strategy combining pixel-level diffusion and bit-level scrambling. Specifically, after XORing the plaintext image with a chaotic sequence, each state value of the correlation matrix is ​​converted into a binary data stream. Then, based on a chaotic pseudo-random sequence generated by a designed two-dimensional discrete hyperchaotic system, each bit in the data stream is randomly scrambled, thereby disrupting the spatial structure of the plaintext image and weakening the correlation between pixels. This process effectively improves the anti-attack capability of the encrypted image. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the method flow in this embodiment;

[0052] Figure 2 This is a schematic diagram comparing the encrypted image and the original sample image in this embodiment;

[0053] Figure 3 This is a pixel histogram of the plaintext image and the ciphertext image in this embodiment;

[0054] Figure 4 This embodiment shows the distribution of adjacent pixels in the plaintext and ciphertext images in the horizontal, vertical, and diagonal directions. Detailed Implementation

[0055] The technical solution of the present invention will be described below with reference to the accompanying drawings and implementation methods.

[0056] Example

[0057] like Figure 1 As shown, an image encryption method based on a two-dimensional discrete hyperchaotic system includes the following steps:

[0058] Step 1: To generate random chaotic sequences, a two-dimensional discrete hyperchaotic system is constructed based on the coupling and modulo operation of logistic mapping and quadratic equations.

[0059] The expression for a two-dimensional discrete hyperchaotic system is as follows:

[0060]

[0061] In the formula, x t Let y be the output state of the first system state variable x in the hyperchaotic system at the current moment; t The output of the second system's state variable y at the current moment in the hyperchaotic system; x t-1 Let y be the output state of the first system state variable x in the hyperchaotic system at the previous moment; t-1 The output of the second system state variable y in the previous moment in the hyperchaotic system; μ, a, b∈(-∞,0)U(0,+∞) are all control parameters; mod1 is the modulo operation performed according to 1.

[0062] Step 2: Randomly select the initial control parameters μ0, a0, b0 and the initial state parameters x0, y0 in the two-dimensional discrete hyperchaotic system.

[0063] Step 3: Input an RGB color plaintext image P with a matrix size of M×N×3. Use the SHA-256 algorithm to generate a 256-bit key K for the plaintext image, and divide it into 16 blocks. The expression of the key K is:

[0064] K = {k1, k2, k3, 3, k}16}

[0065] In the formula, k i This represents the i-th key.

[0066] Step 4: To enhance the correlation between keys K, calculate the intermediate parameter h. i ;

[0067] intermediate parameter h i The formula for calculating (i = 1, 2, 3, 4) is as follows:

[0068]

[0069] In the formula, This indicates the XOR operation.

[0070] Step 5: Utilize the intermediate parameter h i The iterative values ​​of the state parameters x0', y0' and the iterative values ​​of the control parameters μ0', a0', b0' of a two-dimensional discrete hyperchaotic system are calculated using the following formulas:

[0071]

[0072] In the formula, x0 and y0 are the initial state parameters of the two-dimensional discrete hyperchaotic system; μ0, a0, and b0 are the initial control parameters of the two-dimensional discrete hyperchaotic system; and mod is the modulo operation.

[0073] Step 6: Using the key K, randomly generate a first chaotic sequence A1 and a second chaotic sequence A2 with a total length of 3×M×N for the RGB color plaintext image P.

[0074] Step 7: Reorganize the first chaotic sequence A1 into three R-channel chaotic matrices A of size M×N. M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B These three correspond to the R, G, and B color channels, respectively.

[0075] Step 8: Convert the R-channel chaotic matrix A M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B The plaintext matrices P corresponding to the R, G, and B channels of the plaintext image P are respectively... G and the plaintext matrix P of channel B B Performing a pixel-level XOR operation yields the correlation matrix Q1, whose expression is as follows:

[0076]

[0077] Step 9: Convert all elements of the correlation matrix Q1 into an 8-bit binary data stream. Use the chaotic sequence A2 to perform bit-level scrambling on the 8-bit binary data stream to obtain a one-dimensional binary data stream Q2. Reassemble the one-dimensional binary data stream Q2 to obtain a matrix Q3 of size M×N×3, thus obtaining the ciphertext image.

[0078] The following tests assess the encryption effectiveness, key sensitivity, resistance to differential attacks, protection of sensitive information, randomness of pixel distribution, and information entropy of this embodiment.

[0079] Encryption effectiveness test:

[0080] To evaluate the encryption security of this embodiment, three color images of 512×512 pixels, commonly used in image processing, were selected for testing: an airplane, a baboon, and a chili pepper. Figure 2 As shown, this embodiment can successfully encrypt the original sample image.

[0081] Key sensitivity test:

[0082] To verify the key sensitivity in this embodiment, 10 is introduced into the system parameters and initial values ​​respectively. -15 The subtle changes were observed, and the differences between the encrypted images after the two encryptions were investigated. To quantify the differences between the two encryption results, the evaluation metrics used in this embodiment include: signal-to-noise ratio (SNR), mean square error (MSE), and structural similarity index (SSIM).

[0083] Generally, the greater the difference between two images, the higher the MSE, while the lower the SNR and SSIM. If the encryption scheme lacks sensitivity to the keystream, when the keystream changes slightly, the two generated encrypted images may still have a high structural similarity, thus being judged as insecure encryption.

[0084] As shown in Tables 2, 3, 4, 5, and 6, the key sensitivity of this embodiment is robust and has strong key sensitivity. Even if one bit in the key changes, it can effectively prevent attackers from retrieving any valuable information.

[0085] Table 2 Key sensitivity analysis results (with x0 changed)

[0086]

[0087] Table 3 Key sensitivity analysis results (with y0 changed)

[0088]

[0089]

[0090] Table 4. Key sensitivity analysis results (with changes to μ0)

[0091]

[0092] Table 5 Key sensitivity analysis results (with a0 changed)

[0093]

[0094] Table 6 Key Sensitivity Analysis Results (with b0 changed)

[0095]

[0096] Test of resistance to differential attacks:

[0097] In the field of image encryption, differential attack testing is used to evaluate the sensitivity of encryption algorithms to small changes in plaintext images. A secure encryption algorithm should be highly sensitive to small changes in plaintext, that is, if only one pixel changes, the ciphertext image should also change significantly.

[0098] In differential attack testing, Pixel Change Rate (NPCR) and Uniform Average Change Intensity (UACI) are commonly used metrics to measure the resistance of encryption algorithms to differential attacks. NPCR measures the percentage of pixel values ​​that change in two ciphertext images, reflecting the impact of small changes in plaintext on the ciphertext. UACI measures the average degree of pixel value change in two ciphertext images, reflecting the overall level of change in the strength of the encrypted images.

[0099] The theoretical NPCR and UACI values ​​for the encrypted ciphertext image are 99.6094% and 33.4635%, respectively. Table 7 shows the anti-differential attack test results of this embodiment on plaintext images of airplanes, baboons, and chili peppers. As shown in Table 7, this embodiment is closer to the theoretical values ​​in terms of NPCR and UACI, and has the ability to resist differential attacks.

[0100] Table 7. Results of Differential Attack Tests

[0101]

[0102] Test to protect sensitive information:

[0103] Histograms are used to display the frequency of occurrence of different pixel values. The more uniform the distribution of the pixel histogram of an encrypted image, the stronger the encryption algorithm's ability to resist statistical attacks.

[0104] like Figure 3As shown, the histogram distribution of the plaintext image before encryption is uneven, with obvious peaks at certain pixel values, indicating that the plaintext image has clear statistical characteristics. In contrast, the histogram distribution of the ciphertext image is very uniform, indicating that this embodiment can effectively destroy and hide plaintext pixel information and successfully conceal any identifiable patterns or features in the plaintext, thereby significantly enhancing the effectiveness of the encryption algorithm in protecting sensitive information.

[0105] Pixel distribution randomness test:

[0106] Correlation analysis in image encryption refers to measuring whether the encryption algorithm has successfully destroyed and hidden the statistical characteristics of the plaintext image by calculating the correlation between adjacent pixels in the horizontal, vertical and diagonal directions. An effective image encryption algorithm can randomize the pixel distribution of the encrypted image, and the correlation coefficient should be close to 0.

[0107] In this embodiment, 10,000 pairs of adjacent pixels were selected from three directions—horizontal, vertical, and diagonal—for statistical analysis to evaluate the effectiveness of the algorithm in reducing correlation. The calculation results are shown in Table 8, which includes the specific values ​​of the test results of adjacent pixels in the horizontal, vertical, and diagonal directions for the plaintext image before encryption and the encrypted image after encryption in this embodiment.

[0108] Table 8. Correlation analysis of adjacent pixels between plaintext and ciphertext images.

[0109]

[0110] As shown in Table 8, the pixel distribution of the ciphertext image generated in this embodiment is closer to a uniform distribution, and the high randomness of the pixel distribution can effectively reduce the risk of attackers using statistical characteristics to infer plaintext information or keys, further verifying the security and robustness of this embodiment.

[0111] Figure 4 For a visual representation of the calculation results in Table 8, Figure 4 In the pixel space, red represents the horizontal distribution of adjacent pixels, green represents the vertical distribution, and blue represents the diagonal distribution. Since plaintext images contain feature information, their adjacent pixel values ​​are close to 1; since ciphertext images are disordered, their adjacent pixel values ​​are close to 0. Figure 4 It can be seen that the encryption scheme proposed in this embodiment is effective in resisting statistical attacks.

[0112] Information entropy test:

[0113] In image encryption, the information entropy test measures the uncertainty of pixel variables in the ciphertext image. For an image with a grayscale of 256, the theoretical value of its information entropy is 8. The closer the information entropy is to the theoretical maximum value, the more random the distribution of pixel values ​​in the encrypted image, and the more effectively the encryption algorithm can hide the information attributes of the plaintext image.

[0114] As shown in Table 9, the entropy of the encrypted image generated in this embodiment is closer to the theoretical maximum value, indicating that it has a high degree of randomness.

[0115] Table 9. Information Entropy Analysis Results

[0116]

[0117] The test results above show that the pseudo-random key stream generated in this embodiment can pass the NIST test, proving that its time series has sufficiently high complexity and unpredictability, thereby ensuring that the key stream has excellent randomness and robustness, and can effectively resist malicious attacks such as differential attacks and statistical attacks.

Claims

1. An image encryption method based on a two-dimensional discrete hyperchaotic system, characterized in that, Includes the following steps: To generate random chaotic sequences, a two-dimensional discrete hyperchaotic system is constructed based on the coupling and modulo operation of logistic mapping and a univariate quadratic equation. Randomly select the initial control parameters μ0, a0, b0 and the initial state parameters x0, y0 in a two-dimensional discrete hyperchaotic system; Given an RGB color plaintext image P with a matrix size of M×N×3, generate a key K using a hash algorithm; To enhance the correlation between keys K, intermediate parameter h is calculated. i ; Using intermediate parameter h i Calculate the iterative values ​​of the state parameters x0', y0' and the iterative values ​​of the control parameters μ0', a0', b0' of a two-dimensional discrete hyperchaotic system; Using key K, randomly generate a first chaotic sequence A1 and a second chaotic sequence A2 with a total length of 3×M×N for the RGB color plaintext image P; Perform an XOR operation between the plaintext image P and the first chaotic sequence A1 to generate the correlation matrix Q1. Convert all elements in the correlation matrix Q1 into a data stream, and use the second chaotic sequence A2 to perform bit-level scrambling on the data stream to obtain a one-dimensional binary data stream Q2. Reconstruct the one-dimensional binary data stream Q2 to obtain a ciphertext matrix Q3 of size M×N×3, thus obtaining the ciphertext image.

2. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 1, characterized in that, The expression for the two-dimensional discrete hyperchaotic system is as follows: In the formula, x t Let y be the output state of the first system state variable x in the hyperchaotic system at the current moment; t The output of the second system's state variable y at the current moment in the hyperchaotic system; x t-1 Let y be the output state of the first system state variable x in the hyperchaotic system at the previous moment; t-1 The output of the second system state variable y in the previous moment in the hyperchaotic system; μ, a, b∈(-∞,0)U(0,+∞) are all control parameters; mod1 is the modulo operation performed according to 1.

3. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 1, characterized in that, The hash algorithm used is SHA-256.

4. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 3, characterized in that, The generation of key K using a hash algorithm includes: A 256-bit key K is generated for the plaintext image using the SHA-256 algorithm and divided into 16 blocks. The expression for the key K is as follows: K={k1,k2.k3,3,k 16 }, In the formula, k i This represents the i-th key.

5. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 4, characterized in that, The intermediate parameter h i The calculation formula is as follows: In the formula, This indicates the XOR operation.

6. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 5, characterized in that, The calculation formulas for the iterative values ​​of the state parameters x0' and y0' and the iterative values ​​of the control parameters μ0', a0', and b0' are as follows: In the formula, mod represents the modulo operation.

7. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 1, characterized in that, The plaintext image P is XORed with the chaotic sequence A1 to generate an association matrix Q1, including: The first chaotic sequence A1 is reorganized into three R-channel chaotic matrices A1 of size M×N. M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B These three correspond to the R, G, and B color channels, respectively. The chaotic matrix A of channel R M×N,R G-channel chaotic matrix A M×N,G B-channel chaotic matrix A M×N,B The plaintext matrices P corresponding to the R, G, and B channels of the plaintext image P are respectively... G and the plaintext matrix P of channel B B Performing a pixel-level XOR operation yields the correlation matrix Q1, whose expression is as follows:

8. The image encryption method based on a two-dimensional discrete hyperchaotic system according to claim 1, characterized in that, The data stream comprises an 8-bit binary data stream.

Images