Color image encryption method based on mixed heterogeneous single-time-delay chaos and electronic equipment

Abstract

The invention relates to the technical field of image encryption, and particularly discloses a color image encryption method based on hybrid heterogeneous single-time-delay chaos and electronic equipment, and the color image encryption method comprises the following steps: generating a pseudo-random sequence set by using a plurality of heterogeneous single-time-delay chaos systems, according to the heterogeneous single-time-delay chaotic system, time delays are applied to different state variables of a chaotic system, and at least three time-delay chaotic systems with different dynamic behaviors are formed; a color image is layered into three independent pixel matrixes according to R, G and B channels. According to the color image encryption method based on the hybrid heterogeneous single-time-delay chaos, through innovative designs of dynamic sequence extraction, color image layered encryption, key space multi-dimensional expansion and the like of a heterogeneous single-time-delay chaos system, the problems that a traditional chaos encryption algorithm is small in key space, weak in attack resistance, poor in adaptability and the like are effectively solved; and excellent performance is achieved in the aspects of safety, real-time performance and expandability.

Description

Technical Field

[0001] The present invention relates to the technical field of image encryption, and particularly relates to a color image encryption method and an electronic device based on hybrid heterogeneous single-delay chaos. Background Art

[0002] With the development of information technology, images, as important carriers of information dissemination, involve a large amount of private and confidential data. However, they are easily stolen or tampered with during the transmission process, and there is an urgent need for efficient encryption technology.

[0003] Existing encryption technologies are mostly based on the pseudo-random sequences of chaotic systems (with strong pseudo-randomness and initial sensitivity), but they have the following defects:

[0004] Single chaotic system: The generated sequences have strong correlation and are easily simulated and cracked by technologies such as neural networks (for example, the authorized announcement number is: CN114785477B, and the patent name is: Color Image Encryption Algorithm Based on Dynamic Henon-Iterative Mapping and Block Scrambling);

[0005] Low-dimensional chaotic system: There are few key parameters (such as initial values and system parameters), the key space is limited, and it is difficult to resist brute-force attacks;

[0006] Insufficient hierarchical processing: The R / G / B channels of color images are not encrypted hierarchically, resulting in the remaining statistical laws;

[0007] Incomplete application of hybrid chaos: Even if multiple chaotic systems are used, the scrambling and diffusion operations still rely on the sequences of a single system (for example, the authorized announcement number is: CN118200457A, and the patent name is: Image Encryption Algorithm Based on a New Hyperchaotic System and DNA Coding), and the security improvement is limited. Summary of the Invention

[0008] The present invention aims to solve at least one of the technical problems in the related technologies to some extent. To this end, the object of the present invention is to propose a color image encryption method and an electronic device based on hybrid heterogeneous single-delay chaos to improve the image encryption intensity.

[0009] To achieve the above object, a first aspect embodiment of the present invention proposes a color image encryption method based on hybrid heterogeneous single-delay chaos, and the method includes the following steps:

[0010] S1. Generate a set of pseudo-random sequences by using multiple heterogeneous single-delay chaotic systems, and the heterogeneous single-delay chaotic systems form at least three time-delay chaotic systems with different dynamic behaviors by applying time delays to different state variables of the chaotic system;

[0011] S2. Layer the color image into three independent pixel matrices according to the R, G, and B channels;

[0012] S3. For each layer, dynamically extract a first group of sequences from the set of pseudo-random sequences, generate a scrambling index according to the sequence sorting rule, and scramble the positions of the pixel matrix;

[0013] S4. For each scrambled layer, dynamically extract a second group of sequences from the set of pseudo-random sequences to construct a diffusion matrix;

[0014] S5. Merge the diffused layer pixel matrices into a ciphertext image;

[0015] Among them, the key space generated by the set of pseudo-random sequences includes: chaotic system parameters, time-delay positions, initial conditions, sequence extraction numbers, and intercepted position parameters.

[0016] In some embodiments of the present invention, the heterogeneous single-time-delay chaotic system in step S1 is a time-delay type Lorenz system, and its dynamic equation is:

[0017]

[0018] Among them, a, b, c, and d are system parameters; x, y, and z are system state variables.

[0019] In some embodiments of the present invention, the rule for dynamically extracting the first group of sequences in step S3 is:

[0020] Randomly select 3 sequences from the sequence set, and perform rounding operations on the sequence elements according to formula (1):

[0021] x i =(x i * 10 4 ) mod MN + 1 (1)

[0022] Among them, x i is the original value of the chaotic sequence; M and N are the horizontal and vertical pixel numbers of the image;

[0023] After removing duplicate elements, generate a scrambling index to perform a full permutation exchange on the pixel positions.

[0024] In some embodiments of the present invention, the diffusion operation in step S4 is:

[0025] Construct the second group of sequences into a diffusion matrix through formula (2) and perform a multiplication operation with the scrambled pixel matrix:

[0026] C i = C i-1 × x i × P SRi ; (2)

[0027] Among them, C iis the current ciphertext pixel value; C i―1 is the previous ciphertext pixel value; the scrambled image vector is P SR ; i represents the position of the pixel in the one-dimensional vector;

[0028] The dimension of the diffusion matrix is consistent with the size of the pixel matrix, and each element value is determined by the position parameter of the pseudo-random sequence interception.

[0029] In some embodiments of the present invention, the key space includes combinations of the following parameters:

[0030] Chaotic system parameters; a, b, c, d;

[0031] Time-delay position parameters: selected from at least 3 heterogeneous forms among A-I;

[0032] Initial conditions; x(t), y(t), z(t);

[0033] Sequence extraction numbers: 3 independent numbers, with a value range of 1-9;

[0034] Interception position parameter: d≥300.

[0035] In some embodiments of the present invention, the method realizes encryption simulation through MATLAB software, and the encryption performance satisfies:

[0036] The correlation coefficient of adjacent pixels ≤0.02 (horizontal, vertical, diagonal directions);

[0037] NPCR≥99.8%, UACI≥34.0%;

[0038] The ciphertext histogram is uniformly distributed, and the standard deviation ≤5%.

[0039] In some embodiments of the present invention, the generation steps of the pseudo-random sequence set include:

[0040] For each heterogeneous single-time-delay chaotic system, intercept the 1000-5000th iteration value after the initial moment as the sequence basis;

[0041] Intercept a subsequence of length M×N from the sequence according to the image size, where M and N are the horizontal and vertical pixel numbers of the image respectively.

[0042] In some embodiments of the present invention, the method is applicable to an encryption device including a GPU parallel computing architecture, and the encryption response time ≤50ms.

[0043] The second aspect embodiment of the present invention proposes a decryption method corresponding to the above encryption method, including the following steps:

[0044] Layer the ciphertext image by R, G, and B channels;

[0045] For each layer, the scrambled matrix is restored through inverse diffusion operation;

[0046] According to the sequence extraction rule in the key space, the inverse scrambling operation is performed to restore the original pixel matrix;

[0047] The layer matrices are combined to output the plaintext image.

[0048] To achieve the above object, an embodiment of the third aspect of the present invention proposes an electronic device, including a memory, a processor, and a computer program stored on the memory. When the computer program is executed by the processor, the above-mentioned color image encryption method based on hybrid heterogeneous single-delay chaos is implemented.

[0049] The color image encryption method and electronic device based on hybrid heterogeneous single-delay chaos according to the embodiments of the present invention effectively solve the problems of small key space, weak anti-attack ability, and poor adaptability of traditional chaos encryption algorithms through innovative designs such as dynamic sequence extraction of heterogeneous single-delay chaos systems, hierarchical encryption of color images, and multi-dimensional expansion of the key space, and achieve excellent performance in terms of security, real-time performance, and scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the encryption and decryption process and intermediate results of a color image based on hybrid heterogeneous single-delay chaos according to an embodiment of the present invention;

[0051] Figure 2 It is a histogram of the plaintext to be processed according to an embodiment of the present invention;

[0052] Figure 3 It is a histogram of the ciphertext after encryption according to an embodiment of the present invention;

[0053] Figure 4 It is a histogram of the plaintext after decryption according to an embodiment of the present invention;

[0054] Figure 5 It is the correlation coefficients of the image before being processed by this encryption method in the horizontal, vertical, and diagonal directions ((a) horizontal direction, r = 0.9002; (b) vertical direction, r = 0.9412; (c) diagonal direction, r = 0.9423);

[0055] Figure 6 It is the correlation coefficients of the image after being processed by this encryption method in the horizontal, vertical, and diagonal directions ((a) horizontal direction, r = 0.0122; (b) vertical direction, r = 0.0012; (c) diagonal direction, r = 0.0025);

[0056] Figure 7 It is a schematic structural diagram of an electronic device according to another embodiment of the present invention. Detailed implementation manners

[0057] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as a limitation to the present invention.

[0058] The color image encryption method, decryption method and electronic device based on hybrid heterogeneous single-delay chaos according to the embodiments of the present invention will be described below with reference to the accompanying drawings.

[0059] As Figure 1 shown, it is a schematic diagram of the encryption and decryption process and intermediate results of a color image based on hybrid heterogeneous single-delay chaos, showing a complete link of hierarchical division, scrambling, diffusion and inverse operations.

[0060] The color image encryption method based on hybrid heterogeneous single-delay chaos includes the following steps:

[0061] S1. Generate a set of pseudo-random sequences by using multiple heterogeneous single-delay chaos systems. The heterogeneous single-delay chaos systems form at least three delay chaos systems with different dynamic behaviors by applying delays to different state variables of the chaos system;

[0062] S2. Layer the color image into three independent pixel matrices P R 、P G 、P B according to the R, G, and B channels. Compared with the traditional overall processing method, this processing method has the following advantages:

[0063] (1) Increase the encryption complexity, and different encryption parameters can be used for each channel;

[0064] (2) Eliminate the correlation between different channels and improve the anti-statistical analysis ability;

[0065] (3) Facilitate parallel processing and improve the algorithm execution efficiency.

[0066] When the image size is M×N×3 (3 represents the number of channels), each channel forms a two-dimensional matrix of M×N, and then the scrambling operation and diffusion operation are respectively implemented on each matrix.

[0067] S3. For each layer, dynamically extract the first group of sequences from the set of pseudo-random sequences, generate a scrambling index according to the sequence sorting rule, and scramble the positions of the pixel matrix;

[0068] S4. For each scrambled layer, dynamically extract the second group of sequences from the set of pseudo-random sequences and construct a diffusion matrix;

[0069] S5. Merge the diffused layered pixel matrix into a ciphertext image.

[0070] As an example, the method for generating the set of pseudo-random sequences in steps S1, S3, and S4 specifically includes the following steps:

[0071] E1. For each heterogeneous single-delay chaotic system, intercept the sampling of the system after a period of time at the initial moment as a pseudo-random sequence. For example, the 1000 - 5000th iteration values after the initial moment are used as the sequence basis.

[0072] E2. According to the position parameter, intercept the data of the image size from the sequence at the parameter to form a sequence in the set, and perform a rounding operation on each element in the set in a certain form. That is, intercept a subsequence of length M×N from the sequence according to the image size, where M and N are the horizontal and vertical pixel numbers of the image respectively.

[0073] In some embodiments of the present invention, the heterogeneous single-delay chaotic system in step S1 is a delay-type Lorenz system, and its dynamic equation is:

[0074]

[0075] where a, b, c, and d are system parameters, and there are 7 terms in the formula, among which there are only 2 non-linear terms. x, y, and z are system state variables.

[0076] Compared with other chaotic or hyperchaotic systems, the structural form of this system is simpler, so the circuit implementation is easier; in addition, the delay chaotic system is an infinite-dimensional system with complex dynamic behaviors; therefore, this system has potential application value in the fields of secure communication, etc.

[0077] By applying a time delay to the state variables, a delay-type Lorenz chaotic system is obtained. However, different positions of adding the time delay can form functional differential dynamic systems with different dynamic behaviors. By applying a single time delay to the state variables in the formula, 9 forms of heterogeneous single-delay chaotic systems can be formed.

[0078]

[0079] where A - Z represents applying a time delay in the form of t - τ, and τ(>0) is the time delay amount.

[0080] According to the system stability criterion and the Hopf bifurcation analysis method, the Hopf bifurcation critical values of the 9 heterogeneous single-delay type Lorenz systems are obtained respectively under specific parameter values.

[0081] When the parameters are \(a = 10\), \(b=-4\), \(c = 2.5\), \(d = 2\), the Hopf bifurcation critical values of the system when the time delay is applied at different positions are shown in Table 1:

[0082] Table 1 Hopf bifurcation critical values of the heterogeneous single-time-delay-like Lorenz system

[0083] Position Critical value of Hopf bifurcation A 0.2173 B 0.1850 C 0.3276 D 0.3819 E 0.8107 F 0.2765 G 0.6265 H 0.4396 I 0.2253

[0084] The time-delay parameter \(\tau\) is selected to be close to but not exceed its Hopf bifurcation critical value to ensure that the system is in a chaotic state and has a high enough complexity at the same time.

[0085] A pseudo-random sequence set is constructed from the chaotic sequences generated by 9 heterogeneous single-time-delay chaotic systems, and 3 sequences are dynamically selected from them respectively to perform scrambling operations and diffusion operations on the image pixels.

[0086] Before implementing image encryption, a key space is constructed using the relevant information of 9 heterogeneous single-time-delay general Lorenz systems, including the parameters \(a\), \(b\), \(c\), \(d\) of the general Lorenz system, the time-delay position information, and the corresponding Hopf bifurcation value \(\tau\) i (\(i\in[A, I]\)), the initial conditions \(x(t)\), \(y(t)\), \(z(t)\) of the system, and the numbers \(s\) of three sequences selected from the pseudo-random sequence set i (\(i\in[1, 27]\) and the intercept position \(d\) i (\(i = 1, 2, 3\)). The data types in the key space are all integers, so the storage space of the key space is limited and the calculation is convenient. In addition, in the process of generating pseudo-random sequences, not all 9 types of heterogeneity need to be selected. Several of them can be randomly selected to construct the sequence set, thus forming a new encryption scheme using the time-delay position parameters, making the encryption algorithm more secure.

[0087] Before encryption, 27 pseudo-random sequences are generated simultaneously by 9 heterogeneous single-time-delay general Lorenz systems, numbered and put into the sequence set, and then 3 sequences are dynamically extracted from the sequence set respectively to perform scrambling operations and diffusion operations on the images after separating the channels of the color image. This will make the key space of the chaotic cipher larger than that of the previous chaotic ciphers. Taking a color image as an example, if \(M\) and \(N\) are used to represent the horizontal and vertical pixel values of the image respectively, the data volume generated by the time-delay chaotic system far exceeds the value of \(M\times N\). After the pseudo-random sequence set is prepared, the image encryption operation can be carried out.

[0088] In some embodiments of the present invention, the scrambling operation and the diffusion operation in steps S3 and S4 specifically include the following steps:

[0089] The scrambling operation is the first process of the image encryption algorithm. First, it sorts the sequences selected from the sequence set according to the selected number in the key space in ascending order; second, it transforms the pixel positions of the plaintext image according to the sorted sequence, and the transformation method is carried out according to the following formula (1), aiming to disrupt the pixel positions of the plaintext image.

[0090] The diffusion operation is the second process of the image encryption algorithm. It selects three sequences from the sequence set again according to the selected number in the key space, constructs a matrix, and multiplies the matrix by the pixel matrix after the scrambling operation to obtain the pixel matrix of the encrypted image.

[0091] The specific implementation processes of the scrambling operation and the diffusion operation are as follows:

[0092] Suppose the plaintext image is P, with a size of M×N×3, where 3 represents the number of image channels. In the RGB image mode, we divide P into P R 、P G 、P B into three channel layers, and then perform the scrambling operation and the diffusion operation on each layer. Taking the P R layer of the red channel as an example, the P R layer matrix is expanded into a one-dimensional vector by rows or columns, denoted as A. We randomly select a sequence X from the pseudo-random sequence set and perform the following operations:

[0093] T1. According to the position parameter d, intercept M×N data from the X sequence at d to form a set {x i , i = 1, 2, …, MN}; perform the rounding operation on each element in the set according to formula (1);

[0094] x i =(x i *10 4 ) mod MN + 1 (1)

[0095] where x i is the original value of the chaotic sequence; M and N are the horizontal and vertical pixel numbers of the image;

[0096] T2. Remove the duplicate data from the set {x i} obtained in T1, perform the difference operation on the obtained result and the set {1, 2, 3, …, MN}, and perform ascending sorting, and add it to the end of the set {x i};

[0097] T3. Use the result obtained in T2 as the basis for subscript operation of the vector A, and swap the positions of A(x i ) and A(x MN-i+1 ).

[0098] After three steps of operations, the scrambling operation of the image ends, and the scrambled image vector is denoted as P SR Next, we will perform a diffusion operation on the image vector P SR The dimension of the diffusion matrix is the same as the size of the pixel matrix, and each element value is determined by the position parameter of the pseudo-random sequence interception.

[0099] Once again, we randomly select a sequence Y from the sequence set and intercept M×N data from the position parameter d to construct an image matrix, and use Equation (2) for matrix operations to implement the diffusion operation of the image after the scrambling operation. Equation (3) represents the inverse operation of the diffusion operation.

[0100] C i = C i-1 ×x i ×P SRi (2)

[0101] where C i is the current ciphertext pixel value; C i―1 is the previous ciphertext pixel value; the scrambled image vector is P SR ; i represents the position of the pixel in the one-dimensional vector;

[0102] P SRi = C i ÷C i-1 ÷x i (3)

[0103] As an example, here we use a Lena color image with a size of 512×512×3 as the test object to verify the effectiveness of the algorithm. The above heterogeneous single-delay Lorenz system is used to generate a sequence set to implement the encryption and decryption of the color image. The number of sequence elements generated by the time-delay chaotic system is much larger than the size of the color image, and is stored fixedly. A certain number of elements will be intercepted according to the position parameter on the sequence to participate in the scrambling and diffusion operations. The parameters and initial conditions of the heterogeneous single-delay Lorenz system are provided in Table 1 and Figure 4 The position parameter d i ≥300. Next, we evaluate the performance of the encryption algorithm through histogram analysis, adjacent pixel correlation coefficient analysis, NPCR and UACI analysis.

[0104] The simulation environment of the present invention is a computer with AMD Ryzen 9 6900HX with Radeon Graphics CPU@3.30GHz, 16GB of memory, a 64-bit Windows operating system, and MATLAB R2022b software. The simulation uses the Lena image, encrypts it using the algorithm of the present invention, and applies the pseudo-random sequence of dynamic extraction and hybrid single-delay chaos for scrambling and diffusion operations to obtain the encrypted image.

[0105] The encryption performance is analyzed and evaluated from three dimensions as follows.

[0106] 1. Analysis using histograms:

[0107] The encryption and decryption processes of the image are implemented using MATLAB software, and the histograms of the R, G, and B pixels of the hierarchical images during the process are presented. As Figure 2 shows the histogram of the plaintext to be processed; Figure 3 shows the histogram of the ciphertext after encryption; Figure 4 shows the histogram of the plaintext after decryption.

[0108] From Figure 2 it can be seen that the distribution of the pixel values in the R, G, and B channels of the plaintext has obvious statistical laws, and the pixel value change curve of the plaintext image is significant. After scrambling and expansion operations, from Figure 3 it can be known that the ciphertext pixel values are evenly distributed in each gray-level interval. That is to say, the frequency of each pixel in the ciphertext after encryption is very close; and the R, G, and B channels are basically the same, so it cannot be attacked by statistical means. From Figure 4 it can be seen that the distribution of the pixel values in the R, G, and B channels of the plaintext image is basically the same as that of the image after decryption, indicating that the decryption effect is good, and the image can be restored to the plaintext image without being affected by the decryption algorithm. These results show that the information of the plaintext image is effectively diffused, and the encryption algorithm has good anti-statistical attack ability.

[0109] The histogram analysis results show that: the method of the present invention has a good averaging effect, meets the basic requirements of image encryption, and can effectively resist attacks based on statistical characteristics.

[0110] 2. Analysis of the correlation between adjacent pixels:

[0111] Another important evaluation index for image encryption is the correlation between adjacent pixels. In natural images, adjacent pixels usually have a strong correlation, which is an inherent statistical characteristic of images. An effective encryption algorithm should be able to destroy this correlation and make the relationship between adjacent pixels in the ciphertext image tend to be random.

[0112] The present invention calculates the correlation between adjacent pixels in the horizontal, vertical, and diagonal directions through the Pearson correlation coefficient. Table 2 shows the calculation results of the correlation coefficients of the original image and the encrypted image in different directions.

[0113] Table 2 Pearson correlation coefficients between adjacent pixels in different directions

[0114]

[0115] As can be seen from Table 2, for the encryption implemented under the mapping of the heterogeneous single-delay Lorenz system, the correlation coefficients of the encrypted image in the horizontal, vertical, and diagonal directions are all very close to zero. However, these are only some general results. To analyze the correlation between any two adjacent pixels in more detail, we depict the correlations between the plaintext image and the encrypted image in different directions in the form of scatter plots. Figure 5 Shows the correlation coefficient results of the Lena image in the horizontal, vertical, and diagonal directions. Figure 6 Shows the correlation coefficient results of the encrypted image in the horizontal, vertical, and diagonal directions.

[0116] Figure 5 Indicates that there is a high correlation between any two adjacent pixels of the plaintext image in different directions. However, from Figure 6 it can be seen that the correlation between the corresponding adjacent pixels of the encrypted image is very close to 0. Specifically, the correlation coefficients change from 0.9002, 0.9412, 0.9423 to 0.0122, 0.0012, 0.0025 respectively. This means that the encryption algorithm has effectively eliminated the correlation between adjacent pixels of the plaintext image, making it difficult for attackers to obtain any information about the plaintext image through correlation analysis.

[0117] 3. NPCR and UACI Analyses

[0118] The number of pixel change rate (NPCR) and the average change intensity (UACI) of pixels are two metrics for measuring the diffusion effect of the encryption algorithm. NPCR compares the number of changed elements in the pixel matrices corresponding to the plaintext image and the encrypted image to ensure that a sufficient number of elements in the pixel matrix are changed. While UACI reflects the average change magnitude of the pixel values at the corresponding positions of the plaintext image and the encrypted image.

[0119] For two random images, the expected values of NPCR and UACI are 96.6094% and 33.4635% respectively. The NPCR and UACI of the encrypted image being close to their respective expected values indicates that the information of the plaintext image has been well diffused into the encrypted image. Thus, it will be futile for attackers to attempt to obtain information about the plaintext image through differential attacks.

[0120] The NPCR and UACI test results of the method of the present invention are shown in Table 3:

[0121] Table 3 NPCR and UACI Test Results of the Encrypted Image

[0122]

[0123]

[0124] As can be seen from the results in Table 3, the average value of NPCR for the encrypted image is 99.8392%, and the average value of UACI is about 34.2585%. They are both very close to the expected values. If better NPCR and UACI values are desired, only the number of columns of the permutation matrix A needs to be increased. At this time, the size of the required chaotic matrix B will increase, so that the information of the plaintext image will be better diffused into the encrypted image. Therefore, this algorithm can effectively resist differential attacks.

[0125] Under the above simulation conditions, the total time of the image encryption and decryption process for a 512×512×3 image does not exceed 60 ms. In particular, when implementing the GPU parallel computing architecture, the encryption response time can be reduced to less than 50 ms, meeting the requirements of real-time applications.

[0126] To sum up, the image encryption algorithm based on heterogeneous time-delay chaotic systems uses time delays added to different state variables of the chaotic system to form multiple very complex time-delay chaotic systems. The generated sequences form a sequence set, which is used for encryption operations such as image scrambling and diffusion. This paper mainly introduces the designed image encryption scheme from four aspects: encryption algorithm, decryption algorithm, algorithm performance analysis, and comparative analysis. Our main innovation points include: the proposed encryption algorithm is simple, has a large key space, low computational complexity, strong ability to resist statistical attacks and differential attacks, and is easy to implement.

[0127] As an example, the key space generated by the pseudo-random sequence set includes combinations of the following parameters:

[0128] Chaotic system parameters; a, b, c, d;

[0129] Time-delay position parameters: selected from at least 3 heterogeneous forms of A - I, and theoretically there can be C(9,3) = 84 different combinations;

[0130] Initial conditions; x(t), y(t), z(t);

[0131] Sequence extraction numbers: 3 independent numbers, with a value range of 1 - 9;

[0132] Interception position parameter: d ≥ 300, specifying the starting position of intercepting data from the sequence.

[0133] This design of a multi-dimensional and multi-parameter key space greatly improves the security of the algorithm, making brute-force cracking computationally infeasible.

[0134] In addition, due to the use of time-delay chaotic systems, their infinite-dimensional characteristics further enhance the complexity of the system, making it difficult for attackers to accurately predict the system behavior even if they obtain partial key information.

[0135] Summarize the above content. The encryption method realizes encryption simulation through MATLAB software, and the encryption performance meets the following requirements:

[0136] The correlation coefficient of adjacent pixels ≤ 0.02 (horizontal, vertical, diagonal directions);

[0137] NPCR ≥ 99.8%, UACI ≥ 34.0%;

[0138] The ciphertext histogram is uniformly distributed, and the standard deviation ≤ 5%.

[0139] The present invention also provides a decryption method corresponding to the above encryption method, including the following steps:

[0140] V1. Layer the ciphertext image by R, G, and B channels;

[0141] V2. For each layer, restore the scrambling matrix through inverse diffusion operation;

[0142] V3. According to the sequence extraction rule in the key space, perform inverse scrambling operation to restore the original pixel matrix;

[0143] V4. Combine the layered matrices and output the plaintext image.

[0144] The decryption process is the exact inverse operation of the encryption process. As long as the keys are exactly the same, lossless decryption can be achieved. This strict reversibility ensures the complete recoverability of the encrypted image and is applicable to application scenarios with high requirements for image quality.

[0145] Combined with the attached Figure 1 , discuss the encryption and decryption processes;

[0146] Encryption process:

[0147] Step1: Read the plaintext image and construct matrices P R , P G , P B , and respectively form column matrices A R , A G , A B ;

[0148] Step2: According to the key information, generate a sequence set, randomly select 3 sequences (X, Y, Z) from the set, and intercept the sequences according to the position parameters;

[0149] Step3: Perform scrambling operations on P R , P G , P B , perform rounding, sorting, and appending on the intercepted sequence {x i} according to formula (1) to form a new sequence {x i}, and then for AR 、A G 、A B Exchange the pixel positions in it to form the scrambling matrix P SR 、P SG 、P SB ;

[0150] Step4: Perform a diffusion operation on P SR 、P SG 、P SB Once again, randomly select 3 sequences (X, Y, Z) from the set, and intercept the sequences according to the position parameters. Use the intercepted sequence {x i} to perform operations according to Equation (2) to form the diffusion matrix P DR 、P DG 、P DB ;

[0151] Step5: Merge P DR 、P DG 、P DB and output the ciphertext image.

[0152] Decryption process:

[0153] Step1: Read the ciphertext image and construct the matrices C R 、C G 、C B ;

[0154] Step2: Generate a sequence set according to the key information, select 3 sequences (X, Y, Z) from the set according to the sequence selection method, and intercept the pseudo-random sequence {x i};

[0155] Step4: Perform an inverse diffusion operation on C R 、C G 、C B Use the intercepted sequence {x i} to perform operations according to Equation (3) to form the matrices C DR 、C DG 、C DB ;

[0156] Step3: Perform an inverse scrambling operation on C DR 、C DG 、C DB Once again, select 3 sequences (X, Y, Z) from the set according to the sequence selection method, perform rounding, sorting, and appending on the intercepted sequence {x i} according to Equation (1) to form a new sequence {x i}, and then for C DR 、C DG 、C DBThe pixel positions in it are swapped to form matrix C SR , C SG , C SB ;

[0157] Step5: Merge C SR , C SG , C SB and output the decrypted image.

[0158] Corresponding to the above embodiments, the present invention also provides an electronic device.

[0159] As Figure 7 shown is a schematic structural diagram of an electronic device in the present invention. The electronic device 200 includes: a processor 201 and a memory 203. Among them, the processor 201 and the memory 203 are connected, such as through a bus 202. Optionally, the electronic device 200 may further include a transceiver 204. It should be noted that in practical applications, the transceiver 204 is not limited to one, and the structure of the electronic device 200 does not constitute a limitation to the embodiments of the present invention.

[0160] The processor 201 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute various exemplary logical blocks, modules, and circuits described in combination with the disclosure of the present invention. The processor 201 may also be a combination for implementing computing functions, such as a combination including one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0161] The bus 202 may include a path for transmitting information between the above components. The bus 202 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The bus 202 may be divided into an address bus, a data bus, a control bus, etc. For the sake of representation, Figure 7 only a thick line is used to represent it in the figure, but it does not mean that there is only one bus or one type of bus.

[0162] The memory 203 is used to store a computer program corresponding to the color image encryption method based on hybrid heterogeneous single-time-delay chaos in the foregoing embodiments of the present invention, and the execution of this computer program is controlled by the processor 201. The processor 201 is used to execute the computer program stored in the memory 203 to implement the content shown in the foregoing method embodiments.

[0163] Among them, the electronic device 200 includes, but is not limited to: mobile terminals such as laptop computers, PADs (tablet computers), etc. and fixed terminals such as desktop computers, etc. Figure 7 The illustrated electronic device 200 is only an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0164] The electronic device 200 of the embodiments of the present invention effectively solves problems such as small key space, weak anti-attack ability, and poor adaptability of traditional chaotic encryption algorithms through innovative designs such as dynamic sequence extraction of heterogeneous single-time-delay chaotic systems, hierarchical encryption of color images, and multi-dimensional expansion of key spaces, and achieves excellent performance in terms of security, real-time performance, and scalability, providing a new solution for image encryption technology.

[0165] It should be noted that the logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or used in combination with these instruction execution systems, apparatuses, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, image encrypt, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part with one or more wirings (electronic device), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which a program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other suitable processing as necessary, and then stored in a computer memory.

[0166] It should be understood that various parts of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following technologies well known in the art can be used: discrete logic circuits with logic gate circuits for implementing logical functions on data signals, application specific integrated circuits with appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0167] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0168] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" can explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0169] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A color image encryption method based on hybrid heterogeneous single-time-delay chaos, characterized in that, It includes the following steps: S1. Generate a set of pseudo-random sequences using multiple heterogeneous single-delay chaotic systems. The heterogeneous single-delay chaotic systems are formed by imposing delays on different state variables of the chaotic system to constitute at least three delay chaotic systems with different dynamic behaviors. S2. Stratify the color image into three independent pixel matrices according to the R, G, and B channels. S3. For each stratification, dynamically extract a first group of sequences from the set of pseudo-random sequences, generate a scrambling index according to the sequence sorting rule, and scramble the positions of the pixel matrix. S4. For each scrambled stratification, dynamically extract a second group of sequences from the set of pseudo-random sequences and construct a diffusion matrix. S5. Merge the diffused stratified pixel matrices into a ciphertext image. Among them, the key space generated by the set of pseudo-random sequences includes: chaotic system parameters, delay positions, initial conditions, sequence extraction numbers, and intercepted position parameters.

2. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, characterized in that, The heterogeneous single-delay chaotic system in step S1 is a delay-type Lorenz system, and its dynamic equation is: Where a, b, c, d are system parameters; x, y, z are system state variables.

3. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, wherein, The rule for dynamically extracting the first group of sequences in step S3 is: Randomly select 3 sequences from the sequence set, and perform rounding operations on the sequence elements according to formula (1): x i = (x i * 10 4 ) mod MN + 1 (1) where x i is the original value of the chaotic sequence; M and N are the horizontal and vertical pixel numbers of the image; After removing duplicate elements, generate a scrambling index to perform a full permutation exchange on the pixel positions.

4. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, wherein, The diffusion operation in step S4 is: Construct a diffusion matrix from the second group of sequences through formula (2) and perform a multiplication operation with the scrambled pixel matrix. C i = C i-1 × x i × P SRi ; (2) Among them, C i is the current ciphertext pixel value; C i―1 is the previous ciphertext pixel value; the scrambled image vector is P SR ; i represents the position of the pixel in the one-dimensional vector; The dimension of the diffusion matrix is the same as the size of the pixel matrix, and each element value is determined by the intercepted position parameter of the pseudo-random sequence.

5. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, wherein The key space contains combinations of the following parameters: Chaotic system parameters; a, b, c, d; Delay position parameters: selected from at least 3 heterogeneous forms of A-I; Initial conditions; x(t), y(t), z(t); Sequence extraction numbers: 3 independent numbers, with a value range of 1-9; Interception position parameter: d ≥ 300 。 6. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, wherein, The method realizes encryption simulation through MATLAB software, and the encryption performance satisfies: The adjacent pixel correlation coefficient ≤ 0.02; NPCR ≥ 99.8%, UACI ≥ 34.0%; The ciphertext histogram is uniformly distributed, and the standard deviation ≤ 5%.

7. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, characterized in that The generation steps of the set of pseudo-random sequences include: For each heterogeneous single-delay chaotic system, intercept the 1000-5000th iteration value after the initial moment as the sequence basis. Intercept a subsequence of length M×N from the sequence according to the image size, where M and N are the horizontal and vertical pixel numbers of the image respectively.

8. The color image encryption method based on hybrid heterogeneous single-time-delay chaos according to claim 1, wherein The method is applicable to an encryption device with a GPU parallel computing architecture, and the encryption response time ≤ 50ms.

9. A decryption method corresponding to the encryption method described in claim 1, characterized in that, It includes the following steps: Stratify the ciphertext image according to the R, G, and B channels. For each stratification, restore the scrambled matrix through inverse diffusion operation. According to the sequence extraction rule in the key space, perform inverse scrambling operation to restore the original pixel matrix. Merge the stratified matrices and output the plaintext image.

10. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored on the memory. When the computer program is executed by the processor, it realizes the encryption or decryption method as described in any one of claims 1-9.

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