Chaotic image selective encryption method based on facial recognition and key optimization

Abstract

The invention belongs to the technical field of digital image encryption, and discloses a chaos image selective encryption method based on facial recognition and key optimization, which comprises the following steps of: based on an existing chaos mapping system model, adding an exponential term and a complementation function to carry out performance optimization on the system model; establishing a three-dimensional amplitude limiting coupling hyperchaotic mapping system model; and designing a color image face encryption scheme based on the three-dimensional amplitude limiting coupling hyper-chaotic mapping system model. According to the chaotic image selective encryption method based on facial recognition and key optimization, a three-dimensional amplitude limiting coupling hyperchaotic mapping system model is established, and a facial region is selectively encrypted, so that the chaotic range is wide, and the complexity is high; a face recognition encryption scheme based on a DeepFace model is adopted, so that the encryption speed is effectively increased; and a PSO optimization algorithm is used, so that the encryption scheme can effectively resist known plaintext attacks, and compared with traditional encryption, the method has the advantages of relatively high calculation efficiency and encryption quality.

Description

Technical Field

[0001] The invention relates to the technical field of digital image encryption, and in particular to a chaotic image selective encryption method based on face recognition and key optimization. Background Art

[0002] With the continuous advancement of computer technology and artificial intelligence, the amount of information on the Internet has experienced explosive growth. A large amount of data, including images, videos, files, and chat records, needs to be transmitted through public channels, making personal privacy leakage a major challenge for everyone. Therefore, secure communication has become a hot research topic in modern society. Image encryption, with its high redundancy, large data capacity, and strong information correlation, places more stringent requirements on encryption schemes. Therefore, many scholars are committed to finding encryption schemes that are more efficient and less vulnerable to attacks than traditional solutions. Technologies such as DNA coding, compressed sensing, and information hiding have been developed and widely combined for image encryption.

[0003] Since the concept of chaos was first proposed in 1963, chaos theory has developed rapidly and gradually evolved into a mature and practical theoretical framework. Chaotic systems are unpredictable and sensitive to initial conditions. This means that the long-term iteration results of chaotic systems are unpredictable, and a small change in the initial state will lead to a huge change in its dynamic behavior. These characteristics have made it widely used in the field of secure communications, especially in image encryption. In recent years, many image encryption schemes based on chaos theory have been proposed.

[0004] However, many existing chaotic image encryption schemes have some defects. For example, some chaotic systems have insufficient chaotic characteristics, simple structures, and small system parameter ranges, which may lead to chaotic degradation. These problems can lead to reduced security. In addition, traditional encryption methods include two steps: perturbation and diffusion, and diffusion usually involves an XOR operation between the chaotic sequence and the image pixel value. This pixel obfuscation scheme is widely used, making it vulnerable to targeted attacks.

[0005] Most traditional encryption schemes have high time complexity while being effective, making selective encryption particularly important. Facial images carry unique biometric information, which makes their confidentiality extremely important. In applications such as facial recognition and face unlocking, facial images usually contain a lot of redundant information. Therefore, current research focuses on selectively encrypting facial regions. Summary of the invention

[0006] The purpose of the present invention is to provide a chaotic image selective encryption method based on face recognition and key optimization, establish a three-dimensional limited coupled hyperchaotic mapping system model, selectively encrypt the facial area, and solve the defects of the chaotic system parameters proposed in the past, such as small range, long encryption scheme, and insufficient randomness of the generated sequence.

[0007] To achieve the above object, the present invention provides a chaotic image selective encryption method based on face recognition and key optimization, comprising the following steps:

[0008] Step S1, based on the existing chaotic mapping system model, adding exponential terms and modulo functions to optimize the performance of the system model, and establishing a three-dimensional limited-coupled hyperchaotic mapping system model;

[0009] Step S2: design a color image face encryption scheme based on a three-dimensional limited coupled hyperchaotic mapping system model.

[0010] Preferably, in step S1, based on the existing chaotic mapping system model, an exponential term and a remainder function are added to optimize the performance of the system model, and a three-dimensional limited-coupled hyperchaotic mapping system model is established. The specific process is as follows:

[0011] Step S11, based on the existing chaotic mapping system model, adding exponential terms and remainder functions to optimize the performance of the system model; wherein the addition of exponential terms and remainder functions plays a role of limiting;

[0012] Based on this, a three-dimensional limited coupled hyperchaotic mapping system model is established as follows:

[0013]

[0014] Among them, x n ,y n 、z n is the state variable of the system; e g is the control parameter of system complexity; a, b, c, K are conventional parameters that have little effect on system complexity; is an intermediate variable;

[0015] Step S12: Based on the established three-dimensional limited coupled hyperchaotic mapping system model, dynamic behavior analysis is performed, specifically including Lyapunov index diagram, bifurcation diagram, phase diagram, sample entropy and NIST test.

[0016] Preferably, in step S2, a color image face encryption scheme is designed based on a three-dimensional limited coupled hyperchaotic mapping system model, and the specific process is as follows:

[0017] Step 21, read the original image and extract a facial image of size M×N×3 according to the previous facial recognition result, and rearrange it into a size of M×3×N;

[0018] Step 22: Match the recognized face image with the image in the database. If the match is successful, continue the encryption operation;

[0019] Step 23, using a particle swarm optimization algorithm to search for the best system key, and controlling the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence;

[0020] Step 24, performing a circular shift pixel rearrangement and pixel value confusion using a half-tensor product operation on the rearranged face image, and then rearrange it into a size of M×N×3;

[0021] Step 25: embed the encrypted face image back into the original image to obtain the final encryption result.

[0022] Preferably, in step S22, the FaceNet++ model is used to perform face recognition, comparison and region extraction;

[0023] First, a face database is established using the selected images, and all input images to be encrypted are compared with the images in the database;

[0024] Then, in the FaceNet++ model, the Euclidean distance between two images is compared with a preset threshold to determine whether they belong to the same person;

[0025] When the calculated maximum Euclidean distance between the input image and all face images in the database is greater than a preset threshold, it is determined that the match is successful.

[0026] Preferably, in step S23, a particle swarm optimization algorithm is used to search for the best system key, and the three-dimensional limited coupled hyperchaotic mapping system model is controlled to generate the required pseudo-random sequence. The specific process is as follows:

[0027] Step 231, using a particle swarm optimization algorithm to search for an optimal system key;

[0028] During the execution of the particle swarm optimization algorithm, all particles in each generation update their speed and position according to the following formula:

[0029]

[0030] in, is the particle position at time t; is the particle position at time t+1; is the particle velocity vector at time t; is the particle velocity vector at time t; pbest is the best historical position of the particle; best i is the historical best position of the population; w is the inertia weight; c1 and c2 are the holding parameters for controlling the particle speed; r1 and r2 are random numbers before [0,1];

[0031] The particle dimension is set to 8, corresponding to the 8 keys required. A pixel block of 64×64×3 in size is randomly intercepted from the image and encrypted using the key. The peak signal-to-noise ratio and Shannon entropy of the encrypted image are calculated using formulas (4) and (5), respectively, as shown below:

[0032]

[0033] Among them, MSE represents the mean square error of the image; x i For input picture; is the input mean; n is the number of pixels; PSNR is the peak signal-to-noise ratio;

[0034] Next, define the fitness function of the particle swarm optimization algorithm as follows:

[0035]

[0036] Among them, F(p) is the fitness; ω1 and ω2 are control coefficients, which are 0.3 and 0.7 respectively;

[0037] The quality of encryption is judged by the size of this fitness. After multiple rounds of iterations, an optimal solution will be returned, which is the required system key.

[0038] Step 232, controlling the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence;

[0039] According to the above system key, generate the corresponding three chaotic sequences x, y, z; discard the first 500 states of the sequence, and use formula (7) to generate the three sequences line, row and val required later:

[0040]

[0041] Among them, line i 、row i ,val i are three different pseudo-random sequences; floor represents the function of rounding down; x i ,y i 、z i is the original sequence obtained by iterating the chaotic system; n and m are the length and width of the image to be encrypted.

[0042] Preferably, in step S24, the rearranged face image is subjected to pixel rearrangement by circular shift and pixel value confusion by using a half-tensor product operation, and then rearranged into a size of M×N×3. The specific process is as follows:

[0043] Step 241, performing pixel scrambling of alternating rows and columns and cyclic shifting on the rearranged face image;

[0044] Step 242: pixel value obfuscation based on half-tensor product operation;

[0045] Suppose there are two matrices A∈M m×n ,B∈M p×q , and the least common multiple of n and p is t, then T is defined as the semi-tensor product of the two matrices, as shown below:

[0046]

[0047] Where M represents the set of all matrices of size m×n; ∝ represents the semi-tensor product operation; represents the tensor product of matrices; I represents the identity matrix.

[0048] Therefore, the present invention adopts the above-mentioned chaotic image selective encryption method based on face recognition and key optimization, and the beneficial effects are as follows:

[0049] (1) The present invention establishes a three-dimensional limited coupled hyperchaotic mapping system model, which has a controllable Lyapunov exponent, a wide chaotic range, high complexity, and selective encryption of the facial area;

[0050] (2) The present invention adopts a face recognition encryption scheme based on the DeepFace model to effectively improve the encryption speed;

[0051] (3) The present invention uses the PSO optimization algorithm to generate initial values ​​and control parameters in the control system, and generates a key associated with the image to be encrypted, so that the encryption scheme can effectively resist known plaintext attacks;

[0052] (4) In the present invention, STP is used as a new solution to pixel confusion in images, which is very different from the traditional XOR-based obfuscation method, making it effective against traditional attack methods and having greater computational efficiency and encryption quality advantages compared to traditional encryption.

[0053] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is an overall flow chart of a chaotic image selective encryption method based on face recognition and key optimization of the present invention;

[0055] Figure 2 It is a Lyapunov index variation diagram of different parameters of the three-dimensional limited coupled hyperchaotic mapping system model of the present invention; wherein, (a) is variable g; (b) is variable a; (c) is variable b; (d) is variable c; (e) is variable K;

[0056] Figure 3 It is a bifurcation diagram of different parameters of the three-dimensional limited coupled hyperchaotic mapping system model of the present invention in the range of 0 to 10; wherein, (a) is the variable g; (b) is the variable a; (c) is the variable b; (d) is the variable c; (e) is the variable K;

[0057] Figure 4 It is a three-dimensional phase diagram and projection diagrams in three directions of the three-dimensional limited coupled hyperchaotic mapping system model of the present invention; wherein, (a) is a three-dimensional phase diagram; (b) is a projection diagram in the xy direction; (c) is a projection diagram in the xz direction; (d) is a projection diagram in the yz direction;

[0058] Figure 5 It is a sample entropy comparison diagram between the three-dimensional limited coupled hyperchaotic mapping system model of the present invention and other chaotic systems; wherein, (a) is the system used in the present invention; (b) is the two-dimensional cubic mapping; (c) is MILE; (d) is 2D-LTMM; (e) is 2D-LSMCL; (f) is 2D-CSCM;

[0059] Figure 6 Schematic diagram of face recognition encryption and decryption results of the present invention; wherein, (a) is a plaintext image; (b) is a ciphertext image; and (c) is a decryption result. DETAILED DESCRIPTION

[0060] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0061] like Figure 1 As shown, a chaotic image selective encryption method based on face recognition and key optimization comprises the following steps:

[0062] Step S1, based on the existing chaotic mapping system model, adding exponential terms and modulo functions to optimize the performance of the system model, and establishing a three-dimensional limited-coupled hyperchaotic mapping system model;

[0063] Step S2: Based on the three-dimensional limited coupled hyperchaotic mapping system model, a color image face encryption scheme is designed. The specific process is as follows:

[0064] Step 21, read the original image and extract a facial image of size M×N×3 according to the previous facial recognition result, and rearrange it into a size of M×3×N;

[0065] Step 22: Match the recognized face image with the image in the database. If the match is successful, continue the encryption operation;

[0066] Step 23, using a particle swarm optimization algorithm to search for the best system key, and controlling the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence;

[0067] Step 24, performing a circular shift pixel rearrangement and pixel value confusion using a half-tensor product operation on the rearranged face image, and then rearrange it into a size of M×N×3;

[0068] Step 25: embed the encrypted face image back into the original image to obtain the final encryption result.

[0069] Example 1

[0070] The invention discloses a chaotic image selective encryption method based on face recognition and key optimization, which mainly comprises two parts. Firstly, a three-dimensional limited coupled hyperchaotic mapping model is established, and then a novel face image recognition encryption scheme based on the system model is designed.

[0071] Step S1, establishing a three-dimensional limited coupled hyperchaotic mapping system model.

[0072] Step S11, based on the existing chaotic mapping system model, add exponential terms and remainder functions to optimize the performance of the system model; wherein the addition of exponential terms and remainder functions plays a role of limiting.

[0073] Based on this, a three-dimensional limited coupled hyperchaotic mapping system model is established as follows:

[0074]

[0075] Among them, x n ,y n 、z n is the state variable of the system; e g is the control parameter of system complexity; a, b, c, K are conventional parameters that have little effect on system complexity; is an intermediate variable;

[0076] Step S12: Based on the established three-dimensional limited coupled hyperchaotic mapping system model, dynamic behavior analysis is performed, specifically including Lyapunov index diagram, bifurcation diagram, phase diagram, sample entropy and NIST test.

[0077] The Lyapunov exponent (LE) is an important indicator for evaluating the chaotic behavior of a system. An LE value greater than 0 can be used as a reference to determine whether a dynamic system is chaotic, indicating that the trajectory of the system will diverge over time. A system that meets this condition can be called a chaotic system, and the sequence generated by its iteration will also show pseudo-random characteristics.

[0078] A bifurcation diagram is a visual representation used in the study of dynamical systems, including chaotic systems, to illustrate how the behavior of a system changes as a parameter within the system changes. These diagrams show how a system changes from simple, predictable behavior to complex, chaotic dynamics through a series of bifurcations. A bifurcation occurs when a small change in a parameter value leads to an abrupt qualitative change in the behavior of the system.

[0079] Phase diagrams of chaotic systems are a key tool for describing the dynamic behavior of a system. Phase diagrams graphically show the path of a system's state change over time, providing an intuitive perspective for understanding the long-term behavior of a system. If a system exhibits closed-loop trajectories, this often indicates the presence of periodic behavior.

[0080] Sample entropy (SE) is an improved version of approximate entropy (ApEn), which is a statistical measure used to evaluate the complexity of time series data. It mainly evaluates the irregularity and complexity of time series. Figure 5 Figure 2 shows the comparison of SE values ​​between 3D-CIMBA and other systems when the parameters vary within the same range.

[0081] Table 1 Three-dimensional limited coupled hyperchaotic mapping system model NIST test

[0082]

[0083]

[0084] The NIST test can confirm whether the pseudo-random number sequence does have a high level of randomness, which is crucial to ensure the security of the encryption algorithm. Using the default parameters, 100 sets of data generated by the three-dimensional limited coupled hyperchaotic mapping are randomly selected, each with a length of 1 million bits. We performed NIST tests on these data sets, and the results are shown in Table 1. The dynamic behavior analysis results of the three-dimensional limited coupled hyperchaotic mapping system model are shown in Table 1. Figure 2 , Figure 3 and Figure 4 The results show that compared with other chaotic system models, the three-dimensional limited coupled hyperchaotic mapping system model proposed in the present invention has better chaotic performance, and the generated sequence shows good pseudo-random characteristics, which can be applied to the next step of chaotic image encryption.

[0085] Step S2: design a color image face encryption scheme based on a three-dimensional limited coupled hyperchaotic mapping system model.

[0086] Step 21, read the original image and extract a facial image of size M×N×3 according to the previous facial recognition result, and rearrange it to a size of M×3×N.

[0087] Step 22: Match the recognized face image with the image in the database. If the match is successful, continue the encryption operation.

[0088] The FaceNet++ model is used to perform face recognition, comparison, and region extraction. First, a face database is established using the selected images, and all input images to be encrypted are first compared with the images in the database. In the FaceNet++ model, the Euclidean distance between two images is compared with a preset threshold to determine whether they belong to the same person. When the calculated maximum Euclidean distance between the input image and all face images in the database is greater than the preset threshold, it is determined to be a successful match and the next encryption operation is performed.

[0089] Step 23: Use the particle swarm optimization algorithm to search for the best system key, and control the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence.

[0090] Step 231: Use the particle swarm optimization algorithm to search for the best system key.

[0091] The basic idea of ​​the particle swarm optimization (PSO) algorithm is to randomly initialize a group of particles (candidate solutions) in the search space, each particle represents a point in the search space; each particle has two attributes: position and velocity; the position represents a potential solution, and the velocity determines the direction and distance of the particle's movement; the particle updates its position by tracking two "best" solutions: one is the best position experienced by the particle (individual best solution), and the other is the best position experienced by the entire population (global best solution).

[0092] During the execution of the PSO algorithm, all particles in each generation update their velocities and positions according to the following formula:

[0093]

[0094] in, is the particle position at time t; is the particle position at time t+1; is the particle velocity vector at time t; is the particle velocity vector at time t; pbest is the best historical position of the particle; best iis the historical best position of the population; w is the inertia weight; c1 and c2 are the holding parameters for controlling the particle speed; r1 and r2 are random numbers before [0,1];

[0095] The present invention sets the dimension of the particle to 8 dimensions, corresponding to the 8 required keys. Randomly intercept a pixel block of 64×64×3 in the image, encrypt it with the key, and calculate the peak signal-to-noise ratio and Shannon entropy of the encrypted image using formulas (4) and (5), respectively, as shown below:

[0096]

[0097] Among them, MSE represents the mean square error of the image; x i For input picture; is the input mean; n is the number of pixels; PSNR is the peak signal-to-noise ratio.

[0098] Next, define the fitness function of the particle swarm optimization algorithm as follows:

[0099]

[0100] Among them, F(p) is the fitness; ω1 and ω2 are control coefficients, which are 0.3 and 0.7 respectively.

[0101] The quality of encryption is judged by the size of this fitness. After multiple rounds of iterations, an optimal solution will eventually be returned, which is the required system key. Particle swarm optimization can ensure that the generated sequence has good chaotic characteristics, thereby ensuring the encryption quality of subsequent encrypted images. The specific process of generating keys using the particle swarm optimization algorithm is shown in Algorithm 1.

[0102]

[0103]

[0104] Step 232: Control the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence.

[0105] According to the above system key, generate the corresponding three chaotic sequences x, y, z. Discard the first 500 states of the sequence and use formula (7) to generate the three sequences line, row and val required later:

[0106]

[0107] Among them, line i 、row i ,val i are three different pseudo-random sequences; floor represents the function of rounding down; xi ,y i 、z i is the original sequence obtained by iterating the chaotic system; n and m are the length and width of the image to be encrypted.

[0108] Step 24: perform circular shift pixel rearrangement and pixel value confusion using a half-tensor product operation on the rearranged face image, and then rearrange it into a size of M×N×3.

[0109] Step 241: Perform pixel scrambling of the rearranged face image by alternating row and column circular shifts.

[0110] In the operation described in Algorithm 2, the sequence line and row are used to perform row-column alternating cyclic shift operations on the face image. In the following encryption process, the number of iterations is set to 6000.

[0111]

[0112]

[0113] Step 242: pixel value confusion based on half-tensor product operation.

[0114] If there are two matrices A∈M m×n ,B∈M p×q , and the least common multiple of n and p is t, then T is defined as the semi-tensor product of the two matrices, as shown below:

[0115]

[0116] Where M represents the set of all matrices of size m×n; ∝ represents the semi-tensor product operation; represents the tensor product of matrices; I represents the identity matrix.

[0117] Step 25: embed the encrypted face image back into the original image to obtain the final encryption result; wherein, the face recognition encryption and decryption result schematic diagram is as follows: Figure 6 shown.

[0118] Example 2

[0119] This embodiment tests the facial database comparison function.

[0120] The face test set comes from the Internet Movie Database (IMDB). Due to the large total file size, 3,000 images from IMDB.0 with a total size of 1.3GB were used to build the face database.

[0121] The following five images (rm342264064_1964-9-2_2009.jpg, rm304650752_1955-5-16_2001.jpg, rm3388605-44_1961-7-30_1999.jpg, rm3794573056_1985-7-18_2007.jpg, rm848858368_1978-9-23_2010.jpg) are used as input. For convenience, these will be abbreviated as "images 1 to 5". Among them, 4 successfully matched to the image with the smallest Euclidean distance in the database, while 1 failed, as shown in Table 2, and then the encryption operation was performed on these 4 face images with successful recognition and matching.

[0122] Table 2. Matching results of different face recognition

[0123]

[0124] Example 3

[0125] This embodiment provides a specific example of a semi-tensor product operation: Assume that there are two matrices, P∈M 3×4 ,B∈M 2×3 ,

[0126]

[0127] On the contrary, there are

[0128]

[0129] Then, Q can be easily recovered from the equation. It is worth noting that since P is not a square matrix, the operation P -1 Corresponding to finding its generalized inverse matrix. In the encryption step of the present invention, the half tensor product of the double dimension is usually used to simplify the calculation, that is, the special case where n is an integer multiple of p.

[0130] In encryption, take the first n of val 2 elements, thus forming a square matrix R nxn , then, calculate R nxn The semi-tensor product of the image after the confusion is then taken, and all elements in the matrix are divided by 256 to take the remainder to obtain the final encrypted result cipher.

[0131] Since in the decryption process, it is necessary to calculate R nxn The inverse matrix of , so we must ensure that the matrix is ​​invertible. If the first generated R nxnIf it is not reversible, then it should be regenerated by taking values ​​starting from the 101th element of val. If it is still not reversible, then continue to take values ​​from each of the subsequent 100 elements until a reversible full-rank matrix is ​​generated. At this point, the final encryption result is obtained. Since the encryption scheme proposed in the present invention is a symmetric encryption, the decryption process essentially involves the opposite operation of the encryption process.

[0132] Therefore, the present invention adopts the above-mentioned chaotic image selective encryption method based on face recognition and key optimization, and establishes a three-dimensional limited coupled hyperchaotic mapping system model, which has a controllable Lyapunov exponent, a wide chaos range, high complexity, and selective encryption of the facial area; adopts a face recognition encryption scheme based on the DeepFace model to effectively improve the encryption speed; uses a PSO optimization algorithm to control the generation of initial values ​​and control parameters in the system, generates a key associated with the image to be encrypted, and enables the encryption scheme to effectively resist known plaintext attacks; at the same time, STP, as a new solution to pixel confusion in images, is very different from the traditional XOR-based confusion method, making it effective against traditional attack methods and having greater advantages in computational efficiency and encryption quality.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A chaotic image selective encryption method based on face recognition and key optimization, characterized in that: The following steps are involved: Step S1, based on the existing chaotic mapping system model, adding exponential terms and modulo functions to optimize the performance of the system model, and establishing a three-dimensional limited-coupled hyperchaotic mapping system model; Step S2: design a color image face encryption scheme based on a three-dimensional limited coupled hyperchaotic mapping system model.

2. The method for selective encryption of chaotic images based on facial recognition and key optimization according to claim 1, characterized in that: In step S1, based on the existing chaotic mapping system model, exponential terms and remainder functions are added to optimize the performance of the system model, and a three-dimensional limited-coupled hyperchaotic mapping system model is established. The specific process is as follows: Step S11, based on the existing chaotic mapping system model, adding exponential terms and remainder functions to optimize the performance of the system model; wherein the addition of exponential terms and remainder functions plays a role of limiting; Based on this, a three-dimensional limited coupled hyperchaotic mapping system model is established as follows: Among them, x n ,y n 、z n is the state variable of the system; e g is the control parameter of system complexity; a, b, c, K are conventional parameters that have little effect on system complexity; is an intermediate variable; Step S12: Based on the established three-dimensional limited coupled hyperchaotic mapping system model, dynamic behavior analysis is performed, specifically including Lyapunov index diagram, bifurcation diagram, phase diagram, sample entropy and NIST test.

3. The method for selective encryption of chaotic images based on facial recognition and key optimization according to claim 1 is characterized in that: In step S2, a color image face encryption scheme is designed based on the three-dimensional limited coupled hyperchaotic mapping system model. The specific process is as follows: Step 21, read the original image and extract a facial image of size M×N×3 according to the previous facial recognition result, and rearrange it into a size of M×3×N; Step 22: Match the recognized face image with the image in the database. If the match is successful, continue the encryption operation; Step 23, using a particle swarm optimization algorithm to search for the best system key, and controlling the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence; Step 24, performing a circular shift pixel rearrangement and pixel value confusion using a half-tensor product operation on the rearranged face image, and then rearrange it into a size of M×N×3; Step 25: embed the encrypted face image back into the original image to obtain the final encryption result.

4. The method for selective encryption of chaotic images based on facial recognition and key optimization according to claim 3 is characterized in that: In step S22, the FaceNet++ model is used to perform face recognition, comparison and region extraction; First, a face database is established using the selected images, and all input images to be encrypted are compared with the images in the database; Then, in the FaceNet++ model, the Euclidean distance between two images is compared with a preset threshold to determine whether they belong to the same person; When the calculated maximum Euclidean distance between the input image and all face images in the database is greater than a preset threshold, it is determined that the match is successful.

5. The method for selective encryption of chaotic images based on facial recognition and key optimization according to claim 3 is characterized in that: In step S23, the particle swarm optimization algorithm is used to search for the best system key, and the three-dimensional limited coupled hyperchaotic mapping system model is controlled to generate the required pseudo-random sequence. The specific process is as follows: Step 231, using a particle swarm optimization algorithm to search for an optimal system key; During the execution of the particle swarm optimization algorithm, all particles in each generation update their speed and position according to the following formula: in, is the particle position at time t; is the particle position at time t+1; is the particle velocity vector at time t; is the particle velocity vector at time t; pbest is the best historical position of the particle; best i is the historical best position of the population; w is the inertia weight; c1 and c2 are the holding parameters for controlling the particle speed; r1 and r2 are random numbers before [0,1]; The particle dimension is set to 8, corresponding to the 8 keys required. A pixel block of 64×64×3 in size is randomly intercepted from the image and encrypted using the key. The peak signal-to-noise ratio and Shannon entropy of the encrypted image are calculated using formulas (4) and (5), respectively, as shown below: Among them, MSE represents the mean square error of the image; x i For input picture; is the input mean; n is the number of pixels; PSNR is the peak signal-to-noise ratio; Next, define the fitness function of the particle swarm optimization algorithm as follows: Among them, F(p) is the fitness; ω1 and ω2 are control coefficients, which are 0.3 and 0.7 respectively; The quality of encryption is judged by the size of this fitness. After multiple rounds of iterations, an optimal solution will be returned, which is the required system key. Step 232, controlling the three-dimensional limited coupled hyperchaotic mapping system model to generate the required pseudo-random sequence; According to the above system key, generate the corresponding three chaotic sequences x, y, z; discard the first 500 states of the sequence, and use formula (7) to generate the three sequences line, row and val required later: Among them, line i 、row i ,val i are three different pseudo-random sequences; floor represents the function of rounding down; x i ,y i 、z i is the original sequence obtained by iterating the chaotic system; n and m are the length and width of the image to be encrypted.

6. The method for selective encryption of chaotic images based on facial recognition and key optimization according to claim 3 is characterized in that: In step S24, the rearranged face image is subjected to pixel rearrangement by circular shift and pixel value confusion by using a half-tensor product operation, and then rearranged into a size of M×N×3. The specific process is as follows: Step 241, performing pixel scrambling of alternating rows and columns and cyclic shifting on the rearranged face image; Step 242: pixel value obfuscation based on half-tensor product operation; Suppose there are two matrices A∈M m×n ,B∈M p×q , and the least common multiple of n and p is t, then T is defined as the semi-tensor product of the two matrices, as shown below: Where M represents the set of all matrices of size m×n; ∝ represents the semi-tensor product operation; represents the tensor product of matrices; I represents the identity matrix.

Images