Method and system for generating key of image under communication interruption based on symbolic directed graph network

Abstract

The present invention discloses a method and system for generating a key of an image under communication interruption based on a symbolic directed graph network. Based on graph theory, the present invention establishes a mathematical model of a symbolic directed graph network including a virtual leader node and multiple follower nodes, proposes a traction truncated sampling data controller that only uses part of the transmitted data to deal with the occurrence of communication interruption, combines the symbolic directed graph network with the traction truncated sampling data controller based on coordinate transformation to construct a processable error system, designs a dual-interval correlation Lyapunov function, provides a low-conservative sufficient condition to ensure binary synchronization of the virtual leader node and the follower node under the condition of lower coupling strength and higher communication interruption rate between nodes, and obtains a linear matrix inequality condition that is easy to solve; based on the chaotic sequence obtained by binary synchronization control of traction truncated sampling data, it is ensured that the generated key can resist the adverse effects of low coupling strength and high communication interruption rate and reduce network bandwidth occupancy.

Description

Technical Field

[0001] The present invention belongs to the field of network controlled communication security, and in particular relates to a method and system for generating a key of an image under communication interruption based on a symbolic directed graph network. Background Art

[0002] In the field of digital communication and storage, the security and confidentiality of images are of vital importance. Traditional methods of image transmission and storage are subject to the risk of data theft, tampering, or unauthorized access, so protecting the security of image data has become an urgent need. Effective image encryption technology can prevent unauthorized parties from accessing and identifying this information, thereby protecting personal privacy. Image encryption technology ensures the integrity of image data, prevents data from being maliciously tampered with during transmission or storage, and ensures the authenticity and reliability of the image. From the perspective of data security, privacy protection, commercial confidentiality, data integrity, and compliance requirements, the importance of image encryption to modern technology and various fields is becoming increasingly prominent.

[0003] At present, some works combine image encryption technology with leader and follower systems. By integrating encryption and decryption algorithms with leader and follower systems during image processing, more secure encryption keys and decryption keys are obtained. Some researchers have proposed networked control methods to save network bandwidth. There are a large number of literatures designing sampled data controllers to study binary synchronization problems.

[0004] However, sampled data control requires continuous operation of the actuator, and the data generated by the actuator is input into the system through a holder (e.g., zero-order holder, ZOH). In addition, in wireless transmission, the transmission of sampled data will be affected by network communication interruption, resulting in system instability. Therefore, it is crucial to consider the acquisition of encryption and decryption keys under communication interruption. At this point, the two main issues that need to be considered are the update rate and running time of the controller. From the perspective of reducing control costs, alleviating communication burdens, and the existence of communication interruptions, it is necessary to use the advantages of intermittent control and sampled data control to realize the generation of encryption and decryption keys. In other words, under the framework of truncated sampled data control, using only part of the sampling information to study the binary synchronization problem of the signed directed graph network is more conducive to the acquisition of encryption and decryption keys.

[0005] On the other hand, due to the dependence of inter-node coupling on communication hardware, the inter-node coupling strength is often affected by external interference. Therefore, in actual engineering environments, it may be small. At the same time, as the coupling strength increases, the requirements for communication equipment to maintain the connection between the leader node and the follower node also increase, which will lead to an increase in industrial costs. Therefore, it is crucial to achieve binary synchronization control under resource constraints, low coupling strength, and high communication interruption rate, and then obtain secure encryption and decryption keys to achieve image encryption and decryption.

[0006] It should be noted that the above information disclosed in this background technology is only used to increase the understanding of the background technology of the present invention, and therefore, it may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0007] The purpose of the present invention is to propose a key generation method for images under communication interruption based on a symbolic directed graph network, by designing a dual-interval dependent Lyapunov function and a traction truncated data sampling controller, so as to ensure the binary synchronization of the symbolic directed graph network under communication interruption, and then generate a key for image encryption and decryption.

[0008] In order to achieve the above object, the present invention adopts the following technical scheme:

[0009] The method for generating a key based on an image under communication interruption based on a symbolic directed graph network comprises the following steps:

[0010] Step 1. Read the original grayscale image and obtain an image matrix Q of size M*N;

[0011] Step 2. Based on graph theory knowledge, N follower nodes, i.e., N follower systems, which contain competition and cooperation relationships, are represented by a symbolic directed graph, and the dynamic behaviors between the N follower nodes are represented by differential equations. At the same time, the dynamic equation of the leader node, i.e., the leader system, is given;

[0012] Step 3. Design a traction truncated sampling data controller in the case of communication interruption, use the coordinate change to obtain a Laplace matrix with a zero row sum, and establish the error system equations of the leader node and the follower node;

[0013] Step 4. Construct a dual-interval dependent Lyapunov function and obtain sufficient conditions in the form of linear matrix inequalities to ensure binary synchronization of the error system based on Lyapunov stability theory;

[0014] Step 5. According to the sufficient conditions in step 4, solve the control gain that ensures the binary synchronization of the signed directed graph network. Based on the controller designed in step 3 and the communication interruption situation, calculate the state trajectory of the leading node and the follower node under the action of the controller, and use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

[0015] On the basis of the method for generating a key of an image under communication interruption based on a symbolic directed graph network, the present invention also proposes a corresponding system for generating a key of an image under communication interruption based on a symbolic directed graph network, and the technical scheme thereof is as follows:

[0016] A key generation system based on images under communication interruption based on a symbolic directed graph network, comprising:

[0017] The image matrix acquisition module is used to read the original grayscale image and obtain the image matrix Q of size M*N;

[0018] The binary synchronization control module based on the symbolic directed graph network is used to represent N follower nodes, i.e., N follower systems, which contain competition and cooperation relationships, with a symbolic directed graph according to graph theory knowledge, and to represent the dynamic behaviors between the N follower nodes with differential equations; at the same time, the dynamic equation of the leader node, i.e., the leader system, is given;

[0019] The controller design module is used to design the traction truncated sampling data controller in the case of communication interruption, obtain the Laplace matrix with zero row sum by using the coordinate change, and establish the error system equation of the leader node and the follower node;

[0020] Sufficient condition solving module, used to construct dual-interval dependent Lyapunov functions, and based on Lyapunov stability theory, obtain sufficient conditions in the form of linear matrix inequalities to ensure binary synchronization of the error system;

[0021] And a key generation module, which is used to solve the control gain that ensures the binary synchronization of the signed directed graph network according to sufficient conditions, calculate the state trajectory of the leading node and the follower node under the action of the controller based on the designed controller and the communication interruption situation, and use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

[0022] In addition, based on the method for generating a key of an image under communication interruption based on a symbolic directed graph network, the present invention also proposes a computer device, which includes a memory and one or more processors.

[0023] The memory stores executable codes, and when the processor executes the executable codes, it is used to implement the steps of the above-mentioned method for generating a key for an image under communication interruption based on a symbolic directed graph network.

[0024] In addition, based on the method for generating a key for an image under communication interruption based on a symbolic directed graph network, the present invention also proposes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the method for generating a key for an image under communication interruption based on a symbolic directed graph network as described above.

[0025] The present invention has the following advantages:

[0026] As described above, the present invention describes a method for generating a key for an image under communication interruption based on a symbolic directed graph network. This method addresses the problems of communication interruption and limited network bandwidth resources encountered in the key generation process of image encryption, and proposes a design method based on a traction-truncated sampling data controller. With the help of a symbolic directed graph network, the method takes into account the cooperative and competitive relationships to obtain a more concealed and reliable chaotic sequence, so as to obtain a more secure encryption key and decryption key. The method takes into account the cooperative and competitive relationships and the traction-truncated sampling data controller based on coordinate transformation to obtain a processable error system equation. The traction-truncated sampling data control means that only part of the sampling data information is used, and part of the sampling data information due to communication interruption is discarded, which takes into account both communication interruption and saving network bandwidth. In addition, in response to the demand for coupling strength between nodes, the present invention designs a dual-interval dependent Lyapunov function according to the characteristics of the control scheme and network structure. Combining Lyapunov theory and inequality technology, sufficient criteria are proposed to ensure the binary synchronization of the signed directed graph network, that is, the binary synchronization of the leading node and the follower node, and the linear matrix inequality conditions that are easy to solve are obtained; the chaotic sequence obtained based on the binary synchronization control of the traction truncated sampling data ensures that the generated key can resist the adverse effects of low coupling strength and high communication interruption rate and reduce network bandwidth occupancy. Finally, numerical simulation verifies that the method of the present invention can still generate keys under resource constraints, low coupling strength and high communication interruption rate, thereby realizing image encryption and decryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The present invention is a flowchart of a method for generating a key for an image under communication interruption based on a symbolic directed graph network according to an embodiment of the present invention.

[0028] Figure 2 Schematic diagram of control of the traction and truncation sampling data controller in an embodiment of the present invention.

[0029] Figure 3 It is a schematic diagram of a symbol directed graph in an embodiment of the present invention.

[0030] Figure 4 In the embodiment of the present invention, the traction truncation sampling data controller is used, and x i1 Schematic diagram of the state response of s1(t) and s1(t).

[0031] Figure 5 In the embodiment of the present invention, the traction truncation sampling data controller is used, and x i2 Schematic diagram of the state response of s(t) and s2(t).

[0032] Figure 6 In the embodiment of the present invention, the traction truncation sampling data controller is used, and x i3 Schematic diagram of the state response of s3(t) and s4(t).

[0033] Figure 7 These are the original image, the encrypted image and the decrypted image in the embodiment of the present invention.

[0034] in Figure 7 (a) is the original image. Figure 7 (b) in the figure is the encrypted image. Figure 7 (c) in the figure is the decrypted image.

[0035] Figure 8 ] are histograms of the original image and the encrypted image in the embodiment of the present invention.

[0036] in Figure 8 (a) in the figure is the histogram of the original image. Figure 8 (b) in FIG. 5 is the histogram of the encrypted image. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0038] Example 1

[0039] The present invention relates to a method for generating a key for an image under communication interruption based on a symbolic directed graph network. The method establishes a binary synchronization control model based on a symbolic directed graph network based on graph theory, proposes a traction truncated sampling data controller that only uses part of the transmitted data and discards the rest of the data to deal with the occurrence of communication interruption, combines the symbolic directed graph network with the traction truncated sampling data controller based on coordinate transformation, and constructs a processable error system; designs a dual-interval correlation Lyapunov function, provides a low-conservative sufficient condition to ensure binary synchronization of virtual leader nodes and follower nodes under the condition of lower coupling strength and higher communication interruption rate between nodes, and obtains a linear matrix inequality condition that is easy to solve; based on the chaotic sequence obtained by binary synchronization control of traction truncated sampling data, it is ensured that the generated key can resist the adverse effects of low coupling strength and high communication interruption rate and reduce network bandwidth occupancy. Through numerical simulation, it is verified that the present invention can still generate keys under resource constraints, low coupling strength and high communication interruption rate, thereby realizing image encryption and decryption.

[0040] like Figure 1 As shown, the key generation method of the image under communication interruption based on the symbol directed graph network includes the following steps:

[0041] Step 1. Get the pixel matrix.

[0042] Select a grayscale image of size M*N, read the image, and obtain an image matrix Q of size M*N.

[0043] Step 2. Establish a binary synchronization control model based on a symbolic directed graph network.

[0044] Specifically, based on graph theory knowledge, N follower nodes containing competition and cooperation relationships, namely N follower systems, are represented by symbolic directed graphs, and the dynamic behaviors between the N follower nodes are represented by differential equations. At the same time, the dynamic equation of the leading node, namely the leading system, is given.

[0045] According to graph theory, N follower nodes with competition and cooperation relationships are represented by a symbolic directed graph. It is expressed as:

[0046]

[0047] Where V = {1,…,N} represents the node set, N represents the total number of nodes; ε = {(i,j)|i,j∈V} represents the set of edges between nodes; (i,j)∈ε represents a directed edge from node j to node i; is the adjacency matrix representing the relationship between nodes; c ij Represents the adjacency matrix The (i,j)th item of ij > 0, then (i, j) is called a positive edge, and there is a cooperative interaction between nodes i and j; if c ij <0, then (i, j) is called a negative edge, and there is a competitive interaction between nodes i and j; And c ii =0; The symbol means that if and only if, c ii =0 means the node itself cannot interact.

[0048] Based on the symbolic directed graph and the adjacency matrix get l ij The items are:

[0049]

[0050] Among them, nodes i, j = 1, ..., N, N i ={j|(i,j)∈ε} is the set of neighboring edges of node i.

[0051] The differential equation of the follower node including competition and cooperation is established as follows:

[0052]

[0053] where x i (t) = (x i1 (t),…,x in (t)) T ∈R n is the state vector of the ith node, x i1 (t),…,x in (t) respectively represent the 1st,…,nth components of the state vector of the ith node; A=diag(a1,…,a n ) contains n elements a1,…,a n The diagonal matrix of n×n represents the weight matrix; σ represents the coupling strength, x j (t) represents the jth node, sgn(·) represents the symbolic function, and u i (t)∈R n is the input vector of the pull-truncated sampling data controller; R n represents an n′1-dimensional column vector; R n×n represents an n′n-dimensional matrix; the nonlinear term f(x i (t))=(f i1 (x i1 (t)),…,f in (x in (t))) T Represents the activation function.

[0054] For constants u and v, there exists a constant: f ip >0,p=1,…,n, such that:

[0055]

[0056] Among them, f i1 (x i1 (t)),…,f in (x in (t)) represent the activation function f(x i (t))'s 1st to nth components.

[0057] The leader node dynamics equation is as follows:

[0058]

[0059] s(t)=(s1(t),…,s n (t)) T ∈Rn is the state vector of the leader node; where s1(t),…,s n (t) represent the 1st,…,nth components of the leader node state vector respectively.

[0060] Step 3. Design a traction truncation sampling data controller in case of communication interruption.

[0061] Based on the characteristics of communication interruption, a traction truncation sampling data controller is constructed, such as Figure 2 As shown in the figure. The Laplace matrix with zero row sum is obtained by using the coordinate change, and then the error system equations of the leading node and the following node are established.

[0062] Design the traction truncated sampling data controller in the case of communication interruption, as shown in formula (3):

[0063]

[0064] Among them, K i is a diagonal matrix, i=1,…,N, when When K i ≠0, represents the pulling node, and when When K i =0; l is an integer greater than or equal to 2, t k+1 =t k +ls k .

[0065] Among them, s, They are s k The lower and upper limits of w i is a constant with a value of ±1. If node i is in a cooperative relationship with the leader node, w i =1, if node i is in competition with the leader node, w i =-1.

[0066] The above formula (3) shows that within a given time period [t k ,t k+1 ), the controller's behavior changes as follows:

[0067] In [t k ,t k +s k ) time period, the controller starts to operate and outputs K i (x i (t k )-w i s(t k )), and in [t k +s k ,tk +ls k ) time period, that is, the time period of communication interruption, the controller rests and the output is 0.

[0068] Adjacency matrix obtained by coordinate transformation

[0069] in, w j is a constant with a value of ±1. If node j is in a cooperative relationship with the leader node, w j = 1, if node j is in competition with the leader node, w j =-1.

[0070] definition The associated Laplacian matrix

[0071] in,

[0072] The above formula shows that the Laplace matrix is ​​a zero-row-sum matrix, that is, the sum of the elements in each row is zero; furthermore, let the error between the leader node and the follower node be ε i (t), definition

[0073] in is the state vector of the following node, w i is a constant with a value of ±1. If node i is in a cooperative relationship with the leader node, then w i =1; if node i is in a competitive relationship with the leader node, then w i =-1; s(t) is the state vector of the leader node, i=1,…,N.

[0074] The dynamic equation of the error system is given below, as shown in formula (4);

[0075]

[0076] express 1st to nth components; Represents the activation function The 1st to nth components of ;

[0077] f(s(t))=(f1(s1(t)),…,f n (s n (t))) T ,f1(s1(t)),…,f n (s n (t)) represent the 1st to nth components of the activation function f(s(t)); ε i (tk )=(ε i1 (t k ),…,ε in (t k )) T , ε i1 (t k ),…,ε in (t k ) represent ε i (t k )'s 1st to nth components; is the state vector of the following node, express 1st to nth components.

[0078] By expanding formula (4), we get the following form:

[0079]

[0080] Among them, I N represents the N-dimensional identity matrix, I n represents the n-dimensional identity matrix, represents the Kronecker product, diag(K1,…,K N ) represents an N-dimensional diagonal matrix, K1,…,K N represents the elements in an N-dimensional diagonal matrix, (…) T Represents the transpose of a vector.

[0081] Step 4. Establish the binary synchronization criterion of the error system equation.

[0082] A dual-interval dependent Lyapunov function is constructed, and based on the Lyapunov stability theory, sufficient conditions in the form of linear matrix inequalities are obtained to ensure the binary synchronization of the error system.

[0083] Construct a dual-interval-dependent Lyapunov function:

[0084]

[0085] in:

[0086] V1(t)=ε T (t)Pε(t);

[0087]

[0088]

[0089]

[0090]

[0091] in, s represents the time, ε(s) represents the error system state variable, Represents the 1st to nth components of ε(s).

[0092]

[0093]

[0094]

[0095] Among them, U 11 , U 12 , U 13 , X1, X2, X3, X4, X5, Y1, Y2, Y3, Y4, Y5 are all nN×nN dimensional matrices. Based on Lyapunov stability theory, sufficient conditions for ensuring binary synchronization of the error system are obtained.

[0096] Given a scalar a>0,b>0,α>0,l≥2,if there exists an nN×nN-dimensional matrix P>0,R1>0,R2>0,nN×nN-dimensional diagonal matrix Λ m > 0, m = 1, ..., 4, 2nN × 2nN dimensional matrix U > 0, any nN × nN dimensional matrix P1, P2, P3, M pq , p=1,…,6,q=1,…,4, for any 3nN×3nN dimensional matrices X and Y, the following linear matrix inequalities hold:

[0097]

[0098] Π(s k )<0 (8)

[0099]

[0100] Γ(s k )<0 (10)

[0101]

[0102]

[0103]

[0104] Among them, Ξ(s k ),Π(s k )、Y(s k ), Γ(s k )、X(s k) are the unknown variables s k matrix, γ is a constant; * indicates the transposition of the corresponding position element; F = diag(f 11 ,…,f 1n ,…,f N1 ,…,f Nn );f 11 ,…,f 1n ,…,f N1 ,…,f Nn They refer to the activation function f 11 (x 11 (t)),…,f Nn (x Nn (t)) corresponds to the Lipschitz constant.

[0105] Ξ=[Ξ μν ] 7Nn×7Nn , Π=[Π μν ] 7Nn×7Nn , Y=[Y μν ] 7Nn×7Nn , Γ=[Γ μν ] 7Nn×7Nn .

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] Ξ 14 =-U 12 -X3.

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] Ξ 34 =U12 -X4.

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] X 77 =sym{-Λ1}.

[0127] P 11 =Ξ 11 +sym{s k U 12 +as k U 11 +s k X3+as k X1}。

[0128]

[0129]

[0130]

[0131] P 15 =Ξ 15 。

[0132] P 16 =Ξ 16 。

[0133]

[0134]

[0135] P 23 =Ξ 23 -s k X1+s k X2-s k U 11 。

[0136] P 24 =s k X3+s k U 12 。

[0137] P27 =Ξ 27 。

[0138] P 33 =Ξ 33 +sym{as k X1-2as k X2+as k U 11}。

[0139] P 34 =Ξ 34 +2as k X4-2as k U 12 。

[0140] P 35 =Ξ 35 。

[0141] P 36 =Ξ 36 。

[0142] P 44 =Ξ 44 +sym{as k X5+as k U 13}。

[0143] P 55 =Ξ 55 。

[0144] P 56 =Ξ 56 。

[0145] P 66 =Ξ 66 。

[0146] P 77 =sym{-Λ2}.

[0147]

[0148]

[0149]

[0150] Y 14 =-Y3.

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] Y 34 =-Y4。

[0158]

[0159]

[0160]

[0161] Y 55 =-2M 53 -6M 63 。

[0162]

[0163] Y 66 =6M 64 。

[0164] Y 77 =sym{-Λ3}。

[0165] Γ 11 =Y 11 +sym{(l-1)s k Y3-b(l-1)s k Y1}。

[0166]

[0167]

[0168]

[0169] Γ 15 =Y 15 。

[0170] Γ 16 =Y 16 。

[0171]

[0172]

[0173] Γ 23 =-(l-1)s k Y1+(l-1)s k Y2。

[0174] Γ 24 =(l-1)s k Y3.

[0175] Γ 27 =Y 27 .

[0176] Γ 33 =Y 33 +sym{-b(l-1)s k Y1+2b(l-1)s k Y2}.

[0177] Γ 34 =Y 34 -2b(l-1)s k Y4.

[0178] Γ 35 =Y 35 .

[0179] Γ 36 =Y 36 .

[0180] Γ 44 =Y 44 -sym{b(l-1)s k Y5}.

[0181] Γ 55 =Y 55 .

[0182] Γ 56 =Y 56 .

[0183] Γ 66 =Y 66 .

[0184] Γ 77 =sym{-Λ4}.

[0185]

[0186] Step 5. Use the binary synchronization behavior of the symbolic directed graph network to obtain the encryption key and the decryption key, use the encryption key to process the grayscale image to obtain the encrypted image, and use the decryption key to inversely process the encrypted image to obtain the decrypted image.

[0187] According to the sufficient conditions in step 4, write the M file corresponding to the linear matrix inequality, and then solve it based on the MATLAB LMI toolbox to obtain the control gain that ensures the binary synchronization of the signed directed graph network. Based on the controller designed in step 3, considering different communication interruption situations, use the modules in the simulink toolbox module library to simulate the state trajectories of the leading node and the follower node under the action of the controller, and generate multiple groups of chaotic sequences. Use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

[0188] Communication interruption, that is, the period in which data cannot be transmitted accounts for different proportions of the entire transmission period.

[0189] Consider a follower node with the following parameters:

[0190] Where A=diag(1,1,1), f ip (x ip (t)) = 0.5*(|1+x ip (t)|-|-1+x ip (t)|).

[0191] The parameters and activation function of the leader node are the same as those of the follower node, and the cooperation and competition relationship between the leader node and the follower node is as follows: Figure 3 As shown. Set the initial values ​​of the leader node and the three follower nodes to s(0) = (0.1, 0.3, 0.2) T , and x1(0)=(0.5,-0.3,0.1) T , x2(0)=(1,-0.6,-0.5) T , x3(0)=(-0.6,-1,0.3) T .

[0192] According to the theory of symbolic directed graphs, symbolic directed graphs is structurally balanced, the node set can be divided into and According to the definition of Laplace matrix, we can get:

[0193]

[0194] Where W = diag(w1,…w N ), when the coupling strength is 20 and the communication interruption rate is 80%, the control gain obtained by applying traction control to node 3 is: K3=diag(-29.8691,-38.6056,-40.0789), K1=K2=diag(0,0,0).

[0195] Based on the above control gains, the time responses of the leader and follower nodes are as follows: Figure 4-Figure 6 As shown. Figures 4 to 6 It can be seen that the leader node and the follower node achieve binary synchronization under the control of the traction truncated sampling data, that is, the trajectories of follower nodes 1 and 2 are the same as those of the leader node, and the trajectory of follower node 3 is opposite to that of the leader node.

[0196] The image matrix Q generated based on the original grayscale image in step 1 is stored in vector form Follow the encryption steps below to obtain the encryption key:

[0197] (1) Use the leader node status value to generate W×L random sequences J1, J2, …, J WL and a matrix

[0198] (2) Expressed as in Indicates the first A random sequence, Indicates the first A random sequence, Indicates the exclusive OR (XOR) operation;

[0199] (3) Rearrange the matrix V to Z.

[0200] right Figure 7 The original image shown in (a) is encrypted based on the encryption algorithm, as shown in Figure 7 In addition, the histogram analysis of the original image and the encrypted image was performed. Figure 8 (a) and Figure 8 As shown in (b), it can be seen that the histogram distribution of the encrypted image is more uniform, which further proves the effectiveness of the encryption process.

[0201] The decryption key is a pseudo-random sequence of length W×L, which is composed of the negative of the value generated by node 3. The decryption process is the inverse process of the encryption process, and the decrypted image is obtained, such as Figure 7 As shown in (c), the encrypted image is successfully decrypted using the control gain K3 = diag (-29.8691, -38.6056, -40.0789).

[0202] The leader-follower system of the present invention generates a chaotic sequence, wherein the leader system data information is used to generate an encryption key for image encryption. When the encrypted image is received, the follower system data information is used to perform a decryption operation on it. This synchronous combination method not only ensures the security of image processing and transmission, but also realizes the instant response of the leader-follower system to the encrypted image, providing an efficient and secure solution for leader-follower applications involving privacy or sensitive information. When the coupling relationship between the follower nodes is a cooperative relationship, it is represented by an unsigned graph containing only positive edges. However, competition and cooperation usually coexist, therefore, the present invention is based on the signed graph theory, wherein the cooperative and competitive relationships can be represented by positive edges and negative edges. Therefore, the nodes in the structural equilibrium signed graph are divided into two sets. At this time, the corresponding synchronization of the signed directed graph network, i.e., binary synchronization, is very different from the synchronization of the unsigned graph network, and binary synchronization means that the absolute values ​​of all nodes are the same, but the signs are opposite. Therefore, the image encryption based on the binary synchronization control of the signed directed graph network of the present invention is more efficient and secure.

[0203] In order to illustrate the advantages of the dual-interval-dependent Lyapunov function constructed in the present invention, the comparison results between the dual-interval-dependent Lyapunov function in the present invention and the traditional Lyapunov function are given in Table 1 below.

[0204] Table 1 Comparison of the minimum coupling strength and the maximum communication interruption rate allowed

[0205] Traditional Lyapunov function Double interval dependent Lyapunov function Coupling strength 13 11.9 Communication interruption rate 80％ 87.5％

[0206] choose α=0.1,s=0.01s, a = 5.01, b = 5, l = 2. According to the dual interval dependent Lyapunov function, as shown in Table 1, it can be concluded that the derived minimum allowable coupling strength is 11.9. However, if the traditional Lyapunov function is used, the minimum allowable coupling strength is 13.

[0207] Obviously, the minimum allowed coupling strength under the dual-interval dependent Lyapunov function is reduced by 8.46%. Therefore, a smaller coupling strength can be allowed by designing a dual-interval correlation function.

[0208] when Select α = 0.1, s = 0.01s, a = 8, σ = 16. As can be seen from Table 1, the communication interruption rate is increased by 7.5%.

[0209] That is to say, the dual-interval-dependent Lyapunov function proposed in the present invention can allow a larger data truncation rate.

[0210] Example 2

[0211] This embodiment 2 describes a key generation system for images under communication interruption based on a symbolic directed graph network. This system and the key generation method for images under communication interruption based on a symbolic directed graph network in embodiment 1 are based on the same inventive concept.

[0212] Specifically, the key generation system of the image under communication interruption based on the symbol directed graph network includes:

[0213] The image matrix acquisition module is used to read the original grayscale image and obtain the image matrix Q of size M*N;

[0214] The binary synchronization control module based on the symbolic directed graph network is used to represent N follower nodes, i.e., N follower systems, which contain competition and cooperation relationships, with a symbolic directed graph according to graph theory knowledge, and to represent the dynamic behaviors between the N follower nodes with differential equations; at the same time, the dynamic equation of the leader node, i.e., the leader system, is given;

[0215] The controller design module is used to design the traction truncated sampling data controller in the case of communication interruption, obtain the Laplace matrix with zero row sum by using the coordinate change, and establish the error system equation of the leader node and the follower node;

[0216] Sufficient condition solving module, used to construct dual-interval dependent Lyapunov functions, and based on Lyapunov stability theory, obtain sufficient conditions in the form of linear matrix inequalities to ensure binary synchronization of the error system;

[0217] And a key generation module, which is used to solve the control gain that ensures the binary synchronization of the signed directed graph network according to sufficient conditions, calculate the state trajectory of the leading node and the follower node under the action of the controller based on the designed controller and the communication interruption situation, and use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

[0218] It should be noted that in the key generation system of the image under communication interruption based on the symbolic directed graph network, the implementation process of the functions and effects of each functional module is detailed in the implementation process of the corresponding steps in the method in Example 1, and will not be repeated here.

[0219] Example 3

[0220] This embodiment 3 describes a computer device, which includes a memory and one or more processors.

[0221] An executable code is stored in the memory. When the processor executes the executable code, it is used to implement the steps of the method for generating a key for an image under communication interruption based on a symbolic directed graph network in the above-mentioned embodiment 1.

[0222] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0223] Example 4

[0224] This embodiment 4 describes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of a method for generating a key for an image under communication interruption based on a symbolic directed graph network.

[0225] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card, etc. equipped on the device.

[0226] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A method for generating a key from an image under communication interruption based on a symbolic directed graph network, characterized in that: The steps include: Step 1. Read the original grayscale image and obtain an image matrix Q of size M*N; Step 2. Based on graph theory knowledge, N follower nodes, i.e., N follower systems, that contain competition and cooperation relationships are represented by a symbolic directed graph, and the dynamic behaviors between the N follower nodes are represented by differential equations; at the same time, the dynamic equation of the leader node, i.e., the leader system, is given; Step 3. Design a traction truncated sampling data controller in the case of communication interruption, use the coordinate change to obtain a Laplace matrix with a zero row sum, and establish the error system equations of the leader node and the follower node based on the dynamic equations of the follower node and the leader system; Step 4. Construct a dual-interval dependent Lyapunov function, and based on the Lyapunov stability theory, obtain sufficient conditions in the form of linear matrix inequality to ensure the bipartite synchronization of the error system equations of the leader node and the follower node; Step 5. According to the sufficient conditions in step 4, solve the control gain that ensures the binary synchronization of the signed directed graph network. Based on the controller designed in step 3 and the communication interruption situation, calculate the state trajectory of the leading node and the follower node under the action of the controller, and use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

2. The method for generating a key for an image under communication interruption based on a symbolic directed graph network according to claim 1, characterized in that: The step 2 is specifically as follows: According to graph theory, N follower nodes with competition and cooperation relationships are represented by a symbolic directed graph. It is expressed as: Where V = {1,…,N} represents the set of nodes, N represents the total number of follower nodes; ε = {(i,j)|i,j∈V} represents the set of edges between nodes, (i,j)∈ε represents the directed edge from node j to node i; is the adjacency matrix representing the relationship between nodes; c ij Represents the adjacency matrix The (i,j)th item of ; And c ii =0; The symbol means that if and only if, c ii = 0 means the node itself cannot interact; if c ij > 0, then (i, j) is called a positive edge, and there is a cooperative interaction between nodes i and j; if c ij <0, then (i, j) is called a negative edge, and there is a competitive interaction between nodes i and j; Based on the symbolic directed graph and the adjacency matrix get l ij The items are: Among them, nodes i, j = 1, ..., N, N i ={j|(i,j)∈ε} is the set of neighboring edges of node i; The differential equation of the follower node including competition and cooperation is established as follows: where x i (t) = (x i1 (t),…,x in (t)) T ∈R n is the state vector of the ith node, x i1 (t),…,x in (t) respectively represent the 1st to nth components of the state vector of the ith node; A = diag(a1,…,a n ) contains n elements a1,…,a n The diagonal matrix of n×n represents the weight matrix; σ represents the coupling strength, x j (t) represents the jth node, sgn(·) represents the symbolic function, and u i (t)∈R n is the input vector of the pull-truncated sampling data controller; R n represents an n×1-dimensional column vector; R n×n represents an n×n dimensional matrix; the nonlinear term f(x i (t))=(f i1 (x i1 (t)),…,f in (x in (t))) T represents the activation function; For constants u and v, there exists a constant: f ip >0,p=1,…,n, such that: v∈R,u≠v holds; Among them, f i1 (x i1 (t)),…,f in (x in (t)) represent the activation function f(x i (t))'s 1st to nth components; The dynamic equation of the leader node is as follows: s(t)=(s1(t),…,s n (t)) T ∈R n is the state vector of the leader node; s1(t),…,s n (t) represent the 1st to nth components of the leader node state vector respectively.

3. The method for generating a key for an image under communication interruption based on a symbolic directed graph network according to claim 2, characterized in that: The step 3 is specifically as follows: Design the traction truncated sampling data controller in the case of communication interruption, as shown in formula (3): Among them, K i is a diagonal matrix, i=1,…,N, when When K i ≠0, represents the pulling node, and when When K i =0; l is an integer greater than or equal to 2, t k+1 =t k +ls k ; in, s , They are s k The lower and upper limits of w i is a constant with a value of ±1. If node i is in a cooperative relationship with the leader node, then w i =1; if node i is in a competitive relationship with the leader node, then w i = -1; Adjacency matrix obtained by coordinate transformation in, w j is a constant with a value of ±1. If node j is in a cooperative relationship with the leader node, then w j =1; if node j is in a competitive relationship with the leader node, then w j = -1; definition The associated Laplacian matrix Among them, the Laplace matrix is ​​a zero-row-sum matrix, that is, the sum of the elements in each row is zero; Let the error between the leader node and the follower node be ε i (t), definition in, is the state vector of the follower node, s(t) is the state vector of the leader node, i=1,…,N; The dynamic equation of the error system is given below, as shown in formula (4); express 1st to nth components; Represents the activation function The first to nth components of n (s n (t))) T ,f1(s1(t)),…,f n (s n (t)) represent the 1st to nth components of the activation function f(s(t)); ε i (t k )=(ε i1 (t k ),…,ε in (t k )) T , ε i1 (t k ),…,ε in (t k ) represent ε i (t k )'s 1st to nth components; is the state vector of the following node, express 1st to nth components; By expanding formula (4), we get the following form: Among them, I N represents the N-dimensional identity matrix, I n represents the n-dimensional identity matrix, represents the Kronecker product, diag(K1,…,K N ) represents an N-dimensional diagonal matrix, K1,…,K N represents the elements in an N-dimensional diagonal matrix, (…) T Represents the transpose of a vector.

4. The method for generating a key for an image under communication interruption based on a symbolic directed graph network according to claim 3, characterized in that: The step 4 is specifically as follows: Construct a dual-interval-dependent Lyapunov function: in: V1(t)=ε T (t)Pε(t); in, s represents the time, ε(s) represents the error system state variable, represents the 1st to nth components of ε(s); Among them, U 11 , U 12 , U 13 , X1, X2, X3, X4, X5, Y1, Y2, Y3, Y4, Y5 are all nN×nN dimensional matrices; Based on Lyapunov stability theory, sufficient conditions to ensure binary synchronization of the error system are obtained; Given a scalar a>0,b>0,α>0,l≥2,if there exists an nN×nN-dimensional matrix P>0,R1>0,R2>0,nN×nN-dimensional diagonal matrix Λ m > 0, m = 1, ..., 4, 2nN × 2nN dimensional matrix U > 0, any nN × nN dimensional matrix P1, P2, P3, M pq , p=1,…,6,q=1,…,4, for any 3nN×3nN dimensional matrices X and Y, the following linear matrix inequalities hold: P(s k )<0 (8) C(s k )<0 (10) Among them, Ξ(s k ),Π(s k )、Y(s k ),Γ(s k )、X(s k ) are the unknown variables s k , * indicates the transposition of the corresponding position elements; Ξ=[Ξ μν ] 7Nn×7Nn , Π=[Π μν ] 7Nn×7Nn , Y=…Y μν … 7Nn×7Nn , Γ=…Γ μν ] 7Nn×7Nn ;γ is a constant; F=diag(f 11 ,…,f 1n ,…,f N1 ,…,f Nn ), where f 11 ,…,f 1n ,…,f N1 ,…,f Nn They refer to the activation function f 11 (x 11 (t)),…,f 1n (x 1n (t)),…,f N1 (x N1 (t)),…,f Nn (x Nn (t)) corresponding to the Lipschitz constant; 5. The method for generating a key for an image under communication interruption based on a symbolic directed graph network according to claim 1, characterized in that: The step 5 is specifically as follows: According to the sufficient conditions in step 4, the control gain that ensures the binary synchronization of the signed directed graph network is obtained based on the MATLAB LMI toolbox. Based on the controller designed in step 3 and the communication interruption situation, the state trajectory of the leader node and the follower node under the action of the controller is simulated using the simulink toolbox, and multiple groups of chaotic sequences are generated. The encryption key and decryption key are generated respectively using the information of the image matrix Q and the corresponding chaotic sequence.

6. A key generation system for images under communication interruption based on a symbolic directed graph network, characterized in that: include: The image matrix acquisition module is used to read the original grayscale image and obtain the image matrix Q of size M*N; The binary synchronization control module based on the symbolic directed graph network is used to represent N follower nodes, i.e., N follower systems, which contain competition and cooperation relationships, with a symbolic directed graph according to graph theory knowledge, and to represent the dynamic behaviors between the N follower nodes with differential equations; at the same time, the dynamic equation of the leader node, i.e., the leader system, is given; The controller design module is used to design the traction truncated sampling data controller in the case of communication interruption, obtain the Laplace matrix with zero row sum by using the coordinate change, and establish the error system equation of the leader node and the follower node based on the dynamic equation of the follower node and the leader system; Sufficient condition solving module, used to construct dual-interval dependent Lyapunov functions, and based on Lyapunov stability theory, obtain sufficient conditions in the form of linear matrix inequalities to ensure the bipartite synchronization of the error system equations of the leader node and the follower node; And a key generation module, which is used to solve the control gain that ensures the binary synchronization of the signed directed graph network according to sufficient conditions, calculate the state trajectory of the leading node and the follower node under the action of the controller based on the designed controller and the communication interruption situation, and use the information of the image matrix Q and the corresponding chaotic sequence to generate encryption keys and decryption keys respectively.

7. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the method for generating a key for an image under communication interruption based on a symbolic directed graph network as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for generating a key for an image under communication interruption based on a symbolic directed graph network as described in any one of claims 1 to 5 are implemented.

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