DNA color image encryption method and system based on fixed time synchronization of fractional-order chaotic system

Abstract

The present invention discloses a DNA color image encryption method and system based on fixed-time synchronization of a fractional-order chaotic system. The method comprises: setting a synchronization error based on a master system of the fractional-order chaotic system established at a data transmitter and a slave system of the fractional-order chaotic system established at a data receiver; designing a fixed-time synchronization controller based on the synchronization error, and applying the fixed-time synchronization controller to the slave system of the data receiver to synchronize the slave system of the data receiver with the master system of the data transmitter within a fixed time; and synchronizing the slave system of the data receiver with the master system of the data transmitter to enable the data transmitter to implement DNA color image encryption using DNA coding rules based on the color image to be encrypted and the synchronized master system signal. The present invention combines fixed-time synchronization control related to the order of the fractional-order chaotic system with the fractional-order chaotic system to improve the efficiency and security of DNA color image encryption.

Description

Technical Field

[0001] The present invention relates to the field of new generation information technology, and in particular to a DNA color image encryption / processing method, device, system, electronic device and computer-readable storage medium based on fixed-time synchronization of a fractional-order chaotic system. Background Art

[0002] Fractional-order chaotic systems, a generalization of integer-order chaotic systems, are a class of complex nonlinear dynamical systems that are widely found in fields ranging from nature to finance and engineering. Fractional-order chaotic systems combine the characteristics of chaotic systems, such as dependence on initial values ​​and unpredictability, with the hereditary properties of fractional-order systems and the close dependence of system order. Therefore, they have potential applications in secure communications, electromagnetic fields, and biomedicine, and have become a current research hotspot.

[0003] Synchronicity is a key research topic in fractional-order chaotic systems. The convergence of their error systems determines the effectiveness of their synchronization. Currently, many synchronization control methods rely on asymptotic synchronization, meaning that synchronization is achieved as time approaches infinity. However, with the rapid advancement of science and technology, many control systems must complete their tasks in a very short timeframe, making asymptotic synchronization unsuitable for practical engineering applications. While the synchronization time of finite-time synchronization is bounded, it is affected by the initial values ​​of the system. Fixed-time synchronization control overcomes these issues, as its synchronization time depends solely on the system and controller parameters. Currently, fixed-time synchronization is applied in a variety of engineering fields, such as spacecraft attitude adjustment, centrifugal flywheel speed regulators, switching random Rossler systems, and secure communications. Therefore, achieving synchronization of fractional-order chaotic systems within a fixed timeframe would be of great practical value.

[0004] In 1989, Matthews first applied the high complexity, sensitivity, and randomness of chaotic systems to cryptographic research, opening up a new field of chaotic encryption and rapidly establishing chaotic image encryption as a significant technology. In recent years, numerous researchers have investigated the application of chaotic synchronization theory to image encryption. Notably, when using chaotic synchronization theory to generate encryption and decryption keys for images or audio, precise synchronization time is crucial for selecting matching keys. However, quickly obtaining accurate initial conditions is challenging, and these conditions sometimes must be kept secret. Fixed-time synchronization, since the synchronization time is independent of the initial conditions, addresses this shortcoming. Therefore, implementing image encryption and decryption using fixed-time synchronization technology can improve security, but research on this topic remains limited. Summary of the Invention

[0005] In order to address the deficiencies of the above-mentioned prior art, the present invention provides a DNA color image encryption / processing method, device, system, electronic device and computer-readable storage medium based on fixed-time synchronization of a fractional-order chaotic system. By adopting fixed-time synchronization control related to the order of the fractional-order chaotic system in combination with the fractional-order chaotic system, the efficiency and security of DNA color image encryption are improved.

[0006] The first object of the present invention is to provide a DNA color image encryption method based on fixed time synchronization of a fractional order chaotic system.

[0007] The second object of the present invention is to provide a DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system.

[0008] The third object of the present invention is to provide a DNA color image encryption device based on fixed time synchronization of a fractional order chaotic system.

[0009] The fourth object of the present invention is to provide a DNA color image processing system based on fixed-time synchronization of a fractional-order chaotic system.

[0010] A fifth object of the present invention is to provide an electronic device.

[0011] A sixth object of the present invention is to provide a computer-readable storage medium.

[0012] The first object of the present invention can be achieved by adopting the following technical solutions:

[0013] A DNA color image encryption method based on fixed-time synchronization of a fractional-order chaotic system is applied to a data transfer terminal. The method comprises:

[0014] A synchronization error is set according to a master system of a fractional-order chaotic system established at a data transmitting end and a slave system of a fractional-order chaotic system established at a data receiving end;

[0015] A fixed time synchronization controller is designed based on the synchronization error, and the fixed time synchronization controller is applied to the slave system at the data receiving end, so that the slave system at the data receiving end is synchronized with the master system at the data sending end within a fixed time;

[0016] The slave system at the data receiving end is synchronized with the master system at the data sending end, so that the data sending end realizes DNA color image encryption by using DNA coding rules according to the color image to be encrypted and the synchronized master system signal.

[0017] Furthermore, the fixed time synchronization controller is:

[0018]

[0019] Where Π(t) is a fixed time synchronization controller, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q is the order of the fractional-order chaotic system; ζ(t) is the synchronization error; constants α>0, β>0, δ>1, 0<θ<1, matrix Ω=W+L, W∈R n×n , L is a diagonal matrix of constants that satisfy the Lipschitz condition; sign is the sign function, is the gamma function, the indeterminate function ψ(t): R + →R satisfies ψ + (s)=0∨ψ(s) and

[0020] Furthermore, the fixed time synchronization controller is applied to the slave system at the data receiving end, and the synchronization time t e satisfy:

[0021]

[0022] in,

[0023] Furthermore, the synchronization error is:

[0024] ζ(t)=φ * (t)-φ(t)

[0025] Among them, φ * (t) is the state variable of the slave system at the data receiving end, and φ(t) is the state variable of the master system at the data sending end.

[0026] Furthermore, the main system of the fractional-order chaotic system is:

[0027]

[0028] The slave system of the fractional-order chaotic system is:

[0029]

[0030] in, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q is the order of the fractional-order system; φ(t) is the state variable of the main system, φ0 is the initial value of the main system; φ * (t) is the state variable of the slave system, φ * 0 is the initial value of the slave system; W∈R n×n ;η:R n →R n is a nonlinear function, η(0)=0; Π(t) is the synchronous controller to be designed.

[0031] Furthermore, the DNA color image encryption is implemented by using DNA coding rules according to the color image to be encrypted and the synchronized main system signal, including:

[0032] Extract the component matrix I of the red channel, green channel and blue channel of the color image to be encrypted R , I G , I B ; Among them, I R , I G , I B The element value of is one of (0,1,…,255);

[0033] The component matrix I R , I G , I B Pad with zeros, the matrix dimension after padding is M 1 ×N 1 ; The component matrix I R , I G , I B Divide l×l blocks; where l is a positive integer greater than 1;

[0034] Starting from the synchronization time, a chaotic sequence with a length of M is intercepted from the chaotic sequence generated by the main system. 1 ×N 1 The element value of the intercepted sequence is converted into a value between 0 and 255, and then converted into a value that is consistent with the component matrix I R , I G , I B A random matrix S of the same dimension;

[0035] Set the Logistic map L n The parameters κ and L0 are keys, and the sequence L is obtained by continuous iteration X , L Y , L Z , L H , and the sequence L X , L Y , L Z , L H The length of

[0036] L X , L Y , L Z , L H Process and get the corresponding L X 1 , L Y 1 , LZ 1 , L H 1 ;

[0037] Using L X 1 The coding rules determined are respectively for the component matrix I R , I G , I B DNA encoding;

[0038] Using L Y 1 Determine the encoding rules and perform DNA encoding on the random matrix S;

[0039] Using L Z 1 The DNA operation rules determined by DNA encoding are R , I G , I B Perform DNA operations with S;

[0040] Using L H 1 The DNA decoding rules determined by the DNA operation R , I G , I B Perform DNA decoding;

[0041] After DNA decoding, R , I G , I B Merge to get the encrypted image.

[0042] The second object of the present invention can be achieved by adopting the following technical solutions:

[0043] A DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system, the method comprising:

[0044] Encrypting the color image is achieved based on the DNA color image encryption method mentioned above;

[0045] The encrypted color image is decrypted at the data receiving end, including: based on the slave system being synchronized with the master system at the data sending end, DNA color image decryption is achieved using DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

[0046] Furthermore, the decryption process is the inverse process of the encryption process; in the decryption process, the chaotic sequence generated by the master system is replaced by the chaotic sequence generated by the slave system, and the key is the same as the decryption process.

[0047] The third object of the present invention can be achieved by adopting the following technical solutions:

[0048] A DNA color image encryption device based on fixed time synchronization of a fractional-order chaotic system, the device comprising:

[0049] A synchronization error setting module is used to set a synchronization error according to a master system of a fractional order chaotic system established by a data sending end and a slave system of a fractional order chaotic system established by a data receiving end;

[0050] A synchronization controller design module is used to design a fixed-time synchronization controller based on the synchronization error, and apply the fixed-time synchronization controller to the slave system at the data receiving end, so that the slave system at the data receiving end is synchronized with the master system at the data sending end within a fixed time;

[0051] The encryption module is used to synchronize the slave system of the data receiving end with the master system of the data sending end, so that the data sending end can realize DNA color image encryption using DNA coding rules according to the color image to be encrypted and the synchronized master system signal.

[0052] The fourth object of the present invention can be achieved by adopting the following technical solutions:

[0053] A DNA color image processing system based on fixed-time synchronization of a fractional-order chaotic system, the system comprising:

[0054] DNA color image encryption module, used to encrypt color images, based on the above-mentioned DNA color image encryption method;

[0055] The DNA color image decryption module is used to decrypt the encrypted color image at the data receiving end, including: based on the slave system being synchronized with the master system at the data sending end, DNA color image decryption is achieved using DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

[0056] The fifth object of the present invention can be achieved by adopting the following technical solutions:

[0057] An electronic device includes a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, the above-mentioned DNA color image encryption method based on fixed-time synchronization of a fractional-order chaotic system or the DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system is implemented.

[0058] The sixth object of the present invention can be achieved by adopting the following technical solutions:

[0059] A computer-readable storage medium stores a program. When the program is executed by a processor, the method for encrypting DNA color images based on fixed-time synchronization of a fractional-order chaotic system or the method for processing DNA color images based on fixed-time synchronization of a fractional-order chaotic system is realized.

[0060] The present invention has the following beneficial effects compared to the prior art:

[0061] The DNA color image encryption / processing method, device, system, electronic device and computer-readable storage medium based on fixed-time synchronization of a fractional-order chaotic system provided by the present invention can pre-set the synchronization time as needed; based on the correlation between the synchronization time and the order of the fractional-order chaotic system, the synchronization time can be estimated more accurately and effectively, thereby improving the efficiency and security of information transmission; based on the fact that the synchronization controller includes fractional-order terms, the adjustability of the controller can be enhanced, and it has better versatility; since the derivative of the Lyapunov function of the fixed-time synchronization control is indefinite and can even be positive, the conservatism of the algorithm is reduced; combining the fixed-time synchronization control with the DNA encoding operation rules can significantly improve the security of image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0063] Figure 1 This is a diagram illustrating the application environment of the DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system according to an embodiment of the present invention;

[0064] Figure 2 Schematic diagram of a DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system according to an embodiment of the present invention;

[0065] Figure 3 This is a flow chart of a DNA color image encryption method based on fixed time synchronization of a fractional-order chaotic system according to an embodiment of the present invention;

[0066] Figure 4 This is a trajectory comparison diagram of the error system without the controller according to an embodiment of the present invention;

[0067] Figure 5 A trajectory comparison diagram of an error system under the action of a fixed-time synchronization controller according to an embodiment of the present invention;

[0068] Figure 6The following diagrams demonstrate the image encryption effect of an embodiment of the present invention, where (a) is the original image, (b) is the encrypted image, and (c) is the decrypted image.

[0069] Figure 7 are histograms of the original image and the encrypted image according to an embodiment of the present invention, wherein (a) is the histogram of the R, G, and B channels of the original image, and (b) is the histogram of the R, G, and B channels of the encrypted image;

[0070] Figure 8 The decrypted image is obtained by adding salt and pepper noise with a density of 0.15 to the encrypted image according to an embodiment of the present invention;

[0071] Figure 9 This is a structural block diagram of a DNA color image encryption device based on fixed time synchronization of a fractional-order chaotic system according to an embodiment of the present invention;

[0072] Figure 10 This is a structural block diagram of a DNA color image processing system based on fixed-time synchronization of a fractional-order chaotic system according to an embodiment of the present invention;

[0073] Figure 11 2 is a structural block diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0074] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions in this application will be clearly and completely described below in conjunction with the embodiments and drawings. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application. It should be understood that the specific embodiments described are only used to explain this application and are not used to limit this application.

[0075] The DNA color image processing method based on fixed time synchronization of fractional order chaotic system provided by this application can be applied to Figure 1In the application environment shown, the data transmitting end 101 communicates with the data transfer end 102 and the data receiving end 103 via a network, respectively. The data transfer end 102 communicates with the data receiving end 103 via a network. The data transmitting end 101 can establish a master system of a fractional-order chaotic system. The data receiving end 103 can establish a slave system of the fractional-order chaotic system. The data transfer end 102 sets a synchronization error based on the master system of the fractional-order chaotic system of the data transmitting end 101 and the slave system of the fractional-order chaotic system of the data receiving end 103. Based on the synchronization error, a fixed-time synchronization controller is designed. After the fixed-time synchronization controller acts on the slave system of the data receiving end 103, the slave system of the data receiving end 103 synchronizes with the master system of the data transmitting end 101. Based on the synchronization of the slave system of the data receiving end 103 with the master system of the data transmitting end 101, the data transmitting end 101 implements DNA color image encryption using DNA coding rules based on the synchronized master system signal and the color image to be encrypted. Based on the slave system of the data receiving end 103 being synchronized with the master system of the data transmitting end 101 , the data receiving end 103 implements DNA color image decryption using DNA coding rules according to the synchronized slave system signal and the encrypted color image sent by the data transmitting end 101 .

[0076] The data transmitter 101, data transfer terminal 102, and data receiver 103 can be terminals or servers. The terminals can be, but are not limited to, various personal computers, laptops, smartphones, tablet computers, vehicle-mounted terminals, and portable wearable devices. The server can be implemented as an independent server or a server cluster or cloud server consisting of multiple servers. It is understood that there can be at least one data transmitter, at least one data transfer terminal, and at least one data receiver. The data transmitter can establish a master system of a fractional-order chaotic system, and the data receiver can establish a slave system of a fractional-order chaotic system. The data transfer terminal can set a synchronization error based on the master system of the fractional-order chaotic system of the data transmitter and the slave system of the fractional-order chaotic system of the data receiver, and design a fixed-time synchronization controller based on the synchronization error.

[0077] In one embodiment, Figure 2 As shown, a DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system is provided, comprising:

[0078] Encrypt color images;

[0079] The encrypted color image is decrypted at the data receiving end.

[0080] Specifically, color image encryption can be achieved through a DNA color image encryption method based on fixed-time synchronization of a fractional-order chaotic system.

[0081] In one embodiment, Figure 3 As shown in FIG, the DNA color image encryption method based on fixed time synchronization of a fractional-order chaotic system is applied to the data transfer end and specifically includes the following steps:

[0082] S301 , setting a synchronization error according to a master system of a fractional order chaotic system established by a data transmitting end and a slave system of a fractional order chaotic system established by a data receiving end.

[0083] Furthermore, step S301 specifically includes:

[0084] (1) The data sending end establishes the main system of the fractional-order chaotic system.

[0085] Based on the fractional-order chaotic system, the main system of the fractional-order chaotic system is established as:

[0086]

[0087] (2) The data receiving end establishes a slave system of the fractional-order chaotic system.

[0088] Based on the fractional-order chaotic system, the slave system of the fractional-order chaotic system is established as:

[0089]

[0090] in, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q represents the order of the fractional-order chaotic system; φ(t) represents the state variable of the main system, φ0 is the initial value of the main system; φ * (t) represents the state variable of the slave system, φ * 0 is the initial value of the system; W∈R n×n ;η:R n →R n is a nonlinear function, where η(0)=0; Π(t) represents the synchronous controller to be designed.

[0091] (3) Set the synchronization error based on the master system and the slave system.

[0092] The synchronization error is set as:

[0093] ζ(t)=φ * (t)-φ(t)

[0094] According to the master system and the slave system, as well as the synchronization error, the synchronization error system is established as follows:

[0095]

[0096] in, Satisfy η(φ* (t))-η(φ(t))≤L|φ * (t)-φ(t)|=L|ζ(t)|, L is a diagonal matrix of constants that satisfy the Lipschitz condition, ζ(t0)=φ * (t0)-φ(t0).

[0097] S302: Design a fixed time synchronization controller according to the synchronization error, and apply the fixed time synchronization controller to the slave system at the data receiving end.

[0098] According to the synchronization error, a fixed-time synchronization controller is designed and applied to the slave system of the fractional-order chaotic system at the data receiving end, so that the slave system of the fractional-order chaotic system at the data receiving end is synchronized with the master system of the fractional-order chaotic system at the data sending end within a fixed time.

[0099] Furthermore, step S302 specifically includes the following steps:

[0100] (1) Constructing Lyapunov function based on synchronization error The specific expression is:

[0101]

[0102] (2) According to the synchronization error, the fixed time synchronization controller is designed as follows:

[0103]

[0104] Where, the matrix Ω=W+L, the constants α>0, β>0, δ>1, 0<θ<1, sign is the sign function, is the gamma function, the indeterminate function ψ(t): R + →R satisfies ψ + (s)=0∨ψ(s) and

[0105]

[0106] (3) Apply the fixed time synchronization controller to the slave system so that the slave system is synchronized with the master system within a fixed time, and the synchronization time t e satisfy:

[0107]

[0108] in,

[0109] S303: The slave system at the data receiving end is synchronized with the master system at the data sending end, so that the data sending end implements DNA color image encryption using DNA coding rules according to the color image to be encrypted and the synchronized master system signal.

[0110] The data sending end implements DNA color image encryption using DNA coding rules based on the color image to be encrypted and the synchronized main system signal, specifically including the following steps:

[0111] (1) Read the original color image I, image size M×N×3, and extract the red channel component matrix I of the original color image R =I(:,:,1), green channel component matrix I G =I(:,:,2) and the blue channel component matrix I B =I(:,:,3), where, I R , I G , I B The value range of the elements of is one of the values ​​in (0, 1, ..., 255);

[0112] (2) I R , I G , I B Appropriate zero padding is performed, and the dimension of the matrix after zero padding is defined as M 1 ×N 1 , so that the matrix I R , I G , I B Divided into An l×l sized square;

[0113] (3) Extract the chaotic sequence φ1 of the main system from the synchronization time t e Starting from the moment, intercept length M 1 ×N 1 , denoted as φ1 1 Then, the sequence φ1 1 The element value is converted to a value between 0 and 255, and then converted to the value of I R , I G , I B The random matrix S of the same dimension is specifically expressed as follows:

[0114]

[0115] (4) Set the Logistic map L n The parameters κ=3.9999, L0=0.5220, and the sequence L is obtained by continuous iteration. X , L Y , L Z , L H The lengths of the four sequences are The specific description is as follows:

[0116]

[0117] Assume that the grayscale of a pixel is represented as "188" in decimal form, which corresponds to "10111100" in binary form. DNA encoding is performed according to rule 6 in Table 1, and the binary sequence is encoded as "TCCG." DNA decoding is performed according to rule 2 in Table 1, and the binary form is "11010110," which corresponds to the decimal value "214." In the operation of this embodiment, DNA addition and subtraction operations corresponding to encoding rule 1 in Table 1 are used. XOR and XNOR operations select rules 4 and 7 in Table 1, respectively. See Tables 2 and 3 for details.

[0118] Table 1 DNA coding rules

[0119] rule 1 2 3 4 5 6 7 8 A 00 00 11 11 01 01 10 10 T 11 11 00 00 10 10 01 01 G 01 10 01 10 11 00 11 00 C 10 01 10 01 00 11 00 11

[0120] Table 2 DNA addition and subtraction operation rules

[0121] + A T G C - A T G C A A T G C A A G T C T T C A G T T A C G G G A C T G G C A T C C G T A C C T G A

[0122] Table 3 DNA XOR and XNOR operation rules

[0123] ⊕ A T G C ⊙ A T G C A C G T A A A T G C T G C A T T T A C G G T A C G G G C A T C A T G C C C G T A

[0124] (5) L X , L Y , L Z , L H Perform the following processing to obtain L X 1 , L Y 1 , L Z 1 , L H 1 :

[0125]

[0126] Among them, L X 1 The value of determines the three matrices I R , I G , I B Coding rules of L Y 1 The value of determines the encoding rule of the random matrix S; L Z 1 The value of I determines the DNA encoding R , I G , I B DNA operation rules between L and S; H 1 The value of determines the matrix I after DNA operation R, I G , I B DNA decoding rules; L X 1 , L Y 1 , L H 1 The element range of L is 1 to 8, corresponding to the 8 rules in Table 1; Z 1 The elements range from 0 to 3: 0 and 1 correspond to the DNA addition and subtraction operations in Table 2, respectively; 2 and 3 correspond to the DNA XOR operation and DNA XOR operation in Table 3, respectively.

[0127] (6) I obtained in step (5) R , I G , I B Merge to get the encrypted image.

[0128] Specifically, the encrypted color image is decrypted and applied to the data receiving end, including:

[0129] The slave system based on the fractional order chaotic system is synchronized with the master system of the fractional order chaotic system at the data sending end. According to the received encrypted color image and the synchronized slave system signal, the DNA color image decryption is realized using DNA coding rules.

[0130] Specifically, the decryption process is the inverse process of the above encryption process (see step S303). In addition, the sequence φ generated by the fractional order chaotic system needs to be * By replacing the chaotic sequence φ1 of the main system of the fractional-order chaotic system with 1 and keeping other keys the same, the decrypted image can be obtained.

[0131] Specifically, the effectiveness of the fixed-time synchronization control of the fractional-order chaotic system provided by each embodiment is based on the following principles:

[0132] Definition 1: The qth-order Caputo fractional derivative of an mth-order continuously differentiable function φ(t) in a Banach space is defined as:

[0133]

[0134] Among them, the integer m satisfies q <m<q+1, t0 is the initial time;

[0135] Definition 2: For a Lebesgue integrable function φ(t), the p-order fractional integral is defined as:

[0136]

[0137] Lemma 1: If the q-order Caputo fractional derivative is integrable, then:

[0138]

[0139] In particular, when q∈(0,1),

[0140] Definition 3: For the error system of a fractional-order chaotic master system and a fractional-order chaotic slave system, if the synchronization time T(t0,ζ(t0)) is bounded and independent of any ζ(t0), such that For any t ≥ T(t0,ζ(t0)), this holds true. Then the error system is said to be fixed-time stable at the origin, that is, fixed-time synchronization is achieved between the fractional-order chaotic master system and the fractional-order chaotic slave system.

[0141] Assumption 1: Assume that the nonlinear function η(·) is Lipschitz continuous, then for any φ * , φ∈R must have a constant l k >0 such that η(φ(t))=(η1(φ(t)),…,η n (φ(t))) satisfies η k (φ * )-η k (φ)≤l k |(φ * -φ)|, where k=1,2,…,n, and L is composed of l1,…l k ,…,l n The diagonal matrix composed of

[0142] Assumption 2: Continuous function ψ(t):R + →R satisfies where ψ + (s) = 0∨ψ(s);

[0143] Lemma 2: Under Assumption 2, if the locally Lipschitz continuous Lyapunov function U(t,ζ(t)):R×R n →R + With C regularity and U(t,0)=0; when t≥t0, any ζ(t)∈R n , if the following inequality holds:

[0144]

[0145] Among them, constants α>0, β>0, δ>1, 0<θ<1, ψ(t) is an indeterminate function,

[0146] Then the system is stable at the origin for a fixed time, and the stable time

[0147]

[0148] In one embodiment, numerical simulation is used to verify that the fractional-order chaotic master system and the fractional-order chaotic slave system can achieve fixed-time synchronization, and the DNA color image encryption method is effective. The specific process is as follows:

[0149] The fractional-order Chua's circuit is shown below:

[0150]

[0151] Among them, the nonlinear term Assume that the parameters n0 = -1.27, n1 = -0.68, Then there is Available

[0152] Let the order of the fractional-order chaotic master system and the fractional-order chaotic slave system be q = 0.98, and the initial values ​​be φ(0) = [2; 0.5; -1.8], φ * (0) = [0.6; 0.1; -0.6]; Assume Where t∈[0,+∞), then Assuming α=0.5, β=0.9, δ=1.5, θ=0.4, we can get

[0153] The slave system and the master system have achieved fixed time synchronization, and the synchronization time

[0154] The encryption process corresponding to the above DNA color image encryption method is as follows:

[0155] (1) Select a color image Baboon (512×512×3) as the original color image I, set the image block size l×l=4×4; extract the red channel component matrix I of the original color image R =I(:,:,1), green channel component matrix I G =I(:,:,2) and the blue channel component matrix I B =I(:,:,3),where, I R , I G , I B The value range of the elements of is one of the values ​​in (0,1,…,255);

[0156] (2) I R , I G , IB Appropriate zero padding is performed, and the dimension of the matrix after zero padding is defined as M 1 ×N 1 =512×512, so that the matrix I R , I G , I B Divided into A 4×4 sized square;

[0157] (3) Extract the chaotic sequence φ1 of the main system from the synchronization time t e Starting from the moment, intercept length M 1 ×N 1 =512×512, denoted as φ1 1 ; Then the sequence φ1 1 The element value is converted to a value between 0 and 255, and then converted to the value of I R , I G , I B The random matrix S of the same dimension is specifically expressed as follows:

[0158]

[0159] (4) Set the Logistic map L n The parameters κ=3.9999,L0=0.5220, continuous iterations get the sequence L X ,L Y ,L Z ,L H , the lengths of the four sequences are The specific description is as follows:

[0160]

[0161] (5) L X ,L Y ,L Z ,L H Perform the following processing to obtain L X 1 ,L Y 1 ,L Z 1 ,L H 1 , where L X 1 The value of determines the three matrices I R , I G , I B Coding rules of L Y 1 The value of determines the encoding rule of the random matrix S; L Z 1The value of I determines the DNA encoding R , I G , I B DNA operation rules between L and S; H 1 The value of determines the matrix I after DNA operation R , I G , I B DNA decoding rules; L X 1 ,L Y 1 ,L H 1 The element range is 1-8, corresponding to the 8 rules in Table 1; L Z 1 The element range is 0-3: 0 and 1 correspond to the DNA addition and subtraction operations in Table 2, respectively, and 2 and 3 correspond to the DNA XOR operation and DNA XOR operation in Table 3, respectively. The specific expression is as follows:

[0162]

[0163] (6) I obtained in step (5) R , I G , I B Merge to get the encrypted image.

[0164] The decryption process is as follows:

[0165] The decryption process is the reverse process of the encryption process. In addition, the sequence φ generated by the system * 1 replaces the chaotic sequence φ1 of the main system used in the encryption algorithm. The other keys are the same, and the decrypted image can be obtained;

[0166] like Figure 4 As shown in , the synchronization error trajectory oscillates continuously when there is no controller, indicating that the master system and the slave system cannot achieve fixed time synchronization when there is no controller. Figure 5 As shown in the trajectory comparison diagram of the error system under the fixed time synchronization controller provided in this embodiment, the synchronization error under the controller reaches 0 at time 6, which is less than the theoretical value of 13.2788, indicating that the master system and the slave system achieve fixed time synchronization under the synchronization controller designed in this embodiment; Figure 6 (a) is the original image, (b) is the encrypted image, and (c) is the decrypted image, indicating that the DNA encryption and decryption algorithm is effective; Figure 7(a) is the histogram of the R, G, and B channels of the original image, and (b) is the histogram of the R, G, and B channels of the encrypted image; correlation tests were performed on 5000 pairs of adjacent pixels in the original image and the encrypted image from three directions. It can be seen from Table 4 that the correlation coefficients of the R, G, and B channels in the original image in three directions are all greater than 0.9, indicating that the correlation between pixels is very high. However, in the encrypted image, all correlation coefficients are less than 0.1. Obviously, the encryption process greatly destroys the correlation between adjacent pixels, which shows that the DNA encryption and decryption algorithm is effective; it can be seen from Table 5 that the image information entropy of the encrypted image is different from the image information entropy of the original image, and the image information entropy of the encrypted image is close to 8, while the image information entropy of the completely random image is 8, so it can be seen that the encrypted image is close to a completely random image, which reflects the effectiveness of the encryption method provided by this embodiment; Figure 8 The decrypted image is obtained by adding salt-and-pepper noise with a density of 0.15 to the encrypted image. Although the decrypted image is less clear, the overall outline is still clearly discernible, demonstrating the robustness of the decryption algorithm provided in this embodiment. It can be understood that the original image is the color DNA image to be encrypted, the encrypted image is the encrypted version of the original image, and the decrypted image is the decrypted version of the encrypted image.

[0167] Table 4 Correlation coefficients of R, G and B channels in three directions between the original image and the encrypted image

[0168]

[0169] Table 5 Image information entropy of original image and encrypted image

[0170] image R channel information entropy G channel information entropy B channel information entropy Original image 7.7067 7.4744 7.7522 Encrypted Image 7.9992 7.9993 7.9992

[0171] Those skilled in the art will appreciate that all or part of the steps in the method for implementing the above embodiments may be completed by instructing related hardware through a program, and the corresponding program may be stored in a computer-readable storage medium.

[0172] It should be noted that although the method operations of the above embodiments are described in a particular order in the accompanying drawings, this does not require or imply that the operations must be performed in this particular order, or that all of the illustrated operations must be performed to achieve the desired results. Rather, the depicted steps may be performed in a different order. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into a single step, and / or a single step may be broken down into multiple steps.

[0173] In one embodiment, Figure 9As shown, a DNA color image encryption device based on fixed-time synchronization of a fractional-order chaotic system is provided. The device includes a synchronization error setting module 901, a synchronization controller design module 902, and an encryption module 903, wherein:

[0174] A synchronization error setting module 901 is used to set a synchronization error according to the master system of the fractional order chaotic system established by the data sending end and the slave system of the fractional order chaotic system established by the data receiving end;

[0175] A synchronization controller design module 902 is configured to design a fixed-time synchronization controller based on the synchronization error, and apply the fixed-time synchronization controller to the slave system at the data receiving end, so that the slave system at the data receiving end is synchronized with the master system at the data sending end within a fixed time;

[0176] The encryption module 903 is used to synchronize the slave system of the data receiving end with the master system of the data sending end, so that the data sending end can implement DNA color image encryption based on the color image to be encrypted and the synchronized master system signal using DNA coding rules.

[0177] The specific implementation of each module in this embodiment can be found in the above embodiment and will not be described one by one here. It should be noted that the device provided in this embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0178] In one embodiment, Figure 10 As shown, a DNA color image processing system based on fixed-time synchronization of a fractional-order chaotic system is provided, wherein the system includes a DNA color image encryption module 1001 and a DNA color image decryption module 1002, wherein:

[0179] DNA color image encryption module 1001, for encrypting color images, implemented based on the DNA color image encryption method according to any one of claims 1 to 6;

[0180] The DNA color image decryption module 1002 is used to decrypt the encrypted color image at the data receiving end.

[0181] Decrypting the encrypted color image specifically includes: based on the slave system being synchronized with the master system at the data sending end, decrypting the DNA color image using DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

[0182] The implementation process of the above encryption and decryption is specifically referred to the relevant part of the above embodiment and will not be repeated here.

[0183] In one embodiment, an electronic device is provided, which may be a computer, such as Figure 11 As shown, the system comprises a processor 1102, memory, input device 1103, display 1104, and network interface 1105 connected via a system bus 1101. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium 1106 and an internal memory 1107. The non-volatile storage medium 1106 stores an operating system, computer programs, and a database. The internal memory 1107 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 1102 executes the computer program stored in the memory, the DNA color image encryption method based on fixed-time synchronization of a fractional-order chaotic system or the DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system described in Example 1 is implemented. The specific implementation process can refer to the methods described in the aforementioned related embodiments.

[0184] In one embodiment, a computer-readable storage medium is provided, storing a computer program. When executed by a processor, the computer program implements the DNA color image encryption method based on fixed-time synchronization of a fractional-order chaotic system or the DNA color image processing method based on fixed-time synchronization of a fractional-order chaotic system, as described in Example 1. The specific implementation process can refer to the methods described in the aforementioned related embodiments.

[0185] It should be noted that the computer-readable storage medium of the present embodiment may be a computer-readable signal medium or a computer-readable storage medium or any combination thereof. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0186] The above are only preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes based on the technical solution and inventive concept of the present invention within the scope disclosed by the present invention, which falls within the scope of protection of the present invention.

Claims

1. A DNA color image encryption method based on fixed time synchronization of fractional order chaotic system, applied to data transfer end, characterized by: The method comprises: A synchronization error is set according to a master system of a fractional-order chaotic system established at a data transmitting end and a slave system of a fractional-order chaotic system established at a data receiving end; A fixed time synchronization controller is designed based on the synchronization error, and the fixed time synchronization controller is applied to the slave system at the data receiving end, so that the slave system at the data receiving end is synchronized with the master system at the data sending end within a fixed time; The slave system at the data receiving end is synchronized with the master system at the data sending end, so that the data sending end implements DNA color image encryption using DNA coding rules according to the color image to be encrypted and the synchronized master system signal; Wherein, the fixed time synchronization controller is: Where Π(t) is a fixed time synchronization controller, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q is the order of the fractional-order chaotic system; ζ(t) is the synchronization error; constants α>0, β>0, δ>1, 0<θ<1, matrix Ω=W+L, W∈R n×n , L is a diagonal matrix of constants that satisfy the Lipschitz condition; sign is the sign function, is the gamma function, the indeterminate function ψ(t): R + →R satisfies ψ + (s)=0∨ψ(s) and 2. The DNA color image encryption method according to claim 1, characterized in that: Apply the fixed time synchronization controller to the slave system at the data receiving end, and synchronize the time t e satisfy: in, 3. The DNA color image encryption method according to claim 1, characterized in that: The synchronization error is: ζ(t)=φ * (t)-φ(t) Among them, φ * (t) is the state variable of the slave system at the data receiving end, and φ(t) is the state variable of the master system at the data sending end.

4. The DNA color image encryption method according to any one of claims 1 to 3, characterized in that: The main system of the fractional-order chaotic system is: The slave system of the fractional-order chaotic system is: in, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q is the order of the fractional-order system; φ(t) is the state variable of the main system, φ0 is the initial value of the main system; φ * (t) is the state variable of the slave system, φ * 0 is the initial value of the slave system; W∈R n×n ;η:R n →R n is a nonlinear function, η(0)=0; Π(t) is the synchronous controller to be designed.

5. The DNA color image encryption method according to any one of claims 1 to 3, characterized in that: The method of implementing DNA color image encryption using DNA coding rules based on the color image to be encrypted and the synchronized main system signal includes: Extract the component matrix I of the red channel, green channel and blue channel of the color image to be encrypted R , I G , I B ; Among them, I R , I G , I B The element value of is one of (0,1,…,255); The component matrix I R , I G , I B Pad with zeros, the matrix dimension after padding is M 1 ×N 1 ; The component matrix I R , I G , I B Divide l×l blocks; where l is a positive integer greater than 1; Starting from the synchronization time, a chaotic sequence with a length of M is intercepted from the chaotic sequence generated by the main system. 1 ×N 1 The element value of the intercepted sequence is converted into a value between 0 and 255, and then converted into a value that is consistent with the component matrix I R , I G , I B A random matrix S of the same dimension; Set the Logistic map L n The parameters κ and L0 are keys, and the sequence L is obtained by continuous iteration X , L Y , L Z , L H , and the sequence L X , L Y , L Z , L H The length of L X , L Y , L Z , L H Process and get the corresponding L X 1 , L Y 1 , L Z 1 , L H 1 ; Using L X 1 The coding rules determined are respectively for the component matrix I R , I G , I B DNA encoding; Using L Y 1 Determine the encoding rules and perform DNA encoding on the random matrix S; Using L Z 1 The DNA operation rules determined by DNA encoding are R , I G , I B Perform DNA operations with S; Using L H 1 The DNA decoding rules determined by the DNA operation R , I G , I B Perform DNA decoding; After DNA decoding, R , I G , I B Merge to get the encrypted image.

6. A DNA color image processing method based on fixed-time synchronization of fractional-order chaotic systems, characterized in that: The method comprises: Encrypting the color image is achieved based on the DNA color image encryption method according to any one of claims 1 to 5; The encrypted color image is decrypted at the data receiving end, including: based on the slave system being synchronized with the master system at the data sending end, DNA color image decryption is achieved using DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

7. The DNA color image processing method according to claim 6, characterized in that: The decryption process is the inverse process of the encryption process; in the decryption process, the chaotic sequence generated by the master system is replaced by the chaotic sequence generated by the slave system, and the key is the same as the decryption process.

8. A DNA color image encryption device based on fixed time synchronization of fractional order chaotic system, characterized in that: The device comprises: A synchronization error setting module is used to set a synchronization error according to a master system of a fractional order chaotic system established by a data sending end and a slave system of a fractional order chaotic system established by a data receiving end; A synchronization controller design module is used to design a fixed-time synchronization controller based on the synchronization error, and apply the fixed-time synchronization controller to the slave system at the data receiving end, so that the slave system at the data receiving end is synchronized with the master system at the data sending end within a fixed time; An encryption module is used to synchronize the slave system of the data receiving end with the master system of the data sending end, so that the data sending end can realize DNA color image encryption based on the color image to be encrypted and the synchronized master system signal using DNA coding rules; Wherein, the fixed time synchronization controller is: Where Π(t) is a fixed time synchronization controller, is the Caputo differential of the fractional-order system at time t, t0 is the initial time, q is the order of the fractional-order chaotic system; ζ(t) is the synchronization error; constants α>0, β>0, δ>1, 0<θ<1, matrix Ω=W+L, W∈R n×n , L is a diagonal matrix of constants that satisfy the Lipschitz condition; sign is the sign function, is the gamma function, the indeterminate function ψ(t): R + →R satisfies ψ + (s)=0∨ψ(s) and 9. A DNA color image processing system based on fixed-time synchronization of fractional-order chaotic systems, characterized in that: The system comprises: A DNA color image encryption module, for encrypting color images, implemented based on the DNA color image encryption method according to any one of claims 1 to 5; The DNA color image decryption module is used to decrypt the encrypted color image at the data receiving end, including: based on the slave system being synchronized with the master system at the data sending end, DNA color image decryption is achieved using DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

Images