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

Abstract

The invention discloses a DNA color image encryption method and system based on fractional order chaotic system fixed time synchronization, and the method comprises the steps: setting a synchronization error according to a main system of a fractional order chaotic system established at a data transmitting end and a slave system of the fractional order chaotic system established at a data receiving end; designing a fixed time synchronization controller according to the synchronization error, and enabling the fixed time synchronization controller to act on a slave system of the data receiving end, so that the slave system of the data receiving end is synchronized with a main system of the data sending end within fixed time; and the slave system based on the data receiving end is synchronized with the master system of the data sending end, so that the data sending end realizes DNA color image encryption by using a DNA coding rule according to the color image to be encrypted and the synchronized master system signal. According to the method, the fixed time synchronous control related to the order of the fractional order chaotic system is combined with the fractional order chaotic system, so that the efficiency and safety of DNA color image encryption are improved.

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 system is a generalization of integer order chaotic system. It is a kind of complex nonlinear dynamic system, which is widely found in many fields such as nature, finance, engineering, etc. Fractional order chaotic system has the characteristics of chaotic system such as dependence on initial value and unpredictability, and has the hereditary characteristics of fractional order system and the property that is closely related to the order of the system. Therefore, it has potential application prospects in secure communication, electromagnetic field, and biomedicine, and has developed into a current research hotspot.

[0003] Synchronicity is a key research direction of fractional-order chaotic systems. The convergence of its error system determines the synchronization effect of the chaotic system. At present, many synchronization control methods are asymptotic synchronization, that is, synchronization is achieved when time tends to infinity. However, with the comprehensive and efficient development of science and technology, many control systems must complete specified tasks in a very short time, and asymptotic synchronization is no longer conducive to practical engineering applications. However, although the synchronization time of finite-time synchronization is bounded, it is affected by the initial value of the system. Fixed-time synchronization control overcomes these problems, and its synchronization time is only related to the parameters of the system and the controller. At present, fixed-time synchronization is applied to a variety of engineering fields, such as spacecraft attitude adjustment, centrifugal flywheel speed regulator, switching random Rossler system, secure communication, etc. Therefore, if the fractional-order chaotic system can achieve synchronization within a fixed time, it has great practical application 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 quickly making chaotic image encryption an important image encryption technology. In recent years, many scholars have studied the application of chaotic synchronization theory in image encryption. It is worth noting that when using chaotic synchronization theory to generate encryption and decryption keys for images or audio, accurate synchronization time is crucial for selecting matching keys. However, it is not easy to quickly obtain accurate initial conditions, and sometimes these conditions must be kept secret. Since the synchronization time of fixed time synchronization is independent of the initial conditions, it just makes up for this shortcoming. Therefore, implementing image encryption and decryption under fixed time synchronization technology can improve security, but there is still little research on this. 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 a 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 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 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, and the method comprises:

[0014] A synchronization error is set according to a master system of a fractional order chaotic system established at a data sending 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 according to 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 satisfying the Lipschitz condition; sign is the sign function, is the gamma function, the indefinite 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 method of implementing DNA color image encryption by using DNA coding rules according to the color image to be encrypted and the synchronized main system signal includes:

[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 values ​​of the intercepted sequence are converted to values ​​between 0 and 255, and then converted to the same as 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 the 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 Processing, get the corresponding L X 1 , L Y 1 , LZ 1 , L H 1 ;

[0037] Using L X 1 The coding rules determined by 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 the 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] The DNA decoded I R ,I G ,I B Merge them 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, the DNA color image decryption is realized by using the DNA coding rule 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 according to 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 according to the color image to be encrypted and the synchronized master system signal using DNA coding rules.

[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] A DNA color image encryption module is used to encrypt color images, and is implemented 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 main system at the data sending end, the DNA color image decryption is realized by using the 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 comprises 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, which, when executed by a processor, 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.

[0060] The present invention has the following beneficial effects compared with 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, thereby having better versatility; since the derivative of the Lyapunov function of the fixed-time synchronization control is indefinite and can even be a positive value, the conservatism of the algorithm is reduced; combining the fixed-time synchronization control with the DNA coding 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0063] Figure 1 This is an application environment 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;

[0064] Figure 2 This is a 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 It is a trajectory comparison diagram of the error system without the action of the controller according to an embodiment of the present invention;

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

[0068] Figure 6The following is a diagram showing the image encryption effect of an embodiment of the present invention, wherein (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] Fig. 9 It 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] Fig.10 It 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] Fig.11 4 is a structural block diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in combination with the embodiments and drawings. Obviously, the described embodiments 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 creative work 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 in this application can be applied to Figure 1In the application environment shown. Among them, the data sending end 101 communicates with the data transfer end 102 and the data receiving end 103 through the network respectively, and the data transfer end 102 communicates with the data receiving end 103 through the network. The data sending end 101 can establish a master system of the 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 the synchronization error according to the master system of the fractional order chaotic system of the data sending end 101 and the slave system of the fractional order chaotic system of the data receiving end 103; according to 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 is synchronized with the master system of the data sending end 101. Based on the synchronization of the slave system of the data receiving end 103 with the master system of the data sending end 101, the data sending end 101 implements DNA color image encryption using DNA coding rules according to the synchronized master system signal and the color image to be encrypted. Based on the synchronization of the slave system of the data receiving end 103 with the master system of the data sending 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 sending end 101 .

[0076] Among them, the data sending end 101, the data transfer end 102 and the data receiving end 103 can be terminals or servers. The terminal can be, but is not limited to, various personal computers, laptops, smart phones, tablet computers, vehicle-mounted terminals and portable wearable devices, and the server can be implemented by an independent server or a server cluster or cloud server composed of multiple servers. It can be understood that there can be at least one data sending end, at least one data transfer end, and at least one data receiving end. The data sending end can establish a master system of a fractional-order chaotic system, and the data receiving end can establish a slave system of a fractional-order chaotic system. The data transfer end can set the synchronization error according to the master system of the fractional-order chaotic system of the data sending end and the slave system of the fractional-order chaotic system of the data receiving end, and design a fixed-time synchronization controller according to 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, the DNA color image encryption method based on fixed time synchronization of 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 sending 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 according to 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:

[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 satisfying 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 the fixed-time synchronization controller is 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] Further, step S302 specifically includes the following steps:

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

[0101]

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

[0103]

[0104] Among them, 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 indefinite function ψ(t): R + →R satisfies ψ + (s) = 0 ∨ ψ (s) and

[0105]

[0106] (3) Apply a 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, synchronizing the slave system at the data receiving end 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 transmitting end implements DNA color image encryption using DNA coding rules according to the color image to be encrypted and the synchronized main system signal, which specifically includes 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 l×l sized squares;

[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 same value as I R ,I G ,I B The random matrix S of the same dimension is expressed as follows:

[0114]

[0115] (4) Set the Logistic map L n The parameters κ = 3.9999, L0 = 0.5220, continuous iterations to obtain the sequence L 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 gray level of the pixel is expressed 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 Table 2 and Table 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 XOR and XNOR operation rules of DNA

[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 for L Y 1 The value of determines the encoding rule of the random matrix S; L Z 1 The value of determines the DNA encoding I 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 element range is 0 to 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.

[0127] (6) The I obtained in step (5) R ,I G ,I B Merge them 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, and the DNA color image decryption is realized by using the DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

[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 principle of effectiveness of the fixed-time synchronization control of the fractional-order chaotic system provided by each embodiment is as follows:

[0132] Definition 1: The q-order Caputo fractional derivative of an m-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), then For any t ≥ T (t0, ζ (t0)), this is 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 indefinite 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] An example of a fractional-order Chua's circuit is as follows:

[0150]

[0151] Among them, the nonlinear term Assume 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) Choose a color image Baboon (512×512×3) as the original color image I, set the size of the image block to 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 same value as I R ,I G ,I B The random matrix S of the same dimension is expressed as follows:

[0158]

[0159] (4) Set the Logistic map L n The parameters κ = 3.9999, L0 = 0.5220, continuous iteration to obtain 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 for L Y 1 The value of determines the encoding rule of the random matrix S; L Z 1The value of determines the DNA encoding I 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 1-8, corresponding to the 8 rules in Table 1; 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 them 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, and the other keys are the same, and the decrypted image can be obtained;

[0166] like Figure 4 As shown in , the synchronization error trajectory keeps oscillating 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 action of the controller reaches 0 between 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; 5000 pairs of adjacent pixels in the original image and the encrypted image were tested for correlation 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, it can be seen that the encrypted image is close to a completely random image, which reflects the effectiveness of the encryption method provided in this embodiment; Figure 8 The decrypted image is a decrypted image after adding salt and pepper noise with a density of 0.15 to the encrypted image. Although the decrypted image does not look clear enough, the overall outline is still clearly discernible, which proves that the decryption algorithm provided in this embodiment has a certain robustness. It can be understood that the original image is the DNA color image to be encrypted, the encrypted image is the encrypted image of the original image, and the decrypted image is the decrypted image 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 specific order in the accompanying drawings, this does not require or imply that these operations must be performed in this specific order, or that all the operations shown must be performed to achieve the desired results. On the contrary, the steps depicted can be performed in a different order. Additionally or alternatively, some steps can be omitted, multiple steps can be combined into one step, and / or one step can be decomposed into multiple steps.

[0173] In one embodiment, Fig. 9As shown, a DNA color image encryption device based on fixed time synchronization of a fractional order chaotic system is provided, the device comprises 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 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;

[0175] A synchronization controller design module 902 is used to design a fixed time synchronization controller according to the synchronization error, and apply the fixed time synchronization controller to the slave system of the data receiving end, so that the slave system of the data receiving end is synchronized with the master system of 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 refer to the above embodiment, which 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, Fig.10 As shown, a DNA color image processing system based on fixed time synchronization of a fractional order chaotic system is provided, the system comprises a DNA color image encryption module 1001 and a DNA color image decryption module 1002, wherein:

[0179] A DNA color image encryption module 1001, used for encrypting a color image, and 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] The encrypted color image is decrypted, specifically including: based on the slave system being synchronized with the master system at the data sending end, DNA color image decryption is realized by 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, which will not be repeated here.

[0183] In one embodiment, an electronic device is provided, which may be a computer, such as Fig.11 As shown, it is connected to a processor 1102, a memory, an input device 1103, a display 1104 and a network interface 1105 through 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, a computer program and a database. The internal memory 1107 provides an environment for the operation of the operating system and the computer program 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 of the above embodiment 1 is implemented. The specific implementation process can refer to the methods described in the above-mentioned various related embodiments.

[0184] In one embodiment, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, 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 of the above-mentioned embodiment 1 is implemented. The specific implementation process can refer to the methods described in the above-mentioned various 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 of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with 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 of the above.

[0186] The above are only preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solution and inventive concept of the present invention within the scope disclosed by the present invention, which are within the protection scope 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, It is characterized in that The method comprises: A synchronization error is set according to a master system of a fractional order chaotic system established at a data sending end and a slave system of a fractional order chaotic system established at a data receiving end; A fixed time synchronization controller is designed according to 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 realizes DNA color image encryption by using DNA coding rules according to the color image to be encrypted and the synchronized master system signal.

2. The DNA color image encryption method according to claim 1, It is characterized in that 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, t 0 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 satisfying the Lipschitz condition; sign is the sign function, is the gamma function, the indefinite function ψ(t): R + →R satisfies ψ + (s) = 0 ∨ ψ (s) and 3. The DNA color image encryption method according to claim 2, It is 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, 4. The DNA color image encryption method according to claim 2, It is 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.

5. The DNA color image encryption method according to any one of claims 1 to 4, It is 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, t 0 is the initial moment, q is the order of the fractional-order system; φ(t) is the state variable of the main system, φ 0 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.

6. The DNA color image encryption method according to any one of claims 1 to 4, It is characterized in that The method of implementing DNA color image encryption by using DNA coding rules according to 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 values ​​of the intercepted sequence are converted to values ​​between 0 and 255, and then converted to the same as 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 L 0 As the key, 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 Processing, get the corresponding L X 1 , L Y 1 , L Z 1 , L H 1 ; Using L X 1 The coding rules determined by 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 the 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; The DNA decoded I R ,I G ,I B Merge them to get the encrypted image.

7. A DNA color image processing method based on fixed time synchronization of fractional order chaotic system. It is 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 6; 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, the DNA color image decryption is realized by using the DNA coding rule according to the received encrypted color image and the synchronized slave system signal.

8. The DNA color image processing method according to claim 7, It is characterized in that The decryption process is the reverse 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.

9. A DNA color image encryption device based on fixed time synchronization of fractional order chaotic system, It is 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 according to 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; 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 according to the color image to be encrypted and the synchronized master system signal using DNA coding rules.

10. A DNA color image processing system based on fixed time synchronization of fractional order chaotic system. It is characterized in that The system comprises: A DNA color image encryption module, used for encrypting a color image, implemented based on the DNA color image encryption method according to any one of claims 1 to 6; 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 main system at the data sending end, the DNA color image decryption is realized by using the DNA coding rules according to the received encrypted color image and the synchronized slave system signal.

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