Deoxyribose nucleic acid (DNA) strand displacement-based parametric disturbance hyper-chaotic system dislocation projection synchronization and secret communication method and system thereof

Abstract

The invention discloses a DNA strand displacement-based parametric disturbance hyper-chaotic system dislocation projection synchronization and secure communication method and system, and relates to the technical field of chaotic synchronization and secure communication. Constructing a hyperchaotic system by using DNA strand displacement reaction; a Chen hyper-chaotic system is adopted as a parameter disturbance system, parameter disturbance is applied to the hyper-chaotic system, the dynamic performance of the hyper-chaotic system is further improved by means of the hyper-chaotic characteristic of the Chen hyper-chaotic system, and a response system of the same structure is constructed; designing a dislocation disturbance controller, defining a dislocation error system, stabilizing the error system and compensating parameter disturbance through the dislocation disturbance controller, and realizing dislocation projection synchronization of the hyperchaotic system containing the parameter disturbance; a secret communication scheme of double hyperchaotic encryption is constructed, and dislocation transmission and decryption of biological signals are achieved. According to the method, dislocation projection synchronization of the parameter disturbance-containing hyper-chaotic system is realized, and secondary encryption is performed on the driving signal by utilizing the hyper-chaotic characteristic of the parameter disturbance system, so that the encrypted mixed signal is more complex in form and stronger in randomness, and the secrecy performance of the whole system is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of chaotic synchronization and secure communication technology, specifically to a method and system for the synchronization of misaligned projections in a parametrically perturbed hyperchaotic system based on DNA strand substitution and its secure communication. Background Technology

[0002] DNA strand substitution technology, with its precise molecular recognition capabilities and programmable characteristics, has become a core research direction in the field of molecular computing in recent years. This technology achieves precise information control at the molecular scale by dynamically replacing the complementary strand in a double-stranded DNA structure with a single-stranded DNA strand. Based on this unique molecular mechanism, researchers have successfully constructed DNA logic gates, artificial neural network models, and chaotic systems, demonstrating significant application value in areas such as synchronization control and secure communication.

[0003] Chaotic synchronization, as the foundation of secure communication, was first proposed by Pecora and Carroll in 1990. Its core value lies in achieving the gradual convergence of the dynamic trajectories of the driving and responding systems, providing theoretical support for secure information transmission and precise reconstruction. Notably, the breakthrough in DNA strand substitution (DSD) technology has injected new vitality into chaotic synchronization. Research shows that high-precision programming based on base sequences can achieve nanoscale control of chaotic system parameters and initial conditions. This programmable characteristic based on molecular devices can both construct complex chaotic systems and precisely achieve dynamic synchronization between systems. For example, in their 2023 paper titled "Loop synchronization for three four-dimensional chaotic systems based on DNA strand displacement" published in IEEE Transactions on Systems, Man, and Cybernetics: Systems (53(10), 6031-6042), JSun, HJi, and YWang designed multiple DSD reaction modules, successfully constructed a four-dimensional chaotic system, and realized the cascaded loop synchronization of the system, improving the reliability of chaotic synchronization based on DNA computing. In their 2023 paper titled "Projection synchronization of three-dimensional chaotic systems with active control based on DNA strand displacement" published in IEEE Transactions on Nano Bioscience (22(4), 836-844), WangY, SunC, and WangZ designed an active controller based on DNA strand displacement, which realizes proportional scaling synchronization of system state through dynamic scale factor, giving chaotic signals the advantage of programmable parameters in secure communication. However, the aforementioned studies are always limited by the one-to-one coupling mode of state variables. This rigid mapping relationship restricts the communication channel reconstruction capability, resulting in a lack of flexibility in the selection of transmission paths for biological signals. Therefore, it is necessary to improve existing chaotic synchronization methods based on DSD to provide technical support for building more secure multi-channel secure communication systems.

[0004] By using DSD technology to compile chaotic systems, novel bio-communication systems with molecular-level encryption capabilities can be constructed, thereby enabling secure transmission of biological signals. Compared to electronic communication systems that are susceptible to interference from the biological microenvironment, DSD chaotic communication systems, thanks to their molecular self-assembly properties and robust sequence encoding, can achieve encryption and dynamic mapping of biological signals at the nanoscale. For example, in their 2023 paper "Coupling projection synchronization of three chaotic systems and its multilevel secure communication via DNA CRNs" published in IEEE Internet of Things Journal (10(19), 17282-17292), Sun J, Zang M, and Wang Z implemented the coupling projection synchronization of three chaotic systems based on DNA chemical reaction networks (CRNs), and attached biological signals to these chaotic systems. They designed a multilevel secure communication scheme using chaotic masking technology, which effectively improved the security of transmitted signals. In their 2022 paper "Design of a single-channel chaotic secure communication system implemented by DNA strand displacement" published in ACSS Synthetic Biology (11(2), 843-854), An X, Meng Z, and Wang Y implemented chaotic secure communication based on drive-response synchronization using four DSD reaction modules. This system uses chaotic masking communication technology and completes the encryption and decryption of biological signals through a single-channel synchronization scheme. While chaotic masking techniques can effectively conceal target signals, their encryption strength is limited by the underlying chaotic system. This technique relies solely on the state variables of its own chaotic system as the key, leading to insufficient security levels for biosignals during transmission. Therefore, optimizing the chaotic masking key generation mechanism based on DSD is of significant research value for the secure transmission of biosignals.

[0005] In chaotic secure communication based on Disordered Detection (DSD), the inherent parameter sensitivity of chaotic systems means that external nonlinear perturbations can induce fluctuations in system parameters, thereby affecting the stability and security of the communication system. Although such perturbations may disrupt synchronization control mechanisms, precise control of the perturbation parameters can effectively enhance the dynamic characteristics of the chaotic system. This potential threat can be inversely transformed into a key to encryption enhancement. Research shows that perturbing chaotic maps can enhance the ergodicity and quasi-randomness of digital chaotic maps; by using the state variables of the chaotic system as parameter perturbations, the perturbed chaotic system can generate pseudo-random sequences with higher complexity and randomness, effectively improving the shortcomings of traditional chaotic systems such as low randomness and chaotic degradation. This active parameter perturbation strategy is particularly suitable for biomolecular communication scenarios because it can simulate the nonlinear perturbation characteristics in biochemical reaction environments. Therefore, researching misaligned secure communication of hyperchaotic systems under chaotic parameter perturbations is of great significance for constructing secure communication systems adapted to complex biological environments. The purpose of this invention is to propose a method and system for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution, which allows communication between arbitrary state variables of the driving system and the response system, and further enhances the confidentiality of the communication.

[0006] According to a first aspect of the present disclosure, a method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution is provided, comprising the following steps: Constructing hyperchaotic systems using DNA strand displacement reactions; The Chen hyperchaotic system is used as the parameter perturbation system. The parameter perturbation with hyperchaotic characteristics is applied to the hyperchaotic system, thereby improving the dynamic performance of the hyperchaotic system and constructing a response system with the same structure. A misalignment perturbation controller is designed based on DNA strand substitution reaction. A misalignment error system is defined. The error system is stabilized and parameter perturbation is compensated by the misalignment perturbation controller, thereby realizing the misalignment projection synchronization of a hyperchaotic system with parameter perturbation. Based on chaotic masking technology and relying on the misaligned projection synchronization mechanism under parameter perturbation, a secure communication scheme with dual hyperchaotic encryption is constructed to realize the misaligned transmission and decryption of biological signals.

[0007] According to a second aspect of the present disclosure, a misaligned projection synchronization and secure communication system for a parameterized perturbation hyperchaotic system based on DNA strand replacement is provided, comprising: A hyperchaotic system building module that utilizes DNA strand displacement reactions to construct hyperchaotic systems; The parameter perturbation module uses the Chen hyperchaotic system as the parameter perturbation system to apply parameter perturbation to the hyperchaotic system, and utilizes its hyperchaotic characteristics to further improve the dynamic performance of the hyperchaotic system, and constructs a response system with the same structure. The misaligned projection synchronization module designs a misaligned perturbation controller based on DNA strand substitution reaction, defines a misaligned error system, stabilizes the error system and compensates for parameter perturbations through the misaligned perturbation controller, and realizes misaligned projection synchronization of a hyperchaotic system with parameter perturbations. The secure communication module, based on chaotic masking technology and relying on the misaligned projection synchronization mechanism, constructs a secure communication scheme with dual hyperchaotic encryption to achieve misaligned transmission and decryption of biological signals.

[0008] According to a third aspect of the present disclosure, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the memory. When the processor executes the program, it implements the described method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand replacement.

[0009] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the described method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand replacement.

[0010] The advantages of the above technical solutions adopted in this invention compared with the prior art are as follows: 1. This invention realizes misaligned projection synchronization of hyperchaotic systems with parameter perturbation based on DNA strand substitution, allowing the state vector of the driving system to correspond to arbitrary responses. It breaks through the rigid limitation of one-to-one coupling of state variables in traditional chaotic synchronization, provides theoretical support for the flexible transmission of biological signals on arbitrary paths, and greatly improves the flexibility of signal transmission path selection in biological communication.

[0011] 2. This invention employs the Chen hyperchaotic system as the parameter perturbation system, effectively overcoming the shortcomings of traditional chaotic systems such as low randomness and low complexity. By actively perturbing parameters to simulate the nonlinear dynamic characteristics in biochemical reactions, the hyperchaotic system with introduced parameter perturbation exhibits better dynamic behavior, enabling the construction of more complex nonlinear environments for secure communication of biological signals and providing a superior system foundation for subsequent encryption.

[0012] 3. Based on chaotic masking technology, this invention further enhances the confidentiality of the communication system through dual hyperchaotic encryption. The proposed secure communication scheme, while achieving staggered transmission of biological signals, utilizes the hyperchaotic characteristics of the parameter perturbation system to perform secondary encryption on the driving signal. This makes the encrypted mixed signal more complex and more random, significantly improving the overall confidentiality performance of the system and effectively solving the problem of insufficient security level in biological signal transmission in traditional chaotic masking technology. Attached Figure Description

[0013] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0014] Figure 1 The image shows the DSD reaction diagram of the dual-catalytic chemical reaction module. Figure 2 DSD reaction diagram for the annihilation chemical reaction module; Figure 3 Lyapunov exponent diagram for a hyperchaotic system with fixed parameters; Figure 4 For the system to follow A changing Lyapunov bifurcation diagram; Figure 5 For the system Planar phase diagram; Figure 6 For the system Planar phase diagram; Figure 7 The graph shows the evolution of chaotic signal concentration in the driving and response systems. Figure 8 To create a phase diagram for the misaligned projection of the drive system and the response system; Figure 9 Two-dimensional planar phase diagrams for the driving system under different disturbance intensities; Figure 10 For error Concentration evolution graph; Figure 11 Here is a logic block diagram of a secure communication scheme; Figure 12 Initial signal Concentration evolution graph; Figure 13 State variables Evolution of encryption and decryption signal concentration; Figure 14 State variables Evolution of encryption and decryption signal concentration; Figure 15 Decryption signal when leakage occurs Concentration evolution graph; Figure 16 Decryption signal when leakage occurs Concentration evolution graph. Detailed Implementation

[0015] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0016] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0017] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0018] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of this disclosure. It should be noted that each block in a flowchart or block diagram may represent a module, segment, or portion of code, which may include one or more executable instructions for implementing the logical functions specified in the various embodiments. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutively represented blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, may be implemented using a dedicated hardware-based system that performs the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0019] Example 1: This embodiment provides a method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution, including the following steps: S1: Constructing a hyperchaotic system using DNA strand displacement reaction; Bimolecular chemical reactions are used to describe reaction processes such as dual catalysis and annihilation reactions, which can be used to construct hyperchaotic systems. Specifically, the emergent response is as follows:

[0020] in, The reaction rate; while maintaining the reactants , Under constant concentration conditions, both act as catalysts. The synthesis process; the dual-catalytic reaction can be achieved through the DSD reaction. The specific reaction pathway is as follows: DNA strand... Through pivot structure and auxiliary chain A chain displacement reaction occurs, releasing single chains. And form a double chain ; Because of the existence of the fulcrum, continue with A chain displacement reaction occurs, releasing the chain. as well as ;final With auxiliary chain Reaction, generation , , and byproducts Throughout the reaction process, the target product... The concentration of the catalyst continuously increases, while the concentration of the catalyst continuously increases. and The concentration remains in dynamic equilibrium. For example... Figure 1 As shown, the DSD reaction formula for the dual-catalytic reaction can be represented as:

[0021] in, and All are reaction rates. To assist in the initial concentration of DNA species, When the dual-catalytic reaction reaches equilibrium, the reaction rate... .

[0022] The annihilation reaction is:

[0023] in, Represents the annihilation rate. Reactants and The concentration decreases continuously as the reaction proceeds. For example... Figure 2 As shown, the annihilation reaction module can be implemented through the DSD reaction mechanism. The specific reaction path is as follows: as well as Molecular pairs of auxiliary substances and Degradation. Reaction kinetics have two scales: fast and slow. and Through with as well as The rapid reaction was isolated as an intermediate substance, while Through with The slow reaction degrades it into waste; and The initial concentration must be scaled by a factor of 2 to attenuate the isolation effect of rapid kinetics. The annihilation reaction DSD can be specifically represented as:

[0024] The fixed reaction rate of a hyperchaotic system is =36, =1, =20, =1, =3, =1, =0.2, =1. The differential dynamic equation of the hyperchaotic system is as follows:

[0025] in, , , , For the state variables of a hyperchaotic system, the corresponding CRNs are:

[0026] Figure 3 The Lyapunov exponent spectrum of the system under fixed parameters is presented. The system has two Lyapunov exponents greater than 0, fully demonstrating its hyperchaotic characteristics. To investigate the influence of different rates on the system's dynamics, [the following parameters are selected]. As a control parameter Figure 4 Draw the Lyapunov bifurcation diagram of the system. Figure 5 , Figure 6 A three-dimensional projection of the hyperchaotic attractor is described, and its complex structure indicates that the system has highly hyperchaotic properties.

[0027] S2: The Chen hyperchaotic system is used as the parameter perturbation system. The parameter perturbation is applied to the hyperchaotic system to keep the driving system in a hyperchaotic state, and a response system with the same structure is constructed. Specifically, the Chen hyperchaotic system is used as the parametric perturbation system. The Chen hyperchaotic system is a deterministic nonlinear dynamic system, and its complex hyperchaotic behavior can exert perturbations with dynamic nonlinear characteristics on it, thus characterizing the complex external perturbation properties. The differential dynamic equations of the Chen hyperchaotic system are as follows:

[0028] in, , , , The state variables of the parameter-perturbed system are: The specific driving system after applying the parameter perturbation is as follows:

[0029] in, For parameter perturbation. Using the hyperchaotic system as the driving system after adding parameter perturbation, select appropriate... This allows the driving system to remain in a hyperchaotic state. The corresponding isostructural response system is:

[0030] in, , , , The state variables of the response system; , , , These are the four control inputs for the misalignment disturbance controller.

[0031] S3: Design a misalignment perturbation controller based on DNA strand substitution reaction, define the misalignment error system, stabilize the error system and compensate for parameter perturbations through the misalignment perturbation controller, and realize the misalignment projection synchronization of a hyperchaotic system with parameter perturbations; Specifically, when the controller When designed as follows, the error respectively at exponential rates ( ), 、( ), The situation is trending towards stability.

[0032] Among them, the controller Feedback gain needs to be introduced. , Feedback gain Used to stabilize errors, and , .

[0033] In the DSD-based misaligned projection synchronization method, the correspondence between system state variables is no longer a simple one-to-one coupling pattern, but rather proportional projection synchronization is achieved through specific misaligned mappings. Therefore, the error system is defined as:

[0034] in, As a scale factor, , , , This refers to the error component of the error system. Adjustment is made within a certain range. The value of can flexibly control the synchronization relationship between the drive system and the response system. The defined error system differs from the traditional error system in that all state variables in the error system are constructed in a misaligned manner.

[0035] DNA-based misalignment projection synchronization is achieved by assigning corresponding CRNs to the misalignment disturbance controller. The CRNs are constructed as follows:

[0036] Misalignment Disturbance Controller The CRNs are constructed as follows:

[0037] Due to error respectively at exponential rates Converging to zero, choosing different This will determine the convergence rate of the error. This invention selects a larger [value / size]. This allows for fast synchronization; choosing a smaller [size / size]... This can reduce control costs, and designers can choose the appropriate gain according to actual needs. Misalignment disturbance controller The CRNs are constructed as follows:

[0038] Misalignment Disturbance Controller The CRNs are constructed as follows:

[0039] The effectiveness of the misalignment disturbance controller is verified based on the Lyapunov stability principle, and a positive definite function is selected. :

[0040] Obviously Differentiating the above equation, we get

[0041] in,

[0042] It can be seen that, It is a diagonal matrix, when ( ), 、( ), hour, ≤ According to Lyapunov stability theory, the error system is asymptotically stable, meaning that the driving and response systems achieve misaligned projection synchronization under the perturbation of the Chen hyperchaotic system. This is based on the diagonal matrix... It can be seen that even without using Lyapunov's stability theory for proof, it is possible to see... respectively at exponential rates ( ), 、( ), The system tends to stabilize. The nonlinear feedback design of DPC not only simplifies the structure of the error system, but also ensures that the system can stabilize to a synchronous state within the expected time by dynamically adjusting the decay rate of the error term.

[0043] Chaotic signals of the driving system and the corresponding system, such as Figure 7 As shown. When When the scaling factor is 0.5, the driving system and the response system achieve misaligned projection synchronization according to the magnitude of the scaling factor. When = 1, the chaotic signals of the driving system and the response system are completely consistent, achieving complete synchronization. The two-dimensional phase diagram of misaligned projection synchronization is as follows: Figure 8 As shown, it can be seen that there is a certain proportional relationship between the state variables of the driving system and the response system, and the two systems are scaled by a scaling factor. The size is adjusted to achieve synchronized misaligned projection.

[0044] Depend on Figure 9 It is evident that under the influence of parameter perturbation, hyperchaotic systems exhibit more unpredictable chaotic behavior. Due to the hyperchaotic nature of parameter-perturbation systems, the system after introducing parameter perturbation exhibits better dynamic behavior, which can provide good encryption effects for secure communication of biosignals.

[0045] like Figure 10 As shown, the evolution process of misaligned projection synchronization error, state vector , , as well as According to the scaling factor The magnitude of the error is quickly matched with the synchronization. The error system converges to zero, demonstrating the feasibility and effectiveness of the misaligned projection synchronization strategy.

[0046] S4: Based on chaotic masking technology and relying on the misaligned projection synchronization mechanism, a secure communication scheme with dual hyperchaotic encryption is constructed to realize the misaligned transmission and decryption of biological signals and improve the confidentiality of the communication system.

[0047] like Figure 11 As shown, the state variables of the hyperchaotic system are selected. With the initial signal Composition of driving signals ,Right now Its CRNs are:

[0048] in, As a scale factor, =0.5; This is the scaling factor. =0.5; Using a hyperchaotic system as a parameter perturbation is more conducive to the generation of complex dynamic behaviors in the system. To further improve the security of secure transmission of biosignals, the state variables of the parameter perturbation system are selected and nonlinearly combined to obtain... .right The following superposition yields the result. :

[0049] in, , .0045, .0055. State variable and There exists a misaligned mapping ratio relationship, that is... As a sending system, As a receiving system, it receives the mixed signal after nonlinear superposition. Join and In this context, its CRNs are represented as:

[0050] Send mixed signals The drive system is:

[0051] Receive mixed signals The response system is as follows:

[0052] Define the error system: , , , Similarly, based on Lyapunov stability theory, the errors of the driving and response systems can be obtained. respectively at exponential rates ( ), 、( ), Asymptotic stability is achieved. At this point, the drive system and response system achieve misaligned projection synchronization. The initial signal decryption process is based on the error system. For example. First, based on the parameter values ​​of the parameter perturbation system (18), the species Initial concentration, and Restore drive signal Subsequently, based on the misalignment mapping ratio between the driving system and the response system, when At that time, The drive system decrypts the useful signal based on this mapping ratio. If other state variables are selected to form the driving signal, the decryption process is similar to the steps described above, but the mapping ratio should be consistent with the relationship defined in the error system. While achieving misaligned transmission of biological signals, the secure communication scheme utilizes the hyperchaotic characteristics of the parameter perturbation system to perform secondary encryption on the driving signal. The encrypted hybrid signal has a more complex form, significantly improving the overall security performance of the system.

[0053] To verify the feasibility and effectiveness of the secure communication scheme, biological signals were analyzed. , , , Encryption and decryption are performed. Initial signal. , , like Figure 12 As shown, Figure 13 (a) is determined by state variables With the initial signal Constructed driving signal , Figure 13 (b) is the mixed signal encrypted by chaotic perturbation. , Figure 13 (c) is the decryption signal The DPSC scheme improves upon chaotic masked communication methods by leveraging the hyperchaotic characteristics of parameter-perturbed systems to enhance the security level of communication systems. The driving signal, after being encrypted using misaligned perturbation, possesses a more complex form and a more uniform spectral distribution, effectively improving the security performance of the encryption.

[0054] To further illustrate the effectiveness of the secure communication scheme, state variables are selected. With the initial signal Composed of driving signals . Figure 14 (a) is a state variable With the initial signal Constructed driving signal Chaotic masking encryption of the driving signal and Superimposed, = To obtain a mixed signal . Figure 14 (b) is Mixed signal after double encryption Simulation results show that mixed signals The form is also different from the drive signal More complex. Decrypting the signal. like Figure 14 As shown in (c), the receiver can accurately recover the signal without distortion.

[0055] To test the system's robustness to leakage responses, two sets of leakage responses were introduced into the system, treated as disturbances. For example... Figure 15 As shown, the decryption signal After being interfered with, although the decryption signal There were some fluctuations, but overall the original transmission signal was still largely restored. Figure 16 It can be seen that the decryption signal Even after being interfered with, the system can still largely recover valid information. This indicates that even with a leakage reaction, the system can still maintain a certain level of functionality and stability.

[0056] In this invention, the misaligned projection synchronization control method and the chaotic masking encryption method are applied to the field of biomolecules, which can realize misaligned projection synchronization and secure communication of a parameter-perturbed hyperchaotic system based on DNA strand substitution.

[0057] Example 2: This embodiment provides a misaligned projection synchronization and secure communication system for a parameterized perturbation hyperchaotic system based on DNA strand substitution, including: A hyperchaotic system building module that utilizes DNA strand displacement reactions to construct hyperchaotic systems; The parameter perturbation module uses the Chen hyperchaotic system as the parameter perturbation system, applies parameter perturbation to the hyperchaotic system to keep the driving system in a hyperchaotic state, and constructs a response system with the same structure. The misaligned projection synchronization module designs a misaligned perturbation controller based on DNA strand substitution reaction, defines a misaligned error system, stabilizes the error system and compensates for parameter perturbations through the misaligned perturbation controller, and realizes misaligned projection synchronization of a hyperchaotic system with parameter perturbations. The secure communication module, based on chaotic masking technology and relying on the misaligned projection synchronization mechanism, constructs a secure communication scheme with dual hyperchaotic encryption to achieve misaligned transmission and decryption of biological signals.

[0058] Example 3: An electronic device includes a memory, a processor, and a computer program stored in the memory and running thereon. When the processor executes the program, it implements the aforementioned method for synchronizing misaligned projections and secure communication in a parameterized perturbation hyperchaotic system based on DNA strand replacement, comprising: Constructing hyperchaotic systems using DNA strand displacement reactions; The Chen hyperchaotic system is used as the parameter perturbation system. The parameter perturbation is applied to the hyperchaotic system to keep the driving system in a hyperchaotic state, and a response system with the same structure is constructed. A misalignment perturbation controller is designed based on DNA strand substitution reaction. A misalignment error system is defined. The error system is stabilized and parameter perturbation is compensated by the misalignment perturbation controller, thereby realizing the misalignment projection synchronization of a hyperchaotic system with parameter perturbation. Based on chaotic masking technology and relying on the misaligned projection synchronization mechanism, a secure communication scheme with dual hyperchaotic encryption is constructed to realize the misaligned transmission and decryption of biological signals.

[0059] Example 4: A computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand replacement, comprising: Constructing hyperchaotic systems using DNA strand displacement reactions; The Chen hyperchaotic system is used as the parameter perturbation system. The parameter perturbation is applied to the hyperchaotic system to keep the driving system in a hyperchaotic state, and a response system with the same structure is constructed. A misalignment perturbation controller is designed based on DNA strand substitution reaction. A misalignment error system is defined. The error system is stabilized and parameter perturbation is compensated by the misalignment perturbation controller, thereby realizing the misalignment projection synchronization of a hyperchaotic system with parameter perturbation. Based on chaotic masking technology and relying on the misaligned projection synchronization mechanism, a secure communication scheme with dual hyperchaotic encryption is constructed to realize the misaligned transmission and decryption of biological signals.

[0060] Those skilled in the art will understand that the modules or steps described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, which can then be stored in a storage device for execution by a computer device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. This disclosure is not limited to any particular combination of hardware and software.

[0061] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0062] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for synchronized misaligned projections and secure communication in a parametrically perturbed hyperchaotic system based on DNA strand substitution, characterized in that: Includes the following steps: Constructing hyperchaotic systems using DNA strand displacement reactions; The Chen hyperchaotic system is used as the parameter perturbation system. Parameter perturbation is applied to the hyperchaotic system, and a response system with the same structure is constructed. A misalignment perturbation controller is designed based on DNA strand substitution reaction. A misalignment error system is defined. The error system is stabilized and parameter perturbation is compensated by the misalignment perturbation controller, thereby realizing the misalignment projection synchronization of a hyperchaotic system with parameter perturbation. Based on chaotic masking technology and relying on the misaligned projection synchronization mechanism under parameter perturbation, a secure communication scheme with dual hyperchaotic encryption is constructed to realize the misaligned transmission and decryption of biological signals.

2. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 1, characterized in that, The differential dynamic equations of the hyperchaotic system are as follows: ； The corresponding CRNs are: ； in, , , , The four state variables represent the hyperchaotic system; , , , , , , , Represents the fixed reaction rate of a hyperchaotic system; "+" and "-" superscripts are used to distinguish the positive and negative components of reactants; It represents the annihilation of waste.

3. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 1, characterized in that, The differential dynamic equations of the Chen hyperchaotic system are as follows: ； in, , , , These are the four state variables of the Chen hyperchaotic system; the driving system after applying parameter perturbations is specifically as follows: ； in, To represent the parameter perturbation term; The disturbance intensity is determined by selecting a suitable parameter. The Chen hyperchaotic system is treated as a parametric disturbance system. The driving system remains in a hyperchaotic state; the corresponding isomorphic response system is: ； in, , , , These are the four state variables of the response system, which have the same structure as the driving system. , , , It is a control input item in the response system.

4. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 1, characterized in that, The misalignment disturbance controller for: ； in, , , , These are the four control inputs of the misalignment disturbance controller; controller Feedback gain needs to be introduced. , Feedback gain Used to stabilize errors, and , ; is the scale factor.

5. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 1, characterized in that, The error system is defined as: ； in, These are the four error components of the error system. is the scale factor.

6. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 1, characterized in that, To construct a secure communication scheme with dual hyperchaotic encryption, specifically: select the state variables of the hyperchaotic system. With the initial signal Composition of driving signals ,Right now Its CRNs are: ； in, As a scale factor, The scaling factor is used; the state variables of the perturbation system are selected by nonlinear combination to obtain the scaling factor. ;right The following superposition yields the result. : ； in, For the process Superimposed encrypted mixed signal, , , State variables and There exists a misaligned mapping ratio relationship, that is... As a transmission system, As a receiving system.

7. The method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to claim 6, characterized in that, The mixed signal after nonlinear superposition Join and In this context, its CRNs are represented as: ； Send mixed signals The drive system is: ； Receive mixed signals The response system is as follows: ； The "+" and "-" superscripts are used to distinguish the positive and negative components of the reactants.

8. A system for synchronized misaligned projections and secure communication of a parametrically perturbed hyperchaotic system based on DNA strand substitution, characterized in that: include: A hyperchaotic system building module that utilizes DNA strand displacement reactions to construct hyperchaotic systems; The parameter perturbation module uses the Chen hyperchaotic system as the parameter perturbation system, applies parameter perturbation to the hyperchaotic system, and constructs a response system with the same structure. The misaligned projection synchronization module designs a misaligned perturbation controller based on DNA strand substitution reaction, defines a misaligned error system, stabilizes the error system and compensates for parameter perturbations through the misaligned perturbation controller, and realizes misaligned projection synchronization of a hyperchaotic system with parameter perturbations. The secure communication module, based on chaotic masking technology and relying on the misaligned projection synchronization mechanism under parameter perturbation, constructs a secure communication scheme with dual hyperchaotic encryption to achieve misaligned transmission and decryption of biological signals.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and running thereon, characterized in that, When the processor executes the program, it implements the method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for misaligned projection synchronization and secure communication of a parameterized perturbation hyperchaotic system based on DNA strand substitution according to any one of claims 1-7.

Images