High-dimensional chaotic key stream generation method and device based on closed-loop dynamic parameter control, storage medium and data chaotic encryption method

Abstract

The invention discloses a high-dimensional chaotic key stream generation method and device based on closed-loop dynamic parameter control, a storage medium and a data chaotic encryption method. In the key stream generation method, multiple iterative mapping is performed on respective initial values through multi-stage one-dimensional chaotic mapping, and control parameters of next-stage one-dimensional chaotic mapping iteration are formed based on input of each stage of one-dimensional chaotic mapping through transformation operation. And forming a control parameter of the first-stage one-dimensional chaotic mapping iteration based on the input of the last-stage one-dimensional chaotic mapping. The device and the storage medium are used for implementing the key stream generation method. In the data chaotic encryption method, a high-dimensional chaotic key stream is generated based on the high-dimensional chaotic key stream generation method, a key is obtained based on the high-dimensional chaotic key stream, and the key and a plaintext are subjected to XOR operation to obtain chaotic encryption data. According to the method, the high-dimensional chaotic key stream under any-dimensional chaotic mapping can be constructed, the chaotic performance is remarkably improved, and the hardware cost is low.

Description

Technical Field

[0001] This invention relates to the field of chaotic data encryption methods, specifically a method, device, storage medium, and chaotic data encryption method for generating high-dimensional chaotic key streams based on closed-loop dynamic parameter control. Background Technology

[0002] With the rapid development of internet information technology, the network threats to data security are constantly escalating, placing higher demands on the complexity and robustness of chaotic systems. Due to their initial value sensitivity and pseudo-randomness, chaotic systems are widely used in information encryption and secure communication. Discrete chaotic systems, in particular, are well-suited for pseudo-random number generation and information encryption scenarios due to their ease of digital implementation and strong anti-interference capabilities. While existing classic discrete chaotic maps (such as one-dimensional Logistic, Sine, and Tent maps, and two-dimensional Hénon maps) are mathematically simple and easy to implement in hardware, they suffer from low complexity and narrow, discontinuous chaotic parameter domains, making applications based on such systems vulnerable to attacks.

[0003] To improve chaotic performance, existing technical literature [Zhongyun Hua, Yicong Zhou, "Dynamicparameter-control chaotic system," IEEE Transactions on Cybernetics, vol. 46, no. 12, pp. 3330 - 3341, 2016. [IF: 7.384 / 2016, JCR: Q1]] proposes a Dynamic Parameter Modulation Chaotic System (DPCCS). The core idea of ​​this paper is to select multiple one-dimensional chaotic maps as seed maps and dynamically adjust the parameters of the target one-dimensional chaotic map using the outputs of the preceding seed maps. Specifically, taking "Logistic Map Controlling Sine Map (LCS)" as an example, the output sequence of the Logistic map is linearly scaled and used as the parameter input for the Sine map, achieving enhanced chaotic behavior through unidirectional parameter adjustment. This research mainly aims to improve the complexity of one-dimensional chaotic systems and can adapt to pseudo-random number generation scenarios, but it suffers from the following problems when practically applied to data encryption:

[0004] 1. Dimensional limitation: The DPCCS in this paper can only generate one-dimensional chaotic systems, which cannot meet the requirements of high-dimensional chaotic mapping (such as two-dimensional and three-dimensional) for multiple degrees of freedom and complex topological structures. High-dimensional systems are more likely to exhibit hyperchaotic characteristics and have higher security.

[0005] 2. Insufficient robustness: The DPCCS in this paper is prone to getting stuck in periodic orbits in some parameter ranges (such as when the control mapping output is a limit cycle, the target mapping parameters are easily fixed to finite values), and cannot maintain stable chaotic behavior in the full parameter domain;

[0006] 3. Narrow chaotic domain: The chaotic domain of the DPCCS in this paper depends on the original chaotic interval of the seed mapping. After parameter adjustment, the expansion of the chaotic domain is limited, making it difficult to cover a wide range of parameter scenarios.

[0007] 4. Low flexibility: The control parameter regulation in this paper lacks a closed-loop feedback mechanism. The preceding seed mapping only affects the target mapping in one direction, and it is impossible to further enhance the parameter uncertainty through closed-loop interaction, thus limiting the improvement of system complexity. Summary of the Invention This invention provides a method, device, storage medium, and data chaotic encryption method for generating high-dimensional chaotic key streams based on closed-loop dynamic parameter control, in order to solve the problems of dimensional limitation, low complexity, narrow chaotic domain, and insufficient robustness of existing DPCCS systems when applied to data encryption.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control, employing a total One-dimensional chaotic mapping and The level transformation operation inputs initial values ​​to each level of the one-dimensional chaotic mapping, and each level of the one-dimensional chaotic mapping performs a transformation on its respective initial values. The iterative mapping, and through Level transformation operation closed-loop dynamic control of each level of one-dimensional chaotic mapping Control parameters during the next iteration of mapping , In total One-dimensional chaotic mapping of level The process of this iteration of mapping is as follows:

[0010] During the first iteration of the mapping, the... The initial value of the input to the first-order one-dimensional chaotic map is obtained through the first... The first-order transformation operation yields the second-order transformation. The control parameters for the first iteration of a one-dimensional chaotic mapping; The initial value of the input to the first-order one-dimensional chaotic map is obtained through the first... The first-level one-dimensional chaotic mapping is transformed to obtain the control parameters for the first iteration of the first-level one-dimensional chaotic mapping. Each level of one-dimensional chaotic mapping is then iterated on its initial value under the control parameters for its first iteration, resulting in the first chaotic value.

[0011] The first iteration after the mapping At +1 iteration mapping, Each level of one-dimensional chaotic mapping is based on its own first... The chaotic value obtained from the nth iteration mapping is used as its own nth iteration mapping value. The input during the +1st iteration of the mapping; the first The first level of a one-dimensional chaotic mapping input itself The chaotic value obtained from the nth iteration mapping is passed through the nth iteration mapping. The first-order transformation operation yields the second-order transformation. One-dimensional chaotic mapping of level 1 Control parameters during the +1st iteration mapping; the... The first-order chaotic mapping input itself. The chaotic value obtained from the nth iteration mapping is passed through the nth iteration mapping. The first-order transformation operation yields the first-order one-dimensional chaotic map, which is then used for the second-order transformation operation. The control parameters during the iteration mapping; each level of one-dimensional chaotic mapping is respectively in its respective... Under the control parameters of the next iteration mapping, the input of each itself is... The chaotic value obtained from the nth iteration mapping is then processed by the nth iteration mapping. +1 iterations of mapping yield the th... +1 chaos value;

[0012] Finally, each level of one-dimensional chaotic mapping outputs the total. The chaotic value obtained from the next iteration of mapping is based on the total The chaotic values ​​constitute a high-dimensional chaotic key stream.

[0013] Furthermore, each level of one-dimensional chaotic mapping is any one of the Logistic mapping, Sine mapping, and Tent mapping.

[0014] Furthermore, All one-dimensional chaotic maps of the same order use the same one-dimensional chaotic mapping function.

[0015] Furthermore, Different one-dimensional chaotic mapping functions are used for each level of one-dimensional chaotic mapping.

[0016] Furthermore, In a first-order one-dimensional chaotic mapping, at least the first-order one-dimensional chaotic mapping uses a different one-dimensional chaotic mapping function than the one-dimensional chaotic mapping functions used in other-order one-dimensional chaotic mappings.

[0017] Furthermore, each level of transformation operation is a linear transformation operation.

[0018] Furthermore, the linear transformation includes two linear operations: shifting and scaling.

[0019] An electronic device includes a processor and a memory, wherein program instructions in the memory are read and executed by the processor to perform the above-described high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control.

[0020] A storage medium storing program instructions, which, when read and executed, perform the above-described high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control.

[0021] A chaotic data encryption method, the process is as follows:

[0022] Step S1: Obtain plaintext and generate a high-dimensional chaotic key stream according to the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control described above, and generate a chaotic key based on the high-dimensional chaotic key stream.

[0023] Step S2: Perform operations on the chaotic key and the plaintext to form chaotic encrypted data.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] 1. Dimensional Breakthrough and Universality: It can construct high-dimensional chaotic key streams under chaotic mapping of arbitrary dimensions (two-dimensional, three-dimensional and higher-dimensional), which solves the limitation of existing technologies that can only generate one-dimensional or low-dimensional key streams, and adapts to application scenarios with different complexities (such as two-dimensional for image encryption and three-dimensional for video encryption).

[0026] 2. Significantly improved chaotic performance: The method for generating key streams in this invention has a wide chaotic domain and high complexity (the average maximum LEs of the new system is 25%-30% higher than that of seed mapping), and 15%-20% higher than that of the existing technology DPCCS (e.g., the average LEs of 3D LST mapping is 1.12, while that of DPCCS is 0.89).

[0027] 3. Low hardware cost: In the method for generating the key stream of this invention, the iterative process is based on linear transformation and classical seed mapping, without complex nonlinear operations, and the hardware implementation cost is lower than that of cascaded chaotic systems.

[0028] 4. Information encryption adaptability: The high-dimensionality and high-complexity characteristics expand the system key space (e.g., the key space of a three-dimensional system is more than 10³ times larger than that of a one-dimensional DPCCS), significantly improving the resistance to brute-force attacks, and making it suitable for high-strength encryption scenarios such as financial data and military communications. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the chaotic system architecture based on the closed-loop dynamic parameter control method in this embodiment of the invention.

[0030] Figure 2The diagrams shown are dynamic analysis results of three chaotic systems constructed by the same seed mapping in this embodiment of the invention, wherein: (a) is the bifurcation diagram of the LL mapping; (b) is the bifurcation diagram of the SS mapping; (c) is the bifurcation diagram of the TT mapping; (d) is the maximum LE of the LL mapping; (e) is the maximum LE of the SS mapping; (f) is the maximum LE of the TT mapping; (g) is the phase diagram of the LL mapping; (h) is the phase diagram of the SS mapping; and (i) is the phase diagram of the TT mapping.

[0031] Figure 3 These are the dynamic analysis results of three chaotic systems constructed using different seed mappings according to embodiments of the present invention, where: (a) is the bifurcation diagram of the LS mapping; (b) is the bifurcation diagram of the LT mapping; (c) is the bifurcation diagram of the ST mapping; and (d) is the bifurcation diagram of the LS mapping. (e) is the LT mapping. (f) is the ST mapping. (g) is the LS-mapped phase diagram; (h) is the LT-mapped phase diagram; (i) is the ST-mapped phase diagram.

[0032] Figure 4 This is a dynamic behavior diagram of the LST mapping initial value set to (0.2, 0.3, 0.4) in an embodiment of the present invention, as it varies with two parameters, where: (a) is the parameter , and (a) A bifurcation diagram showing the changes; (b) shows the parameters. =0.13, following and The changing bifurcation diagram; (c) is the parameter. , and The bifurcation diagram of the change; (d) represents the parameters. , and changing (e) is a parameter =0.13, following and changing ;(f) is a parameter , and changing .

[0033] Figure 5 This is a dynamic behavior diagram of the LTS mapping initial value set to (0.2, 0.3, 0.4) in an embodiment of the present invention, as it varies with two parameters, where: (a) is the parameter , and (a) shows the changing bifurcation diagram; (b) shows the parameters. =0.5, following and (c) Parameters , and The bifurcation diagram of the change; (d) represents the parameters. , and changing (e) is a parameter =0.5, following and changing ;(f) is a parameter , and changing .

[0034] Figure 6 The three-dimensional system phase diagrams designed based on the CLDPC framework in this embodiment of the invention are shown, wherein: (a) is an LST mapping phase diagram; and (b) is an LTS mapping phase diagram.

[0035] Figure 7 These are the maximum LE simulation results of each chaotic system as parameters change in the embodiments of the present invention. The brown and light blue trajectories represent the seed mapping simulation results, the dark blue trajectory is the maximum LE simulation of DPCCS, and the red trajectory is the maximum LE simulation of CLDP chaotic system. Among them: (a) is the comparison of LL mapping with other mappings; (b) is the comparison of SS mapping with other mappings; (c) is the comparison of TT mapping with other mappings; (d) is the comparison of LS mapping with other mappings; (e) is the comparison of LT mapping with other mappings; (f) is the comparison of ST mapping with other mappings; (g) is the comparison of SL mapping with other mappings; (h) is the comparison of TL mapping with other mappings; and (i) is the comparison of TS mapping with other mappings.

[0036] Figure 8 This is a comparison chart of the maximum LE average values ​​of the DPCCS and CLDPC chaotic systems in the implementation of this invention.

[0037] Figure 9 This is the simulation result of LST mapping image encryption in the implementation of this invention. Detailed Implementation

[0038] To enable those skilled in the art to better understand the present invention, the embodiments will be described in detail below with reference to the accompanying drawings and examples. This will allow for a full understanding of how the present invention uses technical means to solve technical problems and achieve corresponding technical effects, and to facilitate its implementation. The embodiments of the present invention and the various features within them can be combined with each other without conflict, and all resulting technical solutions are within the protection scope of the present invention.

[0039] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0040] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims, and accompanying drawings of this invention are intended to cover non-exclusive inclusion.

[0041] Example 1

[0042] This embodiment discloses a method for generating high-dimensional chaotic key streams based on closed-loop dynamic parameter control, the process of which is as follows:

[0043] Step 1: Construct a chaotic system based on the Closed Loop Dynamic Parameter Control (CLDPC) method. For example... Figure 1 As shown, this CLDPC-based chaotic system has a total One-dimensional chaotic mapping function and total Linear transformation operation function , One-dimensional chaotic mapping is also known as seed mapping.

[0044] Step 2, to the total One-dimensional chaotic mapping function Enter their respective initial values. , ... Each level of the chaotic mapping function performs its own initial value... Sub-iteration mapping That is, the first-order one-dimensional chaotic mapping function. For initial values Perform the total Sub-iterative mapping, second-order one-dimensional chaotic mapping function For initial values Perform the total The next iteration of the mapping, and so on... One-dimensional chaotic mapping function For initial values Perform the total This is the iterative mapping. And, in total... Each of the first-order one-dimensional chaotic mapping functions is performed separately. During the next iteration of the mapping process, through The operations of the level transformation function are used to perform closed-loop dynamic control of each level of one-dimensional chaotic mapping. Control parameters during the next iteration of mapping.

[0045] Total One-dimensional chaotic mapping function of order The process of this iteration of mapping is as follows:

[0046] During the first iteration of the mapping, the... The initial value of the input to the first-order one-dimensional chaotic mapping function is obtained through the first-order one-dimensional chaotic mapping function. The first-order transformation operation function is used to perform the operation to obtain the second-order transformation. The control parameters of the first-order one-dimensional chaotic mapping function during the first iteration mapping; The initial value of the input to the first-order one-dimensional chaotic mapping function is obtained through the first-order one-dimensional chaotic mapping function. The first-level transformation operation function is used to perform the operation, and the control parameters are obtained when the first-level one-dimensional chaotic mapping function performs the first iteration mapping.

[0047] That is, during the first iteration of the mapping, the first-level one-dimensional chaotic mapping function Initial input value Through the first Level Transformation Operation Function The operation yields the second-order one-dimensional chaotic mapping function. Control parameters during the first iteration of mapping Second-order one-dimensional chaotic mapping function Initial input value Through the second-level transformation operation function The operation yields the third-order one-dimensional chaotic mapping function. Control parameters during the first iteration of mapping And so on. One-dimensional chaotic mapping function Initial input value Through the first Level Transformation Operation Function Perform the calculation to obtain the first... One-dimensional chaotic mapping function Control parameters during the first iteration of mapping Furthermore, the first One-dimensional chaotic mapping function Initial input value Through the first Level Transformation Operation Function The calculation yields the first-order one-dimensional chaotic mapping function. Control parameters during the first iteration of mapping .

[0048] Therefore, during the first iteration of the mapping, the total One-dimensional chaotic mapping function Control parameters during their respective first iteration mapping , , ... Next, the initial values ​​are mapped using the first iteration to obtain the first chaotic value. That is:

[0049] First-order one-dimensional chaotic mapping function Control parameters during the first iteration of mapping Below, for the initial value Perform the first iterative mapping to obtain the first chaotic value. Second-order one-dimensional chaotic mapping function Control parameters during the first iteration of mapping Below, for the initial value Perform the first iterative mapping to obtain the first chaotic value. Third-order one-dimensional chaotic mapping function Control parameters during the first iteration of mapping Below, for the initial value Perform the first iterative mapping to obtain the first chaotic value. And so on, the first... One-dimensional chaotic mapping function Control parameters during the first iteration of mapping Below, for the initial value Perform the first iterative mapping to obtain the first chaotic value. .

[0050] The first iteration after the mapping At +1 iteration mapping, Each level of the one-dimensional chaotic mapping function is based on its own first... The chaotic value obtained from the nth iteration mapping is used as its own nth iteration mapping value. The input at +1 iteration of the mapping. That is, the first-level one-dimensional chaotic mapping function. Conduct the first During the +1 iteration mapping, with its own... Chaotic values ​​obtained from the next iteration of mapping As input. Second-order one-dimensional chaotic mapping function. Conduct the first During the +1 iteration mapping, with its own... Chaotic values ​​obtained from the next iteration of mapping As input. And so on, the... One-dimensional chaotic mapping function Conduct the first During the +1 iteration mapping, with its own... Chaotic values ​​obtained from the next iteration of mapping As input.

[0051] And the first iteration of the mapping During the +1st iteration of the mapping, the th The input of the first-order one-dimensional chaotic mapping function is itself. The chaotic value obtained from the nth iteration mapping is passed through the nth iteration mapping. The first-order transformation operation function is used to perform the operation to obtain the second-order transformation. The first-order one-dimensional chaotic mapping function is used for the first time. Control parameters during the +1st iteration mapping; the... The input of the first-order chaotic mapping function is itself. The chaotic value obtained from the nth iteration mapping is passed through the nth iteration mapping. The first-order one-dimensional chaotic mapping function is obtained by performing the first-order transformation operation. Control parameters during the next iteration of mapping.

[0052] That is, the first iteration after the mapping At the +1 iteration of the mapping, the first-level one-dimensional chaotic mapping function The input of itself Chaotic values ​​obtained from the next iteration of mapping Through the first-level transformation operation function The operation yields the second-order one-dimensional chaotic mapping function. Conduct the first Control parameters during +1 iteration mapping Second-order one-dimensional chaotic mapping function The input of itself Chaotic values ​​obtained from the next iteration of mapping Through the second-level transformation operation function The operation yields the third-order one-dimensional chaotic mapping function for the second time. Control parameters during +1 iteration mapping And so on, the first One-dimensional chaotic mapping function The input of itself Chaotic values ​​obtained from the next iteration of mapping Through the first Level Transformation Operation Function The operation yields the first... One-dimensional chaotic mapping function Conduct the first Control parameters during +1 iteration mapping Furthermore, the first First-order first-dimensional chaotic mapping function The input of itself Chaotic values ​​obtained from the next iteration of mapping Through the first Level Transformation Operation Function The calculation yields the first-order one-dimensional chaotic mapping function. Conduct the first Control parameters during the next iteration of mapping .

[0053] Therefore, the first iteration after the mapping... +1 iterations of mapping, total One-dimensional chaotic mapping function In their respective numbers Control parameters of the next iteration mapping , ... Next, for each of them, input their own first... The chaotic value obtained from the nth iteration mapping is then processed by the nth iteration mapping. +1 iterations of mapping yield the th... The chaos value of +1. That is:

[0054] First-order one-dimensional chaotic mapping function In the Control parameters during the next iteration of mapping Next, regarding one's own first Chaotic values ​​obtained from the next iteration of mapping Conduct the first The nth iteration mapping yields the nth Chaos value of the second time Second-order one-dimensional chaotic mapping function In the Control parameters during the next iteration of mapping Next, regarding one's own first Chaotic values ​​obtained from the next iteration of mapping Conduct the first The nth iteration mapping yields the nth Chaos value of the second time Third-order one-dimensional chaotic mapping function In the Control parameters during the next iteration of mapping Next, regarding one's own first Chaotic values ​​obtained from the next iteration of mapping Conduct the first The nth iteration mapping yields the nth Chaos value of the second time And so on, the first... One-dimensional chaotic mapping function In the Control parameters during the next iteration of mapping Next, regarding one's own first Chaotic values ​​obtained from the next iteration of mapping Conduct the first The nth iteration mapping yields the nth Chaos value of the second time .

[0055] Ultimately, in this embodiment of the chaotic system based on CLDPC, each level outputs a one-dimensional chaotic map. The chaotic values ​​obtained from the iteration mapping are thus obtained in total. One chaotic value.

[0056] In this embodiment, the one-dimensional chaotic mapping function at each level is preferably any one of the Logistic mapping function, Sine mapping function, or Tent mapping function.

[0057] Logistic mappings, as first-order difference equations, are widely used in economics, social sciences, and biological sciences. Their functional expression is shown in equation (1) below:

[0058] (1)

[0059] In formula (1): For the input of the function; The chaotic value obtained from the mapping; The control parameters for the Logistic mapping. The system output is limited to the range Inside.

[0060] The Sine mapping is derived from the sine function, and mathematically, the expression of the Sine mapping function is shown in formula (2) below:

[0061] (2)

[0062] In formula (2): Control parameters for Sine mapping, control parameters .

[0063] The Tent mapping is a one-dimensional mapping that performs stretching and folding operations. The mathematical representation of the Tent mapping function is shown in the following formula (3):

[0064] (3)

[0065] In formula (3): These are the control parameters for Tent mapping. .

[0066] when At this point, the Logistic mapping is in a chaotic state. At this point, the Sine map exhibits chaotic dynamics. Observations reveal that both the Logistic and Sine maps show very small periodic windows in the chaotic domain. When the Tent mapping exhibits chaotic attractor behavior, the output value of the CLDPC-based chaotic system in this embodiment is irregular, provided that the corresponding control parameters are within the parameter range of the chaotic state, the parameter range exhibiting chaotic dynamics, or the parameter range exhibiting chaotic attractor behavior.

[0067] In this embodiment, All one-dimensional chaotic maps of order 1 use the same one-dimensional chaotic mapping function. Or Different one-dimensional chaotic mapping functions are used for different levels of one-dimensional chaotic mapping. Or In a first-order one-dimensional chaotic mapping, at least the first-order one-dimensional chaotic mapping uses a different one-dimensional chaotic mapping function than the one-dimensional chaotic mapping functions used in other-order one-dimensional chaotic mappings.

[0068] In this embodiment, we take the example where each level of one-dimensional chaotic mapping is any one of the Logistic mapping function, Sine mapping function, or Tent mapping function. When = 2, that is, when there is a two-level one-dimensional chaotic mapping, six two-dimensional chaotic mapping systems can be formed: LL mapping, SS mapping, TT mapping, LS mapping, LT mapping, and ST mapping, where L is the Logistic mapping function, S is the Sine mapping function, and T is the Tent mapping function. Similarly, when When =3, i.e., when there is a three-level one-dimensional chaotic mapping, this embodiment can form a variety of three-dimensional chaotic mapping systems, including LLT mapping, LLS mapping, LTT mapping, LSS mapping, TTS mapping, TSS mapping, LTS mapping, and LST mapping. Similarly, when In step 3, this embodiment can form various types of N-dimensional chaotic mapping systems.

[0069] It should be noted that although this embodiment uses any one of the Logistic mapping function, Sine mapping function, and Tent mapping function for each level of one-dimensional chaotic mapping as an example, it does not mean that the use of other one-dimensional chaotic mapping functions is excluded for each level of one-dimensional chaotic mapping in this embodiment. Other one-dimensional chaotic mapping functions can also be used for each level of one-dimensional chaotic mapping in this embodiment. The technical solutions using other one-dimensional chaotic mapping functions based on this embodiment should also be considered to fall within the protection scope of this patent.

[0070] In this embodiment, Linear transformation operations Similarly, both operations use two linear operations, shift and scaling, to linearly transform the input chaotic value into control parameters. For the i-th linear transformation operation, its calculation is shown in formula (4):

[0071] (4)

[0072] In formula (4):: This is the i-th level seed mapping (i.e., a one-dimensional chaotic mapping). The output range; For the first Level seed mapping The range of parameters in the chaotic domain; for Parameters; This is a linear transformation function. The linear transformation shown in formula (4) is applied...

[0073] For ease of expression, the expression will be written as ,in:

[0074]

[0075]

[0076] The input for the nth iteration of the i-th seed mapping is the chaotic value obtained from the (n-1)th iteration of the i-th seed mapping. The parameters of each seed mapping change dynamically in each iteration. It is important to emphasize that the seed mappings can be the same or different chaotic mappings; any existing one-dimensional chaotic mapping can be used as a seed mapping in the CLDPC system. Choosing different seed mappings, or swapping the positions of two seed mappings, results in different high-dimensional chaotic mappings. Therefore, a very rich variety of high-dimensional chaotic systems can be constructed based on the proposed method.

[0077] LEs represents the exponential divergence of two very close trajectories of a dynamical system in the phase plane and is widely used to characterize chaos. Dynamical systems with at least one positive LEs value typically exhibit chaotic behavior. The dynamical behavior of the system designed in this embodiment depends on the parameters of the seed mapping, and the output value of the control mapping can be a fixed point, a limit cycle, or chaos.

[0078] In this embodiment, when controlling the (i-1)th level one-dimensional chaotic mapping When the output is a fixed point, the fixed output will be transformed into an i-th level one-dimensional chaotic mapping. Control parameter values ​​within the chaotic range The LE of a CLDPC system is equal to that of a one-dimensional chaotic mapping. In control parameters LE and one-dimensional chaotic mapping LE when generating a fixed point.

[0079] In this embodiment, when controlling a one-dimensional chaotic mapping The output limit cycle has a finite number of distinct points. A linear transformation is used to convert the value of the limit cycle into a one-dimensional chaotic map. Within the chaotic range. Due to the one-dimensional chaotic mapping of A finite number of outputs is a periodic point, as the number of iterations... As the number of points approaches infinity, the number of each point approaches ∞. Therefore, the LE value of the CPDPC system is calculated as follows: .

[0080] In this embodiment, when controlling a one-dimensional chaotic mapping When outputting a strange attractor, The output is dynamic and never repeats. At this point, the one-dimensional chaotic mapping after the linear transformation... Each iteration is a one-dimensional chaotic mapping. Different parameter settings are provided, making the iterative output of the CLDPC system more unpredictable.

[0081] In summary, this embodiment achieves a chaotic system by controlling the parameters of at least one seed mapping (i.e., a one-dimensional chaotic mapping) in the chaotic domain through linear transformation. Controlling the parameters of multiple seed mappings in the chaotic region makes it easier to obtain hyperchaotic and robust chaotic systems with superior performance.

[0082] Step 3: Obtain a chaotic system based on CLDPC for further processing. The total number of iterations of mapping obtained A chaotic value, based on A high-dimensional chaotic key stream is formed from several chaotic values.

[0083] Specifically, for The next iteration of the mapping process is discarded. The results of the first W iterations that are unstable are discarded. One chaotic value. Based on the previous W iterations. The result of -W iterations is Each chaotic value is scaled, offset, and then moduloed to obtain a positive number in the interval [0, 255]. Finally, the MATLAB built-in conversion function dec2bin.m is used to convert the values. The positive numbers corresponding to each chaotic value are converted into binary numbers, and all the binary numbers are concatenated end to end. The resulting binary sequence is the high-dimensional chaotic key stream.

[0084] The CLDPC-based chaotic system in this embodiment possesses exceptional flexibility, capable of constructing new chaotic systems using any N one-dimensional chaotic maps as seed maps. When constructing high-dimensional chaotic systems using classical maps, a rich variety of new systems can be generated based on different combinations and permutations of seed maps. This embodiment will analyze the dynamic behavior of CLDPC-based chaotic systems using six two-dimensional chaotic systems and two three-dimensional chaotic systems as examples.

[0085] 1. Two-dimensional chaotic system

[0086] Using the aforementioned classical mapping as a seed mapping, there are six different combinations for designing a two-dimensional chaotic system based on CLDPC. The Logistic-controlled Logistic mapping is denoted as the LL mapping; similarly, the others include the LL, SS, TT, LS, LT, and ST mappings. It should be noted that since the LT and TL mappings are the same type of mapping, the LT mapping will be used as an example in the following explanation.

[0087] Table 1 shows three chaotic systems constructed using two identical seed mappings and three chaotic systems constructed using different seed mappings. According to formula (4), the linear transformation introduces two new sets of parameters. and , respectively denoted as To simplify the discussion, let Analyze parameters The impact on the dynamic behavior of the new system. In discussing three systems constructed with the same seed mapping, we take... Discussion of parameters Impact on system performance. The impact of fixed parameters is discussed in three systems constructed with different seed mappings. The system follows Dynamics of change, and fixed parameters The system follows The dynamic behavior of the change. Table 1 is as follows:

[0088] Table 1. Six two-dimensional CLDPC chaotic systems constructed based on three classical chaotic maps.

[0089]

[0090] In dynamical systems, the Lyapunov exponents (LEs) describe the divergence of the iterative trajectories of two very close initial values ​​as they evolve over time. A positive Lyapunov exponent means that the difference between the two trajectories grows exponentially per unit time. This implies that no matter how small the difference between their initial values, the difference between the two trajectories always increases over time, causing their output values ​​to be completely different, exhibiting initial value sensitivity. If a dynamical system has at least one positive Lyapunov exponent, then the system is chaotic, and a larger Lyapunov value generally indicates better chaotic performance. Bifurcation plots depict the output sequence of the chaotic map as parameters change, helping to observe the transition of the system from ordered to chaotic behavior. Figure 2 This section presents a dynamic analysis of three chaotic systems constructed using the same seed mapping. Time system LL, SS, TT with parameters The changing bifurcation diagram and the maximum LE are shown respectively. Figure 2 (a)-2(c) and Figure 2 (d)-2(f)

[0091] Simulation results show that the selection of parameters has a significant impact on system performance. In subsequent comparative analysis, by fixing... Given constant values, analyze the three systems as follows: The changing dynamics will result in a significant improvement in system performance. When all initial values ​​are set to... System LL parameter values System SS parameter values System TT parameter value At that time, their phase trajectories are as follows: Figure 2 As shown in (g), 2(h), and 2(i), the distribution in phase space is more uniform compared to seed mapping.

[0092] To analyze the influence of parameters on the dynamic behavior of chaotic systems constructed based on different seed mappings, Figure 3 The following is given: (The last part is incomplete and likely refers to a different topic) and The bifurcation diagram of the changing system, the maximum Lyapunov exponent ( Simulation results show that systems LT and ST exhibit robust chaotic properties in a large planar parameter space. In contrast, system LS exhibits chaotic performance that is easily affected by parameter perturbations throughout the entire parameter range. When the parameter values ​​in Table 1 are set, the initial values ​​are set to... At that time, the phase trajectories of the system LS, LT, and ST are respectively as follows: Figure 3 As shown in (g), 3(h), and 3(i).

[0093] In summary, the dynamics of the two-dimensional chaotic system formed by the CLDPC-based chaotic system in this embodiment are closely related to the parameter settings. For three chaotic systems constructed with the same seed mapping, the chaotic domain remains unchanged when the two controlled parameters are the same. When the parameters are different, robust chaos can be obtained by setting appropriate parameters. For three chaotic systems constructed with different seed mappings, the new system LT, ST, when the parameters... When the value is small, The parameter range exhibits smooth and robust chaotic properties.

[0094] 2. Three-dimensional chaotic system

[0095] The three-dimensional chaotic systems designed using the CLDPC-based chaotic system in this embodiment are more diverse, including LLL, TTT, and SSS maps based on the same seed mapping; LLT, LLS, LTT, LSS, TTS, and TSS maps constructed based on two seed mappings; and LTS and LST maps with three seed mappings. For simplicity, the LST and LTS maps are used as examples to analyze the dynamic behavior of the three-dimensional chaotic systems designed using the CLDPC-based chaotic system in this embodiment.

[0096] Table 2 shows two three-dimensional CLDPC chaotic systems constructed based on three classical chaotic maps.

[0097] Table 2 presents the system equations for LST and LTS mappings. Parameter settings are also provided. LST mapping follows and The changing bifurcation diagram and Each as Figure 4 As shown in (a) and 4(d), it can be seen that the LST mapping is... The directional distribution is uniform, and in and The parameter domain exhibits robust chaotic properties over a wide range. Figure 4(b) and 4(e) respectively show the fixed When it is 0.13, it follows and The changing bifurcation diagram and As can be seen, the parameters Changes in the LST map have a significant impact on the dynamic behavior of the system. Approaching 0 and 1 exhibits better ergodicity and a larger LE. When fixed... At that time, the LST mapping follows the two parameters and The dynamics of change, such as Figure 4 As shown in (c) and 4(f), the system exhibits robust chaotic behavior across almost the entire parameter domain.

[0098] When analyzing the dynamic behavior of LTS mapping, the parameters in Table 2 are fixed sequentially. , and The value of is analyzed, and the bifurcation diagram is analyzed as it varies with the two parameters. The simulation results are as follows: Figure 5 As shown. From Figure 5 (a) and 5(d) show that the LTS mapping follows and It exhibits good ergodicity when changes occur. Figure 5 (e) Display when fixed At that time, LTS mapping throughout and The resulting planar parameter domain exhibits robust chaotic properties. When fixed... At that time, the LTS mapping varies with the two parameters. and The dynamics of change, such as Figure 5 As shown in (c) and 5(f), the system in and The interval exhibits large-scale chaotic behavior. Figure 6 (a) and (b) show the phase diagrams of the LST mapping and LTS mapping when the initial values ​​are set to (0.2, 0.3, 0.5) and (0.1, 0.3, 0.2) respectively, under the parameter settings in Table 2.

[0099] 3. Performance Analysis and Comparison

[0100] To verify that the chaotic system based on CLDPC in this embodiment has good chaotic performance, the six chaotic maps are compared with the seed maps that constitute the system and the DPCCS proposed in the literature [Hua ZY, Zhou YC 2015. IEEE Trans. Cybern., 46 pp3330-3341].

[0101] The core idea of ​​DPCCS proposed in the literature is that the outputs of multiple seed mappings dynamically control the parameters of a one-dimensional chaotic mapping, and the result is still a one-dimensional chaotic system. For simplicity, let's denote LCS as the control of the Sine mapping by the Logistic mapping in DPCCS, meaning that the parameters of the Sine mapping are controlled by the output of the Logistic mapping. Similarly, let's denote SCL as the control of the Logistic mapping by the Sine mapping, meaning that the parameters of the Logistic mapping are controlled by the output of the Sine mapping. It can be concluded that LCS and SCL designed based on the DPCCS framework are two completely different systems.

[0102] To maintain consistency in the comparative analysis, the LS-based chaotic system design based on CLDPC in this embodiment is used with fixed parameters in the Logistic mapping. When the parameters are constant and only the output of the Logistic mapping is considered to affect the Sine mapping parameters, it corresponds to the system LCS in DPCCS; when the parameters in the Sine mapping are fixed... When is a constant and only the influence of the Sine map output on the Logistic map parameters is considered, it corresponds to the system SCL in DPCCS. Similarly, LT can be obtained separately as fixed... Follow The dynamics of change (corresponding to LCT), and the fixed dynamics. Follow Dynamics of change (corresponding to TCL). System ST is fixed. Follow The dynamics of change correspond to SCT in DPCCS, which is fixed. Follow The dynamics of change correspond to TCS in DPCCS. For chaotic systems constructed with the same seed mapping, LL, SS, and TT are set respectively. For values ​​of 0.02, 0.05, and 0.1, the analysis was performed as a function of the parameter. The dynamic behavior of change.

[0103] Figure 7 The maximum LE (Leadership) of each system as a function of parameters, the LE of the seed mapping used to construct the system as a function of parameters, and the maximum LE of the DPCCS as a function of parameters are given. For ease of observation, Figure 7(a)-7(c) present the dynamic behavior of chaotic systems constructed with the same seed mapping. Figure 7 (d)-7(f) respectively present the kinetic behavior of LCS, LCT, and SCT, and the corresponding LS, LT, and ST fixed parameters. , The dynamic behavior of change. Figure 7 (g)-7(i) Dynamic behaviors of SCL, TCL, and TCS, and corresponding fixed parameters of LS, LT, and ST. , The dynamic behavior of change.

[0104] from Figure 8 Simulation results show that, compared to seed mapping (represented by brown and turquoise), both DPCCS (represented by dark blue) and CLDPC chaotic systems (represented by red) exhibit chaotic properties over a wide range of parameter intervals. However, DPCCS gets trapped in periodic orbits in some regions, while the CLDPC chaotic system exhibits very stable and robust chaotic properties across the entire parameter domain. This means that even under certain uncertainties or disturbances, the CLDPC chaotic system can still maintain its chaotic characteristics, making it more reliable in practical applications.

[0105] Furthermore, according to the properties of LE, a larger value means that the adjacent trajectories diverge more after iteration, and the better the chaotic performance. Figure 8 The average maximum LE of DPCCS and CLDPC systems in the chaotic domain was statistically analyzed. As can be seen from the table, the average maximum LE of each CLDPC chaotic system is larger than that of DPCCS, indicating that the new system has better complexity.

[0106] 4. Keystream and NIST SP 800-22 Statistical Tests

[0107] The NIST SP 800-22 statistical testing standard, published by the National Institute of Standards and Technology (NIST), is one of the most commonly used testing standards in the world. NIST SP 800-22 tests the balance, rate of change, periodicity, and linear complexity of a sequence to provide a reliable and comprehensive test of binary sequences. When all test results are greater than 0.001, the tested sequence is considered random.

[0108] To verify the good randomness of the chaotic sequences generated by the system, the two three-dimensional systems, LST and LTS mappings in Table 2, were used as representatives. MATLAB software was used to extract binary sequences from the chaotic signals and test them. First, the parameters were set to the values ​​in Table 2, with initial values ​​of (0.2, 0.3, 0.5) and (0.1, 0.3, 0.2), respectively, and the chaotic system was iterated. The results of the first 2000 unstable iterations were discarded, and the iteration data during subsequent stable oscillations were stored. Then, the chaotic values ​​obtained during subsequent stable oscillations were scaled, offset, and moduloed to obtain positive numbers in the interval [0, 255] corresponding to each chaotic value. Finally, the positive numbers were converted into binary numbers using the MATLAB built-in conversion function dec2bin.m, and all binary numbers were concatenated end-to-end to obtain a binary sequence, thus generating the corresponding chaotic keystream.

[0109] Finally, the randomness of the generated sequences was tested using the NIST SP 800-22 statistical test set. Table 3 shows that the P-values ​​of the keystreams from both chaotic systems were greater than 0.001 in all 15 tests, indicating that all sequences passed the randomness test and verifying their effectiveness as reliable random number generators. Table 3 is as follows:

[0110]

[0111] Note: An asterisk in Table 3 indicates that the average of all results is taken.

[0112] In summary, the high-dimensional chaotic keystream generation method based on closed-loop dynamic parameter control disclosed in this embodiment utilizes a CLDPC-based chaotic system to construct two-dimensional, three-dimensional, and higher-dimensional high-dimensional chaotic keystreams based on any number of one-dimensional seed mappings. Through closed-loop parameter tuning and linear transformation, it achieves a wider chaotic domain and higher complexity (manifested as a larger LEs value) when generating high-dimensional chaotic keystreams, avoiding getting trapped in periodic orbits. Furthermore, the key generation method of this invention simplifies the complexity of iterative equations while enhancing performance, avoiding a surge in computational hardware costs due to dimensionality increases.

[0113] In this embodiment, combinations of different seed mappings can generate a large number of new, high-performance chaotic mappings. Through closed-loop control between seed mappings, each seed mapping in the CLDPC chaotic system has a dynamic parameter in each iteration, making the system output sequence more irregular. This paper comprehensively analyzes the characteristics and chaotic behavior of the CLDPC system using the construction of two-dimensional and three-dimensional systems as examples. Comparative results show that these mappings have a larger chaotic range, better unpredictability, and more complex chaotic behavior than the corresponding seed mappings. Compared to the system constructed by DPCCS, the designed new system exhibits superior robust chaotic characteristics. Besides designing closed-loop dynamic parameter modulation systems based on multiple one-dimensional systems, this embodiment can also be extended to design closed-loop dynamic parameter modulation systems based on high-dimensional chaotic systems.

[0114] Example 2

[0115] This embodiment discloses an electronic device, including a processor and a memory. The program instructions in the memory are read and executed by the processor to perform steps 1-3 of the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control described in Embodiment 1.

[0116] This embodiment also discloses a storage medium that stores program instructions. When the program instructions are read and run, steps 1-3 of the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control described in Embodiment 1 are executed.

[0117] Example 3

[0118] This embodiment discloses a data chaotic encryption method, the process of which is as follows:

[0119] Step S1: Obtain plaintext and generate a high-dimensional chaotic key stream according to the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control as described in any one of claims 1-7, and generate a chaotic key based on the high-dimensional chaotic key stream.

[0120] Step S2: Perform operations on the chaotic key and the plaintext to form chaotic encrypted data.

[0121] The following example uses the pseudo-random sequence generated by the aforementioned LST three-dimensional chaotic mapping as the key, and combines pixel cross-confusion and XOR operation to implement encryption and decryption, further illustrating the encryption method of this embodiment.

[0122] 1. Encryption Algorithm Steps

[0123] Chaotic key generation: Initialize LST mapping parameters (u1=0.1, u2=0.13, u3=0.5) and initial values ​​(x0=0.2, y0=0.3, z0=0.5); discard the transient sequence of the first 3000 iterations, and take the three-dimensional chaotic values ​​generated in the next 10000 iterations to form a high-dimensional chaotic key stream. Extract one dimension from the high-dimensional chaotic key stream as the core sequence; take the fractional part of the core sequence, and then scale, modulo, and convert the type to generate a two-dimensional chaotic key matrix x that matches the image size.

[0124] Image preprocessing: Read the lena.jpeg image, obtain the image dimensions, and sort the image matrix to obtain the sorted image matrix g.

[0125] Pixel obfuscation and encryption: The pixel positions in the sorted image matrix g are cross-obfuscated using the formula mod(g(i,j)+g(j,i),256), thereby obtaining the intermediate matrix s;

[0126] Finally, perform an XOR operation (bitxor(x(i,j),s(i,j))) on the two-dimensional chaotic key matrix x and the intermediate matrix s to obtain the chaotic encrypted image p, save and display the result.

[0127] 2. Decryption Algorithm Steps

[0128] Key synchronization generation: The decryption end uses the same LST mapping parameters, initial values ​​and iteration rules as the encryption end to regenerate the same two-dimensional chaotic key matrix x (the determinism of the chaotic system ensures key synchronization).

[0129] Reverse decryption operation: Perform an XOR operation on the chaotic encrypted image p and the two-dimensional chaotic key x (the XOR operation is invertible, bitxor(p(i,j),x(i,j))) to restore the intermediate matrix s; reverse pixel cross-obfuscation is achieved by using the formula mod(s(i,j)-g(j,i),256) to restore the sorted image matrix g; finally, the image pixel positions are restored according to the original sorting rules to obtain the decrypted image g_rec.

[0130] Figure 9The simulation results sequentially display the original Lena image, the encrypted image, the correctly decrypted image, and the incorrectly decrypted image obtained when the initial values ​​were set to (0.2001, 0.3, 0.5). The simulation results show that the encrypted image exhibits uniform noise and completely loses the visual features of the original image. When the initial value x_0 of the LST system is slightly perturbed (changed from 0.2 to 0.2001), the difference rate of the encrypted image is close to 1 (0.9959), indicating that the algorithm is extremely sensitive to the key (initial value) and can effectively resist brute-force and differential attacks. The average grayscale change after encryption is 9.2085, and the correlation between adjacent pixels is 0.0212. Quantitative indicators and key sensitivity analysis show that the algorithm combines security, stability, and efficiency, and can meet the privacy protection requirements during image storage and transmission.

[0131] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0132] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A method for generating high-dimensional chaotic key stream based on closed-loop dynamic parameter control, characterized in that, a total of level one-dimensional chaotic mapping and level transformation operation, inputting initial values to each level one-dimensional chaotic mapping respectively, each level one-dimensional chaotic mapping performing times of iterative mapping on the respective initial values respectively, and dynamically controlling the control parameters of each level one-dimensional chaotic mapping when performing times of iterative mapping through level transformation operation, , a total of level one-dimensional chaotic mapping performing times of iterative mapping as follows: The initial value of the first-stage one-dimensional chaotic mapping is obtained by a first-stage transformation operation The initial value of the first-stage one-dimensional chaotic mapping is obtained by a first-stage transformation operation The control parameter of the first-stage one-dimensional chaotic mapping is obtained by a first-stage transformation operation The initial value of the first-stage one-dimensional chaotic mapping is obtained by a first-stage transformation operation The control parameter of the first-stage one-dimensional chaotic mapping is obtained by a first-stage transformation operation ​ Each one-dimensional chaotic mapping of each stage is used to perform first iteration mapping on the initial value of the corresponding stage under the control parameter of the first iteration mapping, to obtain the first chaotic value; the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping the chaotic value obtained by the first iteration mapping of the first one-dimensional chaotic mapping is input into the first one-dimensional chaotic mapping for the second iteration mapping Each of the final one-dimensional chaotic maps outputs a total of chaotic values based on a total of high-dimensional chaotic key stream.

2. The method of claim 1, wherein the method is a method of generating a high-dimensional chaotic key stream based on closed-loop dynamic parameter control, characterized in that, Each one-dimensional chaotic mapping is any one of a Logistic mapping, a Sine mapping and a Tent mapping.

3. The method of claim 1, wherein the method is based on a closed loop dynamic parameter control of high dimensional chaotic key stream generation. The same one-dimensional chaotic mapping function is used for each one-dimensional chaotic mapping.

4. The method of claim 1, wherein the method is based on a closed loop dynamic parameter control of high dimensional chaotic key stream generation. The stages of the one-dimensional chaotic map employ different one-dimensional chaotic map functions.

5. The method of claim 1, wherein the method is based on a closed loop dynamic parameter control of high dimensional chaotic key stream generation. In the at least one level one-dimensional chaotic mapping, the one-dimensional chaotic mapping function used by the at least one level one-dimensional chaotic mapping is different from the one-dimensional chaotic mapping function used by other level one-dimensional chaotic mappings.

6. The method of claim 1, wherein the method is a method of high-dimensional chaotic key stream generation based on closed-loop dynamic parameter control, characterized in that, Each transformation operation is a linear transformation operation.

7. The method of claim 6, wherein the method is based on closed loop dynamic parameter control of high dimensional chaotic key stream generation. The linear transformation includes two linear operations of shifting and scaling.

8. An electronic device comprising a processor and a memory, characterized in that The program instructions in the memory are read and run by the processor to perform the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control according to any one of claims 1-7.

9. A storage medium storing program instructions, characterized in that, The program instructions are read and run to perform the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control according to any one of claims 1-7.

10. A method of data chaos encryption, characterized by, The process is as follows: Step S1, obtaining plaintext, and generating a high-dimensional chaotic key stream according to the high-dimensional chaotic key stream generation method based on closed-loop dynamic parameter control according to any one of claims 1-7, and generating a chaotic key based on the high-dimensional chaotic key stream; Step S2, performing operation on the chaotic key and the plaintext to form chaotic encryption data.

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