A spatiotemporal chaotic sequence generation algorithm based on dynamic lattice state vector

Abstract

The present invention discloses a spatiotemporal chaotic sequence generation algorithm based on a dynamic lattice state vector, characterized in that it includes the following steps: S1: random sequence generation; S2: system initialization; initialization of relevant parameters and initial conditions of the system; S3: coupled iterative process, after the relevant parameters and initial conditions of the system are initialized, the chaotic sequence is generated. The present invention relates to the field of information security technology, and in particular, to a spatiotemporal chaotic sequence generation algorithm based on a dynamic lattice state vector. The technical problem to be solved by the present invention is to provide a spatiotemporal chaotic sequence generation algorithm based on a dynamic lattice state vector, which aims to generate an efficient and secure pseudo-random sequence, and can be widely used in image encryption, information hiding and other information security fields.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to a spatiotemporal chaotic sequence generation algorithm based on dynamic lattice state vectors. Background Art

[0002] In the modern information society, secure data transmission and storage have become crucial research topics. As one of the core means of protecting data security, encryption technology is widely used in transportation, industry, healthcare, finance, and other fields. However, due to their linear structure, traditional encryption algorithms (such as AES and DES) may pose security risks when responding to certain attacks. Therefore, researchers are increasingly turning to chaos theory to explore more secure encryption methods.

[0003] Chaotic systems, due to their sensitive dependence on initial conditions, pseudo-randomness, nonlinearity, and complex dynamical behavior, have become a key research topic in the field of cryptography. Small changes in chaotic systems can lead to significant differences in output, and this high degree of unpredictability makes them particularly suitable for cryptographic applications. The development of chaotic systems theory has led to the classification of chaotic systems into low-dimensional chaotic systems, high-dimensional chaotic systems, and spatiotemporal chaotic systems.

[0004] Low-dimensional chaotic systems offer low complexity and high encryption efficiency. Common examples include logistic maps, tent maps, piecewise linear maps, and two-dimensional chaotic systems. However, low-dimensional systems have smaller chaotic intervals and a high number of blank period windows. Because low-dimensional systems have fewer control parameters and a relatively small key space, they may not provide sufficient complexity and security when processing high-dimensional data, such as images.

[0005] Compared to low-dimensional systems, high-dimensional chaotic systems have larger key spaces and more pronounced chaotic characteristics. However, as the system dimension increases, its complexity also increases, leading to higher computational costs and potential challenges in efficiency and resource consumption in practical applications.

[0006] A spatiotemporal chaotic system can be considered an L-dimensional chaotic system. It not only possesses the chaotic characteristics of a high-dimensional chaotic system but also undergoes chaotic iterations simultaneously in both time and space. Therefore, spatiotemporal chaotic systems exhibit more complex nonlinear dynamic behavior, a larger key space, and higher sensitivity to keys and plaintext. However, due to the fixed adjacent coupling method and static coupling coefficients used in classic spatiotemporal chaotic systems (such as coupled mapped lattices, or CMLs), the degree of chaos varies between different lattices in the system, with some lattices exhibiting strong chaotic properties while others exhibit weak or even no chaotic properties at all. Furthermore, the high degree of coupling between adjacent lattices makes the overall chaotic state of the system unstable.

[0007] As research deepened, scholars realized that fixed coupling between adjacent lattices could not meet the requirements of nonlinear propagation with greater randomness in time and space. Consequently, nonlinear coupling methods were proposed. For example, Chen proposed a new random coupled mapped lattice system, while Zhang et al. proposed the Arnold-based coupled mapped lattice (ACLML) and the spatially linear and nonlinear hybrid coupled mapped lattice (MLNCML), opening up new research directions for hybrid adjacent and non-adjacent coupling methods.

[0008] However, spatiotemporal chaotic systems still have some shortcomings in practical applications. While spatiotemporal chaotic systems offer significant advantages in terms of nonlinear dynamic complexity, key space, and key and plaintext sensitivity, in traditional systems, the degree of chaos varies significantly between different grids. Some grids can quickly enter a chaotic state, while others may require more iterations or even fail to enter a chaotic state. This imbalance reduces the system's randomness and overall security.

[0009] The existing technology has the following shortcomings:

[0010] The problem of chaotic differences between different grids in spatiotemporal chaotic systems:

[0011] Although spatiotemporal chaotic systems outperform low- and high-dimensional chaotic systems in terms of key space, the diversity of chaotic sequences, and the complexity of chaotic properties, the degree of chaos in traditional spatiotemporal chaotic systems varies significantly between lattices. Some lattices can produce highly chaotic sequences, while others are less chaotic or even nonexistent. This heterogeneity limits the overall randomness and complexity of the system.

[0012] The time dependence of the states of multiple grid points coupled to inputs in a spatiotemporal chaotic system:

[0013] In traditional spatiotemporal chaotic systems, the states of multiple grid points coupled to the input are time-dependent. Each coupled grid point state is fixed to the same iteration, resulting in a simple approach with limited security. This strong dependency leads to chaotic instability in the system as a whole, compromising both the randomness and security of the sequence. Summary of the Invention

[0014] The technical problem addressed by this invention is to provide an algorithm for generating spatiotemporal chaotic sequences based on dynamic lattice state vectors. This algorithm aims to generate efficient and secure pseudo-random sequences, which can be widely applied in image encryption, information hiding, and other information security fields. By constructing and utilizing vectors that record the latest states of each lattice point, the generated spatiotemporal chaotic sequences possess high complexity, sensitive dependencies, and unpredictability, significantly enhancing the encryption system's resistance to attack.

[0015] The present invention adopts the following technical solutions to achieve the invention objectives:

[0016] A spatiotemporal chaotic sequence generation algorithm based on dynamic lattice state vectors is characterized by comprising the following steps:

[0017] S1: Random sequence generation;

[0018] First, the length of the random sequence rand_map_length is set to log_map_length * lattice * 20, where log_map_length represents the length of the required chaotic sequence and lattice represents the number of grids, ensuring that the sequence can cover the evolution process of the entire system. The random initial value is set to a. After repeated iterations, a random sequence rand_logistic_map with a length of rand_map_length is generated; the actual use part in subsequent calculations is nc ;

[0019] In the present invention, a random sequence is first generated, which is the basis for the subsequent generation of a complex spatiotemporal chaotic sequence. Logistic mapping is a commonly used chaotic mapping model that has a relatively simple mathematical form but can exhibit complex dynamic behaviors. In the present invention, logistic mapping is used, and its recursive formula is as follows:

[0020] (1)

[0021] in: Indicates that at time step The mapping value of

[0022] When the control parameter is 3.4 to 4, the Logistic map will enter a completely chaotic state, that is, its output will be extremely sensitive to the initial conditions and show random characteristics. To ensure that the system is in a completely chaotic state and the generated sequence is unpredictable and highly complex;

[0023] S2: system initialization;

[0024] Initialize the relevant parameters and initial conditions of the system:

[0025] S21: Spatial dimension and time step. The spatial dimension of the system is set to lattice, that is, it is discretized into lattice points in space and has lattice grid points. The time step is set to log_map_length, which means that the state of any lattice system will be iterated to at least log_map_length time steps.

[0026] S22: Chaos Parameters α , α is the control parameter of the system, which directly affects the dynamic behavior of the Logistic map. In this invention, α Varies between 3.4 and 4;

[0027] S23: Coupling strength e , e Represents the coupling strength between spatial points. The introduction of the coupling mechanism causes the states of different points in space to influence each other, increasing the complexity of the system.

[0028] S24: Initial conditions, initialize an array c of length lattice to store the initial chaotic state of each point in space. The initial state is calculated by Logistic mapping:

[0029] (2)

[0030] in: The initial value of is set to 0.345654879, and the initial states of other points are calculated step by step using the above formula;

[0031] S3: Coupled iterative process, after initializing the relevant parameters and initial conditions of the system, the chaotic sequence is generated.

[0032] As a further limitation of this technical solution, the specific steps of S3 are:

[0033] S31: Initialize the grid state vector;

[0034] S311: Create the initial grid state vector cs , set the vector length to the number of lattice points of the chaotic system, and set the array c The value of is assigned to the grid state vector cs As initial value;

[0035] S312: Create the initial grid sequence length vector nx , also set the vector length to the number of lattice points in the chaotic system, the lattice sequence length vector nx It is used to record the number of times each grid point in the chaotic system is coupled. It is also the length of the chaotic sequence in each grid point. Its initial value is set to 0, indicating that no coupling has occurred.

[0036] S32: Select the grid points for coupling;

[0037] Using the random sequence generated above nc , select a grid point ww, and its two adjacent grid points wa and wd , the specific selection method is:

[0038] (3)

[0039] in: nc(n) Is a random sequence nc Middle n numerical values;

[0040] n Indicates the sequence number of the selected value;

[0041] Express nc ( n )× lattice Round down;

[0042] (4)

[0043] (5)

[0044] This selection method ensures that the update of spatial points is random at each iteration, but is also driven by the inherent logical mapping of the system;

[0045] S33: Adjusting coupling strength complexity;

[0046] At each time step, the coupling strength e Updated by a nonlinear function;

[0047] (6)

[0048] in: u is the control parameter;

[0049] Through e The random adjustment further increases the complexity of the system and ensures that the generated chaotic sequence is highly unpredictable in time and space;

[0050] S34: Get grid points ww The coupling state value of

[0051] A random sequence will be used nc Selected grid points ww , and its two adjacent grid points wa and wd The specific coupling method is as follows:

[0052] (7)

[0053] in: f(x)Represents a logical mapping;

[0054] f The function name representing the logical mapping;

[0055] x represents the independent variable;

[0056] nx() represents Elements in the grid point sequence length vector;

[0057] cs() Elements of the grid state vector;

[0058] S35: Update the grid state vector;

[0059] The coupled data is assigned to the corresponding grid points in the grid state vector. At the same time, the grid sequence length vector nx The value of the corresponding grid point in is increased by one, which means that a coupling calculation is performed, so that for the grid state vector cs The data stored in must be the latest status of each grid point;

[0060] S36: Complete space-time chaos iteration;

[0061] Repeat S32-S35 until the grid sequence length vector nx Until the minimum value in is greater than the time step log_map_length, at this time, the first two hundred items that have not yet entered the chaotic state are discarded and the subsequent chaotic sequence is output.

[0062] The grid state vector ensures that the latest state value of each grid point is used for each calculation, and the degree of participation is higher. ww The grid points are all random sequences generated according to the above nc(n) Therefore, the coupling times of each grid point are different. When the coupling times of individual grid points are very small, other grid points may have coupled more times, which increases the complexity of the system and ensures that the generated chaotic sequence is highly unpredictable in time and space.

[0063] As a further limitation of this technical solution, Equation (7) consists of two parts. The first part represents the nonlinear update of the spatial point itself, which is driven by the Logistic map; the second part represents the update from the neighborhood point wa and wd The coupling effect of e By controlling the strength of the coupling, the chaotic behavior of the system is no longer limited to one-dimensional space, but extends to the entire spatial dimension, forming a complex dynamic behavior in time and space.

[0064] As a further limitation of this technical solution, in S32, the random sequencenc Perform a modulo operation and round down to the nearest integer to calculate the grid point for the selected coupling ww , also using the modulo operation to ensure that no matter the grid point ww No matter what value you choose, you can get the adjacent grid points wa and wd .

[0065] As a further limitation of this technical solution, in order to avoid the transient effect of the initial value affecting the result, the random sequence from the 201st item to the last item is finally used as the actual use part in the subsequent calculation. nc ,This can effectively eliminate the non-chaotic behavior in the initial stage of the system, making the generated chaotic ,sequence more robust and reliable.

[0066] Compared with the prior art, the advantages and positive effects of the present invention are:

[0067] By creating a dynamic lattice state vector, the present invention makes the states of multiple coupled input lattice points independent of time, generating a more complex spatiotemporal chaotic sequence. This method not only preserves the nonlinear characteristics of the chaotic system but also increases the complexity and randomness of the sequence through the dynamic lattice state vector, significantly improving the security and attack resistance of the encryption algorithm. The present invention demonstrates enhanced robustness and security against modern cryptanalysis methods (such as chosen-plaintext attacks and differential attacks). The spatiotemporal chaotic sequence generated by the present invention based on the dynamic lattice state vector exhibits high complexity, initial value sensitivity, and unpredictability, making it particularly suitable for applications requiring high security and strong attack resistance, such as image encryption and data encryption. Compared with traditional pseudo-random number generation methods, the present method, by creating a dynamic lattice state vector, ensures that each calculation uses the latest state value at each lattice point, resulting in a higher degree of correlation, better resistance to known attacks, and enhanced security of the encryption system. By properly adjusting parameters, the present method can also be applied to the analysis and simulation of various chaotic systems, showing broad application prospects. DETAILED DESCRIPTION

[0068] A specific embodiment of the present invention is described in detail below, but it should be understood that the protection scope of the present invention is not limited by the specific embodiment.

[0069] The present invention comprises the following steps:

[0070] S1: Random sequence generation;

[0071] First, the length of the random sequence rand_map_length is set to log_map_length * lattice * 20, where log_map_length represents the length of the required chaotic sequence and lattice represents the number of grids, ensuring that the sequence can cover the evolution process of the entire system. The random initial value is set to a. After repeated iterations, a random sequence rand_logistic_map with a length of rand_map_length is generated; the actual use part in subsequent calculations is nc ;

[0072] In order to avoid the transient effect of the initial value affecting the results, the random sequence from the 201st item to the last item is finally used as the actual use part in subsequent calculations. nc ,This can effectively eliminate the non-chaotic behavior in the initial stage of the system, making the generated chaotic ,sequence more robust and reliable.

[0073] In the present invention, a random sequence is first generated, which is the basis for the subsequent generation of a complex spatiotemporal chaotic sequence. Logistic mapping is a commonly used chaotic mapping model that has a relatively simple mathematical form but can exhibit complex dynamic behaviors. In the present invention, logistic mapping is used, and its recursive formula is as follows:

[0074] (1)

[0075] in: Indicates that at time step The mapping value of

[0076] When the control parameter is 3.4 to 4, the Logistic map will enter a completely chaotic state, that is, its output will be extremely sensitive to the initial conditions and show random characteristics. To ensure that the system is in a completely chaotic state and the generated sequence is unpredictable and highly complex;

[0077] S2: system initialization;

[0078] Initialize the relevant parameters and initial conditions of the system:

[0079] S21: Spatial dimension and time step. The spatial dimension of the system is set to lattice, that is, it is discretized into lattice points in space and has lattice grid points. The time step is set to log_map_length, which means that the state of any lattice system will be iterated to at least log_map_length time steps.

[0080] S22: Chaos Parametersα , α is the control parameter of the system, which directly affects the dynamic behavior of the Logistic map. In this invention, α Varies between 3.4 and 4;

[0081] S23: Coupling strength e , e Represents the coupling strength between spatial points. The introduction of the coupling mechanism causes the states of different points in space to influence each other, increasing the complexity of the system.

[0082] S24: Initial conditions, initialize an array c of length lattice to store the initial chaotic state of each point in space. The initial state is calculated by Logistic mapping:

[0083] (2)

[0084] in: The initial value of is set to 0.345654879, and the initial states of other points are calculated step by step using the above formula;

[0085] S3: Coupled iterative process, after initializing the relevant parameters and initial conditions of the system, the chaotic sequence is generated.

[0086] The specific steps of S3 are:

[0087] S31: Initialize the grid state vector;

[0088] S311: Create the initial grid state vector cs , set the vector length to the number of lattice points of the chaotic system, and set the array c The value of is assigned to the grid state vector cs As initial value;

[0089] S312: Create the initial grid sequence length vector nx , also set the vector length to the number of lattice points in the chaotic system, the lattice sequence length vector nx It is used to record the number of times each grid point in the chaotic system is coupled. It is also the length of the chaotic sequence in each grid point. Its initial value is set to 0, indicating that no coupling has occurred.

[0090] S32: Select the grid points for coupling;

[0091] Using the random sequence generated above nc , select a grid point ww , and its two adjacent grid points wa and wd , the specific selection method is:

[0092] (3)

[0093] in: nc(n) Is a random sequence nc Middle n numerical values;

[0094] n Indicates the sequence number of the selected value;

[0095] Express nc ( n )× lattice Round down;

[0096] (4)

[0097] (5)

[0098] This selection method ensures that the update of spatial points is random at each iteration, but is also driven by the inherent logical mapping of the system;

[0099] The S32 is performed by random sequence nc Perform a modulo operation and round down to the nearest integer to calculate the grid point for the selected coupling ww , also using the modulo operation to ensure that no matter the grid point ww No matter what value you choose, you can get the adjacent grid points wa and wd .

[0100] S33: Adjusting coupling strength complexity;

[0101] At each time step, the coupling strength e Updated by a nonlinear function;

[0102] (6)

[0103] in: u is the control parameter;

[0104] Through e The random adjustment further increases the complexity of the system and ensures that the generated chaotic sequence is highly unpredictable in time and space;

[0105] S34: Get grid points ww The coupling state value of

[0106] A random sequence will be used nc Selected grid points ww , and its two adjacent grid points waand wd The specific coupling method is as follows:

[0107] (7)

[0108] Where: f(x) represents the logical mapping;

[0109] f represents the function name of the logical mapping;

[0110] x represents the independent variable;

[0111] nx() represents the element in the grid sequence length vector;

[0112] cs() Elements of the grid state vector;

[0113] Equation (7) consists of two parts. The first part represents the nonlinear update of the spatial point itself, which is driven by the Logistic map. The second part represents the update from the neighboring points. wa and wd The coupling effect of e By controlling the strength of the coupling, the chaotic behavior of the system is no longer limited to one-dimensional space, but extends to the entire spatial dimension, forming a complex dynamic behavior in space and time.

[0114] S35: Update the grid state vector;

[0115] The coupled data is assigned to the corresponding grid points in the grid state vector. At the same time, the grid sequence length vector nx The value of the corresponding grid point in is increased by one, which means that a coupling calculation is performed, so that for the grid state vector cs The data stored in must be the latest status of each grid point;

[0116] S36: Complete space-time chaos iteration;

[0117] Repeat S32-S35 until the grid sequence length vector nx Until the minimum value in is greater than the time step log_map_length, at this time, the first two hundred items that have not yet entered the chaotic state are discarded and the subsequent chaotic sequence is output.

[0118] The grid state vector ensures that the latest state value of each grid point is used for each calculation, and the degree of participation is higher. ww The grid points are all random sequences generated according to the above nc(n) Therefore, the coupling times of each grid point are different. When the coupling times of individual grid points are very small, other grid points may have coupled more times, which increases the complexity of the system and ensures that the generated chaotic sequence is highly unpredictable in time and space.

[0119] The above disclosure is only a specific embodiment of the present invention, but the present invention is not limited thereto. Any changes that can be conceived by those skilled in the art should fall within the scope of protection of the present invention.

Claims

1. A method for generating spatiotemporal chaotic sequences based on dynamic lattice state vectors, characterized in that: The following steps are involved: S1: Random sequence generation; First, the length of the random sequence rand_map_length is set to log_map_length * lattice * 20, where log_map_length represents the length of the required chaotic sequence, lattice represents the number of grids, and the initial value of random is set to a. After repeated iterations, a random sequence rand_logistic_map with a length of rand_map_length is generated; the actual use part in the subsequent calculation is nc ; Using Logistic mapping, the recursive formula is as follows: （1） in: Indicates that at time step The mapping value of To control the parameters; S2: System initialization; Initialize the relevant parameters and initial conditions of the system: S21: spatial dimension and time step. The spatial dimension of the system is set to lattice, that is, it is discretized into lattice points in space and has lattice grid points. The time step is set to log_map_length, which means that the state of any lattice system will be iterated to at least log_map_length time steps. S22: Chaos Parameters α , α is the control parameter of the system; S23: Coupling strength e , e represents the coupling strength between points in space; S24: Initial conditions, initialize an array c of length lattice to store the initial chaotic state of each point in space. The initial state is calculated by Logistic mapping: （2） in: The initial value of is set to 0.345654879; S3: coupled iterative process, after initializing the relevant parameters and initial conditions of the system, the chaotic sequence is generated; The specific steps of S3 are: S31: Initialize the grid state vector; S311: Create the initial grid state vector cs , set the vector length to the number of lattice points in the chaotic system, and set the array c The value of is assigned to the grid state vector cs As initial value; S312: Create the initial grid sequence length vector nx , and similarly set the vector length to be the number of lattice points in the chaotic system; S32: Select the grid points for coupling; Using random sequences nc , select a grid point ww , and its two adjacent grid points w and wd , the specific selection method is: （3） in: nc(n) Is a random sequence nc Middle n numerical values; n Indicates the ordinal number of the selected value; Express nc ( n )× lattice Round down; （4） （5） S33: Adjust coupling strength complexity; At each time step, the coupling strength e Updated by a nonlinear function; （6） in: u To control the parameters; S34: Get grid points ww The coupling state value of A random sequence will be used nc Selected grid points ww , and its two adjacent grid points w and wd The specific coupling method is as follows: （7） in: f(x) Represents a logical mapping; f The function name representing the logical mapping; x represents the independent variable; nx() means Elements in the grid point sequence length vector; cs() Elements of the grid state vector; S35: Update the grid state vector; The coupled data is assigned to the corresponding grid points in the grid state vector. At the same time, the grid sequence length vector nx The value of the corresponding grid point in is increased by one, which means that a coupling calculation is performed, so that for the grid state vector cs The data stored in the grid must be the latest state of each grid point; S36: Complete space-time chaos iteration; Repeat S32-S35 until the grid point sequence length vector nx Until the minimum value in is greater than the time step log_map_length, at this time, the first two hundred items that have not entered the chaotic state are discarded and the subsequent chaotic sequence is output.

2. The method for generating spatiotemporal chaotic sequences based on dynamic lattice state vectors according to claim 1, characterized in that: Formula (7) consists of two parts. The first part represents the nonlinear update of the spatial point itself, driven by the Logistic map; the second part represents the update from the neighborhood point w and wd The coupling effect of e Controls the strength of the coupling.

3. The method for generating spatiotemporal chaotic sequences based on dynamic lattice state vectors according to claim 1, characterized in that: S32 is performed by passing a random sequence nc Perform a modulo operation and round down to the nearest integer to calculate the grid point for the selected coupling. ww , the same modulo operation is used to ensure that no matter the grid point ww No matter what value you choose, you can get the adjacent grid points w and wd .

4. The method for generating spatiotemporal chaotic sequences based on dynamic lattice state vectors according to claim 1, characterized in that: The 201st to the last item of the random sequence is used as the actual part in the subsequent calculations. nc .

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