Vector high-precision map nonlinear encryption method and system

Abstract

The invention discloses a vector high-precision map nonlinear encryption method and system, and belongs to the field of high-precision electronic map manufacturing, and the method comprises the steps: obtaining latitude and longitude coordinates from a vector high-precision map; inputting the latitude and longitude coordinates into a deep neural network for primary encryption to obtain latitude and longitude coordinates after primary encryption; the deep neural network comprises an input layer used for inputting latitude and longitude coordinates; the hidden layer is used for performing nonlinear encryption through network depth and an activation function; the output layer is used for outputting the encrypted latitude and longitude coordinates; and based on the longitude and latitude coordinates after the primary encryption, performing secondary encryption by adopting fragmentation bilinear Peill transform to obtain the finally encrypted longitude and latitude coordinates. According to the method, the depth network model is used for replacing a trigonometric function model to calculate the longitude and latitude variable quantity, the degree of freedom and strength of encryption are improved, and the encryption strength, real-time performance, flexibility and expandability are improved through the depth neural network and fragmentation bilinear Piola transformation.

Description

Technical Field

[0001] This invention belongs to the field of high-precision electronic map production, specifically relating to a nonlinear encryption method and system for vector high-precision maps. Background Technology

[0002] High-precision maps have important applications in autonomous driving, intelligent transportation, and geographic information systems. High-precision map encryption technology is currently a key technology for ensuring the secure application of classified geographic information. The topographic map encryption technology, which has been in use since 2003, has greatly promoted the healthy and orderly development of the navigation electronic map industry and has been applied in digital cities and geographic information public service platforms, achieving significant social and economic benefits. With the rapid development of surveying and mapping geographic information technology in recent years, new geographic information business models, products, and applications have placed higher demands on geographic information encryption technology. High-precision map encryption, by offsetting or transforming the original geographic coordinates, aims to protect geographic information security and prevent unauthorized use and leakage. Self-developed effective encryption algorithms can significantly enhance data protection and achieve precise control over data sovereignty.

[0003] Traditional encryption algorithms do not consider the spatial correlation of map data, which can easily lead to distortions in road geometry after encryption (such as unreasonable bends in straight road segments) and inaccurate distances between adjacent roads, affecting the accuracy of vehicle-side positioning and matching. In addition, while highly nonlinear encryption offers strong security, it also has high computational complexity, putting pressure on the limited computing power of vehicle-side systems. Summary of the Invention

[0004] The purpose of this invention is to address the problem that traditional encryption algorithms do not consider the spatial correlation of map data, which leads to distortions in road geometry after encryption (such as unreasonable bends in straight road segments after encryption) and distortions in the distance between adjacent roads. This invention provides a nonlinear encryption method for high-precision vector maps, which uses deep neural networks and piecewise bilinear Piola transform for encryption, improving encryption strength, real-time performance, flexibility, and scalability. Furthermore, it is easier to implement in the decryption process through user-defined encryption model parameters.

[0005] According to one aspect of this specification, a nonlinear encryption method for high-precision vector maps is provided, comprising:

[0006] Obtain latitude and longitude coordinates from a high-precision vector map;

[0007] The latitude and longitude coordinates are input into a deep neural network (DNN) for encryption to obtain encrypted latitude and longitude coordinates. The deep neural network includes: an input layer for inputting latitude and longitude coordinates; a hidden layer for non-linear encryption using network depth and activation function; and an output layer for outputting the encrypted latitude and longitude coordinates.

[0008] Based on the first encrypted latitude and longitude coordinates, a second encryption is performed using piecewise bilinear Piola transform to obtain the final encrypted latitude and longitude coordinates.

[0009] Furthermore, the latitude and longitude coordinates are input into the deep neural network for encryption, including:

[0010] Use latitude and longitude coordinates as the initial feature space;

[0011] Based on the initial feature space, a rotation transformation is performed using a specified rotation matrix to obtain the rotated feature space; then, a linear displacement superposition is performed on the rotated feature space using a set translation vector to obtain the translated feature space.

[0012] The translated feature space is input into the activation function to obtain the nonlinearly transformed feature space, i.e., the change in latitude and longitude coordinates.

[0013] Furthermore, the first encryption includes:

[0014]

[0015] in, For the input layer, A two-dimensional vector of latitude and longitude coordinates. This is the output of the previous layer. The activation function corresponding to the hidden layer. Indicates a hidden layer. Represents the rotation matrix. Represents the translation vector. Indicates the activation function; This represents the change in latitude and longitude coordinates. Indicates network depth.

[0016] Furthermore, the method also includes:

[0017] The changes in latitude and longitude coordinates are transformed to obtain the encrypted latitude and longitude coordinates, expressed as follows:

[0018]

[0019]

[0020] in, The encrypted latitude and longitude coordinates, c is the coordinate scale conversion factor in m / °, used to convert the change in latitude and longitude from radians to meters. Let e ​​be the major radius of the ellipsoid and e be the eccentricity of the ellipsoid.

[0021] Furthermore, a secondary encryption is performed using piecewise bilinear Piola transform, including:

[0022] The encrypted latitude and longitude coordinates are matched into a preset rectangular cell K, and the center coordinates of the rectangular cell K are set. ;

[0023] Each rectangular element K corresponds to a perturbed quadrilateral element. , The vertex coordinates are The piecewise bilinear Piola transform expression is obtained as follows:

[0024]

[0025] in, The final encrypted latitude and longitude coordinates, vertex coordinates With node basis functions One-to-one correspondence, satisfy .

[0026] Furthermore, the method also includes:

[0027] A rectangular frame E is calculated based on the latitude and longitude range of the map, and then the rectangular frame E is divided into rectangular grids T.

[0028] Based on the rectangular mesh T, any one of the rectangular elements K is obtained.

[0029] According to one aspect of this specification, a vector high-precision map nonlinear encryption system is provided, comprising:

[0030] The data acquisition module is used to obtain latitude and longitude coordinates from vector high-precision maps;

[0031] A primary encryption module is used to input latitude and longitude coordinates into a deep neural network for primary encryption, thereby obtaining the primary encrypted latitude and longitude coordinates. The deep neural network includes: an input layer for inputting latitude and longitude coordinates; a hidden layer for performing non-linear encryption using network depth and an activation function; and an output layer for outputting the primary encrypted latitude and longitude coordinates.

[0032] The secondary encryption module is used to perform secondary encryption based on the encrypted latitude and longitude coordinates using piecewise bilinear Piola transform, to obtain the final encrypted latitude and longitude coordinates.

[0033] According to one aspect of this specification, an electronic device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the vector high-precision map nonlinear encryption method.

[0034] According to one aspect of this specification, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the vector high-precision map nonlinear encryption method.

[0035] According to one aspect of the present invention, a computer program product containing instructions is provided, which, when run on a computer, causes the computer to perform the steps of the vector high-precision map nonlinear encryption method.

[0036] Compared with the prior art, the beneficial effects of the present invention are:

[0037] 1. In this embodiment of the invention, a deep network model is used to replace the trigonometric function model to calculate the changes in latitude and longitude, thereby improving the degree of freedom and strength of encryption.

[0038] 2. The embodiments of the present invention use piecewise bilinear Piola transform for encryption, which avoids the overall deduction function for local offset inversion algorithms.

[0039] 3. The embodiments of the present invention use deep neural networks and piecewise bilinear Piola transform for encryption, which improves encryption strength, real-time performance, flexibility and scalability, and is easier to implement in the decryption process through user-defined encryption model parameters. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of a rectangular / quadrilateral grid according to an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the piecewise bilinear Piola transform encryption according to an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] like Figure 1 As shown, this embodiment of the invention provides a nonlinear encryption method for high-precision vector maps, comprising: obtaining latitude and longitude coordinates from a high-precision vector map; inputting the latitude and longitude coordinates into a deep neural network for primary encryption to obtain primary encrypted latitude and longitude coordinates; wherein the deep neural network comprises: an input layer for inputting latitude and longitude coordinates; a hidden layer for nonlinear encryption using network depth and activation function; an output layer for outputting the primary encrypted latitude and longitude coordinates; and, based on the primary encrypted latitude and longitude coordinates, performing secondary encryption using piecewise bilinear Piola transform to obtain the final encrypted latitude and longitude coordinates.

[0046] Specifically, the input layer of the deep network model takes the longitude and latitude of WGS84 coordinates as input, the output layer takes the coordinate changes as output, and the hidden layer is the core of non-linear encryption. Its functionality depends on two configurable parameters: network depth and activation function sequence. Users can freely select these parameters in the following process according to their needs. The output layer of the deep network model undergoes post-processing to obtain the encrypted longitude and latitude of the coordinates.

[0047] Specifically, the longitude and latitude of the WGS84 coordinates are initialized as follows:

[0048] , (1)

[0049] in, The longitude is in WGS84 coordinates. The dimension of the WGS84 coordinate system.

[0050] Specifically, the user selects the network depth (i.e., the number of hidden layers). Theoretically, users can choose deeper networks to increase the nonlinearity, but this also means an increase in computational cost. Each hidden layer consists of linear transformations and nonlinear activations, where linear transformations refer to rotations and translations. For each layer... Randomly generate the corresponding rotation angle and two-dimensional translation vector ,in The range of values ​​is , The value range for each component is [-100, 100]. For example, for the first layer, you can select...

[0051] , (2)

[0052] Define the weight matrix (i.e., the rotation matrix):

[0053] (3)

[0054] Then, encryption is performed using the following expression:

[0055] (4)

[0056] in, The input layer is a two-dimensional vector composed of the initial coordinates obtained through calculation. This is the output of the previous layer. This is the activation function corresponding to the hidden layer. This indicates that for hidden layers The output of the previous layer As the input to this layer (the input to the first hidden layer, i.e., the input layer), it is processed by a rotation matrix. Translation vector A linear transformation, then passed through an activation function. This yields the output of that layer. Given a two-dimensional vector of latitude and longitude coordinates, after passing through the last hidden layer, the output is the change in latitude and longitude coordinates. , Indicates network depth.

[0057] Specifically, the present invention also provides an embodiment one, in which the selected network depth is The activation function sequence can be selected from the following sequences:

[0058] (5)

[0059] in, The expression is:

[0060] (6)

[0061] If the selected network depth is The activation function sequence can be selected from the following sequences:

[0062] (7)

[0063] Because tanh constrains the range to (-1,1), it preserves the local approximate rigidity.

[0064] Specifically, the present invention also provides an embodiment two.

[0065] (8)

[0066] For the first layer Randomly generated , The linear transformation is:

[0067] (9)

[0068] By activation function ( (Then it becomes:)

[0069] (10)

[0070] The output is:

[0071] (11)

[0072] Then the calculations are performed sequentially for the second layer, the third layer, and so on.

[0073] Specifically, the latitude and longitude coordinates obtained through post-processing are:

[0074] (12)

[0075] (13)

[0076] in c is the coordinate scale transformation factor (dimensions: m / °), used to convert the change in latitude and longitude from radians to meters. Let e ​​be the major radius of the ellipsoid and e be the eccentricity of the ellipsoid.

[0077] Specifically, this embodiment of the invention provides piecewise bilinear Piola transform encryption. The input is the result of deep neural network encryption in the previous steps. and The output is the final encrypted latitude and longitude coordinates. In this step, the data undergoes a second encryption to improve the algorithm's security, where map points are defined by the map's latitude and longitude range. The piecewise bilinear Piola transform achieves quadrilateral mesh mapping through bilinear basis functions and belongs to the isoparametric element transformation in the finite element method.

[0078] Specifically, let E be the rectangular bounding box of the map's latitude and longitude range, and let the set of map points be... Divide E into a rectangular mesh T containing g vertices, store the coordinate matrix G (g×2, where g is the total number of mesh vertices), and assign global-local double-layer numbering to the mesh vertices and cells. The user inputs the perturbation matrix of the mesh vertices. (g×2) yields a quadrilateral mesh. Its vertex coordinate matrix expression is as follows:

[0079] (14)

[0080] The quadrilaterals after perturbation are generally not rectangles; the perturbation breaks the global regularity of the quadrilateral elements, such as... Figure 2 As shown.

[0081] Specifically, this embodiment of the invention also provides a unit looping step, where the rectangular unit is K, and the corresponding quadrilateral unit after perturbation is K. The four vertices of K are A1A2A3A4. The four vertices are B1B2B3B4, as shown below. Figure 3 As shown. Proceed. Transforming the forward arithmetic, we obtain the following expression:

[0082] (15)

[0083] Specifically, this embodiment of the invention also provides a step of filtering the grid, calculating the latitude and longitude range of the input data, and determining which rectangular grid cells can cover this range. Simultaneously, these grid cells are denoted as a cell set L = {L1, L2, ..., Lm} (where L1, L2, ..., Lm are subsets of the rectangular grid T; if the range of the input data is small, performing Piola transformation on the cell set L is more time-efficient than performing transformation on the cell set T). Point-by-point determination of map data shape points. The unit to which it belongs, K∈L (if Just on the grid vertices or common edges, uniformly apply this... (belonging to the rectangular unit with the smallest global number), the calculation expression is:

[0084] (16)

[0085] Save the encrypted map point set .

[0086] Specifically, embodiments of the present invention provide Transformation to forward calculation, let the center coordinates of rectangular element K be... ,like Figure 2 As shown, the length and width are 2h and 2w respectively, then the expression of the node basis function is as follows:

[0087] (17)

[0088] in, For the points to be encrypted, satisfy Also, consider quadrilateral units. The vertex coordinates are ,but The formula for the positive transformation is:

[0089] (18)

[0090] in, The encrypted coordinates, vertex coordinates With node basis functions One-to-one correspondence.

[0091] Specifically, this invention provides a high-precision map encryption method based on the three principles of high-precision map encryption: "high nonlinearity, approximate rigidity, and relative irreversibility (i.e., only the key holder can decrypt, and unauthorized parties cannot reverse-calculate using public information and partial data)." This method is efficient and easy to implement under different parameter systems, thereby improving the security level of geographic information data. The "approximate rigidity" addresses the aforementioned distortion and loss problems, while efficiency and ease of implementation ensure real-time application on the vehicle side. Here, "approximate rigidity" refers to the fact that after combining multi-layer linear transformations (rotation + translation) with nonlinear activation functions, the transformation of local regions approximates the characteristics of a rigid transformation.

[0092] Specifically, the embodiments of the present invention also provide an explanation of relative irreversibility. First, reversibility is explained, then relative irreversibility is explained. Reversibility ensures that two geographically distinct points do not overlap in the encrypted coordinate system. The specific details are as follows:

[0093] 1. The mathematical invertibility of deep neural network encryption. F(Lon,Lat) represents the encrypted latitude and longitude data obtained through DNN transformation. The deep neural network is constructed by coupling each layer with a specific activation function (LeakyReLU, arctan, and tanh, etc.) through a rigid transformation (rotation + translation). It can be proven that... The norm is bounded and less than 1, so the above transformation is injective, thus ensuring that the encryption method is mathematically injective and invertible.

[0094] 2. The mathematical invertibility of piecewise bilinear transformation encryption. This can be derived from the geometric properties of bilinear transformation. Note that given the mapped coordinates of the four vertices of a quadrilateral parallel to the coordinate system, the bilinear transformation within that rectangular region degenerates into a linear transformation along a line parallel to the coordinate system, thus guaranteeing the uniqueness of the transformation within the rectangular region. Finally, utilizing the mapping relationship between vertices, along with the monotonicity along any coordinate within each rectangular region, we can conclude that the piecewise bilinear transformation is mathematically invertible.

[0095] 3. Relative Irreversibility. The non-rigid nature of local DNN encryption leads to inaccuracies in parameter inversion; piecewise bilinear encryption causes significant shifts in the approximate rigid parameters across different regions. When the encryption process is known, DNN inversion requires solving a system of nonlinear equations (complexity increases exponentially with D), while Piola inversion requires global optimization (time complexity is too high). In actual calculations, floating-point errors result in near irreversibility.

[0096] Specifically, the encryption process is as follows: first, encryption is performed using a DNN, followed by encryption using a piecewise bilinear transformation. To accurately obtain the inverse of the encryption process, the following parameters need to be estimated: the DNN architecture (network width, depth, activation function, network parameters), and the control point positions and changes of the piecewise bilinear transformation. Note that the DNN architecture has a very high degree of freedom. Although the last layer is close to a rigid transformation, allowing for relatively accurate estimation, achieving accurate estimation results in an exponential increase in the complexity of calculating the inverse as the estimation precision increases (requiring an extremely accurate estimation of the network architecture). While the piecewise bilinear transformation appears regular, obtaining an accurate estimation formula requires estimating the position of each vertex and its transformed coordinates. The computational complexity increases with the number of vertices; in particular, the parameters introduced by the position and change of each vertex are four times the number of vertices. Therefore, even knowing the encryption process, the system exhibits extremely high security due to the dual limitations of accumulated floating-point errors and exploding computational complexity.

[0097] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a vector high-precision map nonlinear encryption system, which is used to execute a vector high-precision map nonlinear encryption method from the above method embodiments.

[0098] The system includes: a data acquisition module for acquiring latitude and longitude coordinates from a high-precision vector map; a primary encryption module for inputting the latitude and longitude coordinates into a deep neural network for primary encryption to obtain the primary encrypted latitude and longitude coordinates; wherein the deep neural network includes: an input layer for inputting the latitude and longitude coordinates; a hidden layer for performing nonlinear encryption through network depth and activation function; an output layer for outputting the primary encrypted latitude and longitude coordinates; and a secondary encryption module for performing secondary encryption based on the primary encrypted latitude and longitude coordinates using piecewise bilinear Piola transform to obtain the final encrypted latitude and longitude coordinates.

[0099] The vector high-precision map nonlinear encryption system provided in this invention addresses the problem that traditional encryption algorithms do not consider the spatial correlation of map data, leading to distortions in road geometry (such as unreasonable bends in straight road segments after encryption) and inaccurate distances between adjacent roads. The system employs several modules and uses deep neural networks and piecewise bilinear Piola transform for encryption, improving encryption strength, real-time performance, flexibility, and scalability. Furthermore, the user-defined encryption model parameters make it easier to implement in the decryption process.

[0100] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement a vector high-precision map nonlinear encryption method as proposed in the above embodiments.

[0101] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, this program overcomes the problems of traditional encryption algorithms failing to consider the spatial correlation of map data, which leads to distortions in road geometry after encryption (such as unreasonable bends in straight road segments after encryption) and distortions in the distance between adjacent roads. It improves encryption strength, real-time performance, flexibility, and scalability, and is easier to implement in the decryption process through user-defined encryption model parameters.

[0102] The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, or optical disk, used to store computer program code and necessary data files. The stored computer program includes: a data acquisition module, a primary encryption module, and a secondary encryption module.

[0103] This invention also provides a computer program product containing instructions that, when run on a computer, generates, in whole or in part, the vector high-precision map nonlinear encryption method proposed in the above embodiments. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0104] In summary, the present invention uses the input latitude and longitude coordinates as the initial feature space (two-dimensional vector). In each hidden layer, a rotation transformation is first performed using a user-specified rotation matrix to obtain the rotated feature space. Then, a linear displacement superposition is performed using a user-specified translation vector to further obtain the translated feature space. Finally, the feature space after rotation and translation is input into the activation function to obtain the nonlinearly transformed feature space. After passing through the hidden layers, the feature space is no longer latitude and longitude coordinates, but rather the changes in latitude and longitude coordinates.

[0105] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A nonlinear encryption method for high-precision vector maps, characterized in that, include: Obtain latitude and longitude coordinates from a high-precision vector map; The latitude and longitude coordinates are input into a deep neural network for encryption to obtain encrypted latitude and longitude coordinates. The deep neural network includes: an input layer for inputting latitude and longitude coordinates; a hidden layer for non-linear encryption using network depth and activation function; and an output layer for outputting the encrypted latitude and longitude coordinates. Based on the first encrypted latitude and longitude coordinates, a second encryption is performed using piecewise bilinear Piola transform to obtain the final encrypted latitude and longitude coordinates.

2. The nonlinear encryption method for high-precision vector maps according to claim 1, characterized in that, The latitude and longitude coordinates are input into a deep neural network for encryption, including: Use latitude and longitude coordinates as the initial feature space; Based on the initial feature space, a rotation transformation is performed using a specified rotation matrix to obtain the rotated feature space; then, a linear displacement superposition is performed on the rotated feature space using a set translation vector to obtain the translated feature space. The translated feature space is input into the activation function to obtain the nonlinearly transformed feature space, i.e., the change in latitude and longitude coordinates.

3. The nonlinear encryption method for high-precision vector maps according to claim 2, characterized in that, The first encryption includes: ， in, For the input layer, A two-dimensional vector of latitude and longitude coordinates. This is the output of the previous layer. The activation function corresponding to the hidden layer. Indicates a hidden layer. Represents the rotation matrix. Represents the translation vector. Indicates the activation function; This represents the change in latitude and longitude coordinates. Indicates network depth.

4. The nonlinear encryption method for high-precision vector maps according to claim 2, characterized in that, The method further includes: The changes in latitude and longitude coordinates are transformed to obtain the encrypted latitude and longitude coordinates, expressed as follows: , , in, The encrypted latitude and longitude coordinates, c is the coordinate scale conversion factor in m / °, used to convert the change in latitude and longitude from radians to meters. Let e ​​be the major radius of the ellipsoid and e be the eccentricity of the ellipsoid.

5. The nonlinear encryption method for high-precision vector maps according to claim 1, characterized in that, Secondary encryption is performed using piecewise bilinear Piola transform, including: The encrypted latitude and longitude coordinates are matched into a preset rectangular cell K, and the center coordinates of the rectangular cell K are set. ; Each rectangular unit K corresponds to one , The vertex coordinates are The piecewise bilinear Piola transform expression is obtained as follows: , in, The final encrypted latitude and longitude coordinates, vertex coordinates With node basis functions One-to-one correspondence, satisfy .

6. The nonlinear encryption method for high-precision vector maps according to claim 5, characterized in that, The method further includes: A rectangular frame E is calculated based on the latitude and longitude range of the map, and then the rectangular frame E is divided into rectangular grids T. Based on the rectangular mesh T, any one of the rectangular elements K is obtained.

7. A vector high-precision map nonlinear encryption system, characterized in that, include: The data acquisition module is used to obtain latitude and longitude coordinates from vector high-precision maps; A primary encryption module is used to input latitude and longitude coordinates into a deep neural network for primary encryption, thereby obtaining the primary encrypted latitude and longitude coordinates. The deep neural network includes: an input layer for inputting latitude and longitude coordinates; a hidden layer for performing non-linear encryption using network depth and an activation function; and an output layer for outputting the primary encrypted latitude and longitude coordinates. The secondary encryption module is used to perform secondary encryption based on the first-encrypted latitude and longitude coordinates using piecewise bilinear Piola transform, to obtain the final encrypted latitude and longitude coordinates.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the vector high-precision map nonlinear encryption method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the vector high-precision map nonlinear encryption method according to any one of claims 1 to 6.

10. A computer program product containing instructions, characterized in that, When it is run on a computer, it causes the computer to perform the steps of the vector high-precision map nonlinear encryption method according to any one of claims 1 to 6.

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