Vector geographic data encryption and decryption methods based on 3D Arnold transformation
Through the encryption and decryption method of three-dimensional Arnold transform, the problems of complex and low scrambling degree of existing vector geographic data encryption algorithms are solved, and efficient and attack-resistant data protection is achieved, which is suitable for encryption and decryption of multi-dimensional data.
Patent Information
- Application Number
- CN202111130927.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-09-26
- Publication Date
- 2025-09-09
- Estimated Expiration
- 2041-09-26
AI Technical Summary
The existing vector geospatial data encryption algorithms are complex and have low scrambling degree, making it difficult to effectively protect data security.
An encryption and decryption method based on three-dimensional Arnold transform is adopted. By constructing the three-dimensional Arnold transform formula and inverse transform formula, spatial transformation encryption and decryption of vector geographic data are performed. The core key is constructed using parameters such as transformation matrix coefficients, modulus and number of transformations to achieve encryption and decryption of data with high scrambling degree.
It realizes a concise and efficient data encryption and decryption process, has the ability to resist enumeration attacks, supports data processing in different spatial dimensions, adapts to diverse encryption demand scenarios, and has a small amount of computation.
Smart Images
Figure CN113779611B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of geographic information security technology, and in particular relates to a vector geographic data encryption method and a decryption method based on three-dimensional Arnold transformation. Background Art
[0002] Vector geospatial data involves many aspects, including economic operations, military security, organizational management, business operations, and personal life. Information security and copyright protection issues have long plagued its production, storage, transmission, and use. With the development of information technology and the enhancement of spatiotemporal perception, the types, sources, and acquisition methods of geospatial data are becoming increasingly diverse. The speed of data acquisition is accelerating, the amount of data is surging, and the spatiotemporal scale and information scope are gradually expanding into a ternary world where humans, machines, and objects are integrated. As a result, security risks and hazards such as data leaks, infringements, and theft are becoming increasingly prominent. Taking proactive and effective measures to safeguard and promote the healthy and orderly development of the entire geographic information chain, from production, research, processing, to application services, from the perspectives of information security, copyright, and value protection, is an important and urgent task.
[0003] Currently, security measures for vector geospatial data can be broadly categorized into two basic approaches: regulations and technology. Regulations rely on the mandatory binding force of national and departmental governments to regulate, constrain, and hold people accountable. Technology, on the other hand, leverages the data's inherent proactive protection capabilities and is widely adopted by geographic information producers and users. Security technologies for vector geospatial data generally include data declassification, encryption, digital watermarking, data scrambling, access control, data steganography, and data desensitization. However, many current encryption algorithms are complex and have low scrambling levels, making them unsuitable for encrypting vector geospatial data. Summary of the Invention
[0004] The purpose of the present invention is to provide a vector geographic data encryption method and decryption method based on three-dimensional Arnold transform, so as to provide an encryption method with a simple algorithm and a high degree of scrambling and a corresponding decryption method.
[0005] In order to solve the above technical problems, the technical solutions provided by the present invention and the corresponding beneficial effects of the technical solutions are as follows:
[0006] The present invention provides a vector geographic data encryption and decryption method based on three-dimensional Arnold transformation, comprising the following steps:
[0007] 1) Obtain vector geographic plaintext data;
[0008] 2) Determine the vector geographic ciphertext data corresponding to the vector geographic plaintext data according to the constructed three-dimensional Arnold transformation formula; the three-dimensional Arnold transformation formula is:
[0009]
[0010] Where x, y, and z are the coordinate values before the three-dimensional Arnold transformation; x′, y′, and z′ are the coordinate values after the three-dimensional Arnold transformation; P is the modulus; and A is the transformation matrix, whose structure is:
[0011]
[0012] Where a r 、a g 、a b 、c r 、c g 、c b is the transformation coefficient, which is any positive integer, a specified value or a randomly generated value.
[0013] The beneficial effects of the above technical solution are as follows: the encryption method of the present invention is based on the three-dimensional Arnold transformation, which can convert vector geographic plaintext data into corresponding vector geographic ciphertext data. Without changing the original data structure, the vector geographic data is geometrically scrambled based on spatial transformation to achieve the purpose of data encryption. The algorithm of this method has the characteristics of simplicity, high scrambling degree, fast encryption speed, complete reversibility and resistance to enumeration attacks, providing a performance-balanced, lightweight and efficient scrambling encryption protection option for vector geographic data encryption. Moreover, the three-dimensional Arnold transformation formula constructs a core key of more than 9 parameters (inclusive), including the Arnold transformation matrix coefficients, modulus, and number of transformations, which has strong resistance to brute force attacks.
[0014] Furthermore, after step 1), the step of preprocessing the acquired vector geographic plaintext data to obtain vector geographic processed data is also included, and the preprocessing includes offset processing and rounding processing on the vector geographic plaintext data so that the vector geographic processed data is a non-negative integer; accordingly, the means for determining the vector geographic ciphertext data corresponding to the vector geographic plaintext data in step 2) is: substituting the vector geographic processed data into the three-dimensional Arnold transformation formula and performing t Arnold transformations to obtain vector geographic encrypted data corresponding to the vector geographic processed data, t≥1; according to the offset situation during preprocessing, the vector geographic encrypted data is restored and offset processed to obtain the vector geographic ciphertext data.
[0015] The beneficial effect of the above technical solution is: since the coordinate data of vector geographic data can be any integer or floating point type, the vector geographic plaintext data is preprocessed so that the processed vector geographic data is a non-negative integer, so as to ensure the closure, numerical uniqueness and calculation accuracy of subsequent encryption operations.
[0016] Furthermore, if the vector geographic plaintext data is two-dimensional vector geographic plaintext data, then in step 2), for at least two two-dimensional vector geographic plaintext data, a corresponding number of vector geographic processing data are obtained, and the three coordinate value data in all the vector geographic processing data are taken in turn, and substituted into the three-dimensional Arnold transformation formula for t transformations, and when there are less than three coordinate value data at the end, supplementary processing is performed until all the vector geographic processing data are traversed, so as to finally obtain the vector geographic encrypted data corresponding to all the vector geographic processing data.
[0017] The beneficial effects of the above technical solution are: it can accurately realize the encryption of two-dimensional vector geographic plaintext data and support the encryption processing of vector geographic data in different spatial dimensions.
[0018] Furthermore, the three coordinate value data in the obtained vector geoprocessing data are all coordinate value data in the x-direction or all coordinate value data in the y-direction.
[0019] Furthermore, the vector geographic plaintext data is data extracted according to geographic elements or data extracted according to layers in the vector geographic dataset.
[0020] The beneficial effects of the above technical solution are: on the basis of completely maintaining the original vector geographic data structure, according to the characteristics of different feature types, it provides a method of taking values according to geographic features and according to layers, and encryption is performed on this basis. The encryption control granularity can be adjusted to adapt to encryption processing at three granularities, namely single feature, specified feature set and layer, and selective encryption strategies can be used to cope with more flexible and diverse encryption demand scenarios.
[0021] A vector geographic data decryption method based on three-dimensional Arnold transformation of the present invention comprises the following steps:
[0022] 1) Obtain vector geographic encrypted data;
[0023] 2) Determine the vector geographic plaintext data corresponding to the vector geographic ciphertext data according to the constructed three-dimensional inverse Arnold transform formula; the three-dimensional inverse Arnold transform formula is:
[0024]
[0025] Where x, y, and z are the coordinate values after the three-dimensional inverse Arnold transformation; x′, y′, and z′ are the coordinate values before the three-dimensional inverse Arnold transformation; P is the modulus; A -1 is the inverse matrix of the transformation matrix, and its structure is:
[0026]
[0027] Where a r 、ag 、a b 、c r 、c g 、c b is the transformation coefficient, which is any positive integer, a positive value or a randomly generated value.
[0028] The beneficial effects of the above technical solution are as follows: the decryption method of the present invention is implemented based on the corresponding encryption method, which is the inverse process of the encryption method. The encryption method is implemented based on the three-dimensional Arnold transformation, and the corresponding decryption method is also implemented based on the three-dimensional Arnold transformation. It can simply and quickly convert vector geographic ciphertext data into the corresponding vector geographic plaintext data to realize data decryption.
[0029] Furthermore, after step 1), the step of preprocessing the acquired vector geographic ciphertext data to obtain vector geographic encrypted data is also included, and the preprocessing includes offset processing of the vector geographic ciphertext data; accordingly, the means of determining the vector geographic plaintext data corresponding to the vector geographic ciphertext data in step 2) is: substituting the vector geographic encrypted data into the three-dimensional Arnold inverse transformation formula and performing t Arnold inverse transformations to obtain vector geographic processed data corresponding to the vector geographic encrypted data, t≥1; according to the offset situation during preprocessing, the vector geographic processed data is restored and offset processed to obtain the vector geographic plaintext data.
[0030] The beneficial effects of the above technical solution are: since the coordinate data of vector geographic data can be of any integer or floating point type, the vector geographic plaintext data is preprocessed in the encryption processing stage so that the processed vector geographic data is a non-negative integer, so as to ensure the closure, numerical uniqueness and calculation accuracy of subsequent encryption operations. Correspondingly, offset and recovery offset processing are also required in the decryption stage to ensure the correctness of decryption.
[0031] Furthermore, if the vector geographic ciphertext data is two-dimensional vector geographic ciphertext data, then in step 2), for at least two two-dimensional vector geographic ciphertext data, a corresponding number of vector geographic encrypted data are obtained, and the three coordinate value data in all the vector geographic encrypted data are taken in turn, and substituted into the three-dimensional Arnold inverse transformation formula for t times of Arnold inverse transformation, and when there are less than three coordinate value data at the end, supplementary processing is performed until all the vector geographic encrypted data are traversed, so as to finally obtain the vector geographic processed data corresponding to all the vector geographic encrypted data.
[0032] The beneficial effects of the above technical solution are: the encryption of two-dimensional vector geographic plaintext data can be accurately realized in the encryption stage, and accordingly, the decryption of two-dimensional vector geographic plaintext data is realized by adopting a processing method opposite to the encryption method in the encryption stage, thereby realizing encryption processing that supports vector geographic data of different spatial dimensions.
[0033] Furthermore, the three coordinate value data in the obtained vector geographic encryption data are all coordinate value data in the x-direction or all coordinate value data in the y-direction.
[0034] Furthermore, the vector geographic ciphertext data is data obtained after encryption of the vector geographic plaintext data, and the vector geographic plaintext data is data extracted according to geographic elements or data extracted according to layers in the vector geographic dataset.
[0035] The beneficial effects of the above technical solution are: on the basis of completely maintaining the original vector geographic data structure, according to the characteristics of different element types, a method of encryption is provided that can be adopted by taking values according to geographic elements and by taking values according to layers. Accordingly, different decryption methods are realized to meet the decryption requirements of different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] Figure 1 It is a flow chart of the vector geographic data encryption method based on three-dimensional Arnold transformation of the present invention;
[0037] Figure 2 It is a flow chart of the vector geographic data decryption method based on three-dimensional Arnold transformation of the present invention. DETAILED DESCRIPTION
[0038] A vector geographic data encryption method based on three-dimensional Arnold transformation and a vector geographic data decryption method based on three-dimensional Arnold transformation of the present invention are described in detail below with reference to the accompanying drawings and embodiments.
[0039] Encryption method embodiment:
[0040] An embodiment of a vector geographic data encryption method based on three-dimensional Arnold transformation of the present invention is as follows: Figure 1 As shown:
[0041] Step 1: Extract vector geographic data from the vector geographic dataset element by element or layer by layer, and call it vector geographic plaintext data.
[0042] Feature-by-feature extraction: This method iterates over every geographic feature object in the dataset, which can be a point, line, or area. This method controls the granularity of subsequent encryption operations at the feature level, facilitating selective encryption and is suitable for encrypting both linear and area features.
[0043] Layer-by-layer extraction: Encrypt each layer of vector geographic data in turn. This method operates on a layer-by-layer basis and is applicable to different feature types, such as points, lines, and areas.
[0044] Step 2: pre-process the vector geographic plaintext data (including offset processing and rounding processing) to obtain pre-processed vector geographic plaintext data, which is called vector geographic processed data.
[0045] Vector geographic data is a set of coordinate values. In theory, the coordinate value data can be any integer or floating point type. In order to ensure the closure, uniqueness and accuracy of encryption operations, it is necessary to perform offset processing and rounding on the vector geographic plaintext data. The offset processing and rounding are done by expanding the coordinate value by 10 according to the number of digits n in the decimal part of the coordinate value. n times, the resulting coordinate values are non-negative integers. If there is a possibility that the data value exceeds the limit or higher accuracy is required, the original coordinates can be offset from the origin, that is, all coordinate values are subtracted from the minimum coordinate value in the data set. Alternatively, the integer and decimal parts of the coordinate values can be separated and then combined during the transformation.
[0046] Step three, using the constructed three-dimensional Arnold transformation formula and the type of vector geoprocessing data (if it is two-dimensional vector geoprocessing plaintext data, the corresponding vector geoprocessing data is two-dimensional vector geoprocessing data; if it is three-dimensional vector geoprocessing plaintext data, the corresponding vector geoprocessing data is three-dimensional vector geoprocessing data), perform scrambling encryption operations on the vector geoprocessing data to obtain vector geoprocessing encrypted data. The vector geoprocessing encrypted data obtained at this time is not the final vector geociphertext data.
[0047] In this step, the three-dimensional Arnold transformation formula used is as follows:
[0048]
[0049] Where x, y, and z are the coordinate values before the three-dimensional Arnold transformation, which are the coordinate values of the vector geoprocessing data (called processing coordinate values); x′, y′, and z′ are the coordinate values after the three-dimensional Arnold transformation, which are the coordinate values of the vector geoencrypted data (called encrypted coordinate values); P is the modulus, and modulus P X and Model P Y Take the maximum value greater than the x and y coordinate offsets after rounding; A is the transformation matrix, and its structure is:
[0050]
[0051] Where a r 、a g 、a b 、c r 、c g 、c bis the transformation coefficient, which is an arbitrary positive integer. There are two ways to obtain the value of the transformation coefficient. One is to specify the data and keep it confidential and recorded; the other is to generate it randomly by calculation. Common methods include calling a random number generation function in the program, or using a linear chaos model to iterate. The stronger the randomness of the transformation coefficient, the more difficult it is to crack the ciphertext and the better the encryption effect.
[0052] Moreover, in order to increase the complexity of decryption, the vector geoprocessing data can be subjected to multiple three-dimensional Arnold transformations. Therefore, it is necessary to record the number of transformations t, and a corresponding number of inverse transformations are also required during decryption. Since the Arnold transformation is periodic, when the transformation is repeatedly applied, the original input value can be restored at a certain moment. The period of the transformation T is related to P. Therefore, the number of transformations t generally does not exceed the period T. In order to avoid calculating the transformation period, the data can be restored based on the Arnold inverse transformation when the number of transformations t is known. Experiments have shown that the method of the present invention can achieve a high degree of scrambling with a single transformation. Therefore, in this embodiment, a single Arnold forward transformation is used. Accordingly, the data can be restored by calculating the inverse matrix and performing a single inverse transformation, thereby reducing the amount of calculation.
[0053] Therefore, in order to construct the three-dimensional Arnold transform formula, we first need to determine the key, that is, the transformation coefficient in formula (2). The key can be generated by specifying parameters or randomly generating methods; then assign values to the transformation matrix A, perform modulus calculation (P value calculation), determine the number of transformations t, and perform parameter verification.
[0054] The following is an introduction to the scrambling encryption operation processing process, including the scrambling encryption operation processing process for two-dimensional vector geoprocessing data and the scrambling encryption operation processing process for three-dimensional vector geoprocessing data.
[0055] 1) The scrambling and encryption operation process of two-dimensional vector geoprocessing data.
[0056] If it is two-dimensional vector geoprocessing data, the coordinate values of the vector geoprocessing data are (x1, y1), (x2, y2), (x3, y3), ..., (xn, yn), that is, one vector geoprocessing data includes two processing coordinate values. Then, when using the three-dimensional Arnold transformation formula, the three processing coordinate values are taken as x, y, and z in formula (1) and substituted into formula (1). The encrypted coordinate values x′, y′, and z′ corresponding to the three processing coordinate values can be obtained until all the two-dimensional vector geoprocessing data are traversed.
[0057] In specific processing, the three vector geoprocessing data can be grouped together, and all the x-direction coordinate values of the three vector geoprocessing data are taken as the three processing coordinate values, and are substituted into the formula (1) as x, y, and z, respectively, to obtain the encrypted coordinate values corresponding to the three x-direction coordinate values; and all the y-direction coordinate values of the three vector geoprocessing data are taken as the three processing coordinate values, and are substituted into the formula (1) as x, y, and z, respectively, to obtain the encrypted coordinate values corresponding to the three y-direction coordinate values. In this way, the encrypted geographic data corresponding to the three vector geoprocessing data can be finally obtained. Of course, you can also take three vector geoprocessing data, first take the two processing coordinate values of the first vector geoprocessing data and the x-direction coordinate value of the second vector geoprocessing data among the three vector geoprocessing data, and substitute these three processing coordinate values as x, y, and z in formula (1) into formula (1), and you can get the encrypted coordinate values corresponding to these three processing coordinate values. In this way, you can completely get the vector geography ciphertext data corresponding to the first vector geoprocessing data; then take the y-direction coordinate value of the second vector geoprocessing data and the two processing coordinate values of the third vector geoprocessing data, and substitute these three processing coordinate values as x, y, and z in formula (1) into formula (1), and you can get the encrypted coordinate values corresponding to these three processing coordinate values. At this point, you can completely get the vector geography encrypted data corresponding to the second vector geoprocessing data and the third vector geoprocessing data.
[0058] Regardless of the processing method, the key is to take three processing coordinate values and substitute them into formula (1) to obtain the encrypted coordinate values corresponding to these three processing coordinate values. If the remaining processing coordinate values are less than three, a supplementary processing is performed. Specifically, the coordinate value of the last vector geoprocessing data read is assigned to the supplementary coordinate value to participate in the transformation. After all the encrypted coordinate values corresponding to the processing coordinate values are obtained through transformation, new vector geodata need to be assigned according to the original object sequence and coordinate point sequence in the vector geodata set to obtain the vector geodata encryption data corresponding to each vector geodata.
[0059] 2) The scrambling encryption operation process of three-dimensional vector geographic data.
[0060] If it is three-dimensional vector geoprocessing data, the coordinate values of the vector geoprocessing data are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), ..., (xn, yn, zn), that is, one vector geoprocessing data includes three processing coordinate values. Then, when using the three-dimensional Arnold transformation formula, the three coordinate values of this vector geoprocessing data are substituted into formula (1) as x, y, and z, respectively, to obtain the vector geoencrypted data corresponding to the vector geoprocessing data.
[0061] Step 4: Based on the offset during preprocessing in step 2, the vector geographic encrypted data is restored to restore the positive offset and scaling ratio of the transformed coordinate values to obtain vector geographic ciphertext data and realize vector geographic data encryption.
[0062] In summary, the encryption method of the present invention has the following characteristics:
[0063] 1) This method can perform geometric scrambling based on spatial transformation on vector geographic data without changing the original data structure, thereby achieving the purpose of data encryption. Moreover, this method has the characteristics of simple algorithm, high scrambling degree, fast encryption speed, complete reversibility and resistance to enumeration attacks, providing a balanced, lightweight and efficient scrambling encryption protection option for vector geographic data encryption.
[0064] 2) The method of the present invention does not directly encrypt the vector geographic plaintext data through the constructed three-dimensional Arnold transformation formula, but pre-processes it first to ensure the closure, numerical uniqueness and calculation accuracy of the encryption operation.
[0065] 3) A core key with more than 9 parameters, including Arnold transformation matrix coefficients, modulus, and number of transformations, is constructed, which has strong resistance to brute force attacks.
[0066] 4) The present invention can realize the encryption of two-dimensional vector geographic plaintext data, as well as the encryption of three-dimensional vector geographic plaintext data, and supports encryption processing of vector geographic data of different spatial dimensions, and has high practicality.
[0067] 5) When the present invention uses the three-dimensional Arnold transformation formula to perform data encryption, only one Arnold forward transformation is used, which greatly reduces the amount of calculation.
[0068] 6) While completely preserving the original vector geographic data structure, this method adopts encryption by layer value and encryption by feature value according to the characteristics of different feature types. The encryption control granularity can be adjusted to adapt to encryption processing at three granularities: single feature, specified feature set, and layer. Selective encryption strategies can be used to cope with more flexible and diverse encryption demand scenarios.
[0069] Decryption method embodiment:
[0070] The present invention is a method for decrypting vector geographic data based on three-dimensional Arnold transformation. The encryption method is actually the inverse process of the encryption method described in the encryption method embodiment. The process is as follows: Figure 2 As shown:
[0071] Step 1: pre-process the vector geographic ciphertext data (including offset processing) to obtain vector geographic encrypted data. The offset processing here is the inverse process of the offset recovery processing introduced in step 4 of the encryption method embodiment.
[0072] Step 2: Use the constructed three-dimensional Arnold transformation formula and the type of vector geographic ciphertext data (if during the encryption process, the encrypted vector geographic plaintext data is two-dimensional vector geographic plaintext data, the corresponding vector geographic ciphertext data is two-dimensional vector geographic ciphertext data; if the encrypted vector geographic plaintext data is three-dimensional vector geographic plaintext data, the corresponding vector geographic ciphertext data is three-dimensional vector geographic ciphertext data) to perform decryption operation on the vector geographic ciphertext data to obtain vector geographic processed data. The vector geographic processed data obtained at this time is not the vector geographic plaintext data that is ultimately desired.
[0073] In this step, the three-dimensional Arnold inverse transform formula used is as follows:
[0074]
[0075] Where x, y, and z are the coordinate values after the three-dimensional Arnold inverse transformation, which are the coordinate values of the vector geoprocessing data here; x′, y′, and z′ are the coordinate values before the three-dimensional Arnold inverse transformation, which are the coordinate values of the vector geoencryption data here; P is the modulus; A -1 is the inverse matrix of the transformation matrix, and its structure is:
[0076]
[0077] Where a r 、a g 、a b 、c r 、c g 、c b is the transformation coefficient, which is any positive integer.
[0078] Therefore, in order to construct the three-dimensional Arnold inverse transform formula, we first need to obtain the key used in the encryption process, that is, the transformation coefficient in formula (2); then we inverse the transformation matrix A -1 , perform modulus calculation (P value calculation), determine the number of transformations t used in the encryption process, and perform parameter verification.
[0079] The process of performing the decryption operation is actually the reverse process of the scrambling encryption operation process introduced in step 3 of the encryption method embodiment, and will not be described in detail here.
[0080] Step three: Based on the offset condition during preprocessing in step one, the vector geographic processing data is restored and decrypted to obtain vector geographic plaintext data.
[0081] Since the decryption method is actually the reverse process of the encryption method, the entire process and the corresponding beneficial effects will not be described in detail here.
Claims
1. A vector geographic data encryption method based on three-dimensional Arnold transformation, characterized in that: The steps include: 1) Obtaining vector geographic plaintext data and performing preprocessing; the preprocessing includes performing offset processing and rounding processing on the vector geographic plaintext data to obtain vector geographic processed data of non-negative integers; 2) Substituting the vector geoprocessing data into the three-dimensional Arnold transformation formula and performing t Arnold transformations to obtain vector geoencrypted data corresponding to the vector geoprocessing data, where t≥1; performing recovery offset processing on the vector geoencrypted data according to the offset during preprocessing to obtain vector geociphertext data; If the vector geographic plaintext data is two-dimensional vector geographic plaintext data, three coordinate value data from all vector geographic processing data are sequentially taken as vector geographic processing data to be substituted into the three-dimensional Arnold transformation formula; if there are less than three coordinate value data at the end, a supplementary process is performed until all vector geographic processing data are traversed; The three-dimensional Arnold transformation formula is: Where x, y, and z are the coordinate values before the three-dimensional Arnold transformation; x ′ 、y ′ 、z ′ is the coordinate value after three-dimensional Arnold transformation; P is the modulus, modulus P X and Model P Y Take the maximum value greater than the x and y coordinate offsets after rounding; A is the transformation matrix, and its structure is: Where a r 、a g 、a b 、c r 、c g 、c b is the transformation coefficient, which is any positive integer, a specified value or a randomly generated value.
2. The vector geographic data encryption method based on three-dimensional Arnold transformation according to claim 1 is characterized in that: The rounding process is as follows: according to the number of digits n in the decimal part of the coordinate value, the coordinate value is expanded by 10 n times.
3. The vector geographic data encryption method based on three-dimensional Arnold transformation according to claim 1 is characterized in that: The offset process is: all coordinate values minus the minimum coordinate value in the data set.
4. The vector geographic data encryption method based on three-dimensional Arnold transformation according to claim 1 is characterized in that: When the vector geographic plaintext data is two-dimensional vector geographic plaintext data, the three coordinate value data in the obtained vector geographic processing data are all coordinate value data in the x direction or all coordinate value data in the y direction.
5. The vector geographic data encryption method based on three-dimensional Arnold transformation according to any one of claims 1 to 4, characterized in that: The vector geographic plaintext data is data extracted according to geographic elements or data extracted according to layers in the vector geographic dataset.
6. A vector geographic data decryption method based on three-dimensional Arnold transformation, characterized in that: The steps include: 1) Obtaining vector geographic ciphertext data and performing preprocessing; the preprocessing includes performing offset processing on the vector geographic ciphertext data to obtain vector geographic encrypted data; 2) Substituting the vector geo-encrypted data into the three-dimensional inverse Arnold transform formula and performing t inverse Arnold transforms to obtain vector geo-processed data corresponding to the vector geo-encrypted data, where t≥1; performing recovery offset processing on the vector geo-processed data according to the offset during pre-processing to obtain vector geo-plaintext data; Among them, if the vector geographic encrypted data is two-dimensional vector geographic encrypted data, then the three coordinate value data in all the vector geographic encrypted data are taken in turn as the vector geographic encrypted data to be substituted into the three-dimensional Arnold inverse transformation formula; if there are less than three coordinate value data at the end, the data are supplemented until all the vector geographic encrypted data are traversed; The three-dimensional inverse Arnold transform formula is: Where x, y, and z are the coordinate values after the three-dimensional Arnold inverse transformation; x ′ 、y ′ 、z ′ is the coordinate value before the three-dimensional Arnold inverse transformation; P is the modulus, modulus P X and Model P Y Take the maximum value greater than the x and y coordinate offset respectively; A -1 is the inverse matrix of the transformation matrix, and its structure is: Where a r 、a g 、a b 、c r 、c g 、c b is the transformation coefficient, which is any positive integer, a specified value or a randomly generated value.
7. The vector geographic data decryption method based on three-dimensional Arnold transformation according to claim 6 is characterized in that: When the vector geographic encrypted data is two-dimensional vector geographic encrypted data, the three coordinate value data in the vector geographic encrypted data are all coordinate value data in the x-direction or all coordinate value data in the y-direction.
8. The vector geographic data decryption method based on three-dimensional Arnold transformation according to claim 6 is characterized in that: The vector geographic ciphertext data is data obtained after the vector geographic plaintext data is encrypted, and the vector geographic plaintext data is data extracted according to geographic elements or data extracted according to layers in the vector geographic dataset.