DNA dynamic coding-based encryption algorithm for vector map considering global objects

With the rapid development of digitalization and networking, copying and sharing vector map data has become convenient, but it also brings security risks such as data interception and tampering. Current encryption methods focus on partially encrypting objects, which may leave some sensitive and confidential objects unencrypted. Additionally, the encryption effect for the point layers is not satisfactory. This paper proposes an algorithm for encrypting vector maps based on DNA dynamic encoding. Initially, global scrambling is performed on all object coordinates using double random position permutation, and a four-dimensional hyperchaotic system is selected to ensure the complexity of the chaotic sequence. Next, DNA dynamic coding operations are applied to whole layers of the vector map to encrypt all data. Finally, the encrypted data can be decrypted and restored according to the DNA coding rules and the double random position permutation mapping relationship, with the decrypted data being consistent with the original. Experimental results indicate that the proposed algorithm can be applied to the encryption protection of various vector map elements, especially to improve the performance on encrypting point layer data compared with existing encryption algorithms. It improves the security of vector data in the process of storage and transmission, and has potential application value in the protection of vector map.


Introduction
Vector map data is an important strategic resource of the country, and a lot of manpower, material and financial resources are spent in the acquisition process (Wang 2009). It plays an important role in multiple fields including national defense, military affairs, and emergency response. As the Internet of things, cloud computing and other technologies are integrated into human life, great challenges have been brought to the security protection of vector map data (Zhou 2015). Vector map data is usually transmitted and stored in the form of digital files, which facilitates the copying and dissemination of map data, but undoubtedly increases the risk of data leakage. The protection of vector map data security has become an important issue that needs to be solved urgently, (Yan et al. 2011;Zhu et al. 2022). Vector maps are usually encrypted to improve the security in the process of share and use; hence, the algorithm of encrypting vector map data has become a hot research topic (Sun 2017;Yan et al. 2017;Da et al. 2018).
The protection of the copyrights and interests of vector map data producers and legal users can be divided into two categories: post-event accountability and pre-prevention (Zhu 2017). Digital watermark technology (Zhang et al. 2015;Tong et al. 2018Tong et al. , 2019Li and Stefanakis 2020) and digital fingerprint technology (Chen et al. 2020a, b;Yang et al. 2020) belong to post-event accountability. In the event of data copyright disputes, digital watermark technology can authenticate the copyright owner, and digital fingerprint Communicated by: H. Babaie technology can trace the original pirate. Pre-prevention mainly includes user channel control technology (Mao et al. 2017) and data encryption technology (Peng et al. 2019). User channel control technology prevents data leakage by controlling the operating system environment when users use data. The data encryption technology prevented the maps from being illegally intercepted and tampered with during the encapsulation storage and network share. This process converts plaintext data into ciphertext data without clear meaning through secure encryption keys and encryption functions, authorized users use the decryption key and decryption rules to convert ciphertext data into plaintext data containing valid information. The thieves who do not know the key cannot use the data, even if they have stolen it. In order to ensure the security of vector map data in the process of storage and share, this paper focuses on the algorithm of data encryption.
Scholars have done a lot of research on vector map data encryption technologies. Some researchers proposed encryption methods based on cryptographic mechanisms. They can be divided into symmetric encryption and asymmetric encryption according to the difference between keys. Common symmetric encryption algorithms include DES (Data Encryption Standard) algorithm (Coppersmith 1994) and AES (Advanced Encryption Standard) algorithm (Daemen and Rijmen 2002). RSA (RSA Public Key System) is a classic asymmetric encryption algorithm (Rivest et al. 1978). The advantage of encryption algorithms based on the cryptography mechanism lies in their simple implementation and mature key management scheme. However, the encryption efficiency and flexibility are relatively low. In addition, some algorithms only encrypt the partial vector map file. Based on the chaotic system proposed by Fridrich in 1997(Fridrich 1997 some studies proposed image encryption algorithms based on chaotic mechanics (Liu and Wang 2011;Hua et al. 2019;Schmidt and Barron 2020), which can be applied to the encryption of vector maps. Min (2005) proposed an encryption algorithm based on chaos mechanics that considers the characteristics of vector map data. The entire map still needs to be decrypted when extracting part of the data. The chaotic sequence generated by the lowdimensional chaotic system often has poor randomness, low security and small key space. In addition, the limitation of the computer word length leads to the degradation of the dynamic characteristics of the low-dimensional chaotic system. Therefore, A hyperchaotic system that ensures the complexity of the chaotic sequence is proposed, which has more complex dynamical behavior. Wu et al. (2008) proposed a vector map data encryption algorithm based on chaotic maps in the network environment, which can solve the problems of poor randomness of low-dimensional chaotic sequences, low security and easy cracking. Compared with the encryption algorithm based on the cryptography mechanism, the encryption algorithm based on the chaotic system has a larger key space and is easy to implement. However, some chaotic encryption algorithms result in low encryption speed. Encryption methods based on digital images have achieved rapid development (Lu et al. 2023;Zhou et al. 2023), and some researchers have proposed an encryption scheme based on compression coding (Chai et al. 2022;Huang et al. 2023). The basic principle of this encryption scheme is to compress the vector map data first and then encrypt it. Jang et al. (2014) proposed a compressive sensing encryption algorithm for the safe processing of vector maps, which compresses all vector data of polylines and polygons in the unit of lossless minimum coded objects. The perceptual encryption was performed on the two parts of the mean point and the direction of the minimum coded object. Wang (2017) proposed a method based on the unit compression structure. The integer part and the fractional part of the data were processed, and then the position and direction of the data were perceptually encrypted. Encryption technology based on compression coding can speed up data transmission efficiency and improve the ability to resist brute force attacks, but it needs to preprocess the original vector map data, and some preprocessing processes are relatively cumbersome. Bang et al. (2015) proposed a selective encryption algorithm for vector map data based on the chaotic mapping. It selected important objects to encrypt them using the key set generated by chaotic maps before changing them in DWT and DFT domains. Wang et al. (2021b) proposed an algorithm based on a double random position permutation strategy, which uses a four-dimensional hyperchaotic system to generate a key sequence, and uses a double random position permutation strategy to encrypt the coordinates of each layer. The algorithm had high efficiency. Some researchers proposed a vector map data scrambling encryption method, the core of which is to randomize the spatial position of the vector map data objects and change the data organization method and spatial object relationship (Pham et al. 2019). Li et al. (2015) proposed a vector digital map scrambling encryption technology based on a two-dimensional chaotic system. Considering the simplicity of the onedimensional chaotic system and the high complexity of the high-dimensional chaotic map, the two-dimensional Henon chaotic system was selected to destroy the vector map. The domain correlation and spatial order of data form an efficient encryption algorithm. Wang et al. (2021a) achieved the purpose of scrambling and encryption by randomizing Gaussian random numbers and Haar transform to scramble the coordinates of vector map data, and the algorithm has high security and efficiency. Li et al. (2021) proposed a vector map exchange cryptographic watermarking technology based on invariants. The algorithm has strong robustness by arranging scrambled vector data in double random positions, normalizing the coordinates of vertices, and embedding the scrambled watermark into the normalized coordinates.
Although the above studies based on chaos encryption and data scrambling encryption have achieved good performance, they cannot guarantee that all sensitive and confidential objects are encrypted. Therefore, this study aims at encrypting all objects. This type of scrambling encryption is mostly based on layer encryption research. At present, most scrambling algorithms achieve the purpose of encrypting data by disrupting the order and spatial correlation between vector elements, so most existing algorithms are mainly for polyline and polygon. Some special methods can also solve the purpose of point encryption, and there are relatively few researches on point encryption. The introduced of DNA encoding encryption technology in this paper can solve the problem of point encryption protection very well. DNA is an important carrier of genetic information storage in organisms. Due to its ultra-large-scale parallelism, ultrahigh storage density, ultra-low energy consumption, and unique molecular structure and intermolecular recognition mechanism, it determines its outstanding ability of information storage and processing. Encryption based on DNA encoding has both novel calculation methods and unique biological characteristics. It has been widely applied to digital image encryption (Chai et al. 2017(Chai et al. , 2021Yildirim 2022). The DNA sequence studied in bioengineering is similar to the key sequence in data encryption, it has potential to vector data encryption.
In summary, in order to solve the problem that the existing algorithm only encrypts and protects partial objects and cannot encrypt point layers, this paper proposes an algorithm for encrypting vector maps based on DNA dynamic encoding. It first uses double random position permutation to scramble the coordinates of the global objects; then applies DNA dynamic encoding rules to encrypt different coordinates with different encoding rules, which realizes the "onetime-pad" encryption effect of vector map data, once the encrypted data reach the authorized user, the original data can be decrypted and restored with the correct key.

Four-dimensional hyperchaotic system
Encryption algorithms need to be highly sensitive to plaintext data, while chaotic systems are characterized by sensitivity to initial values, pseudo-randomness, and ergodicity. Data encryption algorithms based on chaotic systems have aroused strong interest among researchers. Therefore, based on the Lorenz system, a new four-dimensional quadratic autonomous hyperchaotic system (4D-HCS) using only one equilibrium point to generate two wings and hyperchaotic attractors generates chaotic sequences of scrambled data. Using 4D-HCS to encrypt vector data, its security depends on the randomness of chaotic sequence. Although the attacker can guess the key parameters of the system by reconstructing the phase space, the operation is relatively complicated and difficult. In addition, 4D-HCS is very sensitive to initial values and parameters. Small changes in parameters or initial values may lead to large changes in chaotic dynamics. Its definition is shown in the following formula: where x, y, z, w is state variables, a, b, c, d, e are system parameters. When a = 10, b = 28, c = 8/3, d = 1, e = 16, the system presents a hyperchaotic state, and the trajectory of the attractor is relatively complex, as shown in Fig. 1.

SHA-512 hash algorithm
The SHA-512 hash algorithm uses a message length of 2 128 and can generate a message digest of size 512 bits. In this study, the vector map data and user key are encrypted with the SHA-512 algorithm. The generated 512-bit hash key H k and initial key U k . The message digests H k and U k with a length of 512 bits are grouped into groups of 8 bits, which can be divided into 64, which are represented by [a1, a2, … a63, a64]. Then convert the data in U k into decimal, and then divide it into 16 groups [G 1 , G 2 , … G 15 , G 16 ], the decimal data in each group is represented by k 1 , k 2 , k 3 , k 4 , 16 groups k 1 , k 2 , k 3 , k 4 is summed to obtain U k _sum, and U k _index is calculated by the following formula to select the index sequence.
At the same time k 1 , k 2 , k 3 , k 4 ∈ (0, +∞) are used as four external keys, which makes the message digest more complicated and harder to crack. Figure 2 shows the key grouping process of the SHA-512 hash algorithm.

Double random position permutation (DRPP)
The vertices of each feature in the vector map points, polylines, and polygons have position properties and order properties. The scrambling encryption technology can destroy the correlation between the vector data and the data storage order, so that the plaintext data becomes meaningless garbled data, so as to achieve the purpose of data encryption protection. The traditional sequence scrambling is shown in Fig. 3. The first element in the sequence is traversed to the last element, and then the index sequence D is used to scramble one by one. However, this traditional method of scrambling and encrypting data elements can provide a great convenience for cracking scrambled encryption by analyzing the sequence of the one-to-one mapping relationship between plaintext data and ciphertext data.
Double Random Position Permutation (DRPP) is proposed to solve this problem. As shown in Fig. 4, two index sequences are applied to perform permutation encryption processing. First, use the index sequence D1 to extract the data to be scrambled from the plaintext data; then, use the index sequence D2 to map it to another random bit; finally get the scrambled data, which not only reduces the correlation between the positions of the data elements, but also enhanced security of data element encryption.

DNA encoding and decoding
A DNA sequence is composed of four nucleic acid bases (Nucleic Acid Bases): Adenine (A), Cytosine (Cytosine, C), Guanine (Guanine, G) and Thymine (Thymine, T); Deoxyribose and phosphate in DNA molecules are alternately Fig. 1 Shows the phase diagram of a four-dimensional hyperchaotic system with parameters a = 10, b = 28, c = 8/3, d = 1, e = 16, and the initial values are (1, 1, 1, 1). a projection on x-y-z, b projection on x-y, connected and arranged on the outside to form the basic backbone, and the bases are arranged on the inside. The bases on the two strands are combined by hydrogen bonds, A and T are complementary to G and C, forming a base pair, and the base sequence of one nucleic acid chain is paired with the base sequence of the other nucleic acid chain in antiparallel, forming a base pair. Since 0 and 1 are complementary in the binary system, 00 and 11 are complementary, and 01 and 10 are also complementary. In the process of data encryption, any combination of DNA base pairs can be selected, which improves the security of data encryption. Figure 5 is a schematic diagram of the base pairing of the DNA double helix structure. There are 24 coding types using four nucleic acid bases (A, C, G and T) to code 00, 01, 10 and 11, but only the eight of them conform to the Watson-Crick complementarity rule, as shown in Table 1. It is worth noting that DNA decoding rules are the inverse process of its encoding rules. When DNA coding rule 1 is adopted, the operation rules are listed in Tables 2, 3 and 4.

DNA XOR operation
DNA coding operations are operations such as addition, subtraction, and XOR between codes, and their essence is binary arithmetic operations. The DNA XOR operation is performed through the traditional binary format. There are eight kinds of DNA rules, and there are eight corresponding DNA XOR operation rules. For example, it can be seen from Table 2 that the XOR result of the DNA sequences "GCAT" and "TGAC" is "CTAG".

Introduction to research data types
Vector data and raster data, as the main structure of spatial data in geographic information system, can use computerbased tools GIS to manage, analyze and display geographic information. Raster data is similar to a digital image. It is an image composed of small rectangles, called grid cells or grid points. Each grid cell has a fixed pixel value, representing the color of the grid point or other attribute information. Raster data is usually stored in binary code, and can be managed and stored in spatial databases using grid indexes or spatial grids. Vector map data is to express the geometric position of spatial objects by recording the coordinates and spatial relationships of spatial objects, mainly point, polyline, and polygon. It is also called feature class in ArcGIS. Feature classes have the same spatial cartographic expression. There are two ways to store vector map data in a spatial database: one is to use a coordinate system to represent the position of each point, usually using a spatial reference system to describe geographic coordinates; the other is to use geometric objects to represent lines and polylines and other graphics, usually stored using a vector data type. Vector data not only expresses geometric positions and attributes, but also expresses spatial relationships. Each spatial object contains identification codes and attribute codes. Every time a spatial object is stored, there will be a unique code to connect the geometry and attribute data. Figure 6 shows the legend of vector map data introduction. For city roads in real ground objects, raster data is similar to digital images, and is expressed as grid information composed of small rectangular blocks. Vector data is expressed as coordinates and positional relationships for polyline elements. Vector map data is divided into three basic types: point, polyline, and polygon. Point is most commonly used to represent features that are not adjacent and represent discrete data points. Points have zero size, so you cannot measure length or area with this dataset. Such as schools, scenic spots, manhole covers. Point features are also used to represent abstract points. For example, a point location can represent a city location or a place name. Polyline is used to represent linear features. Common examples are rivers, roads and streets. Polyline features have a start point and an end point. Common examples are representations of road centerlines and rivers. Polygon is used to represent areas, such as administrative divisions, lakes, or forests. Polygon data can be used to measure the area and perimeter of geographic features. Vector map data has a compact structure and low redundancy, which is beneficial to network and retrieval analysis. The graphic display quality is good and the accuracy is high. Vector map data has great application advantages in geographic information research.

Encryption algorithm
As shown in Fig. 7, the proposed encryption algorithm first uses SHA-512 to obtain the external key of the original map file, and as the initial value of the fourdimensional hyperchaotic system, calculates four chaotic sequences X, Y, Z, W, arranges them in ascending order, and then calculates the ascending order. The sequence is represented as an index sequence, which is combined into six sets of index sequence combinations at the same time; then according to the index sequence rules, select the corresponding index sequence combination to perform double random position permutation on the vector map data coordinates x, y using DRPP, and then through the four chaotic sequences Perform calculations to obtain four variables to dynamically determine the DNA encoding rules; finally, perform DNA encoding operations on the double random position permutation data according to the selected DNA encoding rules, and finally obtain the ciphertext map data after the geographic vector data undergoes DNA encoding and decoding operations, reaching The purpose of map vector data encryption protection is achieved.

Permutation encryption (PEE)
Through the four-dimensional hyperchaotic system, two highly random double random position permutation index sequences D1 and D2 are generated, and the data objects are scrambled. First, use D1 to select the object to be scrambled from the original data, and then use the index sequence D2 rule to map it to another random position. All the objects in the entire data are subjected to DRPP operation to obtain the scrambling and encryption effect of the entire data.
Step1: Use SHA-512 to obtain the external key U k , where U x0 , U y0 , U z0 , U w0 are used as the initial values of the four-dimensional hyperchaotic system, and iterate t 0 + L_num times, where L_num represents the sum of the number of vertices under each object. To avoid the periodic influence of the chaotic system, remove the value before t 0 to obtain four chaotic sequences X, Y, Z, W of length L_num, and represent them in ascending order as X 1 , Y 1 , Z 1 , W 1 . The corresponding index  sequence D X , D Y , D Z , D W is obtained by the following formula (3): Step2: In order to enhance the correlation between the encryption algorithm and the plaintext, the index sequences are combined into 6 groups, each of which is: Step3: Obtain the hash value of the original map file according to SHA-512, and convert each hexadecimal .
Substituting the parameters r 1 , r 2 , r 3 , and r 4 calculated by the above formula into the following formula (6) can obtain the information of the initial values U x0 , U y0 , U z0 , U w0 , and U w0 of the four-dimensional hyperchaotic system.
character in the hash value to a decimal number. In order to reduce the correlation between the x-coordinate and the y-coordinate, sum all the converted decimals to obtain H_sum, and process H_sum to obtain Hx_index by the following formula. As shown in the following formula (4): For Hy_index, the parameters r 1 , r 2 , r 3 , and r 4 are first obtained through the following formula (5) (4) Hx_index = mod(H_sum, 6) + 1, Hx_index ∈ [1, 6] . .
With the change of the parameters of the four-dimensional hyperchaotic system, the stability of the system equilibrium point will change, so the system will also be in different states. Fix the parameter a = 10, c = 8/3, d = 1, e = 16, change the parameter b, when b∈[20, 600] changes, the bifurcation diagram of the system about z is shown in Fig. 8, where the black represents b is within the range of [20, 600], the maximum possible chaotic state of z, and the blue color is the chaotic state that b is within the range of [20,600], and the minimum value of z may occur. The chaotic range of the system can be seen from the figure.
Then calculate through formula (7) to get Hy_index: Step4: Select a group of index sequences from Step2, and select the index sequence of the Ai group according to the rule of Hx_index (or Hy_index) = i.
Step5: The coordinate values x i,j , y i,j of the vector map data x and y are respectively replaced by DRPP according to different Ai groups, and the obtained scrambling sequences are S_x i,j and S_yi,j. Take the index sequence combination A1 group and A2 group as an example, where D X ( i ) means to use the index of A1 group to select the object to be scrambled from x i,j , store it in C_x i,j . Then use D Y ( i ) in the combination of index sequence A1 to randomly map C_x i,j to S_x i,j , and complete the DRPP replacement of x i,j . In the same way, the DRPP permuta- Hy_index = fllor(mod( r 1 +r 2 +r 3 +r 4 4 × 10 6 , 6)) + 1, Hy_index ∈ [1, 6] .
tion of the y coordinate is performed according to the index sequence combination A2 group to obtain S_y i, j , i∈ [1, L_num]. Traverse x i, j , y i, j of the entire vector data, and the permutation operation is shown in the following formula (8, 9):

DNA encryption (DNAE)
The traditional XOR operation is a binary XOR operation in two dimensions (either 0 or 1), while the XOR operation after DNA encoding is an XOR operation in four dimensions (it is the XOR operation of the four ATCG), to improve the sensitivity of the XOR operation, enhance the unpredictability of the encoding, and then achieve the purpose of improving the  Fig. 6 Vector map data presentation legend security of the encryption algorithm. DNA encryption is to obtain four variables by performing operations on the four chaotic sequences X, Y, Z, W, and then perform DNA encoding and encryption on the vector data that has completed DRPP replacement according to the DNA encoding rules corresponding to the variables. The DNA coding rules are selected by chaotic sequences, which is more secure and not easy to be cracked. The specific steps are as follows: Step1: It can be seen from the above that U x0 , U y0 , U z0 , and U w0 are used as the initial values of the four-dimensional hyperchaotic system, and are iterated t 0 + L_num times, where L_num represents the sum of the number of vertices under each element. To avoid the periodic influence of the chaotic system, remove the value before t 0 to obtain four chaotic sequences X, Y, Z, W of length L_num.
Step2: According to formulas (10) -(13), operate with each element in X, Y, Z, W to get four variables R x (i), R y (i), R z (i) and R(i).
where X(i), Y(i), Z(i) and W(i) are the ith elements of X, Y, Z, W, i∈ [1,|L_num|], mod(x,y) is the modulo operation of x and y.
Step3: According to the DNA encoding rule corresponding to R z (i), R(i) is encoded by DNA to obtain (10) R x (i) = floor(mod(X(i) × 10 8 , 8)) + 1.   DNA_R(i). At the same time, according to the DNA coding rules corresponding to R y (i), S_x i,j and S_y i,j are encoded by DNA to obtain DNA_S(x i,j ) and DNA_S(y i,j ). Then, New_S(x i,j ) and New_S(y i,j ) are calculated by Eqs. (14) and (15).
a⊕b represents a XOR with b.
Step4: According to the DNA coding rule corresponding to R x (i), New_S(x i,j ) and New_S(y i,j ) are decoded to obtain encrypted coordinate values C_New_S(x i,j ) and C_New_S(y i,j ).

Decryption processing
The decryption process is an inverse process of the encryption process. The key includes the hash value obtained by encrypting the plaintext data according to SHA-512, the hash value obtained by encrypting the user key with SHA-512, the parameters of the fourdimensional chaotic system and the initial value. In the map encryption stage, we encrypt the x-coordinate and y-coordinate separately by layers, using DNA encryption and permutation encryption, respectively. Therefore, first decrypt the DNA encryption of the x-coordinate and y-coordinate; then, decrypt the permutation encryption of the x-coordinate and y-coordinate. In vector map coordinates, x and y is inseparable when expressing space content and objects. When the same key is used to encrypt the x and y value in the same way, and the key is deduced, all can be decrypted. Dividing x and y into two parts and using different keys and different encryption methods can greatly improve the security. Even if part of the key is obtained, only one of the x or y coordinates can be deduced, and the other value's The key could not be pushed out. At this time, the deciphered data is incomplete and cannot express the coordinate values of the feature objects.
If the cipher value of the x coordinate is attacked, the key used to encrypt the x plaintext coordinate is obtained. However, the key obtained by the attack cannot directly decrypt the y-coordinate cipher. If you want to obtain the y-coordinate plaintext value, you need to spend the same time cost as attacking the x-coordinate cipher to obtain the key. The time cost of the attack is greatly increased. Encrypt x and y separately so that the plaintext data of x will not be leaked. By deriving the key, the plaintext data of the y coordinate can be decrypted, which is more secure. The decryption operation is the reverse process of the encryption operation, and the specific decryption steps will not be repeated here.

Visualization of encryption and decryption results
Existing research mostly focuses on local data encryption, which not only needs to consider extracting important data objects, but also needs to ensure the accuracy and feature invariance of encryption, which leads to the introduction of large manual processing costs. In the current big data environment, there are certain limitations. Therefore, in order to reduce the cost of manual processing, the vector data is directly encrypted globally. All the experiments in this study are conducted using Python on an Intel core CPU @2.6 GHz, Windows 10 64-bit operating system, and 16 GB RAM. The experimental results are shown in Figs. 9, 10 and 11. Figure 9 is the point, i.e., the top 100 counties in a certain area are selected. Figure 9a shows the original point, and Fig. 9b shows the data encrypted by our encryption algorithm. Figure 9c is the decrypted points by our decryption algorithm in this paper. It can be found that our algorithm in this paper has a significant effect on encryption and decryption of point. The road network polyline of a city selected in Fig. 10a is the original road network polyline, Fig. 10b is the polyline layer data encrypted by the algorithm in this paper, and Fig. 10c is the polyline layer data after decryption algorithm. The encryption result is significant, and the decrypted polyline layer data is the same as the original polyline. The vector area data can be regarded as closed-end polylines. Therefore, the polygons can be converted into polylines, and then processed by the encryption and decryption algorithm in this paper, and the decrypted polyline can be converted into a polyline combination with end-to-end closure and direction, so as to realize the encryption and decryption operations of the polygon in this paper. As shown in Fig. 11, the polygon of a selected urban building area, Fig. 11a is the original polygon, and the legend of Fig. 11b shows the polyline layer data, which means that the original polygon is converted into open the combined polyline combination, and then the encrypted polyline layer data obtained by using the encryption and decryption algorithm in this paper can be expressed as the encrypted result of polygon. Figure 11c shows that the decrypted polyline layer data is reprocessed into a combination of directional and end-to-end closed polyline data forms decrypted polygon.

Comparative analysis of double random encryption and DNA encryption
In order to improve the randomness of the encrypted vector map data, our study used the double random position permutation vector map data and introduced the DNA algorithm to encrypt the data. Experiments on the points, polylines and polygons were conducted. Figure 12a shows the original points, Fig. 13b shows the data that are randomly encrypted by double random positions permutation, and Fig. 13c shows the data after DNA encryption. The data after the double random position permutation encryption is the same as the original data, which indicates that the double random position permutation encryption cannot encrypt the points. However, after the point layer is encrypted by the DNA algorithm, the encrypted data is completely different from the original data, which achieves the purpose of encrypting points. Figures 13 and 14 show the experimental results of polylines and polygons. Figure  The comparison of the encrypted points, polylines and polygons between double random position permutation encryption and DNA encryption was carried out, including the shape and coordinate value. The shape and coordinate value of the point layer stay the same after double random position permutation encryption. After the DNA algorithm encrypts the point layer, the shape and coordinate value have changed, reaching the effect of encryption. For the polylines and polygons, after double random position permutation encryption and DNA encryption, the shape and coordinate values have changed to a certain extent, and both algorithms can implement the encryption of polyline and polygon. It can be seen that the DNA encryption algorithm can not only solve the problem that existing algorithms cannot encrypt points, but also are suitable to polylines and polygons. Table 5 compares the performance of our algorithm and three existing encryption algorithms on points, polylines and polygons in terms of the shape and coordinate value. In Table 5, √ indicates that there is a change, and × indicates that there is no change. As can be seen, other

Key space analysis
The key space of the algorithm in this paper is large enough to resist various brute force attacks. In this study, the key includes the following contents: (1) the initial value and parameters of the four-dimensional hyperchaotic system; (2) the 512-bit hash value H k of the vector map data obtained by the SHA-512 hash algorithm; (3) four External keys k 1 , k 2 , k 3 , k 4 . Therefore, it is determined that the key space of the hyperchaotic system in this paper is 10 56 , and the calculation accuracy of general computers is 10 − 14 . 2 168 is often studied as a large space key. After comparative analysis, the hyperchaotic system key space 10 56 in this paper is much larger than 2 168 , that is, larger than 2 100 . Therefore, the key space of the algorithm proposed in this paper is much larger than 10 56 , which has a stronger ability to resist brute force attacks and has a higher security level.

Key sensitivity analysis
Key sensitivity refers to the degree of influence on the decryption result when the key changes slightly. The stronger the sensitivity of the key, the higher the security of the algorithm, and the more obvious the impact of the decryption result. In order to verify the sensitivity of the key, the key parameters can be slightly changed, and the sensitivity can be known from the results of the decryption experiment. In this paper, a, b, c, d, e is used as system parameters, and a small change is made when a = 10 + 10 − 16 , b = 28, c = 8/3, d = 1, e = 16. As shown, Fig. 15a is the original vector data, Fig. 15b is the encrypted data using the original key, Fig. 15c is the decrypted data obtained by a small change of the key, and Fig. 15d is the decrypted data obtained by using the correct key. Through the analysis of the key sensitivity experiment, it can be seen that only a small change of 10 − 16 in one of the parameters of the key can obtain the encrypted vector data and the wrong decryption result data as shown in the figure above, which cannot achieve the realization of encrypted 1 3 data. The lossless decryption effect can prove that the key sensitivity of the algorithm in this paper is strong, and it can be used as a vector data protection algorithm with a higher security level.

Conclusion
This paper proposes a vector map data encryption algorithm based on four-dimensional hyperchaotic system, double random position permutation and DNA code calculation, which takes global factors into account. In view of the fact that existing algorithms focus on the encryption of partial objects, it is difficult to ensure that all sensitive and confidential objects are encrypted. This paper chooses encryption research based on global objects to ensure that all objects can be encrypted and protected. Some algorithm encryption is mainly based on layer encryption research, and most algorithms can only encrypt polyline and polygon, but cannot encrypt point layer data. Therefore, this study introduces DNA encoding encryption technology, which solves the encryption protection of point well. At the same time, the chaotic sequence dynamics generated by the four-dimensional hyperchaotic system The selection of DNA encoding operation rules enhances the security of the algorithm. The encryption algorithm system in this paper is associated with the original vector map data, and achieves the encryption effect of "onetime padding". Theoretical and experimental analysis shows that the algorithm proposed in this paper has a large enough key space, strong key sensitivity, and appropriate complexity, has a high security level, not only can solve the problem that some existing algorithms cannot encrypt vector map point, but also can be applied to the protection of various vector space data whose geometric shape is polyline and polygon. In the next work, the copyright information of vector geographic data can be combined with the data encryption method in this paper, and the copyright information of the data can be confirmed while encrypting, so as to protect the security of vector geographic data from the source. This is also an ongoing scientific research project that the author participates in.
Author contributions Yan Qingbo contributed to the design and implementation of the algorithm. Yan Qingbo, Yan Haowen and Zhang Liming cooperatively collect data, design the experiments and analyze the results. The first draft of the manuscript was written by Yan Qingbo and were mainly commented by Yan Haowen and Zhang Liming. All authors read and approved the final manuscript.
Funding This study is supported by National Natural Science Foundation of China (NO. 42271430). This work is also supported by The Industrial Support and Guidance Project of Universities in Gansu Province, China (NO. 2019 C-04).

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.