CN103067159B

CN103067159B - A kind of reversible DecryptDecryption method of GIS vector data

Info

Publication number: CN103067159B
Application number: CN201210586283.3A
Authority: CN
Inventors: 周卫; 闫娜
Original assignee: Nanjing Normal University
Current assignee: Nanjing Normal University
Priority date: 2012-12-28
Filing date: 2012-12-28
Publication date: 2016-03-02
Anticipated expiration: 2032-12-28
Also published as: CN103067159A

Abstract

The invention discloses a reversible decryption method for GIS vector data, which belongs to the field of geographic information security. The method includes the following processes: (1) The key generation process, including determining the data range, determining the data transformation amount, calculating the medium error caused by the linear transformation quantity and determining the parameters, calculating the medium error caused by the nonlinear transformation quantity and determining the parameters, and using The asymmetric encryption algorithm RSA encrypts the key Key and stores it in the key file; (2) Decryption process, including reading the key file, decrypting and extracting the key; opening the original vector data; obtaining the coordinate set of feature points; Normalization; loop processing; (3) recovery process. The method of the present invention has the characteristics of randomness, gradual change, reversibility, etc., improves the reliability of GIS vector data decryption, improves the theory and method system of geographic information security protection, and can be used for the public release of GIS vector data and the like.

Description

A Reversible Decryption Method for GIS Vector Data

技术领域technical field

本发明属于地理信息安全领域，具体涉及一种针对GIS矢量数据的可逆脱密方法。The invention belongs to the field of geographic information security, and in particular relates to a reversible decryption method for GIS vector data.

背景技术Background technique

测绘地理信息事关拓展发展空间，事关国家安全。尤其在全球信息化的大趋势下，地理信息安全保护问题越来越突出。矢量数据具有精度高、输出质量好、数据量小等特点，应用十分广泛，其安全保护研究十分重要。Surveying and mapping geographic information is related to expanding development space and national security. Especially under the general trend of global informatization, the issue of geographic information security protection is becoming more and more prominent. Vector data has the characteristics of high precision, good output quality, and small data volume. It is widely used, and its security protection research is very important.

根据国家相关法律法规，矢量数据公开使用需要经过脱密处理，脱密包括空间精度脱密和属性脱密两个方面。空间精度脱密使用专业脱密技术进行要素的位移，降低其精度，且脱密后的数据在没有密钥的情况下不易恢复。目前常用的空间精度脱密方法包括投影转换法、空间变换法、随机误差干扰法等。投影转换法是可逆的；数据空间变换法包括相似变换、仿射变换和射影变换等，这几种变换方法是线性变换，易于恢复，脱密处理的可靠性差；随机误差干扰法有的会存在不能保证要素的拓扑关系或算法不可逆等缺点。According to the relevant laws and regulations of the country, the public use of vector data needs to be declassified. The declassification includes two aspects: spatial precision declassification and attribute declassification. Spatial precision decryption uses professional decryption technology to displace elements, reducing its accuracy, and the declassified data is not easy to recover without a key. At present, the commonly used spatial precision declassification methods include projection transformation method, spatial transformation method, random error interference method and so on. The projection transformation method is reversible; the data space transformation method includes similar transformation, affine transformation and projective transformation, etc. These transformation methods are linear transformations, easy to recover, and the reliability of decryption processing is poor; some random error interference methods will exist Disadvantages such as the topological relationship of the elements or the irreversibility of the algorithm cannot be guaranteed.

发明内容Contents of the invention

本发明针对现有脱密方法存在的缺陷，提供一种非线性混合模型对矢量数据进行脱密处理的方法，具有误差的随机性、要素关系的拓扑性、算法的可逆性和难以破解等特点。Aiming at the defects existing in the existing decryption methods, the present invention provides a method for decrypting vector data with a nonlinear mixed model, which has the characteristics of randomness of errors, topology of element relationships, reversibility of algorithms, and difficulty in deciphering. .

一种GIS矢量数据可逆脱密方法，以线图层为例，包括如下过程：A method for reversible decryption of GIS vector data, taking a line layer as an example, includes the following process:

(一)密钥生成过程(1) Key generation process

步骤11，确定数据范围：获取原始矢量数据V的最小外接矩形R，R左下角坐标为(x_min，y_min)，右上角坐标为(x_max，y_max)，根据公式(1)得数据中心点坐标(x_mid，y_mid)、数据长度XL和数据宽度YL；Step 11, determine the data range: obtain the minimum circumscribed rectangle R of the original vector data V, the coordinates of the lower left corner of R are (x _min , y _min ), the coordinates of the upper right corner are (x _max , y _max ), and the data are obtained according to formula (1) Center point coordinates (x _mid , y _mid ), data length XL and data width YL;

$\{\begin{matrix} {x x}_{mid middle} = = (({x x}_{min min} + + {x x}_{max max})) / / 22 \\ {y the y}_{mid middle} = = (({y the y}_{min min} + + {y the y}_{max max})) / / 22 \\ XL XL = = {x x}_{max max} - - {x x}_{min min} \\ YL YL = = {y the y}_{max max} - - {y the y}_{min min} \end{matrix} - - - - - - ((11))$

步骤12，确定数据变换量：具体步骤如下：输入数据总体变换量offset，offset＞0，非线性变换量nonlinear，0＜nonlinear＜＝offset，根据公式(2)得到线性变换量linear；Step 12, determine the amount of data transformation: the specific steps are as follows: the overall transformation amount offset of the input data, offset>0, the nonlinear transformation amount nonlinear, 0<nonlinear<=offset, and the linear transformation amount linear is obtained according to formula (2);

$linear linear = = \sqrt{{offset offset}^{22} - - {nonlinear nonlinear}^{22}} - - - - - - ((22))$

步骤13，计算线性变换量linear引起的中误差，确定影响变换效果的参数：焦距f、航高H、偏角倾角ω、旋角κ，具体步骤如下：Step 13, calculate the medium error caused by the linear transformation amount linear, and determine the parameters that affect the transformation effect: focal length f, flying height H, deflection angle Inclination ω, rotation κ, the specific steps are as follows:

c)焦距f∈(0，1)，c) focal length f ∈ (0, 1),

d)根据公式(3)计算航高H，d) Calculate flight height H according to formula (3),

$H h = = \sqrt{XL XL * * YL YL} / / f f - - - - - - ((33))$

c)根据公式(4)计算线性变化量linear的扰动范围linearExtent，c) Calculate the disturbance range linearExtent of the linear variation linear according to formula (4),

$linearExtent linearExtent = = \sqrt{linear linear} - - - - - - ((44))$

d)生成控制点集合，具体步骤如下：在最小外接矩形R范围内生成m*n(m*n＞＝6)个均匀控制点组成源控制点集合FromPoints＝{(Fx_i，Fy_i)|i＝1，2，...m*n}；根据公式(5)计算每个目标控制点坐标(Tx_i，Ty_i)组成目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...m*n}，d) Generate a set of control points, the specific steps are as follows: Generate m*n (m*n>=6) uniform control points within the range of the smallest circumscribed rectangle R to form a source control point set FromPoints={(Fx _i , Fy _i )| i=1, 2,...m*n}; Calculate each target control point coordinates (Txi, Ty _i _{) according to the formula (5) to form a set of target control points ToPoints={(Txi, Ty i} ₎ | _i =1,2,...m*n},

$\{\begin{matrix} {Tx Tx}_{i i} = = {Fx Fx}_{i i} + + {dir dir}_{11} \times \times linear linear + + {random random}_{11} \times \times linearExtent linearExtent \\ {Ty Ty}_{i i} = = {Fy Fy}_{i i} + + {dir dir}_{22} \times \times linear linear + + {random random}_{22} \times \times linearExtent linearExtent \end{matrix} - - - - - - ((55))$

其中：方向参数dir₁在[0.0，1.0]范围内，方向参数控制点扰动参数random₁和random₂在[-1.0，1.0]范围内随机选取，Among them: the direction parameter dir ₁ is in the range of [0.0, 1.0], the direction parameter The control point disturbance parameters random ₁ and random ₂ are randomly selected in the range [-1.0, 1.0],

e)坐标归一化，根据公式(6)对源控制点集合FromPoints和目标控制点集合ToPoints进行归一化处理得到新坐标集合FromPoints’＝{(Fx_i’，Fy_i’)|i＝1，2，...m*n}，ToPoints’＝{(Tx_i’，Ty_i’)|i＝1，2，...m*n}，e) Coordinate normalization, according to the formula (6), the source control point set FromPoints and the target control point set ToPoints are normalized to obtain a new coordinate set FromPoints'={(Fx _i ', Fy _i ')|i=1 , 2,...m*n}, ToPoints'={(Tx _i ', Ty _i ')|i=1, 2,...m*n},

$\{\begin{matrix} {Fx Fx}_{i i}^{' '} = = (({Fx Fx}_{i i} - - {x x}_{mid middle})) * * f f / / H h \\ {Fy Fy}_{i i}^{' '} = = (({Fy Fy}_{i i} - - {y the y}_{mid middle})) * * f f / / H h \\ {Tx Tx}_{i i}^{' '} = = (({Tx Tx}_{i i} - - {x x}_{mid middle})) * * f f / / H h \\ {Ty Ty}_{i i}^{' '} = = (({Ty Ty}_{i i} - - {y the y}_{mid middle})) * * f f / / H h \end{matrix} - - - - - - ((66))$

f)计算偏角倾角ω、旋角κ，根据公式(7)利用最小二乘法对FromPoints’中源控制点和ToPoints’中目标控制点进行拟合解算得到偏角倾角ω、旋角κ，f) Calculation of declination Inclination ω and rotation κ, according to the formula (7), use the least squares method to fit and solve the source control point in FromPoints' and the target control point in ToPoints' to obtain the deflection angle Inclination ω, rotation κ,

g)计算线性变换中误差accuracy₁，具体步骤如下：根据公式(8)转换源控制点集合FromPoints’坐标得到目标控制点集合ToPoints”＝{(Tx_i”，Ty_i”)|i＝1，2，...m*n}，g) Calculating the error accuracy ₁ in the linear transformation, the specific steps are as follows: convert the coordinates of the source control point set FromPoints' according to the formula (8) to obtain the target control point set ToPoints"={(Tx _i ", Ty _i ")|i=1, 2,...m*n},

根据公式(9)计算中误差accuracy1，Calculate the medium error accuracy1 according to the formula (9),

${accuracy accuracy}_{11} = = \sqrt{Σ Σ (({(({Tx Tx}_{i i}^{' '' '} - - {Fx Fx}_{i i}))}^{22} + + {(({Ty Ty}_{i i}^{' '' '} - - {Fy Fy}_{i i}))}^{22})) / / ((m m * * n no))} - - - - - - ((99))$

h)调节目标控制点集合，具体步骤如下：如果|linear/accuracy₁-1|＞0.01，则根据公式(10)调节每个原目标控制点坐标(Tx_i，Ty_i)，得到新的目标控制点坐标(NTx_i，NTy_i)，用新的目标控制点替代原目标控制点即Tx_i＝NTx_i、Ty_i＝NTy_i，得到目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...m*n}，h) Adjust the set of target control points, the specific steps are as follows: If |linear/accuracy ₁ -1|>0.01, adjust the coordinates (Tx _i , Ty _i ) of each original target control point according to formula (10) to obtain a new target Control point coordinates (NTx _i , NTy _i ), replace the original target control point with a new target control point, that is, Txi _{= NTxi , Ty i} _{= NTy i} _, _and get the set of target control points ToPoints={(Txi , Ty _i ₎ |i=1,2,...m*n},

$\{\begin{matrix} {NTx NTx}_{i i} = = {Fx Fx}_{i i} + + ((linear linear / / accuracy accuracy)) (({Tx Tx}_{i i} - - {Fx Fx}_{i i})) \\ {NTy NTy}_{i i} = = {Fy Fy}_{i i} + + ((linear linear / / accuracy accuracy)) (({Ty Ty}_{i i} - - {Fy Fy}_{i i})) \end{matrix} - - - - - - ((1010))$

i)循环步骤e)-h)直至|linear/accuracy₁-1|＜＝0.01，得到最终的偏角倾角ω、旋角κ；i) Repeat steps e)-h) until |linear/accuracy ₁ -1|<=0.01 to get the final declination Inclination ω, rotation κ;

步骤14，计算非线性变换量nonlinear引起的中误差，确定参数j₀-j₅，具体步骤如下：Step 14, calculate the medium error caused by the nonlinear transformation amount nonlinear, and determine the parameters j ₀ -j ₅ , the specific steps are as follows:

b)生成控制点高程，利用公式(11)计算源控制点集合FromPoints每个点位移nonlinear所需的高程Fz_i，生成三维源控制点集合FromPoints＝{(Fx_i，Fy_i，Fz_i)|i＝1，2，...m*n}，b) Generate control point elevations, use formula (11) to calculate the elevation Fz _i required for each point displacement nonlinear of the source control point set FromPoints, and generate a three-dimensional source control point set FromPoints={(Fx _i , Fy _i , Fz _i )| i=1,2,...m*n},

${Fz Fz}_{i i} = = H h * * nonlinear nonlinear / / \sqrt{{(({x x}_{mid middle} - - {Fx Fx}_{i i}))}^{22} + + {(({y the y}_{mid middle} - - {Fy Fy}_{i i}))}^{22}} - - - - - - ((1111))$

b)根据公式(12)对生成的三维源控制点集合FromPoints进行最小二乘解算，得到参数j₀-j₅，b) According to the formula (12), perform the least squares calculation on the generated 3D source control point set FromPoints, and obtain the parameters j ₀ -j ₅ ,

Fz_i＝j₀+j₁Fx_i+j₂Fy_i+j₃Fx_i ²+j₄Fy_i ²+j₅Fx_iFy_i(12)Fz _i ＝j ₀ +j ₁ Fx _i +j ₂ Fy _i +j ₃ Fx _i ² +j ₄ Fy _i ² +j ₅ Fx _i Fy _i (12)

c)计算非线性变换中误差accuracy₂，具体步骤如下：根据公式(12)和参数j₀-j₅解算每个源控制点的Fz_i值，保存到三维源控制点集合FromPoints中，根据公式(13)对三维源控制点集合FromPoints进行计算得到目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...m*n}，c) Calculating the error accuracy ₂ in the nonlinear transformation, the specific steps are as follows: Calculate the Fz _i value of each source control point according to formula (12) and parameters j ₀ -j ₅ , save it in the three-dimensional source control point set FromPoints, according to Formula (13) calculates the three-dimensional source control point set FromPoints to obtain the target control point set ToPoints={(Tx _i , Ty _i )|i=1, 2,...m*n},

$\{\begin{matrix} {Tx Tx}_{i i} = = ((- - f f (({Fx Fx}_{i i} - - {x x}_{mid middle})) / / (({Fz Fz}_{i i} - - H h)))) * * H h / / f f + + {x x}_{mid middle} \\ {Ty Ty}_{i i} = = ((- - f f (({Fy Fy}_{i i} - - {y the y}_{mid middle})) / / (({Fz Fz}_{i i} - - H h)))) * * H h / / f f + + {y the y}_{mid middle} \end{matrix} - - - - - - ((1313))$

根据公式(14)计算中误差accuracy₂，Calculate the medium error accuracy ₂ according to formula (14),

${accuracy accuracy}_{22} = = \sqrt{Σ Σ (({(({Tx Tx}_{i i} - - {Fx Fx}_{i i}))}^{22} + + {(({Ty Ty}_{i i} - - {Fy Fy}_{i i}))}^{22})) / / ((m m * * n no))} - - - - - - ((1414))$

d)调节源控制点高程值，如果|nonlinear/accuracy₂-1|＞0.01，则根据公式(15)调节每个源控制点坐标高程值，得到新的高程值NFzi，用新高程值替代原高程值即Fzi＝NFzi，得到三维源控制点集合FromPoints＝{(Fx_i，Fy_i，Fz_i)|i＝1，2，...m*n}，d) Adjust the elevation value of the source control point. If |nonlinear/accuracy ₂ -1|>0.01, adjust the coordinate elevation value of each source control point according to formula (15) to obtain a new elevation value NFzi, and replace the original elevation value with the new elevation value The elevation value is Fzi=NFzi, and the three-dimensional source control point set FromPoints={(Fx _i , Fy _i , Fz _i )|i=1, 2,...m*n} is obtained,

$\{\begin{matrix} {NFz NFz}_{i i} &Element; &Element; (({Fz Fz}_{i i} / / 22,, (({nonlinear nonlinear / / accuracy accuracy}_{22})) * * {Fz Fz}_{i i})) & if if (({nonlinear nonlinear / / accuracy accuracy}_{22} > > 11)) \\ {NFz NFz}_{i i} &Element; &Element; (((({nonlinear nonlinear / / accuracy accuracy}_{22})) * * {Fz Fz}_{i i} / / 22,, {Fz Fz}_{i i})) & if if (({nonlinear nonlinear / / accuracy accuracy}_{22} < < 11)) \end{matrix} - - - - - - ((1515))$

e)循环步骤b)-d)，直至|nonlinear/accuracy₂-1|＜＝0.01，得到最终参数j₀-j₅；e) Repeat steps b)-d) until |nonlinear/accuracy ₂ -1|<=0.01, to obtain the final parameters j ₀ -j ₅ ;

步骤15，焦距f、航高H、偏角倾角ω、旋角κ、数据中心点坐标(x_mid，y_mid)、参数j₀-j₅组成密钥Key，用非对称加密算法RSA对密钥Key进行加密并存入密钥文件Key.txt；Step 15, focal length f, flying height H, deflection angle Inclination ω, rotation κ, data center point coordinates (x _mid , y _mid ), and parameters j ₀ -j ₅ form the key Key, which is encrypted with the asymmetric encryption algorithm RSA and stored in the key file Key. txt;

(二)脱密过程(2) Decryption process

步骤21，读取密钥文件Key.txt，解密后提取密钥Key，打开原始矢量数据V；Step 21, read the key file Key.txt, extract the key Key after decryption, and open the original vector data V;

步骤22，生成每个点高程值z_j，转换坐标，具体步骤如下：Step 22, generate the elevation value z _j of each point, and transform the coordinates, the specific steps are as follows:

a)提取矢量数据V的要素点坐标，得到要素点坐标集合P＝{(x_j，y_j，z_j)|j＝1，2，...，k}，其中k为要素包含的点个数，a) Extract the element point coordinates of the vector data V, and obtain the element point coordinate set P={(x _j , y _j , z _j )|j=1, 2, ..., k}, where k is the point contained in the element number,

b)根据密钥Key和公式(16)循环计算集合P中每一个点坐标p_j(x_j，y_j，z_j)的高程值z_j并保存到集合P中，b) According to the key Key and the formula (16), the elevation value z _j of each point coordinate p _j (x _j , y _j , z _j ) in the set P is cyclically calculated and saved in the set P,

z_j＝j₀+j₁x_j+j₂y_j+j₃x_j ²+j₄y_j ²+j₅x_jy_j(16)z _j =j ₀ +j ₁ x _j +j ₂ y _j +j ₃ x _j ² +j ₄ y _j ² +j ₅ x _j y _j (16)

c)根据公式(17)和密钥Key，对每个点坐标p_j(x_j，y_j，z_j)进行计算，得到点坐标集合P’＝{(x_j’，y_j’，z_j)|j＝1，2，...，k}；c) According to the formula (17) and the key Key, calculate the coordinates p _j (x _j , y _j , z _j ) of each point, and obtain the set of point coordinates P'={(x _j ', y _j ', z _j )|j=1,2,...,k};

步骤23，坐标归一化，根据密钥Key和公式(18)对每个点坐标p_j’(x_j’，y_j’，z_j)进行归一化处理得到脱密后点坐标集合P”＝{(x_j”，y_j”，z_j)|j＝1，2，...，k}；Step 23, coordinate normalization, according to the key Key and formula (18), normalize each point coordinate p _j '(x _j ', y _j ', z _j ) to obtain the decrypted point coordinate set P "={(x _j ", y _j ", z _j )|j=1, 2, ..., k};

$\{\begin{matrix} {x x}_{j j}^{' '' '} = = {x x}_{mid middle} + + {x x}_{j j}^{' '} * * H h / / f f \\ {y the y}_{j j}^{' '' '} = = {y the y}_{mid middle} + + {y the y}_{j j}^{' '} * * H h / / f f \end{matrix} - - - - - - ((1818))$

步骤24，循环步骤22到23，直至每个要素处理完毕，保存脱密后的数据文件W；Step 24, loop steps 22 to 23, until each element is processed, save the data file W after decryption;

(三)恢复过程(3) Recovery process

步骤31，读取密钥文件Key.txt，解密后提取密钥Key，打开脱密后的矢量数据W；Step 31, read the key file Key.txt, extract the key Key after decryption, and open the decrypted vector data W;

步骤32，坐标归一化，具体步骤如下：Step 32, coordinate normalization, the specific steps are as follows:

a)提取矢量数据W的要素点坐标，得到坐标集合P”＝{(x_j”，y_j”，z_j)|j＝1，2，...，k}，a) Extract the coordinates of the element points of the vector data W, and obtain the coordinate set P”={(x _j ”, y _j ”, z _j )|j=1, 2, ..., k},

b)根据密钥Key和公式(19)，对集合P”集合中每个点坐标p_j”(x_j”，y_j”，z_j)进行归一化处理生成点坐标集合P’＝{(x_j’，y_j’，z_j)|j＝1，2，...，k；b) According to the key Key and formula (19), normalize the coordinates p _j ”(x _j ”, y _j ”, z _j ) of each point in the set P” to generate a set of point coordinates P’={ (x _j ', y _j ', z _j )|j=1, 2, ..., k;

$\{\begin{matrix} {x x}_{j j}^{' '} = = (({x x}_{j j}^{' '' '} - - {x x}_{mid middle})) * * f f / / H h \\ {y the y}_{j j}^{' '} = = (({y the y}_{j j}^{' '' '} - - {y the y}_{mid middle})) * * f f / / H h \end{matrix} - - - - - - ((1919))$

步骤33，转换坐标，根据公式(20)和密钥Key对每个点坐标p_j’(x_j’，y_j’，z_j)进行计算，然后将高程值z_j置零，得到恢复后的点坐标p_j(x_j，y_j，0)，生成坐标集合P＝{(x_j，y_j，0)|j＝1，2，...，k}；Step 33, convert the coordinates, calculate the coordinates p _j '(x _j ', y _j ', z _j ) of each point according to the formula (20) and the key Key, and then set the elevation value z _j to zero, and get the recovered Point coordinates p _j (x _j , y _j , 0), generate coordinate set P={(x _j , y _j , 0)|j=1, 2,..., k};

步骤34，循环步骤32到33，直至每个要素处理完毕，保存恢复后的数据文件Q。Step 34, loop steps 32 to 33 until each element is processed, and save the restored data file Q.

本发明提出了一种非线性混合模型对GIS矢量数据进行脱密与恢复处理。本方法针对GIS矢量数据的安全保护问题，在保证矢量数据拓扑关系不发生改变的前提下，根据密钥可对数据进行脱密，脱密后的数据依据密钥可进行无损恢复。本方法具有随机性、渐变性、可逆性等特点，提高了GIS矢量数据脱密的可靠性，完善了地理信息安全保护的理论与方法体系，可用于GIS矢量数据的公开发布等方面。The invention proposes a nonlinear mixed model to decipher and recover GIS vector data. This method aims at the security protection problem of GIS vector data, under the premise of ensuring that the topological relationship of the vector data does not change, the data can be decrypted according to the key, and the decrypted data can be restored without loss according to the key. This method has the characteristics of randomness, gradual change, and reversibility, which improves the reliability of GIS vector data decryption, improves the theory and method system of geographic information security protection, and can be used in the public release of GIS vector data.

附图说明Description of drawings

图1是本发明方法脱密过程流程图。Fig. 1 is a flow chart of the decryption process of the method of the present invention.

图2是本发明方法恢复过程流程图。Fig. 2 is a flowchart of the recovery process of the method of the present invention.

图3是本发明实施例选用的原始矢量数据。Fig. 3 is the original vector data selected by the embodiment of the present invention.

图4是本发明原始数据和脱密后矢量数据叠加的效果图。Fig. 4 is an effect diagram of superposition of the original data and the decrypted vector data according to the present invention.

具体实施方式detailed description

下面结合附图对本发明的实施例做详细说明。Embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

本实施例选择shp格式矢量数据，对数据进行读取、脱密与恢复操作，进一步详细说明本发明。本实施例选择某一建筑的shp线图层数据(如图3)作为原始矢量数据，包括以下步骤：In this embodiment, the vector data in shp format is selected, and operations of reading, deciphering and restoring the data are performed, and the present invention is further described in detail. The present embodiment selects the shp line layer data (as Fig. 3) of a certain building as original vector data, comprises the following steps:

(一)密钥生成过程(1) Key generation process

步骤11，确定数据范围：获取原始矢量数据V的最小外接矩形R，R左下角坐标为(123451.63676768，142705.11870332)，右上角坐标为(123726.302067681，142994.494303319)，根据公式(1)得数据中心点坐标(123588.969417681，142849.80650332)、数据长度XL＝274.665300000459和数据宽度YL＝289.375599998981；Step 11, determine the data range: obtain the minimum circumscribed rectangle R of the original vector data V, the coordinates of the lower left corner of R are (123451.63676768, 142705.11870332), the coordinates of the upper right corner are (123726.302067681, 142994.494303319), and the coordinates of the data center point ( 123588.969417681, 142849.80650332), data length XL=274.665300000459 and data width YL=289.375599998981;

步骤12，确定数据变换量：具体步骤如下：输入数据总体变换量offset＝50，非线性变换量nonlinear＝7，根据公式(2)得到线性变换量linear＝49.5075751779463；Step 12, determine the amount of data transformation: the specific steps are as follows: the overall transformation amount of input data offset=50, the nonlinear transformation amount nonlinear=7, and the linear transformation amount linear=49.5075751779463 is obtained according to formula (2);

e)焦距f＝0.15，e) focal length f=0.15,

f)根据公式(3)计算航高H＝1879.49681193348，f) According to the formula (3), calculate flight height H=1879.49681193348,

c)根据公式(4)计算线性变化量linear的扰动范围linearExtent＝7.03616196359537，c) Calculating the disturbance range linearExtent=7.03616196359537 of the linear variation linear according to the formula (4),

d)生成控制点集合，具体步骤如下：在最小外接矩形R范围内生成4*4个均匀控制点组成源控制点集合FromPoints＝{(Fx_i，Fy_i)|i＝1，2，...4*4}；根据公式(5)计算每个目标控制点坐标(Tx_i，Ty_i)组成目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...4*4}，d) Generate a set of control points, the specific steps are as follows: Generate 4*4 uniform control points within the range of the smallest circumscribed rectangle R to form a source control point set FromPoints={(Fx _i , Fy _i )|i=1, 2, .. .4*4}; According to the formula (5), calculate the coordinates (Txi, Ty _i ) of each target control point to form the set of target control points ToPoints={(Txi, Ty _i ₎ | _i =1, 2,... 4*4},

e)坐标归一化，根据公式(6)对源控制点集合FromPoints和目标控制点集合ToPoints进行归一化处理得到新坐标集合FromPoints’＝{(Fx_i’，Fy_i’)|i＝1，2，...4*4}，ToPoints’＝{(Tx_i’，Ty_i’)|i＝1，2，...4*4}，e) Coordinate normalization, according to the formula (6), the source control point set FromPoints and the target control point set ToPoints are normalized to obtain a new coordinate set FromPoints'={(Fx _i ', Fy _i ')|i=1 , 2,...4*4}, ToPoints'={(Tx _i ', Ty _i ')|i=1, 2,...4*4},

f)计算偏角倾角ω、旋角κ，根据公式(7)利用最小二乘法对FromPoints’中源控制点和ToPoints’中目标控制点进行拟合解算得到偏角倾角ω＝0.00921638185358357、旋角κ＝0.0206308078601073，f) Calculation of declination Inclination ω and rotation κ, according to the formula (7), use the least squares method to fit and solve the source control point in FromPoints' and the target control point in ToPoints' to obtain the deflection angle Inclination ω=0.00921638185358357, rotation κ=0.0206308078601073,

g)计算线性变换中误差accuracy₁，具体步骤如下：根据公式(8)转换源控制点集合FromPoints’坐标得到目标控制点集合ToPoints”＝{(Tx_i”，Ty_i”)|i＝1，2，...4*4}，根据公式(9)计算中误差accuracy₁＝50.6202842886151，g) Calculating the error accuracy ₁ in the linear transformation, the specific steps are as follows: convert the coordinates of the source control point set FromPoints' according to the formula (8) to obtain the target control point set ToPoints"={(Tx _i ", Ty _i ")|i=1, 2, ... 4*4}, the error accuracy ₁ = 50.6202842886151 in the calculation according to the formula (9),

h)调节目标控制点集合，具体步骤如下：如果|linear/accuracy₁-1|＞0.01，则根据公式(10)调节每个原目标控制点坐标(Tx_i，Ty_i)，得到新的目标控制点坐标(NTx_i，NTy_i)，用新的目标控制点替代原目标控制点即Tx_i＝NTx_i、Ty_i＝NTy_i，得到目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...4*4}，h) Adjust the set of target control points, the specific steps are as follows: If |linear/accuracy ₁ -1|>0.01, adjust the coordinates (Tx _i , Ty _i ) of each original target control point according to formula (10) to obtain a new target Control point coordinates (NTxi, NTy _i ), replace the original target control points with new target control points, that is _{, Txi = NTxi, Ty i} ₌ _{NTy i} _, _and obtain the target control point set ToPoints={(Txi, Ty _i ₎ |i=1,2,...4*4},

i)循环步骤e)-h)，当accuracy₁＝49.5075776592392时|linear/accuracy₁-1|＜＝0.01，得到最终的偏角倾角ω＝0.00901382354283439、旋角κ＝0.0201770830635741；i) Cycle steps e)-h), when accuracy ₁ =49.5075776592392 |linear/accuracy ₁ -1|<=0.01, the final declination angle is obtained Inclination ω=0.00901382354283439, rotation κ=0.0201770830635741;

a)生成控制点高程，利用公式(11)计算源控制点集合FromPoints每个点位移nonlinear所需的高程Fz_i，生成三维源控制点集合FromPoints＝{(Fx_i，Fy_i，Fz_i)|i＝1，2，...4*4}，a) Generate control point elevations, use formula (11) to calculate the elevation Fz _i required for each point displacement nonlinear of the source control point set FromPoints, and generate a three-dimensional source control point set FromPoints={(Fx _i , Fy _i , Fz _i )| i=1,2,...4*4},

b)根据公式(12)对生成的三维源控制点集合FromPoints进行最小二乘解算，得到参数j₀＝-134576645.0625、j₁＝957.075539588928、j₂＝1056.14212036133、j₃＝-0.00386110281764473、j₄＝-0.00368852281107479、j₅＝-1.88736757991137E-05，b) According to formula (12), perform least squares calculation on the generated three-dimensional source control point set FromPoints, and obtain parameters j ₀ =-134576645.0625, j ₁ =957.075539588928, j ₂ =1056.14212036133, j ₃ =-0.00386110281764473, j ₄ = -0.00368852281107479, j ₅ =-1.88736757991137E-05,

c)计算非线性变换中误差accuracy₂，具体步骤如下：根据公式(12)和参数j₀-j₅解算每个源控制点的Fz_i值，保存到三维源控制点集合FromPoints中，根据公式(13)对三维源控制点集合FromPoints进行计算得到目标控制点集合ToPoints＝{(Tx_i，Ty_i)|i＝1，2，...4*4}，根据公式(14)计算中误差accuracy₂＝8.33449148774509，c) Calculating the error accuracy ₂ in the nonlinear transformation, the specific steps are as follows: Calculate the Fz _i value of each source control point according to formula (12) and parameters j ₀ -j ₅ , save it in the three-dimensional source control point set FromPoints, according to Formula (13) calculates the three-dimensional source control point set FromPoints to obtain the target control point set ToPoints={(Tx _i , Ty _i )|i=1, 2, ... 4*4}, according to formula (14) calculation Error accuracy ₂ = 8.33449148774509,

d)调节源控制点高程值，如果|nonlinear/accuracy₂-1|＞0.01，则根据公式(15)调节每个源控制点坐标高程值，得到新的高程值NFzi，用新高程值替代原高程值即Fzi＝NFzi，得到三维源控制点集合FromPoints＝{(Fx_i，Fy_i，Fz_i)|i＝1，2，...4*4}，d) Adjust the elevation value of the source control point. If |nonlinear/accuracy ₂ -1|>0.01, adjust the coordinate elevation value of each source control point according to formula (15) to obtain a new elevation value NFzi, and replace the original elevation value with the new elevation value The elevation value is Fzi=NFzi, and the three-dimensional source control point set FromPoints={(Fx _i , Fy _i , Fz _i )|i=1, 2,...4*4} is obtained,

e)循环步骤b)-d)，当accuracy₂＝6.9961779687363时|nonlinear/accuracy₂-1|＜＝0.01，得到最终参数j₀＝-92384371.34375、j₁＝544.834728956223、j₂＝822.104847669601、j₃＝-0.00253963583136851、j₄＝-0.00312865154306508、j₅＝0.000580351679673186；e) Cycle steps b)-d), when accuracy ₂ =6.9961779687363 |nonlinear/accuracy ₂ -1|<=0.01, the final parameters j ₀ =-92384371.34375, j ₁ =544.834728956223, j ₂ ₌ 822.104847669601, j -0.00253963583136851, j ₄ =-0.00312865154306508, j ₅ =0.000580351679673186;

(二)脱密过程(2) Decryption process

a)提取矢量数据V的要素点坐标，得到要素点坐标集合P＝{(x_j，y_j，z_j)|j＝1，2，...，k}，其中k为要素包含的点个数，下面以P中一点p(123677.937667681，142928.252103319，0)为例进行说明，a) Extract the element point coordinates of the vector data V, and obtain the element point coordinate set P={(x _j , y _j , z _j )|j=1, 2, ..., k}, where k is the point contained in the element The number, the following takes a point p(123677.937667681, 142928.252103319, 0) in P as an example to illustrate,

b)根据密钥Key和公式(16)循环计算集合P中每一个点坐标p_j(x_j，y_j，z_j)的高程值z_j并保存到集合P中，示例点p的高程值z＝119.892017556354，b) According to the key Key and formula (16), the elevation value z _j of each point coordinate p _j (x _j , y _j , z _j ) in the set P is cyclically calculated and saved in the set P, the elevation value of the example point p z=119.892017556354,

c)根据公式(17)和密钥Key，对每个点坐标p_j(x_j，y_j，z_j)进行计算，得到点坐标集合P’＝{(x_j’，y_j’，z_j)|j＝1，2，...，k}，示例点p(123677.937667681，142928.252103319，119.892017556354)转换后的点坐标为p’(0.00402027927973795，0.00517358718854751，119.892017556354)；c) According to the formula (17) and the key Key, calculate the coordinates p _j (x _j , y _j , z _j ) of each point, and obtain the set of point coordinates P'={(x _j ', y _j ', z _j )|j=1, 2,..., k}, example point p(123677.937667681, 142928.252103319, 119.892017556354) and the converted point coordinates are p'(0.00402027927973795, 0.00517358718854751, 119.865);

步骤23，坐标归一化，根据密钥Key和公式(18)对每个点坐标p_j’(x_j’，y_j’，z_j)进行归一化处理得到脱密后点坐标集合P”＝{(x_j”，y_j”，z_j)|j＝1，2，...，k}，点p’归一化后点坐标为p”(123639.34343161，142914.631440834，119.892017556354)；Step 23, coordinate normalization, according to the key Key and formula (18), normalize each point coordinate p _j '(x _j ', y _j ', z _j ) to obtain the decrypted point coordinate set P "={(x _j ", y _j ", z _j )|j=1, 2, ..., k}, the point p' coordinates after normalization is p" (123639.34343161, 142914.631440834, 119.892017556354);

(三)恢复过程(3) Recovery process

a)提取矢量数据W的要素点坐标，得到坐标集合P”＝{(x_j”，y_j”，z_j)|j＝1，2，...，k}，下面以点P”中一点p”(123639.34343161，142914.631440834，119.892017556354)为例进行说明，a) Extract the coordinates of the element points of the vector data W, and obtain the set of coordinates P”={(x _j ”, y _j ”, z _j )|j=1, 2, ..., k}, the following is the point P” One point p" (123639.34343161, 142914.631440834, 119.892017556354) as an example to illustrate,

b)根据密钥Key和公式(19)，对集合P”集合中每个点坐标p_j”(x_j”，y_j”，z_j)进行归一化处理生成点坐标集合P’＝{(x_j’，y_j’，z_j)|j＝1，2，...，k}，对示例点p”进行归一化处理得到点p’(0.00402027927973827，0.00517358718854753，119.892017556354)；b) According to the key Key and formula (19), normalize the coordinates p _j ”(x _j ”, y _j ”, z _j ) of each point in the set P” to generate a set of point coordinates P’={ (x _j ', y _j ', z _j )|j=1, 2, ..., k}, normalize the example point p" to get point p'(0.00402027927973827, 0.00517358718854753, 119.892017556354);

步骤33，转换坐标，根据公式(20)和密钥Key对每个点坐标p_j’(x_j’，y_j’，z_j)进行计算，然后将高程值z_j置零，得到恢复后的点坐标p_j(x_j，y_j，0)，生成坐标集合P＝{(x_j，y_j，0)|j＝1，2，...，k}，转换p’坐标得到恢复后的点坐标为p(123677.937667681，142928.252103319，0)；Step 33, convert the coordinates, calculate the coordinates p _j '(x _j ', y _j ', z _j ) of each point according to the formula (20) and the key Key, and then set the elevation value z _j to zero, and get the restored Point coordinates p _j (x _j , y _j , 0), generate coordinate set P={(x _j , y _j , 0)|j=1, 2,..., k}, transform p' coordinates to be recovered The final point coordinates are p(123677.937667681, 142928.252103319, 0);

本发明实施例中仅以线图层为例进行矢量数据的脱密与恢复，该方法也可用于点图层和面图层的脱密与恢复。In the embodiment of the present invention, only the line layer is used as an example to decrypt and restore vector data, and this method can also be used for decryption and restoration of point layers and surface layers.

本发明在保证矢量数据拓扑关系不发生改变的前提下对矢量数据进行脱密和恢复，并可根据需求设定参数以达到所需的脱密效果，脱密后的数据根据密钥可进行无损恢复。The present invention deciphers and restores the vector data on the premise that the topological relationship of the vector data does not change, and can set parameters according to requirements to achieve the required deciphering effect, and the deciphered data can be deciphered according to the key. recover.

Claims

1. A GIS vector data reversible deciphering method, is characterized in that, comprises following process:

(1) Key generation process

Step 11, determine the data range: obtain the minimum circumscribed rectangle R of the original vector data V, the coordinates of the lower left corner of R are (x _min , y _min ), the coordinates of the upper right corner are (x _max , y _max ), and the data are obtained according to formula (1) Center point coordinates (x _mid , y _mid ), data length XL and data width YL;

\{\begin{matrix} {x x}_{m m i i d d} = = (({x x}_{m m i i n no} + + {x x}_{m m a a x x})) / / 22 \\ {y the y}_{m m i i d d} = = (({y the y}_{m m i i n no} + + {y the y}_{m m a a x x})) / / 22 \\ X x L L = = {x x}_{max max} - - {x x}_{m m i i n no} \\ Y Y L L = = {y the y}_{max max} - - {y the y}_{m m i i n no} \end{matrix} - - - - - - ((11))

Step 12, determine the amount of data transformation: the specific steps are as follows: the overall transformation amount offset of the input data, offset>0, the nonlinear transformation amount nonlinear, 0<nonlinear<=offset, obtain the linear transformation amount linear according to formula (2);

l l i i n no e e a a r r = = \sqrt{{offset offset}^{22} - - {nonlinear nonlinear}^{22}} - - - - - - ((22))

Step 13, calculate the medium error caused by the linear transformation amount linear, and determine the parameters that affect the transformation effect: focal length f, flying height H, deflection angle Inclination ω, rotation κ, the specific steps are as follows:

131) focal length f ∈ (0,1),

132) Calculate flight height H according to formula (3),

H h = = \sqrt{X x L L * * Y Y L L} / / f f - - - - - - ((33))

133) Calculate the perturbation range linearExtent of the linear transformation amount linear according to formula (4),

l l i i n no e e a a r r E E. x x t t e e n no t t = = \sqrt{l l i i n no e e a a r r} - - - - - - ((44))

134) Generate a set of control points, the specific steps are as follows: Generate m*n uniform control points within the range of the smallest circumscribed rectangle R to form a set of source control points FromPoints={(Fx _i , Fy _i )|i=1, 2, .. .m*n}, m*n>=6; Calculate each target control point coordinates (Tx _i , Ty _i ) according to formula (5) to form a set of target control points ToPoints={(Tx _i , Ty _i )|i= 1, 2, ...m*n},

\{\begin{matrix} {Tx Tx}_{i i} = = {Fx Fx}_{i i} + + {dir dir}_{11} \times \times l l i i n no e e a a r r + + {random random}_{11} \times \times l l i i n no e e a a r r E E. x x t t e e n no t t \\ {Ty Ty}_{i i} = = {Fy Fy}_{i i} + + {dir dir}_{22} \times \times l l i i n no e e a a r r + + {random random}_{22} \times \times l l i i n no e e a a r r E E. x x t t e e n no t t \end{matrix} - - - - - - ((55))

Among them: the direction parameter dir ₁ is in the range of [0.0,1.0], the direction parameter The control point disturbance parameters random ₁ and random ₂ are randomly selected in the range of [-1.0,1.0],

135) Coordinate normalization, according to the formula (6), the source control point set FromPoints and the target control point set ToPoints are normalized to obtain a new coordinate set FromPoints'={(Fx _i ', Fy _i ')|i=1 , 2,...m*n}, ToPoints'={(Tx _i ', Ty _i ')|i=1, 2,...m*n},

\{\begin{matrix} {Fx Fx}_{i i}^{' '} = = (({Fx Fx}_{i i} - - {x x}_{m m i i d d})) * * f f / / H h \\ {Fy Fy}_{i i}^{' '} = = (({Fy Fy}_{i i} - - {y the y}_{m m i i d d})) * * f f / / H h \\ {Tx Tx}_{i i}^{' '} = = (({Tx Tx}_{i i} - - {x x}_{m m i i d d})) * * f f / / H h \\ {Ty Ty}_{i i}^{' '} = = (({Ty Ty}_{i i} - - {y the y}_{m m i i d d})) * * f f / / H h \end{matrix} - - - - - - ((66))

136) Calculate declination Inclination ω and rotation κ, according to the formula (7), use the least squares method to fit and solve the source control point in FromPoints' and the target control point in ToPoints' to obtain the deflection angle Inclination ω, rotation κ,

137) Calculate the error accuracy ₁ in the linear transformation, and the specific steps are as follows: convert the source control point set FromPoints' coordinates according to the formula (8) to obtain the target control point set ToPoints"={(Tx _i ", Ty _i ")|i=1, 2,...m*n},

Calculate the medium error accuracy ₁ according to the formula (9),

{accuracy accuracy}_{11} = = \sqrt{Σ Σ (({(({Tx Tx}_{i i}^{' '' '} - - {Fx Fx}_{i i}))}^{22} + + {(({Ty Ty}_{i i}^{' '' '} - - {Fy Fy}_{i i}))}^{22})) / / ((m m * * n no))} - - - - - - ((99))

138) Adjust the set of target control points, the specific steps are as follows: If |linear/accuracy ₁ -1|>0.01, then adjust the coordinates (Tx _i , Ty _i ) of each original target control point according to the formula (10) to obtain a new target Control point coordinates (NTx _i , NTy _i ), replace the original target control points with new target control points, that is, Txi _{= NTxi , Ty i} _{= NTy i} _, _and obtain a new set of target control points NTToPoints={(NTx _i , NTy _i )|i=1,2,...m*n},

\{\begin{matrix} {NTx NTx}_{i i} = = {Fx Fx}_{i i} + + ((l l i i n no e e a a r r / / {accuracy accuracy}_{11})) (({Tx Tx}_{i i} - - {Fx Fx}_{i i})) \\ {NTy NTy}_{i i} = = {Fy Fy}_{i i} + + ((l l i i n no e e a a r r / / {accuracy accuracy}_{11})) (({Ty Ty}_{i i} - - {Fy Fy}_{i i})) \end{matrix} - - - - - - ((1010))

139) Repeat steps 135)-138) until |linear/accuracy ₁ -1|<=0.01 to get the final declination Inclination ω, rotation κ;

Step 14, calculate the medium error caused by the nonlinear transformation amount nonlinear, and determine the parameters j ₀ , j ₁ , j ₂ , j ₃ , j ₄ and j ₅ , the specific steps are as follows:

141) Generate control point elevations, use the formula (11) to calculate the elevation Mz _i required for the nonlinear displacement of each point in the source control point set FromPoints, and generate a three-dimensional source control point set MFromPoints={(Mx _i , My _i , Mz _i )| i=1,2,...m*n},

{Mz Mz}_{i i} = = H h * * n no o o n no l l i i n no e e a a r r / / \sqrt{{(({x x}_{m m i i d d} - - {Mx Mx}_{i i}))}^{22} + + {(({y the y}_{m m i i d d} - - {My My}_{i i}))}^{22}} - - - - - - ((1111))

142) According to the formula (12), perform the least squares calculation on the generated 3D source control point set MFromPoints, and obtain the parameters j ₀ , j ₁ , j ₂ , j ₃ , j ₄ and j ₅ ,

Mz _i '＝j ₀ +j ₁ Mx _i +j ₂ My _i +j ₃ Mx _i ² +j ₄ My _i ² +j ₅ Mx _i My _i (12)

143) Calculate the error accuracy ₂ in the nonlinear transformation, the specific steps are as follows: calculate the Mz _i ' of each source control point according to formula (12) and parameters j ₀ , j ₁ , j ₂ , j ₃ , j ₄ and j ₅ The value is stored in the three-dimensional source control point set MFromPoints, and the three-dimensional source control point set MFromPoints is calculated according to formula (13) to obtain the target control point set NToPoints={(Nx _i , Ny _i )|i=1, 2, .. .m*n},

\{\begin{matrix} {Nx nx}_{i i} = = ((- - f f (({Mx Mx}_{i i} - - {x x}_{mi mi d d})) / / (({Mz Mz}_{i i}^{' '} - - H h)))) * * H h / / f f + + {x x}_{m m i i d d} \\ {Ny Ny}_{i i} = = ((- - f f (({My My}_{i i} - - {y the y}_{m m i i d d})) / / (({Mz Mz}_{i i}^{' '} - - H h)))) * * H h / / f f + + {y the y}_{m m i i d d} \end{matrix} - - - - - - ((1313))

Calculate the medium error accuracy ₂ according to formula (14),

{accuracy accuracy}_{22} = = \sqrt{Σ Σ (({(({Nx nx}_{i i} - - {Mx Mx}_{i i}))}^{22} + + {(({Ty Ty}_{i i} - - {My My}_{i i}))}^{22})) / / ((m m * * n no))} - - - - - - ((1414))

144) Adjust the elevation value of the source control point, if |nonlinear/accuracy ₂ -1|>0.01, then adjust the elevation value of each source control point coordinate according to the formula (15) to obtain a new elevation value NMz _i , replace it with the new elevation value The original elevation value is Mz _i =NMz _i , and the three-dimensional source control point set MFromPoints={(Mx _i ,My _i ,Mz _i )|i=1,2,...m*n} is obtained,

\{\begin{matrix} {NMz NM}_{i i} &Element; &Element; (({Mz Mz}_{i i}^{' '} / / 22,, ((n no o o n no l l i i n no e e a a r r / / {accuracy accuracy}_{22})) * * {Mz Mz}_{i i}^{' '})) & i i f f ((n no o o n no l l i i n no e e a a r r / / {accuracy accuracy}_{22} > > 11)) \\ {NMz NM}_{i i} &Element; &Element; ((((n no o o n no l l i i n no e e a a r r / / {accuracy accuracy}_{22})) * * {Mz Mz}_{i i}^{' '} / / 22,, {Mz Mz}_{i i}^{' '})) & i i f f ((n no o o n no l l i i n no e e a a r r / / {accuracy accuracy}_{22} < < 11)) \end{matrix} - - - - - - ((1515))

145) loop steps 142)-144), until |nonlinear/accuracy _2-1 |<=0.01, to obtain the final parameters j ₀ ', j ₁ ', j ₂ ', j ₃ ', j ₄ ' and j ₅ ';

Step 15, focal length f, flying height H, deflection angle Inclination ω, rotation κ, data center point coordinates (x _mid , y _mid ), parameters j ₀ ', j ₁ ', j ₂ ', j ₃ ', j ₄ ' and j ₅ ' form the key Key, and use non The symmetric encryption algorithm RSA encrypts the key Key and stores it in the key file Key.txt;

(2) Decryption process

Step 21, read the key file Key.txt, extract the key Key after decryption, and open the original vector data V;

Step 22, generate the elevation value z _j of each point, and transform the coordinates, the specific steps are as follows:

221) Extract the element point coordinates of the vector data V, and obtain the element point coordinate set P={(x _j ,y _j ,z _j )|j=1,2,...,k}, where k is the number of points contained in the element ,

222) According to the key Key and formula (16), the elevation value z _j of each point coordinate p _j (x _j , y _j , z _j ) in the set P is cyclically calculated and stored in the set P,

z _j =j ₀ '+j ₁ 'x _j +j ₂ 'y _j +j ₃ 'x _j ² +j ₄ 'y _j ² +j ₅ 'x _j y _j (16)

223) Calculate each point coordinate p _j (x _j , y _j , z _j ) according to the formula (17) and the key Key, and obtain the point coordinate set P'={(x _j ', y _j ', z _j )|j=1,2,...,k};

Step 23, coordinate normalization, according to the key Key and formula (18), normalize each point coordinate p _j '(x _j ', y _j ', z _j ) to obtain the decrypted point coordinate set P "={(x _j ",y _j ", z _j )|j=1,2,...,k};

\{\begin{matrix} {x x}_{j j}^{' '' '} = = {x x}_{m m i i d d} + + {x x}_{j j}^{' '} * * H h / / f f \\ {y the y}_{j j}^{' '' '} = = {y the y}_{m m i i d d} + + {y the y}_{j j}^{' '} * * H h / / f f \end{matrix} - - - - - - ((1818))

Step 24, loop through steps 22 to 23 until each element is processed, and save the decrypted vector data W;

(3) Recovery process

Step 31, read the key file Key.txt, extract the key Key after decryption, and open the decrypted vector data W;

Step 32, coordinate normalization, the specific steps are as follows:

321) Extract the coordinates of the element points of the vector data W, and obtain the coordinate set WP"={(wx _j ", wy _j ", wz _j )|j=1,2,...,k},

322) According to the key Key and formula (19), each point coordinate wp _j "(wx _j ", wy _j ", wz _j ) in the set WP" set is normalized to generate a point coordinate set WP'={ (wx _j ',wy _j ',wz _j )|j=1,2,...,k}};

\{\begin{matrix} {wx wx}_{j j}^{' '} = = (({wx wx}_{j j}^{' '' '} - - {x x}_{m m i i d d})) * * f f / / H h \\ {wy wy}_{j j}^{' '} = = (({wy wy}_{j j}^{' '' '} - - {y the y}_{m m i i d d})) * * f f / / H h \end{matrix} - - - - - - ((1919))

Step 33, convert the coordinates, calculate the coordinates wp _j '(wx _j ', wy _j ', wz _j ) of each point according to the formula (20) and the key Key, and then set the elevation value wz _j to zero to obtain the recovered Point coordinates wp _j (wx _j ,wy _j ,0), generate coordinate set WP={(wx _j ,wy _j ,0)|j=1,2,...,k};

\{\begin{matrix} {wx wx}_{j j} = = {x x}_{m m i i d d} + + \frac{(({wz w}_{j j} - - H h)) ((ω ω f f κ κ - - f f φ φ - - {ω ω}^{22} {wx wx}_{j j}^{' '} - - {wx wx}_{j j}^{' '} + + {φωwy φωwy}_{j j}^{' '} + + {κwy κwy}_{j j}^{' '}))}{(({fκ fκ}^{22} - - {ωwy ωwy}_{j j}^{' '} - - {φwx φwx}_{j j}^{' '} + + f f - - {ωκwx ωκwx}_{j j}^{' '} + + {φκwy φκwy}_{j j}^{' '}))} \\ {wy wy}_{j j} = = {y the y}_{m m i i d d} + + \frac{(({wz w}_{j j} - - H h)) (({ωφwx ωφwx}_{j j}^{' '} - - {φ φ}^{22} {wy wy}_{j j}^{' '} - - {wy wy}_{j j}^{' '} - - f f ω ω - - {κwx κwx}_{j j}^{' '} - - φ φ f f κ κ))}{(({fκ fκ}^{22} - - {ωwy ωwy}_{j j}^{' '} - - {φwx φwx}_{j j}^{' '} + + f f - - {ωκwx ωκwx}_{j j}^{' '} + + {φκwy φκwy}_{j j}^{' '}))} \end{matrix} - - - - - - ((2020))

Step 34, loop steps 32 to 33 until each element is processed, and save the restored vector data Q.