CN111192361A - Geographic vector field data decryption and recovery method based on geometric algebra - Google Patents

Geographic vector field data decryption and recovery method based on geometric algebra Download PDF

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CN111192361A
CN111192361A CN201911297697.2A CN201911297697A CN111192361A CN 111192361 A CN111192361 A CN 111192361A CN 201911297697 A CN201911297697 A CN 201911297697A CN 111192361 A CN111192361 A CN 111192361A
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CN111192361B (en
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袁林旺
王赟
车骁宇
闫振军
张正方
罗文�
俞肇元
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Nanjing Fanzai Geographic Information Industry Research Institute Co ltd
Nanjing Normal University
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Abstract

本发明公开了一种基于几何代数的地理向量场数据脱密与恢复方法，包括：密钥生成中地理向量场数据坐标点及其扰动量的确定、脱密中误差的计算、脱密参数的确定和密钥的加密保存；脱密处理中密钥文件解密读取、打开地理向量场数据、遍历待脱密地理向量场数据要素并获取坐标点、归一化坐标并进行脱密处理、保存脱密后的地理向量场数据；恢复处理中密钥文件解密处理，脱密后地理向量场数据的恢复处理、恢复后地理向量场数据保存。本发明具有抗攻击能力强、脱密后地理向量场数据可以利用密钥进行恢复、且具有全局扰动随机、有效快捷等特性，可为地理向量场数据在共享、传输、存储等多方面提供技术支持。

Figure 201911297697

The invention discloses a method for deciphering and restoring geographic vector field data based on geometric algebra. Determining and encrypting and saving the key; decrypting and reading the key file during the decryption process, opening the geographic vector field data, traversing the elements of the geographic vector field data to be decrypted, obtaining coordinate points, normalizing the coordinates, performing decryption processing, and saving Decrypted geographic vector field data; key file decryption processing in recovery processing, recovery processing of decrypted geographic vector field data, and storage of recovered geographic vector field data. The present invention has strong anti-attack capability, can recover geographic vector field data after deciphering by using a key, and has the characteristics of global disturbance randomness, effectiveness and speed, etc., and can provide technology for sharing, transmission, storage and other aspects of geographic vector field data. support.

Figure 201911297697

Description

Geographic vector field data decryption and recovery method based on geometric algebra
Technical Field
The invention relates to the technical field of geographic information security, in particular to a geographic vector field data decryption and recovery method based on geometric algebra.
Background
The geographic vector field data is an important component of geographic information data and is also an important data source for geoscience research. In recent years, with the continuous expansion of global space-to-ground observation means, the continuous improvement of computer processing capability and the continuous deepening of climate mode simulation research. A large amount of geographic vector field data are being rapidly generated, transmitted and applied, and the simulation and analysis research of global or large-area climate and environmental changes is greatly promoted. On the other hand, a large amount of digitized geographic information data includes sensitive information in a large number of fields such as resources and environments. Particularly, some important geographic information space-time data relate to the national mastery and the homeland security, and have very important significance for the national modernization construction, so that secret-level geographic vector field data need to be converted into geographic vector field data meeting the requirement of public precision through technical means such as a decryption technology and the like for shared application.
① linear decryption method is relatively simple, lacks random disturbance and has low safety, ② nonlinear decryption method cannot effectively control random disturbance quantity, so that decrypted geographic vector field data cannot meet decryption requirements, ③ some nonlinear decryption methods are difficult to accurately recover reversely under the support of a secret key, use value of the decrypted geographic vector field data is reduced, and integration application of the decrypted geographic vector field data and original geographic vector field data is not facilitated.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides a geographic vector field data decryption and recovery method based on geometric algebra, wherein the geometric algebra is based on dimensional operation and can conveniently realize the mathematical operation of dimensional expansion and indentation. The multi-dimensional operation of geometric algebra can support the quick decryption operation of geographic vector field data. The method increases global random disturbance while considering the integral transformation of the geographic vector field data, and has the characteristics of strong attack resistance and safety, controllable error, capability of accurately recovering the geographic vector field data through a secret key, effectiveness, rapidness and the like.
The technical scheme is as follows: in order to realize the purpose, the invention adopts the following technical scheme:
a geographic vector field data decryption and recovery method based on geometric algebra comprises the following steps:
(1) and (3) key generation: the method comprises the steps of determining geographic vector field data coordinate points and disturbance quantities thereof in key generation, normalizing target coordinate points in a decryption process, calculating errors in the decryption process, determining decryption parameters and encrypting and storing keys;
(2) and (3) decryption treatment: the method comprises the steps of decrypting and reading a key file in decryption processing, opening geographic vector field data to be decrypted, traversing geographic vector field data elements to be decrypted, acquiring coordinate points, normalizing the coordinate points and performing decryption processing, and storing the decrypted geographic vector field data;
(3) and (3) recovery processing: the method comprises the steps of decryption processing of a key file in recovery processing, recovery processing of decrypted geographic vector field data and storage of recovered geographic vector field data.
Further, the determination of the coordinate point of the geographic vector field data and the disturbance amount thereof in the step (1) comprises the following steps:
(101) determining a geographic vector field data range to be decrypted
Is opened to be taken offAnd (3) acquiring dense geographic vector field data, wherein the minimum circumscribed rectangle R is obtained, and the angular coordinate of the upper left corner of R is (x)min，ymin) And the corner point coordinate of the lower right corner of R is (x)max，ymax) (ii) a Calculating the Length and the width Height of the data range of the geographic vector field to be decrypted according to the following formula;
Figure BDA0002321001780000021
(102) determination of geographic vector field data coordinate points and disturbance amounts thereof in key generation
Taking the index subscript from the geographic vector field data to be decrypted as a Coordinate point Coordinate (pX) of a geographic vector field data source in the decryption processi，pYi) And according to the decryption index, the disturbance quantity delta X of the coordinate point of the geographic vector field data source in each decryption process is giveniAnd Delta Yi(ii) a The geographic vector field data target Coordinate point Coordinate (tX) in the decryption processi，tYi) The coordinates of (a) are:
Figure BDA0002321001780000022
(103) geographic vector field data target coordinate point normalization in decryption process
Normalizing the geographic vector field data target coordinate point in the decryption process of the step (102) to [ -1,1 ] according to the following formula]Within the interval, wherein tXmean，tYmeanRespectively a geographic vector field data target Coordinate point Coordinate (tX) in the decryption processi，tYi) Middle tXi，tYiTo obtain a normalized geographic vector field data target Coordinate point Coordinate (nX)i，nYi)：
Figure BDA0002321001780000023
Further, the calculation of the error in decryption, the determination of decryption parameters and the encrypted storage of the secret key in the step (1) comprises the following steps:
(111) error calculation during decryption
Coordinate point Coordinate (nX) of normalized geographic vector field datai，nYi) And attribute data nZiInto formula (4), where N1，N2，N3，N4Four arbitrary decryption parameters, e1，e2，e3Obtaining Coordinate point Coordinate (RX) of the decrypted geographic vector field data as a unit vectori，RYi) And attribute data RZi；
Figure BDA0002321001780000031
Calculating a decryption error MSE according to a formula (5);
Figure BDA0002321001780000032
wherein n represents the number of coordinate points of a geographic vector field data source in the decryption process; Δ XiAnd Delta YiRespectively representing the disturbance quantity of a coordinate point of a geographic vector field data source in the decryption process; pXi，pYiA geographic vector field data source coordinate point in the decryption process is obtained;
(112) decker error control
Adjusting disturbance quantity of a target coordinate point of geographic vector field data in a decryption process: comparing the decryption error MSE with the decryption index, if MSE is larger than the decryption index sigma, the disturbance variable delta X of the target coordinate point of the geographic vector field data in the decryption process needs to be adjustediAnd Delta YiTo control errors in decryption; and controlling the offset of the target coordinate point of the geographic vector field data in the decryption process according to a formula (6), wherein delta Yinew，ΔXinewThe disturbance quantity of the target coordinate point of the adjusted geographic vector field data in the decryption process is as follows:
Figure BDA0002321001780000033
iterating steps (111) to (112) until the decryption error MSE is smaller than the decryption index sigma, and then executing step (113);
(113) and (3) generating a secret key: the final decryption parameter N1，N2，N3，N4And geographic vector field data target coordinate point offset delta X in decryption processiAnd Delta YiEncrypted using RSA (Rivest-Shamir-Adleman) algorithm and stored as a key file.
Further, the step (2) comprises the following steps:
(21) key file decryption reading
Decrypting and reading the key file by using RSA (Rivest-Shamir-Adleman) algorithm, and extracting decryption parameter N1，N2，N3，N4Opening the geographic vector field data to be decrypted;
(22) geo-vector field data read to be descreased
Traversing the geographic vector field data to be decrypted to obtain Coordinate point Coordinate (pX) of the geographic vector field data source in the decryption processi，pYi)；
(23) Normalizing the geographic vector field data coordinate points and performing decryption processing
Coordinate point Coordinate (pX) of geographic vector field data source in decryption processi，pYi) Normalized to [ -1,1 [ ]]Within the interval, obtaining a normalized geographic vector field data Coordinate point Coordinate (nX)i，nYi) (ii) a The normalized formula is:
Figure BDA0002321001780000041
(24) decrepitation treatment
Coordinate point Coordinate (nX) of the normalized geographic vector field datai，nYi) And attribute data nZiSubstituting the formula to obtain Coordinate point Coordinate (RX) of the decrypted geographic vector field datai，RYi) And attribute data RZi：
Figure BDA0002321001780000042
The error MSE in the decryption is calculated as:
Figure BDA0002321001780000043
(25) preserving decrypted geographic vector field data
And (5) circulating the steps (22) to (24) until all the coordinate points of the geographic vector field data after normalization are processed, and the error MSE in decryption is smaller than the decryption index sigma, and storing the decrypted geographic vector field data.
Further, the step (3) comprises the following steps:
(31) key file decryption reading
Decrypting and reading the key file by using an RSA (Rivest-Shamir-Adleman) algorithm, and encoding Coordinate (pX) of a geographic vector field data source in the decryption processi，pYi) As the recovered geographic vector field data target Coordinate point, the geographic vector field data target Coordinate point Coordinate (tX) in the decryption process is usedi，tYi) As the recovered geographic vector field data source Coordinate point, the geographic vector field data target Coordinate point Coordinate (tX) in the decryption processi，tYi) Amount of disturbance Δ XiAnd Delta YiCoordinate point Coordinate (tX) of geographic vector field data source in recovery processi，tYi) Amount of disturbance Δ XriAnd Delta YriMutually opposite numbers, and a decryption parameter N in the process of decryption simultaneously1，N2，N3，N4And a recovery parameter N in a recovery procedurer1，Nr2，Nr3，Nr4Mutually opposite numbers;
(32) recovery processing of decrypted geographic vector field data
Traversing the data of the decrypted geographic vector field to obtain Coordinate point Coordinate (RX) of the data of the decrypted geographic vector fieldi，RYi)；
(33) Recovering the decrypted geographic vector field data;
(34) post-recovery geographic vector field data preservation
And (4) processing all the geographic vector field data in the circulating step (33) until all the elements are processed, and storing the recovered geographic vector field data.
Further, the step (33) comprises the steps of:
(a) coordinate point Coordinate (RX) to be recovered in the recovery process in step (32)i，RYi) And attribute RZ after decryptioniAnd its recovery parameter Nr1，Nr2，Nr3，Nr4Substituting the formula into the formula, and solving to obtain geographic vector field data Coordinate point Coordinate (nX) in the recovery processi，nYi) And attribute data nZi：
Figure BDA0002321001780000051
(b) Reverse normalization: coordinate point Coordinate (nX) of geographic vector field data Coordinate point in the recovery process solved in the step (a)i，nYi) Substituting the formula into the data source Coordinate point Coordinate (tX) of the geographic vector field in the recovery processi，tYi)：
Figure BDA0002321001780000061
(c) Coordinate point Coordinate (tX) of geographic vector field data source in the recovery process solved in the step (b)i，tYi) Substituting the formula into the formula, and solving to obtain geographic vector field data target Coordinate point Coordinate (pX) in the recovery processi，pYi)：
Figure BDA0002321001780000062
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) according to the method, decryption is carried out on the geographic vector field data to generate a secret key, and lossless recovery can be carried out on the decrypted geographic vector field data according to the secret key;
(2) the invention considers the integral transformation of the geographic vector field data and increases the overall random disturbance;
(3) the method has the characteristics of strong attack resistance and safety, controllable error, capability of accurately recovering the geographic vector field data through the secret key, effectiveness, rapidness and the like, improves the reliability of decryption of the geographic vector field data, is favorable for perfecting a geographic information safety protection theory and method system, and can be used for aspects of public sharing, transmission and the like of the geographic vector field data.
Drawings
FIG. 1 is a flow chart of geographic vector field data decryption according to the present invention;
FIG. 2 is a flow chart of the recovery of the decrypted geographic vector field data of the present invention;
FIG. 3 illustrates geo-vector field data selected for use in embodiments of the present invention;
FIG. 4 is a graph of the effect of the data of the decrypted geographic vector field in the practice of the present invention;
FIG. 5 is a diagram illustrating the effect of recovered geovector field data in the practice of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
The geographic vector field data decryption process is shown in fig. 1, and the geographic vector field data recovery process is shown in fig. 2. The method comprises the following steps:
the present example uses a global wind field as the geographic vector field data to be compromised (see fig. 3), with the coordinate system being a grid coordinate system.
This example includes the following steps:
(1) key generation
The specific processes of determining geographic vector field data coordinate points and disturbance quantities thereof in key generation, target coordinate point normalization in the decryption process, error calculation in the decryption process, decryption parameter determination and encryption storage of keys are as follows:
(11) determining a geographic vector field data range to be decrypted
Opening the geographic vector field data to be decrypted, and acquiring the minimum external rectangle R of the geographic vector field data, wherein the corner point coordinate of the upper left corner of the R is (x)min，ymin) In this embodiment, (1, 1), the corner point coordinate of the lower right corner of R is (x)max，ymax) In the present embodiment, (180, 91); calculating the Length and the width Height of a geographic vector field data range to be decrypted according to the formula (1);
Figure BDA0002321001780000071
in this embodiment, the following are calculated:
Figure BDA0002321001780000072
(12) determination of geographic vector field data coordinate points and disturbance amounts thereof in key generation
Taking the index subscript from the geographic vector field data to be decrypted as a Coordinate point Coordinate (pX) of a geographic vector field data source in the decryption processi，pYi) In this embodiment, 16380 Coordinate points Coordinate (pX) of geographic vector field data sources in the decryption process are obtainedi，pYi) And according to the decryption index, giving a proper disturbance quantity delta X of a coordinate point of the geographic vector field data source in each decryption processiAnd Delta Yi(ii) a The geographic vector field data target Coordinate point Coordinate (tX) in the decryption processi，tYi) The coordinates of (a) are:
Figure BDA0002321001780000073
(13) geographic vector field data target coordinate point normalization in decryption process
Coordinate point Coordinate (tX) of geographic vector field data target in the decryption process of the step (12)i，tYi) Normalized to [ -1,1 ] according to equation (3)]Within the interval, wherein tXmean，tYmeanAre respectively asGeographic vector field data target Coordinate point Coordinate (tX) in decryption processi，tYi) Middle tXi，tYiTo obtain a normalized geographic vector field data target Coordinate point Coordinate (nX)i，nYi)：
Figure BDA0002321001780000074
(14) Error calculation during decryption
Normalizing the geographic vector field data to obtain a target Coordinate point Coordinate (nX)i，nYi) And attribute data tZiInto formula (4), where N1，N2，N3，N4(120, 1,1,1 in this example) are four arbitrary decryption parameters, e1，e2，e3As a unit vector, obtaining a Coordinate point Coordinate (RX) of the data of the decrypted geographic vector fieldi,RYi) And attribute data RZi。
Figure BDA0002321001780000081
In this example N1，N2，N3，N4Respectively taking 120,1,1 and 1 as:
Figure BDA0002321001780000082
calculating a decryption error MSE according to formula (5), wherein n is 16380;
Figure BDA0002321001780000083
the density removal error MSE is 74.1217.
(15) Decker error control
Adjusting disturbance quantity of a target coordinate point of geographic vector field data in a decryption process: comparing the decryption error MSE with the decryption index sigma, if the decryption error MSE is larger than the decryption index sigma, adjusting the decryptionDisturbance quantity delta X of target coordinate point of geographic vector field data in processiAnd Delta YiTo control the decryption error; and controlling the offset of the target coordinate point of the geographic vector field data in the decryption process according to a formula (6), wherein delta Yinew，ΔXinewThe disturbance quantity of the target coordinate point of the adjusted geographic vector field data in the decryption process is as follows:
Figure BDA0002321001780000084
iterating steps (14) to (15) until the decryption error MSE is smaller than the decryption index sigma, and then executing step (16);
finally obtained geographic vector field data target coordinate point offset delta Y in decryption processinew，ΔXinewComprises the following steps:
Figure BDA0002321001780000085
Figure BDA0002321001780000091
(16) and (3) generating a secret key: the final decryption parameters 120,1,1,1 and the offset delta Y of the target coordinate point of the geographic vector field data in the decryption processinew，ΔXinewEncrypted using RSA (Rivest-Shamir-Adleman) algorithm and stored as a key file.
(2) Decrepitation treatment
The specific processes of decrypting and reading the key file in the decryption processing, opening the geographic vector field data to be decrypted, traversing the geographic vector field data elements to be decrypted, acquiring a target coordinate point in the decryption process, normalizing the target coordinate point in the decryption process, performing decryption processing and storing the decrypted geographic vector field data are as follows:
(21) key file decryption reading
Decrypting and reading the key file by using RSA (Rivest-Shamir-Adleman) algorithm, and extracting decryption parameter N1，N2，N3，N4(in the present embodiment)120,1,1,1), opening the geographic vector field data to be decrypted;
(22) geo-vector field data read to be descreased
Traversing the geographic vector field data to be decrypted to obtain Coordinate point Coordinate (pX) of the geographic vector field data source in the decryption processi，pYi)；
(23) Normalizing the geographic vector field data coordinate points and performing decryption processing
Adding a disturbance quantity to a Coordinate point of a geographic vector field data source in the decryption process according to a formula (2) to generate a Coordinate point Coordinate (tX) of a geographic vector field data target in the decryption processi，tYi) According to the formula (3), Coordinate point Coordinate (tX) of geographic vector field data target in the decryption process is determinedi，tYi) Normalized to [ -1,1 [ ]]Within the interval, obtaining a normalized geographic vector field data Coordinate point Coordinate (nX)i，nYi)；
(24) Decrepitation treatment
Coordinate point Coordinate (nX) of normalized geographic vector field datai，nYi) And normalized geographic vector field attribute data nZiSubstituting the formula (4) to obtain a Coordinate point Coordinate (RX) of the decrypted geographic vector field datai，RYi) And the decrypted geographic vector field attribute data RZiAnd calculating an error MSE in decryption;
(25) preserving decrypted geographic vector field data
And (5) circulating the steps (22) to (24) until all the coordinate points of the geographic vector field data after normalization are processed, and the error MSE in decryption is smaller than the decryption index sigma, and storing the decrypted geographic vector field data.
(3) Recovery process
The specific processes of the steps of decryption processing of the key file in the recovery processing, recovery processing of the decrypted geographic vector field data, storage of the recovered geographic vector field data and the like are as follows:
(31) key file decryption reading
Decrypting and reading the key file by using RSA (Rivest-Shamir-Adleman) algorithm, and decrypting the key fileCoordinate point Coordinate (pX) of geographic vector field data sourcei，pYi) As the recovered geographic vector field data target Coordinate point, the geographic vector field data target Coordinate point Coordinate (tX) in the decryption process is usedi，tYi) As the recovered geographic vector field data source Coordinate point, the geographic vector field data target Coordinate point Coordinate (tX) in the decryption processi，tYi) Amount of disturbance Δ XiAnd Delta YiCoordinate point Coordinate (tX) of geographic vector field data source in recovery processi，tYi) Amount of disturbance Δ XriAnd Delta YriMutually opposite numbers, and a decryption parameter N in the process of decryption simultaneously1，N2，N3，N4And a recovery parameter N in a recovery procedurer1，Nr2，Nr3，Nr4Mutually opposite numbers;
(32) recovery processing of decrypted geographic vector field data
Traversing the data of the decrypted geographic vector field to obtain Coordinate point Coordinate (RX) of the data of the decrypted geographic vector fieldi，RYi)；
(33) Recovery processing of decrypted geographic vector field data
(a) Coordinate point Coordinate (RX) of the decrypted geographic vector field data in the step (32)i，RYi) And the attribute data RZ of the decrypted geographic vector field dataiAnd their recovery parameters-120, -1, -1, -1 into formula (7):
Figure BDA0002321001780000101
obtaining:
Figure BDA0002321001780000102
solving the above formula to obtain a geographic vector field data Coordinate point Coordinate (nX) in the recovery processi，nYi) And attribute data nZi。
(b) Reverse normalization: the number of geographic vector fields in the recovery process solved in step (a)Coordinate point Coordinate (nX)i，nYi) Substituting the data into a formula (8), and solving to obtain a Coordinate point Coordinate (tX) of the geographic vector field data source in the recovery processi，tYi)：
Figure BDA0002321001780000111
(c) Coordinate point Coordinate (tX) of geographic vector field data source in the recovery process solved in the step (b)i，tYi) Substituting into a formula (9), and solving to obtain geographic vector field data target Coordinate point Coordinate (pX) in the recovery processi，pYi)：
Figure BDA0002321001780000112
(34) Post-recovery geographic vector field data preservation
And (4) processing all the geographic vector field data in a circulating step (33) until all the elements are processed, and storing the recovered data.
The effect graph of the data of the decrypted geographic vector field in the implementation of the invention is shown in FIG. 4; the effect graph of the recovered geographic vector field data in the implementation of the present invention is shown in fig. 5.
The method has the characteristics of strong attack resistance and safety, controllable error, capability of accurately recovering the geographic vector field data through the secret key, effectiveness, rapidness and the like, improves the reliability of decryption of the geographic vector field data, and provides technical support for geographic information safety and geographic vector field data sharing.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (6)

1.一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，包括以下步骤：1. a method for deciphering and recovering geographic vector field data based on geometric algebra, is characterized in that, comprises the following steps: (1)密钥生成：包括密钥生成中地理向量场数据坐标点及其扰动量的确定、脱密过程中的目标坐标点归一化、脱密过程中误差的计算、脱密参数的确定、密钥的加密保存；(1) Key generation: including the determination of geographic vector field data coordinate points and their disturbances in key generation, the normalization of target coordinate points in the process of decryption, the calculation of errors in the process of decryption, and the determination of decryption parameters , encryption and storage of the key; (2)脱密处理：包括脱密处理中密钥文件解密读取、打开待脱密地理向量场数据、遍历待脱密地理向量场数据要素并获取坐标点、归一化坐标点并进行脱密处理、保存脱密后的地理向量场数据；(2) Decryption processing: including decrypting and reading the key file in the decryption process, opening the geographic vector field data to be decrypted, traversing the elements of the geographic vector field data to be decrypted and obtaining coordinate points, normalizing the coordinate points and performing decryption Encrypt and save the de-encrypted geographic vector field data; (3)恢复处理：包括恢复处理中密钥文件解密处理，脱密后地理向量场数据的恢复处理、恢复后地理向量场数据保存。(3) Recovery processing: including decryption processing of the key file in the recovery processing, recovery processing of the geographic vector field data after deciphering, and storage of the recovered geographic vector field data. 2.根据权利要求1所述的一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，步骤(1)中地理向量场数据坐标点及其扰动量的确定，包括以下步骤：2. a kind of geographic vector field data deciphering and recovery method based on geometric algebra according to claim 1, is characterized in that, in step (1), the determination of geographic vector field data coordinate point and disturbance amount thereof, comprises the following steps : (101)确定待脱密的地理向量场数据范围(101) Determine the geographic vector field data range to be decrypted 打开待脱密的地理向量场数据，获取其最小外接矩形R，R左上角的角坐标为(xmin，ymin)，R的右下角的角点坐标为(xmax，ymax)；并按照以下公式计算待脱密的地理向量场数据范围的长度Length和宽度Height；Open the geographic vector field data to be deciphered, obtain its minimum circumscribed rectangle R, the corner coordinates of the upper left corner of R are (x min , y min ), and the corner coordinates of the lower right corner of R are (x max , y max ); and Calculate the length Length and width Height of the geographic vector field data range to be decrypted according to the following formulas;
Figure FDA0002321001770000011
Figure FDA0002321001770000011
 (102)密钥生成中地理向量场数据坐标点及其扰动量的确定(102) Determination of geographic vector field data coordinate points and their disturbances in key generation 从待脱密的地理向量场数据中将索引下标作为脱密过程中地理向量场数据源坐标点Coordinate(pXi，pYi)，并根据脱密指标给定每个脱密过程中地理向量场数据源坐标点的扰动量ΔXi与ΔYi；则脱密过程中地理向量场数据目标坐标点Coordinate(tXi，tYi)的坐标为：From the geographic vector field data to be decrypted, the index subscript is taken as the coordinate (pX i , pY i ) of the data source coordinate point of the geographic vector field in the decrypting process, and each geographic vector in the decrypting process is given according to the decrypting index The disturbances ΔX i and ΔY i of the source coordinate point of the field data; then the coordinates of the target coordinate point Coordinate (tX i , tY i ) of the geographic vector field data in the process of deciphering are:
Figure FDA0002321001770000012
Figure FDA0002321001770000012
 (103)脱密过程中地理向量场数据目标坐标点归一化(103) Normalization of target coordinate points of geographic vector field data in the process of deciphering 将步骤(102)脱密过程中地理向量场数据目标坐标点按照以下公式归一化至[-1，1]区间内，其中tXmean，tYmean分别为脱密过程中地理向量场数据目标坐标点Coordinate(tXi，tYi)中tXi，tYi的均值，得到归一化后的地理向量场数据目标坐标点Coordinate(nXi，nYi)：In the step (102) deciphering process, the geographic vector field data target coordinate points are normalized to the [-1, 1] interval according to the following formula, wherein tX mean , tY mean are respectively the geographic vector field data target coordinates in the deciphering process. The mean value of tX i , tY i in the point Coordinate(tX i , tY i ), the normalized geographic vector field data target coordinate point Coordinate(nX i , nY i ):
Figure FDA0002321001770000021
Figure FDA0002321001770000021
 3.根据权利要求1所述的一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，步骤(1)中脱密中误差的计算、脱密参数的确定和密钥的加密保存，包括以下步骤：3. a kind of geographic vector field data decryption and recovery method based on geometric algebra according to claim 1, it is characterized in that, in step (1), the calculation of error in decryption, the determination of decryption parameter and the encryption of key Encrypted storage, including the following steps: (111)脱密过程中误差的计算(111) Calculation of errors in the declassification process 将归一化后的地理向量场数据坐标点Coordinate(nXi，nYi)以及属性数据nZi代入公式(4)，其中N1，N2，N3，N4为四个任意脱密参数，e1，e2，e3为单位向量，得到脱密后的地理向量场数据坐标点Coordinate(RXi，RYi)以及属性数据RZi；Substitute the normalized geographic vector field data coordinate point Coordinate(nX i , nY i ) and attribute data nZ i into formula (4), where N 1 , N 2 , N 3 , N 4 are four arbitrary decryption parameters , e 1 , e 2 , and e 3 are unit vectors, and the deciphered geographic vector field data coordinate points Coordinate (RX i , RY i ) and attribute data RZ i are obtained;
Figure FDA0002321001770000022
Figure FDA0002321001770000022
 按照公式(5)计算脱密误差MSE；Calculate the declassification error MSE according to formula (5);
Figure FDA0002321001770000023
Figure FDA0002321001770000023
 其中，n表示脱密过程中地理向量场数据源坐标点的个数；ΔXi与ΔYi分别为脱密过程中地理向量场数据源坐标点的扰动量；pXi，pYi为脱密过程中地理向量场数据源坐标点；Among them, n represents the number of coordinate points of the geographic vector field data source in the deciphering process; ΔX i and ΔY i are the disturbances of the geographic vector field data source coordinate points in the deciphering process; pX i , pY i are the deciphering process The coordinate point of the data source of the medium geographic vector field; (112)脱密误差控制(112) Decryption error control 调整脱密过程中地理向量场数据目标坐标点扰动量：将脱密误差MSE与脱密指标σ进行比较，若MSE大于脱密指标σ，则需要调整脱密过程中地理向量场数据目标坐标点的扰动量量ΔXi与ΔYi来控制脱密中误差；并按照公式(6)对脱密过程中地理向量场数据目标坐标点的偏移量进行控制，其中ΔYinew，ΔXinew为脱密过程中调整后的地理向量场数据目标坐标点的扰动量：Adjust the disturbance amount of the target coordinate point of the geographic vector field data during the deciphering process: compare the deciphering error MSE with the deciphering index σ. If the MSE is greater than the deciphering index σ, the target coordinate point of the geographic vector field data needs to be adjusted during the deciphering process. The disturbance amount ΔX i and ΔY i to control the error in deciphering; and according to formula (6) to control the offset of the target coordinate point of the geographic vector field data in the deciphering process, where ΔY inew , ΔX inew are deciphering The disturbance amount of the target coordinate point of the adjusted geographic vector field data in the process:
Figure FDA0002321001770000031
Figure FDA0002321001770000031
 迭代步骤(111)至(112)，直到脱密误差MSE小于脱密指标σ，然后执行步骤(113)；Iterate steps (111) to (112) until the decryption error MSE is less than the decryption index σ, and then execute step (113); (113)生成密钥：将最终的脱密参数N1，N2，N3，N4和脱密过程中地理向量场数据目标坐标点偏移量ΔXi与ΔYi利用RSA(Rivest-Shamir-Adleman)算法进行加密并存储为密钥文件。(113) Generate key : use RSA ( Rivest - Shamir -Adleman) algorithm is encrypted and stored as a key file. 4.根据权利要求1所述的一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，步骤(2)包括以下步骤：4. a kind of geographic vector field data deciphering and recovery method based on geometric algebra according to claim 1, is characterized in that, step (2) comprises the following steps: (21)密钥文件解密读取(21) Decryption and reading of the key file 使用RSA(Rivest-Shamir-Adleman)算法解密并读取密钥文件，提取脱密参数N1，N2，N3，N4，打开待脱密地理向量场数据；Use the RSA (Rivest-Shamir-Adleman) algorithm to decrypt and read the key file, extract the decryption parameters N 1 , N 2 , N 3 , N 4 , and open the geographic vector field data to be decrypted; (22)待脱密地理向量场数据读取(22) Read the geographic vector field data to be deciphered 遍历待脱密地理向量场数据，获取脱密过程中地理向量场数据源坐标点Coordinate(pXi，pYi)；Traverse the geographic vector field data to be deciphered, and obtain the coordinate points of the geographic vector field data source coordinate (pX i , pY i ) in the deciphering process; (23)归一化地理向量场数据坐标点并进行脱密处理(23) Normalize the coordinate points of geographic vector field data and perform decryption processing 将脱密过程中地理向量场数据源坐标点Coordinate(pXi，pYi)归一化至[-1，1]区间内，得到归一化后的地理向量场数据坐标点Coordinate(nXi，nYi)；归一化公式为：Normalize the coordinate points of the geographic vector field data source coordinate (pX i , pY i ) to the interval [-1, 1] in the process of deciphering, and obtain the normalized coordinate points of the geographic vector field data Coordinate (nX i , nY i ); the normalization formula is:
Figure FDA0002321001770000032
Figure FDA0002321001770000032
 (24)脱密处理(24) Decryption treatment 将归一化之后的地理向量场数据坐标点Coordinate(nXi，nYi)以及属性数据nZi代入以下公式，得到脱密后地理向量场数据坐标点Coordinate(RXi，RYi)和属性数据RZi：Substitute the normalized geographic vector field data coordinate point Coordinate(nX i , nY i ) and attribute data nZ i into the following formula to obtain the deciphered geographic vector field data coordinate point Coordinate(RX i , RY i ) and attribute data RZ i :
Figure FDA0002321001770000033
Figure FDA0002321001770000033
 计算脱密中误差MSE为：The error MSE in deciphering is calculated as:
Figure FDA0002321001770000041
Figure FDA0002321001770000041
 (25)保存脱密后的地理向量场数据(25) Save the deciphered geographic vector field data 循环步骤(22)至(24)，直至所有归一化之后的地理向量场数据坐标点处理完毕，并且脱密中误差MSE小于脱密指标σ，保存脱密后的地理向量场数据。Steps (22) to (24) are repeated until all normalized geographic vector field data coordinate points are processed, and the error MSE in deciphering is less than the deciphering index σ, and the deciphered geographic vector field data is saved. 5.根据权利要求1所述的一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，步骤(3)包括以下步骤：5. a kind of geographic vector field data deciphering and recovery method based on geometric algebra according to claim 1, is characterized in that, step (3) comprises the following steps: (31)密钥文件解密读取(31) Decryption and reading of the key file 使用RSA(Rivest-Shamir-Adleman)算法解密并读取密钥文件，将脱密过程中地理向量场数据源坐标点Coordinate(pXi，pYi)作为恢复的地理向量场数据目标坐标点，将脱密过程中地理向量场数据目标坐标点Coordinate(tXi，tYi)作为恢复的地理向量场数据源坐标点，则脱密过程中地理向量场数据目标坐标点Coordinate(tXi，tYi)的扰动量ΔXi与ΔYi与恢复过程中地理向量场数据源坐标点Coordinate(tXi，tYi)的扰动量ΔXri与ΔYri互为相反数，同时脱密过程中的脱密参数N1，N2，N3，N4与恢复过程中的恢复参数Nr1，Nr2，Nr3，Nr4互为相反数；Use the RSA (Rivest-Shamir-Adleman) algorithm to decrypt and read the key file, and use the coordinate point Coordinate (pX i , pY i ) of the geographic vector field data source during the decryption process as the target coordinate point of the recovered geographic vector field data. In the process of deciphering, Coordinate(tX i , tY i ) of the geographic vector field data target coordinate point is used as the recovered geographic vector field data source coordinate point, then during the deciphering process, Coordinate(tX i , tY i ) The disturbances ΔX i and ΔY i and the disturbances ΔX ri and ΔY ri of the coordinate point Coordinate(tX i , tY i ) of the geographic vector field data source during the recovery process are opposite numbers to each other, and the deciphering parameter N in the deciphering process 1 , N 2 , N 3 , N 4 and the recovery parameters N r1 , N r2 , N r3 , and N r4 in the recovery process are opposite numbers to each other; (32)脱密后地理向量场数据的恢复处理(32) Recovery processing of geographic vector field data after deciphering 遍历待恢复地理向量场数据，获取恢复过程中待恢复的坐标点Coordinate(RXi，RYi)；Traverse the geographic vector field data to be restored, and obtain the Coordinate (RX i , RY i ) of the coordinate points to be restored during the restoration process; (33)脱密后地理向量场数据的恢复处理；(33) Recovery processing of geographic vector field data after deciphering; (34)恢复后地理向量场数据保存(34) Save geographic vector field data after recovery 循环步骤(33)处理全部地理向量场数据，直到所有要素都处理完毕，保存恢复后的地理向量场数据。The loop step (33) processes all the geographic vector field data until all elements are processed, and saves the restored geographic vector field data. 6.根据权利要求5所述的一种基于几何代数的地理向量场数据脱密与恢复方法，其特征在于，步骤(33)包括以下步骤：6. a kind of geographic vector field data deciphering and recovery method based on geometric algebra according to claim 5, is characterized in that, step (33) comprises the following steps: (a)将步骤(32)中恢复过程中待恢复的坐标点Coordinate(RXi，RYi)和脱密后的属性RZi及其恢复参数Nr1，Nr2，Nr3，Nr4代入以下公式，求解得到恢复过程中地理向量场数据坐标点Coordinate(nXi，nYi)以及属性数据nZi：(a) Substitute the coordinate points to be restored in the restoration process in step (32) (RX i , RY i ), the deciphered attribute RZ i and its restoration parameters N r1 , N r2 , N r3 , N r4 into the following Formula, solve to obtain the coordinate point Coordinate (nX i , nY i ) and attribute data nZ i of the geographic vector field data during the recovery process:
Figure FDA0002321001770000051
Figure FDA0002321001770000051
 (b)反归一化：将步骤(a)求解出的恢复过程中地理向量场数据坐标点坐标点Coordinate(nXi，nYi)代入以下公式，求解得恢复过程中地理向量场数据源坐标点Coordinate(tXi，tYi)：(b) Inverse normalization: Substitute the Coordinate (nX i , nY i ) of the coordinate points of the geographic vector field data coordinate points in the recovery process obtained in step (a) into the following formula, and solve the coordinates of the geographic vector field data source during the recovery process. Point Coordinate(tX i , tY i ):
Figure FDA0002321001770000052
Figure FDA0002321001770000052
 (c)将步骤(b)求解出的恢复过程中地理向量场数据源坐标点Coordinate(tXi，tYi)代入以下公式，求解得恢复过程中地理向量场数据目标坐标点Coordinate(pXi，pYi)：(c) Substitute the coordinate point Coordinate(tX i , tY i ) of the geographic vector field data source coordinate point in the recovery process obtained in step (b) into the following formula, and solve to obtain the coordinate point Coordinate(pX i ) of the geographic vector field data target coordinate point during the recovery process, pY i ):
Figure FDA0002321001770000053
Figure FDA0002321001770000053
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