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

The invention discloses a geographic vector field data decryption and recovery method based on geometric algebra, which comprises the following steps: determining geographic vector field data coordinate points and disturbance quantities thereof in key generation, calculating errors in decryption, determining decryption parameters and encrypting and storing keys; in decryption processing, a key file is decrypted and read, geographic vector field data are opened, elements of the geographic vector field data to be decrypted are traversed, coordinate points are obtained, coordinates are normalized and decryption processing is carried out, and the decrypted geographic vector field data are stored; and in the recovery processing, the key file is decrypted, the geographic vector field data after decryption is recovered, and the recovered geographic vector field data is stored. The method has the advantages of strong attack resistance, capability of recovering the decrypted geographic vector field data by using the secret key, random global disturbance, effectiveness, rapidness and the like, and capability of providing technical support for the geographic vector field data in various aspects such as sharing, transmission, storage and the like.

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. A geographic vector field data decryption and recovery method based on geometric algebra is characterized by comprising 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.
2. The geometric algebra-based geographic vector field data decryption and recovery method of claim 1, wherein the determination of the coordinate points of the geographic vector field data and their disturbance amounts in step (1) comprises the following steps:
(101) determining a geographic vector field data range to be decrypted
Opening the geographic vector field data to be decrypted, and acquiring the minimum circumscribed rectangle R of the geographic vector field data, wherein the angular coordinate of the upper left corner of the 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 FDA0002321001770000011
(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 Then the geographic vector field data object sits during the decryption processPunctuation Coordinate (tX)i，tYi) The coordinates of (a) are:
Figure FDA0002321001770000012
(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 FDA0002321001770000021
3. The geometric algebra-based geographic vector field data decryption and recovery method of claim 1, wherein the calculation of the error in decryption, the determination of decryption parameters and the encrypted storage of the secret key in 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 FDA0002321001770000022
Calculating a decryption error MSE according to a formula (5);
Figure FDA0002321001770000023
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 sigma, 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 FDA0002321001770000031
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.
4. The geometric algebra-based geographic vector field data decryption and recovery method of claim 1, wherein the step (2) comprises the steps of:
(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 FDA0002321001770000032
(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 FDA0002321001770000033
The error MSE in the decryption is calculated as:
Figure FDA0002321001770000041
(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.
5. The geometric algebra-based geographic vector field data decryption and recovery method of claim 1, wherein the step (3) comprises the steps of:
(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 geographic vector field data to be recovered to acquire Coordinate point Coordinate (RX) to be recovered in the recovery processi，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.
6. A geometric algebra-based geographic vector field data decryption and recovery method according to claim 5, wherein 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 FDA0002321001770000051
(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 FDA0002321001770000052
(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 FDA0002321001770000053
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