Spatial object data hash check method using spatial point cloud set disorder

Abstract

The application provides a spatial object data Hash check method using spatial point cloud set disorder, which comprises the following steps: S1, obtaining spatial object data to be processed; S2, serializing the spatial object data to be processed; S3, distributing the serialized elements to multiple devices; S4, performing element authentication code calculation on the serialized elements distributed to each device; and S5, calculating a set authentication code by using the calculated element authentication codes. The application can realize fast verification of spatial data, reduce waiting time, and ensure data consistency.

Description

Technical Field

[0001] This invention relates to the field of spatial object data technology, and in particular to a spatial object data hash verification method that utilizes the unordered nature of spatial point cloud sets. Background Technology

[0002] Spatial object data is a crucial basis for national economic development and scientific research. Its copyright involves the interests of data production units, and tampering with high-precision data can endanger national security. While the development of the internet has brought convenience, it has also generated some negative effects, including infringement of spatial data and insecure data authentication. Common authentication methods include digital watermarking and hash authentication algorithms. Most current authentication algorithms treat spatial object data as vector data, which can effectively utilize its spatial semantics. However, this also means that the algorithm is sensitive to the order of data coordinate points. Because governments and companies use different systems to manage and acquire data, the same data may appear in different orders under different systems, leading to more cumbersome data processing or invalid authentication results. To address this issue, we combine the principle of pixel-based image semantics. That is, when the coordinate points of a data object reach a certain density, spatial semantics can be expressed using points instead of vector topological relationships, transforming the approach of verifying vector data into verifying high-density points. Therefore, this paper treats spatial data as a high-density set of points and proposes a hash authentication algorithm for spatial object data based on the unordered nature of sets. Experiments verify the effectiveness of the algorithm and the rationality of the proposed hash function. Summary of the Invention

[0003] This invention aims to at least solve the technical problems existing in the prior art, and in particular, it innovatively proposes a spatial object data hash verification method that uses the unordered nature of spatial point cloud sets.

[0004] To achieve the above-mentioned objectives of this invention, this invention provides a spatial object data hash verification method using the unordered nature of spatial point cloud sets, comprising the following steps:

[0005] S1, Obtain the spatial object data to be processed;

[0006] S2, serialize the spatial object data to be processed into elements;

[0007] S3 distributes serialized elements to multiple devices;

[0008] S4, multiple devices calculate the element authentication code for the serialized elements they are allocated;

[0009] S5 calculates the set authentication code using the calculated element authentication codes.

[0010] In a preferred embodiment of the present invention, the method for calculating element serialization in step S2 is as follows:

[0011] ,

[0012] in, Indicates a serialized string;

[0013] Functions for converting real numbers to strings;

[0014] Represents the x-coordinate of two-dimensional point cloud data;

[0015] For string concatenation;

[0016] The vertical coordinate represents the two-dimensional point cloud data.

[0017] In a preferred embodiment of the present invention, the method for calculating element serialization in step S2 is as follows:

[0018] ,

[0019] in, Indicates a serialized string;

[0020] Functions for converting real numbers to strings;

[0021] Represents the X-axis coordinates of 3D point cloud data;

[0022] For string concatenation;

[0023] Represents the Y-axis coordinate of 3D point cloud data;

[0024] The Z-axis coordinate represents the 3D point cloud data.

[0025] In a preferred embodiment of the present invention, the serialization element allocation method in step S3 is as follows:

[0026] The serialization elements are divided according to the computing power of different devices.

[0027] In a preferred embodiment of the present invention, the method for calculating the element authentication code in step S4 is as follows:

[0028] ,

[0029] in, Indicates the element's authentication code;

[0030] This represents the MD5 hash function;

[0031] This represents the serialized string obtained from the allocation.

[0032] In a preferred embodiment of the present invention, the method for calculating the set authentication code in step S5 is as follows:

[0033] ,

[0034] in, Represents a collection authentication code;

[0035] This represents the MD5 hash function;

[0036] This represents the authentication code of the first element;

[0037] This represents the XOR operation;

[0038] This represents the authentication code for the second element;

[0039] This represents the third element's authentication code;

[0040] Indicates the first Element authentication code.

[0041] In a preferred embodiment of the present invention, after verifying with the set authentication code in step S4 and the set authentication code calculated elsewhere, a quantitative indicator is also included. The quantitative indicator includes the number of bits of average change, the probability of average change, one of the sample standard deviations of the two indicators, or any combination thereof.

[0042] Number of digits of average change

[0043] (4.1)

[0044] in, The number of digits representing the average change;

[0045] This indicates the number of times each tampering operation is executed;

[0046] This indicates the change in the number of bits in the initial 128-bit authentication message after each tampering.

[0047] Probability of average change

[0048] (4.2)

[0049] in, Represents the probability of average change;

[0050] The number of digits representing the average change;

[0051] Indicates the length of the message;

[0052] Sample standard deviation of the two indicators

[0053] (4.3)

[0054] in, This represents the sample standard deviation of the first indicator;

[0055] This indicates the number of times each tampering operation is executed;

[0056] This indicates the change in the number of bits in the initial 128-bit authentication message after each tampering.

[0057] The number of digits representing the average change;

[0058] (4.4)

[0059] in, This represents the sample standard deviation of the second indicator;

[0060] Indicates the length of the message;

[0061] This indicates the number of times each tampering operation is executed;

[0062] This represents the rate of change of the initial 128-bit authentication message after each tampering.

[0063] This represents the probability of average change.

[0064] This invention also discloses a method for hash verification of spatial object data using the unordered nature of spatial point cloud sets, comprising the following steps:

[0065] S1, Obtain the spatial object data to be processed;

[0066] S2 distributes the spatial object data to be processed to multiple devices;

[0067] S3, each device serializes the spatial object data to be processed that it has been allocated to;

[0068] S4, Each device calculates the element authentication code for the serialized element;

[0069] S5 calculates the set authentication code using the calculated element authentication codes.

[0070] In a preferred embodiment of the present invention, the allocation method in step S2 is as follows:

[0071] The spatial object data to be processed is divided according to the computing power of different devices.

[0072] The sending end obtains the sending end set authentication code through the above steps, and the receiving end obtains the receiving end set authentication code through the above steps. By comparing whether the sending end set authentication code and the receiving end set authentication code are consistent, the spatial data can be quickly verified.

[0073] In summary, by adopting the above technical solutions, the present invention can achieve rapid verification of spatial data, reduce waiting time, and ensure data consistency.

[0074] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0075] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0076] Figure 1 These are schematic diagrams showing different descriptions of the same two-dimensional region of the present invention ((a) A to I, (b) F to G).

[0077] Figure 2 This is a schematic diagram illustrating different descriptions of the same point cloud rabbit in this invention (using different point sequence descriptions does not affect the final generated spatial object).

[0078] Figure 3 This is a schematic diagram of the framework for creating a hash authentication code for collection data according to the present invention.

[0079] Figure 4 This is a schematic diagram of the distribution of 256 small 1E-5 changes in this invention.

[0080] Figure 5 This is a schematic diagram (added) showing the distribution of the number of bits B and the rate of change P in this invention.

[0081] Figure 6 This is a schematic diagram showing the distribution of the number of bits B and the rate of change P in this invention (deleted).

[0082] Figure 7This is a schematic diagram (replaced) showing the distribution of the number of bits B and the rate of change P in this invention. Detailed Implementation

[0083] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0084] 1 Introduction

[0085] To address the problem that existing methods can lead to cumbersome data processing or invalid authentication results when accessing spatial objects as vector data through different systems, this paper treats spatial data as a high-density set of points and proposes a spatial object hash authentication algorithm based on the unordered nature of sets.

[0086] Before introducing the algorithm, it is necessary to briefly understand some existing methods. This will begin with "Digital Watermarking and Hash Function Authentication Algorithms," followed by an analysis of the shortcomings of existing methods and potential transformation strategies based on the characteristics of spatial objects. Finally, the paper's structure will be presented.

[0087] 1.1 Digital Watermarking and Hash Authentication Algorithm

[0088] Digital watermarking is mainly divided into spatial domain algorithms and transform domain algorithms. However, both of these algorithms embed digital watermarks by modifying vector data, which affects data accuracy and makes them easy to erase. Some scholars have proposed zero-watermarking algorithms that construct watermarks by selecting important features of the original data, rather than modifying the data to embed the watermark, thus solving the accuracy problem. Other scholars have proposed multi-watermarking algorithms based on multiple features or combinations of multiple watermarks. All these methods that do not affect accuracy take into account the characteristics of spatial object data. However, digital watermarks from zero-watermarking algorithms that reference simple features are easily forged, while multi-watermarking algorithms can effectively prevent forgery, but the more features referenced, the more complex the processing becomes.

[0089] Some scholars have designed hash functions based on chaotic systems to process data. Due to the one-way nature of hash functions and the unpredictability of chaotic systems, hash authentication algorithms have a significant advantage in solving authentication problems. These studies mainly utilize these characteristics to generate hash authentication codes corresponding to the data for subsequent authentication. However, hash authentication algorithms are extremely sensitive to input; the topological order obtained from accessing spatial object data differs in different systems, which can lead to inconsistent authentication inputs and consequently, algorithm failure.

[0090] 1.2 Characteristics of Spatial Objects

[0091] exist Figure 1 In the planning process of the two-dimensional region shown, changing the order of coordinate points in the same coordinate system does not affect human judgment of the final planned region. However, if these data points are given to the computer as vector data, the different topological sequences will lead to inconsistent authentication results. For ease of understanding, this article will... Figure 1 The relevant information for (a) and (b) is recorded in Table 1, including the region sequence (Seq), longitude (Lng), and latitude (Lat). In actual data manipulation and management, although the topological sequence of the data is not manually altered, companies and governments use different systems to operate on the data. Factors such as the database access order and operating system encoding can lead to potential changes in the topological sequence, which to some extent limits the universality of the authentication algorithm. To address this potential issue, we attempt to shift our approach from treating data as a vector to a more detailed discussion in subsequent paragraphs.

[0092] Table 1 Figure 1 Coordinate point record

[0093]

[0094] Hash authentication algorithms are extremely sensitive to input. The process of storing data generated from spatial objects varies from system to system, which may lead to inconsistent authentication inputs and thus algorithm failure. However, completely abandoning topological spatial semantics is not advisable. Similar to the principle that digital images can be semantically represented by high-density pixels, a certain density of coordinate points of spatial objects can replace topological order to represent spatial semantics.

[0095] We can better understand this from the perspective of three-dimensional objects. For example, in Figure 2 When drawing a rabbit in the point cloud shown, we can start from the ears or the tail depending on the dataset, but this does not affect the final generated rabbit. The high density of points shows obvious spatial semantic information, that is, the object is a "rabbit".

[0096] Therefore, we can change the approach of authentication vectors and instead authenticate high-density points, that is, treat the data as a set of high-density points, and propose a new authentication algorithm.

[0097] 1.3 Text Structure

[0098] The structure of this paper is as follows: Chapter II introduces the Hash authentication algorithm; Chapter III provides experimental results of the algorithm; and Chapter IV summarizes the work presented in this paper.

[0099] 2 Algorithm Framework

[0100] 2.1 Algorithm Description

[0101] The problem posed in the previous section was to authenticate a set whose element order should not affect the authentication code. Therefore, the key to this algorithm is designing a hash authentication function (HAF) that is insensitive to the element order.

[0102] Definition 1: Let It is a set whose elements It is a finite dataset, that is ,in For data objects, it is called This refers to the authentication function on the set. For a finite field, for A 3D vector space. The function is denoted as set_hash.

[0103] Note 1: The input to the function set_hash is a set A. Since the set is deterministic and unordered, it is required that changing the order of the elements in set A does not affect the value of the function.

[0104] Note 2: Data elements in set A Duplicates are not allowed.

[0105] Note 3: In Generally, 128, 196, and 256 can be selected as needed.

[0106] Definition 2: If we can find another If a collision occurs, then set_hash(A) = set_hash(B).

[0107] The authentication key for a set is a fixed-length numerical value generated by the `set_hash` function after set A is processed by the set_hash function. The key to authenticating set data is a well-designed `set_hash` function, and it must be applicable to any set of data. It is computationally impossible to find a set that conflicts with set A. .

[0108] Algorithm design idea: Consider set data ,in It refers to data objects. First, for each data object in the data collection... Serialization is performed to generate a character sequence closely related to the element, and an authentication code for each sequence is generated using a hash function, thus obtaining the identity of each data object. Unique authentication code Then, perform a bitwise XOR operation on the authentication codes of all data objects, i.e. Since the XOR operation satisfies commutativity, the value of M is independent of the order of the authentication codes. Finally, M is calculated using a hash algorithm to obtain the final authentication code Mac = hash(M). The framework for creating a hash authentication code for a set of data is as follows: Figure 3 As shown.

[0109] The framework's process is as follows:

[0110] 1) Element serialization

[0111] Elements in set A It might be a more complex data object, so to facilitate the next step of calculating the element's authentication code, we need to first process the element. Serialization, i.e., selecting a function Data objects Convert to string And the function It should be unidirectional, that is, if Then there must be .

[0112] 2) Calculate the authentication code of a single set element.

[0113] Elements in set A After serialization, we get Its elements All are strings. For each element in set B, generate an authentication code for that element. Its length is N=128,192,256 bits of binary data, that is . It can be any type of hash function, such as MD5, SHA, SM3, or other hash functions with key authentication.

[0114] 3) Calculate the hash authentication code of the entire set.

[0115] Authentication codes for all elements A XOR operation will be performed, and then... After performing a hash operation, the authentication information for dataset A is obtained, i.e. .

[0116] Note 4: For dataset A, its elements should satisfy the basic property of uniqueness, meaning that set A should not contain duplicate elements. If duplicate elements exist, such as in set A... In Then there is .

[0117] Therefore, if duplicate elements are allowed in dataset A, an attacker can add pairs of identical data objects to set A, and the hash authentication code will not be changed.

[0118] 2.2 Implementation of Planar Point Cloud Set Authentication

[0119] Using the set authentication framework proposed above, authentication codes are generated for two-dimensional point cloud data, thereby enabling authentication of such set data.

[0120] Let set ,in . Figure 3 The authentication code framework diagram and its steps are as follows:

[0121] Step 1: Serialize the set elements. (Serialize the elements...) Serialization The function str converts a real number into a string. For string concatenation operators, let's call them... .

[0122] Step 2: Calculate the element authentication code. Use the MD5 hash function to calculate the authentication code for each element in set B. ,in N=128 bits of binary data.

[0123] Step 3: Calculate the set authentication code. Perform an XOR operation on all element authentication codes, then apply the MD5 algorithm for hashing to obtain the authentication information for data set A. .

[0124] 2.3 Algorithm Parallelism Analysis and Implementation

[0125] This algorithm has a natural advantage in parallel implementation. If there are t machines, it can be implemented in parallel as follows:

[0126] Point sets are adjusted according to the computing power of different machines. Partitioning yields a set. ,in It is a set non-empty subset And satisfy .

[0127] subset Placed in the first The computer performs the calculations: First, it calculates... Authentication codes for all elements Then, perform an XOR operation on all authentication codes to obtain a subset. Authentication information.

[0128] Calculate the point set according to formula (3.1) Authentication code:

[0129] (3.1)

[0130] Since the computations on each machine are completely independent, and the final result is simply calculated according to (3.1), the algorithm is well-suited for parallel implementation, which is extremely advantageous for the validation of large-scale planar datasets.

[0131] 3. Experimental Analysis

[0132] A hash function is a one-way function that can compress plaintext of any finite length into a fixed-length hash value. Finding its inverse mapping is computationally difficult. In this paper, firstly, it must also be insensitive to the order of elements in the set, so it's necessary to verify whether the encryption result of the algorithm is unique under random order. Secondly, reasonably secure hash algorithms typically possess good sensitivity, obfuscation, and diffusion properties, so these characteristics need to be tested to evaluate the algorithm's reasonableness and security.

[0133] In these experiments, we used two-dimensional data from real-world regional planning work as the experimental data for testing the algorithms. This data consisted of a total of 4464 points.

[0134] 3.1 Uniqueness Analysis of Encryption Results

[0135] The experiments used a dataset of 4464 points, with 44 rounds of data selection, adding 100 points in each round and performing 10 randomized encryption operations per round. The 44th round added 164 points because subsequent rounds had fewer than 100 operations. The number of data points in each round, the number of randomization operations, and whether the result was unique were recorded (true if the requirement was met, false if not).

[0136] Experimental results show that the encryption result of this algorithm is still unique under random order, thus satisfying the requirement of "insensitive to the order of elements in the set". For specific results, please refer to Table 2.

[0137] Table 2 Uniqueness Analysis Results

[0138] 1 100 TRUE 2 200 TRUE 3 300 TRUE 4 400 TRUE 5 500 TRUE 6 600 TRUE 7 700 TRUE 8 800 TRUE 9 900 TRUE 10 1000 TRUE 11 1100 TRUE 12 1200 TRUE 13 1300 TRUE 14 1400 TRUE 15 1500 TRUE 16 1600 TRUE 17 1700 TRUE 18 1800 TRUE 19 1900 TRUE 20 2000 TRUE 21 2100 TRUE 22 2200 TRUE 23 2300 TRUE 24 2400 TRUE 25 2500 TRUE 26 2600 TRUE 27 2700 TRUE 28 2800 TRUE 29 2900 TRUE 30 3000 TRUE 31 3100 TRUE 32 3200 TRUE 33 3300 TRUE 34 3400 TRUE 35 3500 TRUE 36 3600 TRUE 37 3700 TRUE 38 3800 TRUE 39 3900 TRUE 40 4000 TRUE 41 4100 TRUE 42 4200 TRUE 43 4300 TRUE 44 4464 TRUE

[0139] 3.2 Sensitivity Analysis of the Algorithm

[0140] Sensitivity refers to the degree to which a hash value is sensitive to the plaintext message. If every tiny change in the plaintext message results in a significant change in the encryption result, the algorithm has high initial value sensitivity, which in turn indicates that the algorithm has good one-way hashing performance.

[0141] In this experiment, the coordinate value of a certain dimension of a point in the original data was slightly changed. The change range was 1E-5, 1E-4 or 1E-3. Each change operation was repeated 256 times. Finally, the changed result was compared with the original result to obtain the average number of bits changed and its sample standard deviation. The specific results are shown in Table 3.

[0142] Table 3. Impact of Small Changes of Different Degrees on Results (Number of digits changed)

[0143]

[0144] Experimental results show that even small changes in plaintext data, such as 1E-05, can lead to significant changes in the results, indicating that the algorithm has good initial sensitivity. Specific sensitivity experimental records are as follows... Figure 4 As shown in the figure, the bit change distribution under 256 1E-5 changes is displayed. The two rows record the number of changed bits (purple line) and the bit change rate under a total of 128 bits (red line), respectively.

[0145] 3.3 Analysis of Algorithm Confusion and Diffusion

[0146] Diffusion refers to the phenomenon where a change in each bit of the plaintext of a designed function affects many bits of the ciphertext. For a binary result, each bit has only two possibilities: 1 or 0. A good diffusion effect is observed when a small change in the initial value results in a 50% probability of a change in any bit of the result. Furthermore, confusion implies that the designed algorithm should make the dependencies between the plaintext and ciphertext quite complex.

[0147] The specific quantitative indicators are as follows:

[0148] Number of digits of average change

[0149] (4.1)

[0150] Probability of average change

[0151] (4.2)

[0152] Sample standard deviation of the two indicators

[0153] (4.3)

[0154] (4.4)

[0155] in The absolute value is the change in the number of bits in the initial 128-bit authentication message after each tampering. The number of times each tampering operation is executed. This represents the change rate of the initial 128-bit authentication message after each tampering. This represents the length of the message; in this experiment, it is 128 bits.

[0156] , This indicates the stability of the hash's disorder and dispersion properties; the smaller the value, the more stable the hash. If the calculated value... The values ​​are all very small, indicating that the algorithm has a strong and stable ability to handle plaintext confusion and diffusion.

[0157] Therefore, we modified the two-dimensional data in different ways, such as adding, deleting, and replacing, and recorded the corresponding indicators to test the algorithm's ability to tamper with and spread the data. For each method, we randomly selected a point and repeated the process 2048 times.

[0158] 1) Add one arbitrary point

[0159] Experimental results are as follows Figure 5 As shown, a distribution diagram of the number of bit changes and the transformation rate under this tampering method is drawn. The purple line represents the number of bits that change, and the red line represents the transformation rate of each bit. For a good diffusion effect, each bit should change with a 50% probability, so the transformation rate should be close to 50% and the number of bits that change should be close to 64.

[0160] Table 2 provides the specific indicators. ΔB and ΔP indicate the stability of the hash disorder and diffusion properties. If the calculated Δ values ​​are all small, it means that the algorithm has a strong and stable ability to handle the disorder and diffusion of plaintext.

[0161] Table 4. Indicators for Test E (Increased)

[0162]

[0163] according to Figure 5 As shown in Table 4, the algorithm's rate of change is stable at around 50%, averaging 50.04%, and the number of changes is stable at around 64, averaging 64.06. The Δ values ​​are also relatively small, averaging 5.57 and 4.35 respectively, indicating that the algorithm has good ability to create confusion and spread this type of tampering.

[0164] 2) Delete any point

[0165] Experimental results are as follows Figure 6 As shown, the distribution of the sum of the values ​​obtained by deleting this type of tampering is plotted again. Similarly, Table 5 of this paper presents the specific metrics for the deletion experiments.

[0166] Table 5. Indicators for Test E (deleted)

[0167]

[0168] according to Figure 6 And Table 5, Algorithm Change Rate The average was 50.31%, with a change in the number of digits. The average value is 64.39, while the average Δ value is 5.80 and 4.53, indicating that the algorithm also has good obfuscation and diffusion capabilities in eliminating this type of tampering.

[0169] 3) Replace one arbitrary point

[0170] Experimental results are as follows Figure 7 As shown, the method of replacing this tampering was drawn again. and The distribution of the substitution experiments is shown in Table 6 of this paper.

[0171] Table 6. Indicators for Test E (with replacements)

[0172]

[0173] according to Figure 7 And Table 6, Algorithm Change Rate The average is 50.1%, with a change in the number of digits. The average value is 64.13, while the average Δ value is 5.71 and 4.37, indicating that the algorithm, as a tampering method, also has good obfuscation and diffusion capabilities.

[0174] Overall Conclusion

[0175] Finally, combining the three sets of experiments, although the methods of tampering were different, the rate of change of the algorithm was consistent. It remains stable at around 50%, with a change in the number of digits. It also remains stable at around 64. Moreover, the Δ value is relatively small, meaning that the algorithm has good obfuscation and diffusion capabilities for plaintext data.

[0176] 4. Conclusion

[0177] Unlike previous authentication methods, this paper treats spatial object data as a high-density point set instead of vector data, and designs a corresponding hash authentication algorithm. This solves the potential problem of invalid authentication results due to different data topology orders accessed by different systems, resulting in a more universal authentication algorithm. Through testing the algorithm's sensitivity, diffusion, and probabilistic properties, the paper concludes that the algorithm is reasonable and secure.

[0178] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for hash verification of spatial object data using the unordered nature of spatial point cloud sets, characterized in that, Includes the following steps: S1, Obtain the spatial object data to be processed; S2, serialize the spatial object data to be processed element by element; the calculation method for element serialization is as follows: ， in, Indicates a serialized string; Functions for converting real numbers to strings; Represents the X-axis coordinates of 3D point cloud data; For string concatenation; Represents the Y-axis coordinate of 3D point cloud data; Represents the Z-axis coordinate of 3D point cloud data; S3 distributes the serialization elements to multiple devices, specifically as follows: according to The computing power of different devices on the point set Partitioning yields the partitioned set. ,in It is a set non-empty subset And satisfy ; subset Assigned to the On the equipment; S4, multiple devices perform parallel calculations of element authentication codes on their respective assigned serialized elements; the calculation method for the element authentication code is as follows: ， in, Indicates the element's authentication code; This represents the MD5 hash function; This represents the serialized string obtained from the allocation; S5. Calculate the set authentication code using the calculated element authentication code. The calculation method for the set authentication code is as follows: ， in, Represents a collection authentication code; This represents the MD5 hash function; This represents the authentication code of the first element; This represents the XOR operation; This represents the authentication code for the second element; This represents the third element's authentication code; Indicates the first Element authentication code.

2. The spatial object data hash verification method using the unordered nature of spatial point cloud sets according to claim 1, characterized in that, After verifying using the set authentication code in step S4 and the separately calculated set authentication code, it also includes quantitative indicators, which include the number of bits of average change, the probability of average change, the sample standard deviation of the two indicators, or any combination thereof. Number of digits of average change: ， in, The number of digits representing the average change; This indicates the number of times each tampering operation is executed; This indicates the change in the number of bits in the initial 128-bit authentication message after each tampering. Probability of average change: ， in, Represents the probability of average change; The number of digits representing the average change; Indicates the length of the message; Sample standard deviations of the two indicators: ， in, This represents the sample standard deviation of the first indicator; This indicates the number of times each tampering operation is executed; This indicates the change in the number of bits in the initial 128-bit authentication message after each tampering. The number of digits representing the average change; ， in, This represents the sample standard deviation of the second indicator; Indicates the length of the message; This indicates the number of times each tampering operation is executed; This represents the rate of change of the initial 128-bit authentication message after each tampering. This represents the probability of average change.

Images