Industrial Internet of Things multi-dimensional privacy protection data aggregation method based on homomorphic proxy re-encryption

Abstract

The invention discloses an industrial Internet of Things multi-dimensional privacy protection data aggregation method based on homomorphic proxy re-encryption, and the method comprises the steps: carrying out the data reporting of an intelligent sensor at a data reporting stage; the aggregation gateway performs proxy re-encryption and data aggregation; and in the data decryption stage, the power control center decrypts the data. The invention provides a reliable and flexible data aggregation framework based on a hyper-incremental sequence, homomorphic encryption and proxy re-encryption, and the framework supports multi-dimensional data aggregation and dynamic management of an intelligent sensor, an aggregation gateway and a power control center. According to the privacy protection data aggregation scheme based on the modified Paillier cryptographic algorithm, proxy re-encryption is supported, and the problem of internal attacks is solved through the scheme. According to the method, privacy, integrity, authenticity, external aggression resistance and fault tolerance are guaranteed, and more functions are provided under the condition that similar overhead is kept.

Description

Technical Field

[0001] The present invention relates to homomorphic encryption technology and proxy re-encryption technology, and in particular to an industrial Internet of Things multi-dimensional privacy protection data aggregation method based on homomorphic proxy re-encryption. Background Art

[0002] Smart grid is a key component of the modern Industrial Internet of Things (IIoT). It uses real-time data and intelligent control technology to achieve reliable, efficient and sustainable operation of the power system, which is very helpful for industrial production scheduling. Usually the infrastructure of smart grid in IIoT includes smart sensors (SS), aggregation gateways (AG) and power control centers (ECC). Smart sensors in factories are deployed in industrial equipment to collect power usage data and transmit this data to the aggregation gateway regularly. The aggregation gateway operates within the industrial area network, collects and integrates data, reduces the frequency of data transmission, and reduces system load and cost. The power control center uses mathematical and statistical algorithms to analyze this data to support decisions such as load optimization, fault warning, electricity price adjustment and emergency response measures.

[0003] Although smart grid in IIoT provides advantages in power management and dispatch, it also introduces serious privacy and security issues. Most data transmission of smart grid in IIoT is carried out through wireless communication links, which may contain sensitive information such as the production capacity of the factory. Attackers can exploit privacy leakage to gain benefits. Therefore, it is necessary to develop effective security schemes to protect the fine-grained data of IIoT from unauthorized access.

[0004] Privacy-preserving data aggregation (PPDA) can ensure the effectiveness of data analysis and mining while minimizing the risk of privacy leakage. Studies have shown that homomorphic encryption is an effective technology. However, most homomorphic encryption schemes only focus on power consumption scenarios, preventing the power control center from conducting multidimensional analysis and managing regional power usage patterns. In real environments, there are many types of power usage information. Existing single-dimensional aggregation schemes must process multidimensional power usage data separately. In addition, since smart sensors report data to the aggregation gateway periodically, the reported plaintext data is usually much smaller than the plaintext space of the encryption algorithm, resulting in a lot of computing resources being wasted when encrypting single-dimensional data. To address these challenges, some studies have proposed multidimensional data aggregation schemes.

[0005] However, most existing schemes are designed to defend the system from external attacks, while modern smart grid infrastructure is also at risk of internal attacks. For example, in some schemes, smart sensors use the public key of the power control center to encrypt plaintext data. This allows a semi-honest power control center to decrypt the private energy consumption data of a single device using its private key. Since smart grids in IIoT involve a variety of devices and a complex user group, the impact of internal attacks can be widespread. Therefore, mitigating internal attacks becomes a key challenge to ensure the security of smart grids. Most existing multi-dimensional schemes based on traditional public key encryption fail to defend against the risk of internal attacks or private key leakage.

[0006] To address these internal attack issues, some studies have modified the Paillier encryption system, where smart sensors use their own independent keys to encrypt the collected data. At the same time, the power control center holds the aggregate key and can only decrypt the aggregated data. This design effectively prevents the curious control center from decrypting the sensitive data of registered devices. Even if the attacker leaks the private key of a single device, the data of other devices can still be prevented from being leaked. However, these public key encryption schemes lack sufficient reliability and require significant additional overhead to recover the system in the event of the loss of aggregation participants. Smart sensors and their communication lines, which are usually deployed at the edge of the power grid system, are vulnerable. In addition, the addition, removal, and update of entities in the industrial power grid system are more in line with real-world usage scenarios. Therefore, the designed scheme should have sufficient fault tolerance and flexibility to adapt to real-world conditions. Summary of the invention

[0007] Purpose of the invention: The purpose of the present invention is to address the deficiencies in the prior art and to provide an industrial Internet of Things multi-dimensional privacy protection data aggregation method based on homomorphic proxy re-encryption.

[0008] Technical solution: The present invention provides a method for industrial Internet of Things multi-dimensional privacy protection data aggregation based on homomorphic proxy re-encryption, comprising the following steps:

[0009] Step (1), during the system initialization phase, the trusted authority TA generates and publishes public parameters Ω for the system, and distributes secret parameters to the power control center ECC, the aggregation gateway AG, and the smart sensor SS;

[0010] in,

[0011] N represents the upper limit of the number of smart sensors. The trusted authority TA selects large prime numbers p and q based on the security parameter λ, calculates N=pq, g=N+1, and selects a random r0 that satisfies Bilinear Map Pairing are all prime v-order cyclic groups, choose The generator g1, H is a collision-resistant hash function, p ag is the signature public key of the aggregation gateway AG, {p i} i＝1，2，...，n Refers to the signature convention set of all smart sensors, there are n smart sensors in total, p i Refers to a single smart sensor SS i The signature public key of i} 1≤i≤k refers to a super-increasing sequence that satisfies

[0012] Step (2), reporting data, refers to the smart sensor SS performing preliminary aggregation of multi-dimensional data and encrypting and signing the data before reporting the data to the aggregation gateway AG; the specific method is:

[0013] First, the i-th smart sensor SS i Preliminary aggregation of collected plaintext messages, calculation of aggregated plaintext message m i =d i1 S1+d i2 ·S2+…+d ik ·S k ;d ij Indicates SS i The j-th dimension data collected; then, the smart sensor SS i Encrypt the original plaintext and calculate the primary ciphertext C′ i :

[0014]

[0015] Then the smart sensor SS i Sign the primary ciphertext and generate a signature Last SS i {C′ i , σ i , T} is packaged and sent to the aggregation gateway AG, where T is the current timestamp used to resist replay attacks;

[0016] Step (3), re-encrypting and aggregating the ciphertext, including the aggregation gateway AG verifying, re-encrypting and aggregating the reported data, the specific method is:

[0017] Step (3.1), the aggregation gateway AG receives data from each smart sensor SS i Verify the received data;

[0018] Step (3.2), the aggregation gateway AG performs a proxy re-encryption operation on the verified ciphertext, that is, for the received primary ciphertext C′ i , re-encrypt it and calculate the first-level ciphertext

[0019] Step (3.3), the aggregation gateway AG aggregates the first-level ciphertext obtained by re-encryption to obtain the aggregated ciphertext C; and signs the aggregated ciphertext C to calculate Finally, the aggregation gateway AG reports the data {C, σ ag , n0, T} are packaged and sent to the power control center ECC;

[0020] Step (4): In the data decryption phase, the power control center ECC decrypts the data report {C, σ ag , n0, T} to verify and decrypt, and finally obtain the plaintext aggregate data D i .

[0021] Furthermore, the detailed method of step (1) is:

[0022] Step (1.1), the trusted authority TA sets system parameters and collision-resistant hash function For the super-increasing sequence S = {S1, S2, ..., S k},satisfy

[0023] k is the dimension of the reported data, M j Represents the upper limit value of the j-th dimension data;

[0024] Step (1.2), the trusted authority TA sets the system key and selects a random number As the key of the power control center ECC; select a random number As a smart sensor SS i The key of As the key of the aggregation gateway AG;

[0025] Step (1.3), re-encryption key setting, TA calculates the re-encryption key rk i→ecc ;

[0026]

[0027] Step (1.4), the trusted authority TA sets the signature key of other entities, Public parameters

[0028] Step (1.5), the trusted authority TA distributes secret parameters:

[0029] Send the private key x through a secure channel ecc Send to ECC; send the private key x through a secure channel ag and RK i→eccSend to AG; i = 1, 2, ..., n; send the private key x through a secure channel i Send to SS i .

[0030] The collected multi-dimensional plaintext data is aggregated into one plaintext through the super-increment sequence, and the device SS i The collected multi-dimensional plaintext data (d i1 , d i2 , …, d ik ), k is the dimension of the plaintext, and the device initially aggregates k data into one data m i , saving the transmission cost, the initially aggregated data is restored to the original data through step (4.3).

[0031] Furthermore, in step (3), before re-encryption and aggregation, the aggregation gateway AG first verifies the data received from the smart sensor, and the verification method is:

[0032] The aggregation gateway AG verifies whether the timestamp T is fresh. If the verification fails, it refuses to receive the data. If the timestamp T is verified, it continues to verify whether the digital signature is valid. If the equation e(σ i , g) = e(H(C′ i ), p i ) is established, the verification passes and continues to execute;

[0033] To make signature verification more efficient, AG performs batch signature verification and calculates Batch verification reduces the number of pairing operations from 2n to n+1;

[0034] The detailed process of the aggregation gateway AG performing the aggregation operation on the first-level ciphertext obtained by re-encryption is as follows:

[0035] First, count the smart devices participating in the aggregation, and record n0 as the number of devices that correctly participate in the aggregation. The counting operation can prevent the edge device from being damaged and unable to upload data normally, resulting in aggregation decryption failure; then the aggregation gateway AG calculates the aggregation ciphertext

[0036] Furthermore, the specific process of step (4) is as follows:

[0037] Step (4.1), the power control center ECC performs data verification, the specific process is as follows:

[0038] First, verify whether the timestamp T is fresh. If the verification fails, refuse to receive the data. If the timestamp T is verified, continue to verify whether the digital signature is valid, that is: if the equation e(σ, g) = e(H(C), p ag) is established, the digital signature verification is successful. Here, ECC can perform batch signature verification and verify data from multiple AGs at the same time;

[0039] Step (4.2), ECC performs data decryption, that is, ECC first calculates According to the binomial expansion, we can get gm: Get the aggregated plaintext message m;

[0040] g m =(1+N) m mod N 2 =(1+Nm)mod N 2 ;

[0041] Step (4.3), ECC processes the aggregated plaintext message, the specific process is as follows:

[0042] Get aggregate plaintext message Set the loop variable i to decrease from i=k to i=1;

[0043] Then calculate the sum of the data of the current i-th dimension D i ,

[0044] Next, the value of the ECC update message m is: m = m mod S i , the updating of m aims to remove the data of the dimension that has been processed;

[0045] ECC repeats steps (4.3.2) and (4.3.3) until the sum of data of all dimensions is obtained

[0046] Step (4.4), ECC performs data analysis and mining applications on the data of each dimension.

[0047] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0048] (1) Considering the low fault tolerance and weak scalability of existing solution frameworks, the present invention proposes a reliable and flexible data aggregation framework based on super-incremental sequences, homomorphic encryption, and proxy re-encryption. The proposed framework supports multi-dimensional data aggregation and dynamic management of smart sensors, aggregation gateways, and power control centers.

[0049] (2) Aiming at the internal attack problem that is rarely addressed in the prior art, the present invention designs a privacy-preserving data aggregation scheme based on the modified Paillier cryptographic algorithm that supports proxy re-encryption. In this way, no entity can obtain a single plaintext, thereby protecting the privacy of individual data in IIoT.

[0050] (3) The present invention adopts formal correctness and security analysis. The analysis results show that our invention guarantees privacy, integrity, authenticity, resistance to external attacks and fault tolerance. The present invention provides more functions while maintaining similar overhead. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a system model diagram of the present invention;

[0052] Figure 2 It is a data flow chart in the embodiment;

[0053] Figure 3 is a computational cost diagram of the smart sensor in the embodiment;

[0054] Figure 4 A diagram showing the computational overhead of an aggregation gateway in an embodiment;

[0055] Figure 5 Graph showing the computational overhead of the power computing center in the embodiment. DETAILED DESCRIPTION

[0056] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0057] In order to solve the problems of low fault tolerance, low scalability and internal attack in the existing solutions of industrial Internet of Things security aggregation, the present invention proposes a data aggregation method for industrial Internet of Things multi-dimensional privacy protection based on homomorphic proxy re-encryption, and realizes the dynamic management of industrial Internet of Things entities through a reliable and flexible data aggregation framework based on super-incremental sequence, homomorphic encryption and proxy re-encryption, and then uses the modified Paillier cryptographic algorithm to effectively resist internal attacks. Specifically, this paper combines super-incremental sequence, homomorphic encryption and proxy re-encryption, and supports higher fault tolerance on the basis of supporting multi-dimensional data aggregation, which greatly improves the scalability of the system. Even if the entity in the system suffers natural damage or human attack and cannot correctly participate in data aggregation, the design framework of the present invention can still run correctly. Then, the present invention modifies the Paillier cryptographic algorithm, and adds support for proxy re-encryption under the premise of ensuring that its homomorphic properties remain unchanged. The modified cryptographic system of the present invention enables the system to prevent more security threats. Even if a few devices are cracked by the enemy, the sensitive data of other unbroken smart sensors will not be leaked.

[0058] like Figure 1As shown, this embodiment involves four types of entities: smart sensors (SS), aggregation gateways (AG), power control centers (ECC), and trusted authorities (TA). Smart sensors are network edge devices. In the Industrial Internet of Things (IIOT), they are responsible for collecting multi-dimensional power data generated by users and aggregating them into initial plaintext using super-increment sequences, and then encrypting the initial plaintext using their own keys and sending it to the aggregator gateway. After the aggregation gateway collects the initial ciphertext encrypted by the SS, it performs proxy re-encryption on it and converts it into a ciphertext form that can be decrypted by ECC. The re-encrypted ciphertext is then aggregated to obtain the aggregated ciphertext and send it to the ECC. The power computing center is responsible for receiving and decrypting the aggregated ciphertext sent by the AG. After obtaining the aggregated plaintext, the algorithm is used to obtain the sum of the data of each dimension, and analysis and decision-making are performed on this basis. The trusted authority is responsible for generating the keys, re-encryption keys, signature keys of each major entity, and publishing public parameters. After the system initialization is completed, the TA is generally offline.

[0059] In order to facilitate the understanding of the technical solution of this embodiment, the meanings of the relevant variables are explained, and the specific contents are shown in Table 1.

[0060] Table 1

[0061]

[0062]

[0063] The industrial Internet of Things multi-dimensional privacy protection data aggregation method based on homomorphic proxy re-encryption of this embodiment includes the following steps:

[0064] Step (1), during the system initialization phase, the trusted authority TA generates and publishes public parameters Ω for the system, and distributes secret parameters to the power control center ECC, the aggregation gateway AG, and the smart sensor SS;

[0065] in,

[0066] N represents the upper limit of the number of smart sensors. The trusted authority TA selects large prime numbers p and q based on the security parameter λ, calculates N=pq, g=N+1, and selects a random r0 that satisfies Bilinear Map Pairing are all prime v-order cyclic groups, choose The generator g1, H is a collision-resistant hash function, p ag is the signature public key of the aggregation gateway AG, p i For n smart sensors SS i The corresponding signature public key, {S i} 1≤i≤k middle;

[0067] Step (2), reporting data, refers to the smart sensor SS performing preliminary aggregation of multi-dimensional data and encrypting and signing the data before reporting the data to the aggregation gateway AG; the specific method is:

[0068] First, the i-th smart sensor SS i Preliminary aggregation of collected plaintext messages, calculation of aggregated plaintext message m i =d i1 ·S1+d i2 ·S2+…+d ik ·S k ;d ij Indicates SS i The j-th dimension data collected; then, the smart sensor SS i Encrypt the original plaintext and calculate the primary ciphertext C′ i :

[0069]

[0070] Then the smart sensor SS i Sign the primary ciphertext and generate a signature Last SS i {C′ i , σ i , T} is packaged and sent to the aggregation gateway AG, where T is the current timestamp used to resist replay attacks;

[0071] Step (3), re-encrypting and aggregating the ciphertext, including the aggregation gateway AG verifying, re-encrypting and aggregating the reported data, the specific method is:

[0072] Step (3.1), the aggregation gateway AG receives data from each smart sensor SS i Verify the received data;

[0073] Step (3.2), the aggregation gateway AG performs a proxy re-encryption operation on the verified ciphertext, that is, for the received primary ciphertext C′ i , re-encrypt it and calculate the first-level ciphertext

[0074] Step (3.3), the aggregation gateway AG aggregates the first-level ciphertext obtained by re-encryption to obtain the aggregated ciphertext C; and signs the aggregated ciphertext C to calculate Finally, the aggregation gateway AG reports the data {C, σ ag , n0, T} are packaged and sent to the power control center ECC;

[0075] Step (4): In the data decryption phase, the power control center ECC decrypts the data report {C, σag , n0, T} to verify and decrypt, and finally obtain the plaintext aggregate data D i .

[0076] In this embodiment, the detailed method of step (1) is:

[0077] Step (1.1), the trusted authority TA sets system parameters and collision-resistant hash function For the super-increasing sequence S = {S1, S2, ..., S k},satisfy

[0078] k is the dimension of the reported data, M j Represents the upper limit value of the j-th dimension data;

[0079] Step (1.2), the trusted authority TA sets the system key and selects a random number As the key of the power control center ECC; select a random number As a smart sensor SS i The key of As the key of the aggregation gateway AG;

[0080] Step (1.3), re-encryption key setting, TA calculates the re-encryption key rk i→ecc ;

[0081]

[0082] Step (1.4), the trusted authority TA sets the signature key of other entities, Public parameters

[0083] Step (1.5), the trusted authority TA distributes secret parameters:

[0084] x ecc Send to ECC; send x through a secure channel ag and RK i→ecc Send to AG; i = 1, 2, ..., n; send x through a secure channel i Send to SS i .

[0085] In this embodiment, before re-encryption and aggregation, the aggregation gateway AG first verifies the data received from the smart sensor, and the verification method is:

[0086] The aggregation gateway AG verifies whether the timestamp T is fresh. If the verification fails, it refuses to receive the data. If the timestamp T is verified, it continues to verify whether the digital signature is valid. If the equation e(σ i , g) = e(H(C′ i ), p i ) is established, the verification passes and continues to execute; in order to make signature verification more efficient, AG performs batch signature verification and calculates

[0087] The detailed process of the aggregation gateway AG performing the aggregation operation on the first-level ciphertext obtained by re-encryption is as follows:

[0088] First, count the smart devices participating in the aggregation, and record n0 as the number of devices that correctly participate in the aggregation. Then the aggregation gateway AG calculates the aggregation ciphertext

[0089] In this embodiment, the specific process of step (4) is as follows:

[0090] Step (4.1), the power control center ECC performs data verification, the specific process is as follows:

[0091] First, verify whether the timestamp T is fresh. If the verification fails, refuse to receive the data. If the timestamp T is verified, continue to verify whether the digital signature is valid, that is: if the equation e(σ, g) = e(H(C), p ag ) is established, the digital signature verification is successful;

[0092] Step (4.2), ECC performs data decryption, that is, ECC first calculates According to the binomial expansion, we can get gm: Get the aggregated plaintext message m;

[0093] g m =(1+N) m mod N 2 =(1+Nm)mod N 2 ;

[0094] Step (4.3), ECC processes the aggregated plaintext message, the specific process is as follows:

[0095] Get aggregate plaintext message Set the loop variable i to decrease from i=k to i=1;

[0096] Then calculate the sum of the data of the current i-th dimension D i ,

[0097] Next, the value of the ECC update message m is: m = m mod Si ;

[0098] ECC repeats steps (4.3.2) and (4.3.3) until the sum of data of all dimensions is obtained

[0099] Step (4.4), ECC performs data analysis and mining applications on the data of each dimension.

[0100] This example is run on a computer equipped with an AMD Ryzen 76800H 3.2GHz processor, 16GB memory and Windows 11 (64-bit) operating system. The proposed scheme is implemented using Python programming language and miracl core library, and the security parameters of the Paillier cryptographic system and its modified version are set to 2048 bits. The cryptographic primitive execution time symbol and theoretical overhead analysis of this method are shown in Table 2_1 and Table 2_2:

[0101] Table 2_1

[0102] Logo illustrate <![CDATA[T h ]]> The time of a hash operation <![CDATA[T mm ]]> The time of a modular multiplication operation <![CDATA[T me ]]> Time for one modular exponentiation operation <![CDATA[T pa ]]> One-click operation time <![CDATA[T pm ]]> The time of one point multiplication operation

[0103] Table 2_2

[0104] entity Theoretical computational overhead <![CDATA[SS i ]]> <h2 style=";text-align:left;direction:ltr"><![CDATA[(k+1)·T <h2 style=";text-align:left;direction:ltr"> mm <h2 style=";text-align:left;direction:ltr"> +2T<h2 style=";text-align:left;direction:ltr"> me <h2 style=";text-align:left;direction:ltr"> ]]><h2 style=";text-align:left;direction:ltr"> AG <![CDATA[2(n-1)·T mm ]]> ECC <![CDATA[2T mm +T me ]]>

[0105] In this embodiment, each smart sensor first performs preliminary aggregation and calculates the plaintext message m i =d i1 S1+d i2 ·S2+…+d ik ·S k During this process, SS i k modular multiplication operations need to be performed. During the encryption process, SS i One modular multiplication operation and two modular exponentiation operations need to be performed. Therefore, SS i The total encryption computation cost is (k+1)·T mm +2T me .

[0106] At the aggregation gateway, assuming that the number of users participating in the aggregation is n, in the present invention, AG first performs proxy re-encryption on the primary ciphertext of n devices and calculates C i =C′ i ·rk i→ecc This process involves n modular multiplication operations. Then, AG aggregates the re-encrypted ciphertext This includes n-1 modular multiplication operations. The total computational cost is 2(n-1)·T mm .

[0107] The ECC at the power computing center performs decryption operations and calculates Involves 1 modular exponential operation and 2 modular multiplication operations. The total computational cost is 2T mm +T me .

[0108] According to the above operations, the communication overhead results of each entity in the practical application stage of the technical solution of the present invention are shown in Table 3. The ciphertext size of the Paillier cipher variant algorithm in this embodiment is 4096 bits, and the signature algorithm of the scheme is implemented on the BLS12-383 curve, and the signature size is 392 bits. In order to ensure the correctness and consistency of the theoretical analysis results, the size of the identifier and timestamp is set to 32 bits, and n is the number of smart sensors participating in the aggregation.

[0109] Table 3

[0110] entity Communication overhead (bytes) <![CDATA[SS i to AG]]> 4520n AG to ECC 4552

[0111] In this embodiment, SS i The computational overhead of AG and ECC is used to measure the performance of the present invention. i First, the collected multi-dimensional data is preliminarily aggregated, and then the aggregated single plaintext data is encrypted. i The collected plaintext dimensions k = 2, 4, 6, 8, 10, for SS i Repeat the above operation 100 times to calculate the average value. The result is as follows Figure 3 shown.

[0112] In the proxy re-encryption and aggregation stage, after verifying the signature, AG first re-encrypts the reported ciphertext data, and then aggregates the aggregated ciphertext. The plaintext dimension k = 10, the number of aggregated users n = 200, 400, 600, 800, 1000, and the above operation is repeated 100 times for AG to calculate the average value. The results are as follows: Figure 4 shown.

[0113] In the data decryption stage, the ECC performs decryption on the received ciphertext after signature verification, and then uses the algorithm to extract the sum of each dimension data from the aggregated plaintext. In this embodiment, the dimension k is set to 10, and the number of aggregated users n is set to 200, 400, 600, 800, 1000. The above operation is repeated 100 times for ECC to calculate the average value. The result is as follows: Figure 5 shown.

[0114] Experimental results show that the computational overhead of this embodiment is very light and has obvious advantages over existing methods.

Claims

1. A method for industrial Internet of Things multi-dimensional privacy protection data aggregation based on homomorphic proxy re-encryption, characterized in that: The following steps are involved: Step (1), during the system initialization phase, the trusted authority TA generates and publishes public parameters Ω for the system, and distributes secret parameters to the power control center ECC, the aggregation gateway AG, and the smart sensor SS; in, N represents the upper limit of the number of smart sensors. The trusted authority TA selects large prime numbers p and q based on the security parameter λ, calculates N=pq, g=N+1, and selects a random r0 that satisfies Bilinear map pairing e: are all prime v-order cyclic groups, choose The generator g1, H is a collision-resistant hash function, p ag is the signature public key of the aggregation gateway AG, {p i } i＝1，2，...，n refers to the signature convention set of all smart sensors, {S i } 1≤i≤k It refers to the super-increasing sequence; Step (2), reporting data, refers to the smart sensor SS performing preliminary aggregation of multi-dimensional data and encrypting and signing the data before reporting the data to the aggregation gateway AG; the specific method is: First, the i-th smart sensor SS i Preliminary aggregation of collected plaintext messages, calculation of aggregated plaintext message m i =d i1 ·S1+d i2 ·S2+…+d ik ·S k ;d ij Indicates SS i The j-th dimension data collected; Then, the smart sensor SS i Encrypt the original plaintext and calculate the primary ciphertext C′ i : Then the smart sensor SS i Sign the primary ciphertext and generate a signature Last SS i {C′ i , σ i , T} is packaged and sent to the aggregation gateway AG, where T is the current timestamp used to resist replay attacks; Step (3), re-encrypting and aggregating the ciphertext, including the aggregation gateway AG verifying, re-encrypting and aggregating the reported data, the specific method is: Step (3.1), the aggregation gateway AG receives data from each smart sensor SS i Verify the received data; Step (3.2), the aggregation gateway AG performs a proxy re-encryption operation on the verified ciphertext, that is, for the received primary ciphertext C′ i , re-encrypt it and calculate the first-level ciphertext Step (3.3), the aggregation gateway AG aggregates the first-level ciphertext obtained by re-encryption to obtain the aggregated ciphertext C; and signs the aggregated ciphertext C to calculate Finally, the aggregation gateway AG reports the data {C, σ ag , n0, T} are packaged and sent to the power control center ECC; Step (4): In the data decryption phase, the power control center ECC decrypts the data report {C, σ ag , n0, T} to verify and decrypt, and finally obtain the plaintext aggregate data D i .

2. The method for industrial Internet of Things multi-dimensional privacy protection data aggregation based on homomorphic proxy re-encryption according to claim 1 is characterized in that: The detailed method of step (1) is as follows: Step (1.1), the trusted authority TA sets system parameters and collision-resistant hash function For the super-increasing sequence S = {S1, S2, ..., S k },satisfy k is the dimension of the reported data, M j Represents the upper limit value of the j-th dimension data; Step (1.2), the trusted authority TA sets the system key and selects a random number As the key of the power control center ECC; select a random number As the key of the smart sensor SSi; select a random number As the key of the aggregation gateway AG; Step (1.3), re-encryption key setting, TA calculates the re-encryption key rk i→ecc ; Step (1.4), the trusted authority TA sets the signature key of other entities, Public parameters Step (1.5), the trusted authority TA distributes secret parameters: Send the private key x through a secure channel ecc Send to ECC; send the private key x through a secure channel ag and RK i→ecc Send to AG; i = 1, 2, ..., n; send the private key x through a secure channel i Send to SS i .

3. A multi-dimensional privacy-preserving data aggregation method for industrial IoT based on homomorphic proxy re-encryption, characterized in that: In step (3), before re-encryption and aggregation, the aggregation gateway AG first verifies the data received from the smart sensor. The verification method is: The aggregation gateway AG verifies whether the timestamp T is fresh. If the verification fails, it refuses to receive the data. If the timestamp T is verified, it continues to verify whether the digital signature is valid. If the equation e(σ i , g) = e(H(C′ i }, p i ) is established, the verification passes and continues to execute; in order to make signature verification more efficient, AG performs batch signature verification and calculates The detailed process of the aggregation gateway AG performing the aggregation operation on the first-level ciphertext obtained by re-encryption is as follows: First, count the smart devices participating in the aggregation, and record n0 as the number of devices that correctly participate in the aggregation. Then the aggregation gateway AG calculates the aggregation ciphertext 4. A multi-dimensional privacy-preserving data aggregation method for industrial Internet of Things based on homomorphic proxy re-encryption, characterized in that: The specific process of step (4) is as follows: Step (4.1), the power control center ECC performs data verification, the specific process is as follows: First, verify whether the timestamp T is fresh. If the verification fails, refuse to receive the data. If the timestamp T is verified, continue to verify whether the digital signature is valid, that is: if the equation e(σ, g) = e(H(C), p ag ) is established, the digital signature verification is successful; Step (4.2), ECC performs data decryption, that is, ECC first calculates According to the binomial expansion, we can get gm: Get the aggregated plaintext message m; g m =(1+N) m mod N 2 =(1+Nm)mod N 2 ; Step (4.3), ECC processes the aggregated plaintext message, the specific process is as follows: Get aggregate plaintext message Set the loop variable i to decrease from i=k to i=1; Then calculate the sum of the data of the current i-th dimension Next, the value of the ECC update message m is: m = m mod S i ; ECC repeats steps (4.3.2) and (4.3.3) until the sum of data of all dimensions is obtained

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