Multi-dimensional privacy-preserving data aggregation method for industrial IoT based on homomorphic proxy re-encryption

Abstract

The present invention discloses a multi-dimensional privacy-preserving data aggregation method for the industrial Internet of Things based on homomorphic proxy re-encryption. In the data reporting stage, smart sensors perform data reporting; the aggregation gateway performs proxy re-encryption and data aggregation; and in the data decryption stage, the power control center decrypts the data. The present invention proposes a reliable and flexible data aggregation framework based on super-increasing 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. The present invention supports a privacy-preserving data aggregation scheme based on a modified Paillier cipher algorithm with proxy re-encryption, which solves the problem of internal attacks. The present invention ensures privacy, integrity, authenticity, resistance to external attacks, and fault tolerance, and provides more functions while maintaining similar overhead.

Description

Technical Field

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

[0002] The smart grid is a key component of the modern Industrial Internet of Things (IIoT). It leverages real-time data and intelligent control technologies to achieve reliable, efficient, and sustainable operation of power systems, which is very helpful for industrial production scheduling. The smart grid infrastructure in the IIoT typically includes smart sensors (SS), aggregation gateways (AG), and power control centers (ECCs). Smart sensors in factories are deployed in industrial equipment to collect power usage data and regularly transmit this data to the aggregation gateway. The aggregation gateway operates within the industrial area network, collecting and integrating data, reducing the frequency of data transmission and lowering system load and costs. 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] While smart grids in the IIoT offer advantages in power management and dispatch, they also introduce significant privacy and security concerns. Most data transmission in IIoT smart grids occurs over wireless communication links, which may contain sensitive information such as a plant's production capacity. Attackers can exploit this privacy leakage to their advantage. Therefore, it is necessary to develop effective security solutions to protect fine-grained IIoT data 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. Research has 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-world 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 large amount of computing resources being wasted when encrypting single-dimensional data. To address these challenges, some studies have proposed multidimensional data aggregation schemes.

[0005] While most existing schemes are designed to defend systems from external attacks, modern smart grid infrastructure also faces the risk of insider attacks. For example, in some schemes, smart sensors encrypt plaintext data using the public key of the power control center. This allows a semi-honest power control center to decrypt the private energy consumption data of individual devices using its private key. Because smart grids in the IIoT involve a wide variety of devices and a complex user base, the impact of insider attacks can be widespread. Therefore, mitigating insider attacks has become a key challenge in ensuring smart grid security. Most existing multi-dimensional schemes based on traditional public key cryptography fail to protect against insider attacks or the risk of 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 curious control centers from decrypting sensitive data from registered devices. Even if an 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 typically deployed at the edge of the power grid system, are vulnerable. In addition, the addition, removal, and update of entities in industrial power grid systems are more in line with real-world usage scenarios. Therefore, the designed scheme should be sufficiently fault-tolerant and flexible 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 provide an industrial Internet of Things multi-dimensional privacy-preserving data aggregation method based on homomorphic proxy re-encryption.

[0008] Technical solution: The present invention provides a method for aggregating multi-dimensional privacy-preserving data in the industrial Internet of Things 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, aggregation gateway AG, and 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, 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, encrypting and signing the data, and then reporting the data to the aggregation gateway AG; the specific method is:

[0013] First, the i-th smart sensor SS i Initially aggregate the collected plaintext messages and calculate the 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, specifically:

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

[0018] Step (3.2), the aggregation gateway AG performs 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 performs an aggregation operation on 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 the system parameters and the anti-collision hash function For the super-increasing sequence S={S1, S2, ..., S k},satisfy

[0023] k is the dimension of the reported data, M j Indicates 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; choose a random number 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 the secret parameters:

[0029] The private key x is sent via a secure channel ecc Send to ECC; send private key x through 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] Aggregate the collected multi-dimensional plaintext data into one plaintext through the super-increment sequence, and the device SS i Collected multi-dimensional plaintext data (d i1 , d i2 ,…,d ik ), k is the dimension of the plaintext, the device initially aggregates k data into one data m i , saving the transmission cost, the preliminary 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. 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 re-encrypted first-level ciphertext 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 avoid the failure of aggregation decryption caused by damage to the edge device and inability to upload data normally; 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, the data is rejected. If the timestamp T is verified, the digital signature is verified to be 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 aggregated plaintext message Set the loop variable i to decrease from i=k to i=1;

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

[0044] Then, the value of the ECC update message m is: m = m mod S i , the update 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 for all dimensions is obtained

[0046] In step (4.4), ECC performs data analysis and mining 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 frameworks, this paper proposes a reliable and flexible data aggregation framework based on super-increasing sequences, homomorphic encryption, and proxy re-encryption. The proposed framework supports multidimensional data aggregation and dynamic management of smart sensors, aggregation gateways, and power control centers.

[0049] (2) This paper addresses the problem of insider attacks, which is rarely addressed in existing technologies. It designs a privacy-preserving data aggregation scheme based on a modified Paillier cipher algorithm that supports proxy re-encryption. This scheme prevents any entity from obtaining a single plaintext, thus protecting the privacy of individual data in the 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, and 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 diagram in the embodiment;

[0053] Figure 3 Graph showing the computational overhead of the smart sensor in the embodiment;

[0054] Figure 4 This is a diagram of the computational overhead of the aggregation gateway in the 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] To address the low fault tolerance, low scalability, and internal attack issues of existing industrial Internet of Things security aggregation solutions, the present invention proposes a multi-dimensional privacy-preserving data aggregation method for the industrial Internet of Things based on homomorphic proxy re-encryption. This method implements dynamic management of industrial Internet of Things entities through a reliable and flexible data aggregation framework based on super-incremental sequences, homomorphic encryption, and proxy re-encryption. Furthermore, a modified Paillier cryptographic algorithm is used to effectively resist internal attacks. Specifically, this paper combines super-incremental sequences, homomorphic encryption, and proxy re-encryption to support higher fault tolerance while supporting multi-dimensional data aggregation, greatly improving the scalability of the system. Even if entities in the system suffer natural damage or human attacks and are unable to participate in data aggregation correctly, the framework designed by the present invention can still operate correctly. The present invention then modifies the Paillier cryptographic algorithm, adding support for proxy re-encryption while ensuring that its homomorphic properties remain unchanged. The modified cryptographic system of the present invention enables the system to guard against more security threats. Even if a few devices are hacked by an adversary, the sensitive data of other unhacked smart sensors will not be leaked.

[0058] like Figure 1As shown, this embodiment involves four types of entities: smart sensors (SS), aggregation gateways (AGs), power control centers (ECCs), and trusted authorities (TAs). 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 it into initial plaintext using a super-incremental sequence. The initial plaintext is then encrypted using its own key and sent to the aggregator gateway. The aggregation gateway collects the initial ciphertext encrypted by the SS and performs proxy re-encryption on it, converting it into ciphertext decryptable by the ECC. The re-encrypted ciphertext is then aggregated to obtain the aggregated ciphertext and sent 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, an algorithm is used to obtain the sum of the data for each dimension, based on which analysis and decision-making are performed. The trusted authority is responsible for generating the keys, re-encryption keys, and signature keys for each key entity and publishing public parameters. After system initialization is complete, the TA typically goes offline.

[0059] In order to facilitate 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 method for aggregating multi-dimensional privacy-preserving data in the industrial Internet of Things based on homomorphic proxy re-encryption in 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, aggregation gateway AG, and 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, encrypting and signing the data, and then reporting the data to the aggregation gateway AG; the specific method is:

[0068] First, the i-th smart sensor SS i Initially aggregate the collected plaintext messages and calculate the 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, specifically:

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

[0073] Step (3.2), the aggregation gateway AG performs 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 performs an aggregation operation on 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 the system parameters and the anti-collision hash function For the super-increasing sequence S={S1, S2, ..., S k},satisfy

[0078] k is the dimension of the reported data, M j Indicates 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; choose a random number 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 the secret parameters:

[0084] x through a secure channel ecc Send to ECC; send x through a secure channel ag and rk i→ecc Send to AG; i = 1, 2, ..., n; x 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. 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 is passed and continues to execute; in order to make the 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 re-encrypted first-level ciphertext 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:

[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, the data is rejected. If the timestamp T is verified, the digital signature is verified to be 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 aggregated plaintext message Set the loop variable i to decrease from i=k to i=1;

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

[0097] Then, 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 for all dimensions is obtained

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

[0100] This example was run on a computer equipped with an AMD Ryzen 76800H 3.2GHz processor, 16GB of RAM, and Windows 11 (64-bit). The proposed scheme was implemented using the Python programming language and the miracl core library. The security parameter of the Paillier cryptosystem and its modified versions was set to 2048 bits. The symbolic and theoretical cost analysis of the cryptographic primitive execution time of this method is shown in Tables 2_1 and 2_2:

[0101] Table 2_1

[0102] Logo illustrate <![CDATA[T h ]]> Time for one hash operation <![CDATA[T mm ]]> Time for one modular multiplication operation <![CDATA[T me ]]> Time for one modular exponentiation operation <![CDATA[T pa ]]> Time for one click-add operation <![CDATA[T pm ]]> The time of one dot 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"><!-- 7 --> ]]><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 It includes n-1 modular multiplication operations. The total computational cost is 2(n-1)·T mm .

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

[0108] Based on the above operations, the communication overhead results for each entity during the practical application phase 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 solution is implemented on the BLS12-383 curve, with a signature size of 392 bits. 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 performance of the present invention is measured by the computational overhead of AG and ECC. 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 phase, after verifying the signature, the 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, repeat the above operation 100 times for the AG and calculate the average value. The results are as follows: Figure 4 shown.

[0113] In the data decryption phase, the ECC decrypts the received ciphertext after signature verification, and then uses an 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, and 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 lightweight and has obvious advantages over existing methods.

Claims

1. A method for multi-dimensional privacy-preserving data aggregation in industrial IoT 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 for the system. and distribute secret parameters to the power control center ECC, aggregation gateway AG, and smart sensor SS; in, ; Indicates the upper limit of the number of smart sensors, trusted authority Based on safety parameters Select a large prime number , ,calculate , , select random and satisfy ; Bilinear map pairing , , All are prime numbers Cyclic group of order, choose Generators of , is a collision-resistant hash function, Aggregation Gateway The signature public key, Refers to the signature convention set of all smart sensors, 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 as follows: First, the i-th smart sensor Initially aggregate the collected plaintext messages and calculate the aggregated plaintext messages ; express The collection dimensional data; then, smart sensors Encrypt the original plaintext and calculate the primary ciphertext : ； Then by smart sensor Sign the primary ciphertext and generate a signature ;at last Will Pack and send to aggregation gateway , Is the current timestamp used to resist replay attacks; Step (3) re-encrypts and aggregates the ciphertext, including the aggregation gateway AG verifying, re-encrypting and aggregating the reported data. The specific method is: Step (3.1), aggregation gateway From each smart sensor Verify the received data; Step (3.2), aggregation gateway Perform proxy re-encryption on the verified ciphertext, that is, for the received primary ciphertext , re-encrypt it and calculate the first-level ciphertext ; Step (3.3), aggregation gateway Perform aggregation operation on the first-level ciphertext obtained by re-encryption to obtain the aggregated ciphertext ; and aggregate ciphertext Sign and calculate ; Final aggregation gateway Report the data Pack and send to the power control center ; To correctly determine the number of devices participating in the aggregation; Step (4): In the data decryption phase, the power control center ECC reports the data Perform verification and decryption to finally obtain the plaintext aggregate data .

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), trusted authority Set system parameters and anti-collision hash function For super-increasing sequences ,satisfy ; is the dimension of the report data, Indicates the The upper limit value of the dimension data; Step (1.2), trusted authority Set the system key and select a random number As a power control center The key; choose a random number As a smart sensor The key; choose a random number As an aggregation gateway The key of Step (1.3), re-encryption key setting, Calculate the re-encryption key ; ； Step (1.4), Trusted Authority Set the signing key of another entity, , ; Public parameters ; Step (1.5), Trusted Authority Distribute secret parameters: The private key is sent via a secure channel Send to ; Send the private key through a secure channel and Send to ; ; Send the private key through a secure channel Send to .

3. 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: In step (3), before re-encryption and aggregation, the aggregation gateway First, verify the data received from the smart sensor. The verification method is: Aggregation Gateway Verify Timestamp Is it fresh? If the verification fails, the data will be rejected. If the timestamp If the verification is successful, continue to verify whether the digital signature is valid. If the equation If it is established, the verification is passed and the execution continues; in order to make the signature verification more efficient, Perform batch signature verification and calculation ; Aggregation Gateway The detailed process of 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 To correctly determine the number of devices participating in the aggregation, the aggregation gateway Calculate aggregate ciphertext .

4. 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 specific process of step (4) is as follows: Step (4.1), Power Control Center Perform data verification. The specific process is as follows: Verify the timestamp first Is it fresh? If the verification fails, the data will be rejected. If the timestamp If the verification is successful, continue to verify whether the digital signature is valid, that is: if the equation If it is established, the digital signature verification is successful; Step (4.2), Decrypt the data, that is Calculate first ; According to the binomial expansion, we get :calculate , get the aggregated plaintext message ; ； Step (4.3), The aggregated plaintext message is processed as follows: Get aggregated plaintext message , set the loop variable from arrive Decreasing; Then calculate the current The sum of the dimension data , .

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