Security control method, device and system based on homomorphic encryption

Abstract

The application discloses a kind of security control method, device and system based on homomorphic encryption, method includes the following steps: using BGN encryption algorithm to generate encryption table, the BGN encryption algorithm is finite times homomorphism, support once multiplication homomorphic operation and infinite times addition homomorphic operation;Multiple homomorphic operations are carried out in parallel, first parallel calculation ciphertext homomorphic multiplication operation, then execute ciphertext homomorphic addition operation;Calculate to generate decryption table, the ciphertext in the decryption table is not the same as the ciphertext form in the encryption table.Form.BGN encryption algorithm used in the application has higher security level relative to semi-homomorphic encryption algorithm, supports protecting encryption controller parameter and transmission signal simultaneously;BGN encryption algorithm is optimized by pre-computation lookup table and parallel calculation mode, the control efficiency of encryption controller is guaranteed;Encoding and decoder are used to quantize data in encryption control system, the asymptotic stability of encryption control system is ensured.

Description

Technical Field

[0001] This invention relates to a security control method, apparatus, and system based on homomorphic encryption, belonging to the field of network security technology. Background Technology

[0002] Networked control systems integrate sensing, networking, computing, and control methods with physical systems, and are widely used in industry and modern critical infrastructure. With the development of cloud computing and control theory, traditional networked control systems face challenges in handling large datasets. The computational power required to collect large amounts of data and run these systems has led to the outsourcing of estimation and control tasks to third-party platforms. However, the transmission and sharing of sensitive data through network systems, communication networks, and third-party clouds are vulnerable to cyberattacks involving eavesdropping and data manipulation. Attacks on control systems can harm physical equipment and the surrounding environment. Therefore, networked control system solutions should not only achieve high-quality control but also ensure the security and privacy of data involved in the entire control loop.

[0003] Encryption technology has been used in network control systems to improve data confidentiality during transmission, thereby achieving secure communication. Currently, most solutions for enhancing the security of network control systems are based on traditional encryption and decryption techniques. However, this design has a significant drawback: data needs to be decrypted before being transmitted to the controller, and private keys used for the decryption process need to be managed simultaneously. Since the data inside the controller is in plaintext, if a malicious user gains unauthorized access to the control or decryption equipment, they could potentially record and steal the system's most important and confidential information, such as controller parameters, measurements, and control commands. Using homomorphic encryption to perform encrypted computations on the data can address this security vulnerability and provide data confidentiality throughout the control loop. Homomorphic encryption is a form of encryption that allows computation on ciphertext without decryption; the encrypted data undergoes privacy-preserving computations directly within the controller. Therefore, using homomorphic encryption significantly improves the security of network control systems.

[0004] A key issue is that in a control system, the controller must obtain a calculation result within a set sampling period. However, the computational efficiency of homomorphic encryption algorithms is slow, and the encryption and decryption processes involve a significant workload and communication overhead, which may prevent the control task from being completed within the sampling period. Therefore, selecting a fast homomorphic encryption algorithm or optimizing the encryption control algorithm is one of the technical problems that urgently need to be solved. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a security control method, apparatus, and system based on homomorphic encryption, which can guarantee the control efficiency of the encryption controller and ensure the asymptotic stability of the encryption control system.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] In a first aspect, the present invention provides a security control method based on homomorphic encryption, comprising the following steps:

[0008] An encryption table is generated using the BGN encryption algorithm, which is a finite number of fully homomorphic operations and supports one homomorphic multiplication operation and an infinite number of homomorphic addition operations.

[0009] Multiple homomorphic operations are performed in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed.

[0010] A decryption table is generated, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table.

[0011] As one possible implementation of this embodiment, the step of generating the encryption table using the BGN encryption algorithm includes:

[0012] A key is generated using a key generation algorithm, the key including a public key for encryption and a private key for decryption;

[0013] Generate an encryption table, determine the range of values ​​for the encrypted plaintext, calculate the encrypted ciphertext for the encrypted plaintext within the range of values, and store the encrypted plaintext as an index in the encryption table and the encrypted ciphertext in pairs.

[0014] As one possible implementation of this embodiment, the key generation using the key generation algorithm includes:

[0015] Input security parameters Run the key generation algorithm Get tuple , Is the order as cyclic group It is a bilinear mapping, with two generators randomly selected. and order ,but It's a group of The random generator of the subgroup of order is used to determine the public key. private key .

[0016] As one possible implementation of this embodiment, the step of generating an encryption table, determining the value range of the encrypted plaintext, calculating the encrypted ciphertext for the encrypted plaintext within the value range, and storing the encrypted plaintext as an index and the encrypted ciphertext in the encryption table in pairs, includes:

[0017] Establish an encryption table to store pairs of encrypted plaintext and encrypted ciphertext;

[0018] Assuming message space Depend on The set consists of integers, where q2, Enter the public key and messages At that time, randomly select one Calculate encrypted ciphertext using encryption algorithms ;

[0019] The range of values ​​for the encrypted plaintext is determined based on the control function. Each encrypted plaintext within the range of values ​​is encrypted to obtain the corresponding ciphertext. The encrypted plaintext is then used as an index to directly look up the encryption table and obtain the corresponding encrypted ciphertext.

[0020] As one possible implementation of this embodiment, the method of performing multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation, includes:

[0021] To perform multiple ciphertext multiplication operations in parallel using multiple threads, let... , ,but The order is , The order is And there must be Make Set the message ciphertext , Then we get The ciphertext:

[0022]

[0023] in, ;

[0024] Perform ciphertext homomorphic addition: Let the message ciphertext be... , , can be obtained ciphertext .

[0025] As one possible implementation of this embodiment, the calculation and generation of the decryption table specifically involves:

[0026] Establish a decryption table to store pairs of decrypted ciphertext and decrypted plaintext, and determine the range of values ​​for the decrypted plaintext based on a control function. For each decrypted plaintext within the range of values calculate ,use By creating an index, you can directly look up the decryption table to obtain the corresponding decryption result.

[0027] Secondly, an embodiment of the present invention provides a security control device based on homomorphic encryption, comprising:

[0028] An encryption table generation module is used to generate an encryption table using the BGN encryption algorithm, wherein the BGN encryption algorithm is a finite number of fully homomorphic operations and supports one multiplication homomorphic operation and an infinite number of addition homomorphic operations.

[0029] The homomorphic operation parallel module is used to perform multiple homomorphic operations in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed.

[0030] The decryption table generation module is used to calculate and generate a decryption table, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table.

[0031] Thirdly, the embodiments of the present invention provide a security control system based on homomorphic encryption, comprising:

[0032] The controlled object is the device being controlled, and it is represented as follows:

[0033]

[0034] in, These are parameters for the control object. It is the time step. It controls the state of the object. It is the control input and It controls the output;

[0035] Sensors are used to measure data of controlled objects. And send it to the encryption controller;

[0036] An encoder is used to quantize and map transmitted data and encrypted controller parameters to the plaintext message space;

[0037] The encryption module is used to look up the encryption table based on the data and then encrypt it.

[0038] The encryption controller is used to perform multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation.

[0039] The decryption module is used to look up the decryption table and decrypt the ciphertext result calculated by the encryption controller.

[0040] A decoder is used to recover and restore data;

[0041] Actuator, used to execute control signals transmitted by the encryption controller. This is used to adjust and control the object.

[0042] As one possible implementation of this embodiment, the encoder includes:

[0043] Encoder design module, used to design encoders The design is as follows:

[0044]

[0045] in, , and ;

[0046] Right now:

[0047]

[0048] in, , , , , and .

[0049] As one possible implementation of this embodiment, the encryption controller includes:

[0050] The control function module is used to dynamically output the control functions of the feedback encryption controller.

[0051]

[0052] in, and These are encrypted controller parameters. It is the time step. It is the state of the encryption controller. It is the input of the encryption controller and It is the output of the encryption controller;

[0053] control function Rewritten as:

[0054]

[0055] in, , and ;

[0056] The ciphertext calculation module is used to process the ciphertext obtained from the encryption table. and The encrypted result is obtained through parallel computation internally. and ;

[0057] The ciphertext homomorphic computation module is used to perform ciphertext homomorphic computations.

[0058]

[0059] The parallel computing module is used to perform parallel computation of homomorphic multiplication first:

[0060]

[0061] Then retrieve the result asynchronously. and ,

[0062] Then, when performing homomorphic addition, get , get ;

[0063] Data transmission module, used to transmit The data is sent to the decryption module. The data is sent to the decryption module to be decrypted by looking up the decryption table, and then sent to the encryption table for encryption before being transmitted.

[0064] The technical solutions of the embodiments of the present invention can have the following beneficial effects:

[0065] The technical solution of this invention provides a security control method based on homomorphic encryption. The BGN encryption algorithm used has a higher security level than the semi-homomorphic encryption algorithm and supports the simultaneous protection of encryption controller parameters and transmission signals. The BGN encryption algorithm is optimized by pre-calculation lookup table and parallel computing to ensure the control efficiency of the encryption controller. The encryption control system uses encoders and decoders to quantize data, ensuring the asymptotic stability of the encryption control system.

[0066] The security control device based on homomorphic encryption in the technical solution of this invention has the same beneficial effects as the security control method based on homomorphic encryption in the technical solution of this invention.

[0067] This invention provides a security control system based on homomorphic encryption. The scheme uses the BGN homomorphic encryption algorithm to encrypt the encryption controller, comprehensively enhancing the security of the network control system based on the characteristics of additive and multiplicative homomorphism. The BGN encryption algorithm is optimized through fast table lookup for encryption / decryption and parallel computation of ciphertext, keeping the processing time of the encryption controller within the sampling period and ensuring the control efficiency of the closed-loop system. Encoders and decoders are used to quantize the data, making the quantization error caused by encryption negligible, thus guaranteeing the control performance and stability of the closed-loop system. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating a security control method based on homomorphic encryption according to an exemplary embodiment;

[0069] Figure 2 This is a schematic diagram illustrating a security control device based on homomorphic encryption according to an exemplary embodiment;

[0070] Figure 3 This is a schematic diagram illustrating a security control system based on homomorphic encryption according to an exemplary embodiment;

[0071] Figure 4 This is a flowchart illustrating a privacy computation process based on homomorphic encryption according to an exemplary embodiment. Detailed Implementation

[0072] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0073] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure of the invention, components and arrangements of specific examples are described below. Furthermore, reference numerals and / or letters may be repeated in different examples. This repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. Descriptions of well-known components, processing techniques, and processes are omitted in this invention to avoid unnecessarily limiting the invention.

[0074] Terminology Explanation:

[0075] Homomorphic encryption refers to the process of homomorphically encrypting the original data, performing specific operations on the resulting ciphertext, and then homomorphically decrypting the result to obtain plaintext that is equivalent to the data obtained by directly performing the same operations on the original plaintext data.

[0076] To achieve secure data computation, encrypted control requires redesigning classic control algorithms based on the homomorphic properties of homomorphic encryption algorithms. Besides computational overhead and communication load, different homomorphic encryption algorithms offer varying security levels for the control system. Therefore, a more secure and comprehensive homomorphic encryption algorithm needs to be selected to achieve an efficient, real-time, and highly secure encrypted control system. Furthermore, encrypted controllers involve quantization issues; improper quantization leading to significant errors directly impacts the stability of the control system's performance. Therefore, selecting an appropriate quantization technique is crucial. Thus, this invention proposes a secure control method based on homomorphic encryption.

[0077] like Figure 1As shown in the figure, an embodiment of the present invention provides a security control method based on homomorphic encryption, which includes the following steps:

[0078] An encryption table is generated using the BGN encryption algorithm, which is a finite number of fully homomorphic operations and supports one homomorphic multiplication operation and an infinite number of homomorphic addition operations.

[0079] Multiple homomorphic operations are performed in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed.

[0080] A decryption table is generated, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table.

[0081] As one possible implementation of this embodiment, the step of generating the encryption table using the BGN encryption algorithm includes:

[0082] A key is generated using a key generation algorithm, the key including a public key for encryption and a private key for decryption;

[0083] Generate an encryption table, determine the range of values ​​for the encrypted plaintext, calculate the encrypted ciphertext for the encrypted plaintext within the range of values, and store the encrypted plaintext as an index in the encryption table and the encrypted ciphertext in pairs.

[0084] As one possible implementation of this embodiment, the key generation using the key generation algorithm includes:

[0085] Input security parameters Run the key generation algorithm Get tuple , Is the order as cyclic group It is a bilinear mapping, with two generators randomly selected. and order ,but It's a group of The random generator of the subgroup of order is used to determine the public key. private key .

[0086] As one possible implementation of this embodiment, the step of generating an encryption table, determining the value range of the encrypted plaintext, calculating the encrypted ciphertext for the encrypted plaintext within the value range, and storing the encrypted plaintext as an index and the encrypted ciphertext in the encryption table in pairs, includes:

[0087] Establish an encryption table to store pairs of encrypted plaintext and encrypted ciphertext;

[0088] Assuming message space Depend on The set consists of integers, where q2, Enter the public key and messages At that time, randomly select one Calculate encrypted ciphertext using encryption algorithms ;

[0089] The range of values ​​for the encrypted plaintext is determined based on the control function. Each plaintext within the specified value range is encrypted to obtain the corresponding ciphertext. The plaintext is then used as an index to directly look up the encryption table and obtain the corresponding ciphertext, thus avoiding the time consumption of encryption. The encryption table is represented as follows:

[0090]

[0091] As one possible implementation of this embodiment, the method of performing multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation, includes:

[0092] To perform multiple ciphertext multiplication operations in parallel using multiple threads, let... , ,but The order is , The order is And there must be Make Set the message ciphertext , Then we get The ciphertext:

[0093]

[0094] in, ;

[0095] Perform ciphertext homomorphic addition: Let the message ciphertext be... , , can be obtained ciphertext .

[0096] As one possible implementation of this embodiment, the calculation and generation of the decryption table specifically involves:

[0097] Establish a decryption table to store pairs of decrypted ciphertext and decrypted plaintext, and determine the range of values ​​for the decrypted plaintext based on a control function. For each decrypted plaintext within the range of values calculate ,use By directly querying the decryption table using an index, the corresponding product decryption result is obtained, thus avoiding the time loss in decryption. The decryption table is represented as follows:

[0098]

[0099] This invention optimizes ciphertext computation by using a parallel approach. Multiple ciphertext multiplication operations are added to a multithreaded system, which performs ciphertext homomorphic multiplication operations in parallel, obtains the results asynchronously, and then performs ciphertext homomorphic addition operations, thereby improving the running speed.

[0100] The BGN encryption algorithm has high encryption efficiency but low decryption efficiency. The security control of this invention uses a strategy of generating encryption and decryption tables for fast table lookup during encryption and decryption, avoiding the time loss in encryption and decryption. Furthermore, it performs homomorphic operations on ciphertext in parallel, improving the efficiency of privacy computation.

[0101] The BGN encryption algorithm used has a higher security level than the semi-homomorphic encryption algorithm, and supports the simultaneous protection of encryption controller parameters and transmission signals. The BGN encryption algorithm is optimized by pre-calculation lookup table and parallel computing to ensure the control efficiency of the encryption controller. The encryption control system uses encoders and decoders to quantize data, ensuring the asymptotic stability of the encryption control system.

[0102] like Figure 2 As shown, an embodiment of the present invention provides a security control device based on homomorphic encryption, comprising:

[0103] An encryption table generation module is used to generate an encryption table using the BGN encryption algorithm, wherein the BGN encryption algorithm is a finite number of fully homomorphic operations and supports one multiplication homomorphic operation and an infinite number of addition homomorphic operations.

[0104] The homomorphic operation parallel module is used to perform multiple homomorphic operations in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed.

[0105] The decryption table generation module is used to calculate and generate a decryption table, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table.

[0106] like Figure 3 As shown in the figure, an embodiment of the present invention provides a security control system based on homomorphic encryption, including a controlled object, a sensor, an encoder, an encryption module, an encryption controller, a decryption module, a decoder, and an actuator.

[0107] 1. The controlled object is the device being controlled, and it is represented as follows:

[0108]

[0109] in, These are parameters for the control object. It is the time step. It controls the state of the object. It is the control input and It controls the output.

[0110] 2. Sensors, used to measure data of the controlled object. And send it to the encryption controller.

[0111] 3. Encoder, used to quantize and map transmitted data and encrypted controller parameters to plaintext message space.

[0112] Data must be quantized and mapped to the plaintext message space before it can be encrypted. Therefore, the encoder is based on the control function. The design is as follows:

[0113]

[0114] in, , and ;

[0115] Right now:

[0116]

[0117] in, , , , , and .

[0118] 4. Encryption module, used to look up the encryption table based on the data and encrypt it.

[0119] Data measured by the sensor and encryption controller status During encryption, the corresponding ciphertext is obtained by referring to the encryption table. and .

[0120] 5. Encryption controller, used to perform multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation.

[0121] Ciphertext obtained from the encryption table and The ciphertext result is obtained through parallel computation within the encryption controller. and ;

[0122] The following formula is used for ciphertext homomorphic computation:

[0123]

[0124] The parallel computing process begins with parallel computation of homomorphic multiplication:

[0125]

[0126] Then retrieve the result asynchronously. and ,

[0127] Then, when performing homomorphic addition, get , get ;

[0128] Will The data is transmitted to the decryption module. Since the BGN encryption algorithm only supports one homomorphic multiplication operation, the state of the encryption controller cannot be iterated within the encryption controller itself. Therefore, it is necessary to... The data is sent to the decryption module to be decrypted from the decryption table, and then sent to the encryption table for encryption to complete the data transmission.

[0129] The encryption controller also has control functions for dynamic output feedback encryption controllers:

[0130]

[0131] in, and These are encrypted controller parameters. It is the time step. It is the state of the encryption controller. It is the input of the encryption controller and It is the output of the encryption controller;

[0132] control function Rewritten as:

[0133]

[0134] in, , and .

[0135] This invention encrypts both the parameters of the encryption controller and the transmitted data, ensuring the security of the network control system by calculating and transmitting data in ciphertext form.

[0136] 6. Decryption module, used to look up the decryption table and decrypt the ciphertext result calculated by the encryption controller.

[0137] according to and The corresponding plaintext values ​​are obtained by decrypting the tables respectively. and .

[0138] 7. Decoder, used to recover and restore data.

[0139] Will and Restore to and ,in and ;

[0140] Will Transmitted to the actuator, and simultaneously It is passed to the encoder for encryption in the encryption module.

[0141] 8. Actuator, used to execute control signals transmitted by the encryption controller. This is used to adjust and control the object.

[0142] Figure 4 This is a flowchart illustrating a privacy computation process based on homomorphic encryption, according to an exemplary embodiment. Figure 4 As shown, this invention utilizes the homomorphism of the BGN encryption algorithm to perform privacy calculations on data within the controller. The privacy calculation process mainly includes the following steps: encrypting the data by looking up an encryption table; performing parallel ciphertext calculations within the encryption controller; and decrypting the ciphertext result calculated by the encryption controller by looking up a decryption table. The controller based on the optimized BGN encryption algorithm of this invention completes the control task within the sampling period. The BGN encryption algorithm used in this invention has a higher security level than semi-homomorphic encryption algorithms, supporting the simultaneous protection of encryption controller parameters and transmitted signals; the BGN encryption algorithm is optimized through pre-calculation lookup and parallel computation, ensuring the control efficiency of the encryption controller; the encryption control system uses encoders and decoders to quantize the data, ensuring the asymptotic stability of the encryption control system.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A security control method based on homomorphic encryption, characterized in that, Includes the following steps: An encryption table is generated using the BGN encryption algorithm, which is a finite number of fully homomorphic operations and supports one homomorphic multiplication operation and an infinite number of homomorphic addition operations. Multiple homomorphic operations are performed in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed. A decryption table is generated, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table; The process of generating an encryption table using the BGN encryption algorithm includes: A key is generated using a key generation algorithm, the key including a public key for encryption and a private key for decryption; Generate an encryption table, determine the range of values ​​for the encrypted plaintext, calculate the encrypted ciphertext for the encrypted plaintext within the range of values, and store the encrypted plaintext as an index in the encryption table and the encrypted ciphertext in pairs.

2. The security control method based on homomorphic encryption according to claim 1, characterized in that, The key generation algorithm includes: Input security parameters Run the key generation algorithm Get tuple , Is the order as cyclic group It is a bilinear mapping, with two generators randomly selected. and order ,but It's a group of The random generator of the subgroup of order is used to determine the public key. private key .

3. The security control method based on homomorphic encryption according to claim 2, characterized in that, The process of generating an encryption table, determining the range of values ​​for the plaintext to be encrypted, calculating the ciphertext for the plaintext within the range, and storing the plaintext as an index and the ciphertext in the encryption table in pairs, includes: Establish an encryption table to store pairs of encrypted plaintext and encrypted ciphertext; Assuming message space Depend on The set consists of integers, where q2, Enter the public key and messages At that time, randomly select one Calculate encrypted ciphertext using encryption algorithms ; The range of values ​​for the encrypted plaintext is determined based on the control function. Each encrypted plaintext within the range of values ​​is encrypted to obtain the corresponding ciphertext. The encrypted plaintext is then used as an index to directly look up the encryption table and obtain the corresponding encrypted ciphertext.

4. The security control method based on homomorphic encryption according to claim 3, characterized in that, The method of performing multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation, includes: To perform multiple ciphertext multiplication operations in parallel using multiple threads, let... , ,but The order is , The order is And there must be Make Set the message ciphertext , Then we get The ciphertext: in, ; Perform ciphertext homomorphic addition: Let the ciphertext of the message be... , ,have to ciphertext .

5. The security control method based on homomorphic encryption according to claim 4, characterized in that, The calculation to generate the decryption table is specifically as follows: Establish a decryption table to store pairs of decrypted ciphertext and decrypted plaintext, and determine the range of values ​​for the decrypted plaintext based on a control function. For each decrypted plaintext within the range of values calculate ,use By creating an index, you can directly look up the decryption table to obtain the corresponding decryption result.

6. A security control device based on homomorphic encryption, characterized in that, include: An encryption table generation module is used to generate an encryption table using the BGN encryption algorithm, wherein the BGN encryption algorithm is a finite number of fully homomorphic operations and supports one multiplication homomorphic operation and an infinite number of addition homomorphic operations. The homomorphic operation parallel module is used to perform multiple homomorphic operations in parallel. First, the ciphertext homomorphic multiplication operation is calculated in parallel, and then the ciphertext homomorphic addition operation is performed. The decryption table generation module is used to calculate and generate a decryption table, wherein the ciphertext in the decryption table is different from the ciphertext in the encryption table. The process of generating an encryption table using the BGN encryption algorithm includes: A key is generated using a key generation algorithm, the key including a public key for encryption and a private key for decryption; Generate an encryption table, determine the range of values ​​for the encrypted plaintext, calculate the encrypted ciphertext for the encrypted plaintext within the range of values, and store the encrypted plaintext as an index in the encryption table and the encrypted ciphertext in pairs.

7. A security control system based on homomorphic encryption, characterized in that, include: The controlled object is the device being controlled, and it is represented as follows: in, These are parameters for the control object. It is the time step. It controls the state of the object. It is the control input and It controls the output; Sensors are used to measure data of controlled objects. And send it to the encryption controller; An encoder is used to quantize and map transmitted data and encrypted controller parameters to the plaintext message space; The encryption module is used to look up the encryption table generated by the BGN encryption algorithm according to the data and encrypt it. The encryption table determines the value range of the encrypted plaintext according to the control function, calculates the encrypted ciphertext for the encrypted plaintext within the value range, and stores the encrypted plaintext as the index of the encryption table and the encrypted ciphertext in the encryption table in pairs. The encryption controller is used to perform multiple homomorphic operations in parallel, first calculating the ciphertext homomorphic multiplication operation in parallel, and then performing the ciphertext homomorphic addition operation. The decryption module is used to look up the decryption table generated by the BGN encryption algorithm based on the ciphertext result calculated by the encryption controller for decryption. The decryption table determines the range of plaintext values ​​to be decrypted according to the control function, and calculates the decryption of each plaintext value within the range. ,use By creating an index, you can directly look up the decryption table to obtain the corresponding decryption result. A decoder is used to recover and restore data; Actuator, used to execute control signals transmitted by the encryption controller. This is used to adjust and control the object.

8. The security control system based on homomorphic encryption according to claim 7, characterized in that, The encoder includes: Encoder design module, used to design encoders The design is as follows: in, , and ; Right now: in, , , , , and .

9. The security control system based on homomorphic encryption according to claim 8, characterized in that, The encryption controller includes: The control function module is used to dynamically output the control functions of the feedback encryption controller. in, and These are encrypted controller parameters. It is the time step. It is the state of the encryption controller. It is the input of the encryption controller and It is the output of the encryption controller; control function Rewritten as: in, , and ; The ciphertext calculation module is used to process the ciphertext obtained from the encryption table. and The encrypted result is obtained through parallel computation internally. and ; The ciphertext homomorphic computation module is used to perform ciphertext homomorphic computations. The parallel computing module is used to perform parallel computation of homomorphic multiplication first: Then retrieve the result asynchronously. and , Then, when performing homomorphic addition, get , get ; Data transmission module, used to transmit The data is sent to the decryption module. The data is sent to the decryption module to be decrypted from the decryption table, and then sent to the encryption table for encryption and status update.

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