Multi-secret confusion mode component homomorphic encryption method, system and device and medium

Abstract

The invention provides a multi-secret confusion mode component homomorphic encryption method, system and device and a medium, and relates to the technical field of homomorphic encryption, and the method comprises the steps: generating a coding mode base set and an encryption mode base set according to safety parameters and system configuration; generating a key associated with the encrypted modulo set; coding the plurality of secret messages to be encrypted and the random number into a plaintext; calculating a real modulo component of the plaintext for each encryption modulo to generate a random list, and replacing a specified column element of a corresponding row in the random list with each real modulo component according to the key to obtain a ciphertext; performing homomorphic operation on the at least two ciphertexts under the encryption mode base to obtain a result ciphertext; and extracting a real mode component from the result ciphertext according to the key, reconstructing a plaintext, and decoding to obtain a secret message after homomorphic operation. According to the method, while multi-message parallel homomorphic calculation is supported, the ciphertext security is enhanced through a confusion mode component structure, and correct recovery of an operation result is ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of homomorphic encryption, in particular to a multi-secret obfuscated modulus component homomorphic encryption method, system, device and medium. BACKGROUND

[0002] In the fields of cloud computing, security outsourcing computing and privacy protection data analysis, homomorphic encryption allows direct execution of computing tasks in the ciphertext state, especially suitable for multi-party collaborative computing, privacy protection machine learning and other scenarios, which can support effective ciphertext operation of remote servers while ensuring data privacy.

[0003] At present, the mainstream homomorphic encryption scheme is mostly based on the difficulty problem on the lattice, which has the potential to resist quantum attacks in theory, but faces significant challenges in practical application. On the one hand, its computational complexity is high, and a large number of polynomial operations and noise growth control result in insufficient efficiency when processing large-scale data. On the other hand, existing schemes often require complex noise management of ciphertext, increasing the difficulty of engineering implementation and system integration, and limiting its practicalization process in real-time or high-concurrency scenarios.

[0004] In addition, although the existing homomorphic encryption method based on obfuscated modulus component has good parallel computing characteristics, its design is usually only for encryption and operation of a single secret message. In actual application, users often need to encrypt and homomorphically process multiple related messages or data vectors at the same time. If only single-secret encryption is used, the encryption process needs to be repeated, resulting in communication overhead and waste of computing resources, which cannot fully utilize the potential efficiency advantage of this method in batch processing.

[0005] Further, the existing obfuscated modulus component scheme still has room for improvement in security enhancement. Although the obfuscation of ciphertext can be improved by randomizing the modulus component, its hiding mechanism is relatively fixed and lacks flexible support for dynamic configuration of security isolation and obfuscation position between different messages in the multi-secret case. Attackers may infer part of the key information or message correlation by analyzing the ciphertext structure or repeated encryption pattern, thereby weakening the anti-attack ability of the overall scheme.

[0006] Therefore, how to design a multi-secret obfuscated modulus component homomorphic encryption method, system, device and medium that can support multi-message parallel encryption and have higher obfuscation security to meet the encryption computing needs of multi-secret, high security and high efficiency in actual scenarios is a problem that needs to be solved by those skilled in the art. SUMMARY

[0007] Therefore, the present application provides a multi-secret obfuscated modular component homomorphic encryption method, system, device and medium, aiming at solving the problem that the existing obfuscated modular component scheme only supports single secret encryption and is limited in efficiency; by introducing a random obfuscated modular component structure to hide the real data position, the anti-analysis capability is enhanced, and it is ensured that the addition and multiplication homomorphic operations can still be correctly performed in the ciphertext state, so that reliable secure outsourcing calculation is supported while the encryption efficiency and security are improved.

[0008] In order to achieve the above object, the present application adopts the following technical solutions:

[0009] In a first aspect, the present application provides a multi-secret obfuscated modular component homomorphic encryption method, comprising the following steps: S1. Generating an encoding modular base set and an encryption modular base set according to security parameters and system configuration; S2. Generating a key associated with the encryption modular base set, and defining a hiding rule of real modular components in the ciphertext structure; S3. Encoding a plurality of secret messages to be encrypted and a random number into plaintext based on the encoding modular base set; S4. Calculating the real modular components of the plaintext for each encryption modular base, generating a random list, and replacing each real modular component with a specified column element in the corresponding row of the random list according to the key to obtain ciphertext; S5. Homomorphically operating at least two ciphertexts under the encryption modular base to obtain a result ciphertext; S6. Extracting real modular components from the result ciphertext according to the key, and decoding the plaintext after reconstruction to obtain the secret messages after homomorphic operation.

[0010] Preferably, the S1 comprises: Setting security parameters K and encoding random number length b, calculating the number of encoding random numbers ; Setting the number of secret messages to be encrypted as m, the number of encryption modular bases as n, and the number of obfuscated modular components as t; Generating s=r+m prime numbers with length b as encoding modular bases , and generating n encryption modular bases .

[0011] Preferably, the S2 comprises: Generating a key W={W[1], W[2], …, W[n]}, wherein 1≤W[j]≤t, n is the number of encryption modular bases, t is the number of obfuscated modular components, and W[j] is the column index where the jth real modular component should be placed in the random matrix.

[0012] Preferably, the S3 comprises: Based on m secret messages to be encrypted Generate r random numbers ; make , and calculate satisfy ; Calculate plaintext X using the Chinese Remainder Theorem:

[0013] in, , Let i and n represent the i-th message to be encrypted and the random number, respectively.

[0014] Preferably, S4 includes: For the j-th encryption module Calculate the true modulus components ; The generated size is A random list R of t, where ; Based on key W, the true modulus components Replace random list The Middle The element in row W[j] and column W[j] is used to obtain the ciphertext C.

[0015] Preferably, S5 includes: Receive at least two ciphertexts and Perform modulo operation on the elements at their corresponding positions. Addition or modulo Multiplication yields the ciphertext of the homomorphic computation result. .

[0016] Preferably, S6 includes: From the encrypted result Extracted real modulus component sequence ; make , and calculate satisfy ; Calculate the plaintext corresponding to the homomorphic result :

[0017] Decoding yields the message after homomorphic operation:

[0018] Where k = 1, 2, ..., m.

[0019] Secondly, the present invention provides a multi-secret, confused modal component homomorphic encryption system, comprising: System parameter initialization module: Generates a set of encoding templates and a set of encryption templates based on security parameters and system configuration; Key generation module: Generates a key associated with the cryptographic modulus set and defines the hiding rules of the real modulus components in the ciphertext structure; Message encoding module: Encodes multiple secret messages to be encrypted and random numbers into plaintext based on the encoding module set; Ciphertext generation module: Calculates the real modulus component of the plaintext for each encryption modulus, generates a random list, and replaces the specified column element of the corresponding row in the random list with each real modulus component according to the key to obtain the ciphertext; Homomorphic operation module: Performs homomorphic operations on at least two ciphertexts under the encryption model base to obtain the result ciphertext; Result decryption module: Extracts the real modulus component from the ciphertext based on the key, reconstructs the plaintext, and then decodes it to obtain the secret message after homomorphic operation.

[0020] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the above-described multi-secret obfuscated modal component homomorphic encryption method.

[0021] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-secret obfuscated modal component homomorphic encryption method.

[0022] The descriptions of the second to fourth aspects of this invention can be referred to the detailed description of the first aspect; and the beneficial effects described in the second to fourth aspects can be referred to the analysis of the beneficial effects of the first aspect, which will not be repeated here.

[0023] As can be seen from the above technical solution, compared with the prior art, the present invention has the following beneficial effects: 1. This solution constructs a set of encoding modal bases and uses the Chinese Remainder Theorem to encode multiple messages to be encrypted and random numbers into a single plaintext, thereby supporting the encryption of multiple secret messages at one time. During the homomorphic computation stage, addition or multiplication operations can be performed directly on multiple sets of encrypted messages in the ciphertext state, realizing efficient multi-secret parallel processing capabilities, which is suitable for secure outsourcing computing scenarios for batch data.

[0024] 2. By introducing a confused modulo component structure, the real modulo component is hidden in a randomly generated matrix, and its position is indicated only by the key. This design increases the randomness and structural complexity of the ciphertext, making it difficult for attackers to directly infer the real modulo component or key information from the ciphertext, thereby improving the data confidentiality of the scheme in untrusted environments.

[0025] 3. Under the control of the encryption modulus, homomorphic operations between ciphertexts can be performed directly under the modulus operation without decryption intervention. During decryption, the real modulus component is extracted through the key, and the plaintext is recovered based on the Chinese Remainder Theorem. Finally, the correct operation result is obtained by decoding, which ensures the mathematical consistency of homomorphic computation. This allows the scheme to support ciphertext computation without affecting the correctness and usability of the final result. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0027] Figure 1 A flowchart of a multi-secret obfuscated modal component homomorphic encryption method provided in an embodiment of the present invention; Figure 2 A framework diagram of a multi-secret, obfuscated modal component homomorphic encryption system provided in this embodiment of the invention; Figure 3 This is a schematic diagram of the electronic device structure provided in an embodiment of the present invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] The homomorphic comparison method provided in this application can be applied to a homomorphic comparison server. The homomorphic comparison server can be hardware or software. When the homomorphic comparison server is hardware, it can be implemented as a distributed server cluster providing homomorphic comparison services, or it can be implemented as a single server. When the homomorphic comparison server is software, it can be installed on the servers listed above. It can be implemented as multiple software programs or software modules, or it can be implemented as a single software program or software module; no specific limitations are made here.

[0030] Example 1; like Figure 1 As shown, this embodiment provides a multi-secret, confused modal component homomorphic encryption method, including the following steps: S1. Generate a set of encoding templates and a set of encryption templates based on security parameters and system configuration; S2. Generate a key associated with the cryptographic modulus set and define the hiding rules of the real modulus components in the ciphertext structure; S3. Encode multiple secret messages to be encrypted and random numbers into plaintext based on the encoding modulus set; S4. Calculate the real modulus component of the plaintext for each encryption modulus, generate a random list, and replace the specified column element of the corresponding row in the random list with each real modulus component according to the key to obtain the ciphertext; S5. Perform homomorphic operations on at least two of the ciphertexts under the encryption model to obtain the result ciphertext; S6. Extract the real modulus component from the ciphertext based on the key, reconstruct the plaintext, and then decode it to obtain the secret message after homomorphic operation.

[0031] This method achieves efficient parallel encryption and homomorphic processing of multiple sets of messages by encoding multiple secret messages into a single plaintext and encrypting it using a confused modulo component structure. At the same time, by randomly hiding the real modulo component in the matrix, the obfuscation and anti-attack capabilities of the ciphertext are enhanced. During the homomorphic computation process, the computability of the ciphertext is maintained based on the modulo operation, and the correctness of the decryption result is ensured by combining the key extraction and reconstruction mechanism.

[0032] The following provides a further detailed explanation of each step in the above method; In this embodiment S1, based on security parameters and system configuration, an encoding model set and an encryption model set are generated; including: Set the security parameter K and the length b of the encoded random numbers, and calculate the number of encoded random numbers. ; Let m be the number of messages to be encrypted, n be the number of encryption moduli, and t be the number of confusion moduli; the number t of confusion moduli at this point satisfies Furthermore, the value of t does not affect the correctness of encryption and decryption, and is positively correlated with the system's security strength; Generate s = r + m prime numbers of length b as the encoding basis. And generate n encryption model bases .

[0033] Furthermore, when generating the encoding module set and the encryption module set, the encoding module... With encryption module They are pairwise coprime.

[0034] This step, by defining the quantity and coprime relationship between the encoding and encryption modulo bases, provides the correct mathematical foundation for subsequent encoding / decoding and homomorphic computation, ensuring the feasibility and consistency of multi-message encoding and modulo operations in the overall system.

[0035] In this embodiment, S2, a key associated with the encrypted modulus set is generated, and the hiding rules of the real modulus components in the ciphertext structure are defined; including: Generate a key W={W[1],W[2],…,W[n]}, where 1≤W[j]≤t, n is the number of encryption modal bases, t is the number of confusion modal components, and W[j] is the column index in which the j-th real modal component should be placed in the random matrix.

[0036] Furthermore, element W[j] is an integer that is independently and uniformly randomly selected from the set {1,2,…,t}.

[0037] The randomization mechanism of key generation makes the hidden position of the real modulus component in the ciphertext matrix unpredictable, thereby enhancing the scheme's ability to resist position analysis attacks at the algorithm level.

[0038] In this embodiment, S3, multiple secret messages to be encrypted and random numbers are encoded into plaintext based on the encoding modulus set; including: Based on m messages to be encrypted Generate r random numbers Random number at this location For the interval [0, Uniformly randomly generated integers within ) make , and calculate satisfy ; Calculate plaintext X using the Chinese Remainder Theorem:

[0039] in, , Let i and n represent the i-th message to be encrypted and the random number, respectively.

[0040] By using the Chinese Remainder Theorem to fuse multiple messages with random noise into a single plaintext, simultaneous processing of multiple secrets is achieved. Furthermore, the introduction of random numbers effectively masks the statistical characteristics of the original messages, thereby improving both encryption throughput and semantic security.

[0041] In this embodiment, S4, the true modulus component of the plaintext is calculated for each encryption modulus, a random list is generated, and the specified column element of the corresponding row in the random list is replaced by each true modulus component according to the key to obtain the ciphertext; including: For the j-th encryption module Calculate the true modulus components ; The generated size is A random list R of t, where ; Based on key W, the true modulus components Replace random list The Middle The element in row W[j] and column W[j] is used to obtain the ciphertext C.

[0042] Furthermore, when generating the random list R, for the j-th row, all elements in that row are in the interval [0, ..., ... The random integers generated independently within the range are used for obfuscation only, except for the replaced position, and do not contain any valid information. By embedding the real modulus components into a randomly generated list, with only a very few positions carrying valid information and the vast majority of elements being random masks, this structure increases the entropy and resistance to analysis of the ciphertext, making it difficult for attackers to distinguish the real components from noise in the ciphertext.

[0043] In this embodiment S5, homomorphic operations are performed on at least two ciphertexts under the encryption model to obtain the result ciphertext; including: Receive at least two ciphertexts and Perform modulo operation on the elements at their corresponding positions. Addition or modulo Multiplication yields the ciphertext of the homomorphic computation result. .

[0044] In this step, homomorphic operations support parallel execution, meaning that for multiple ciphertext pairs or multiple sets of ciphertexts, the same encryption modulus { Under the control of}, batch modular addition or modular multiplication operations can be performed on the elements at their respective corresponding positions simultaneously; Homomorphic operations perform element-wise operations on the ciphertext matrix directly in the modular domain, ensuring the correctness of the operation results after decryption. Its highly regular and independent computational characteristics are particularly suitable for parallel computing architectures such as GPUs, enabling efficient batch ciphertext processing.

[0045] In this embodiment, S6 involves extracting the real modulo component from the ciphertext based on the key, reconstructing the plaintext, and then decoding it to obtain the secret message after homomorphic operation; including: From the encrypted result Extracted real modulus component sequence ; make , and calculate satisfy ; Calculate the plaintext corresponding to the homomorphic result :

[0046] Decoding yields the message after homomorphic operation:

[0047] Where k = 1, 2, ..., m.

[0048] This method can process m independent messages simultaneously during a single encryption process, and after homomorphic computation and decryption, it can correctly recover the homomorphic operation results corresponding to these m messages.

[0049] By locating the key and extracting the real modulus components, and then reconstructing and decoding using the Chinese Remainder Theorem, the homomorphic computation results of each message are accurately recovered. This completes the closed loop from encryption and computation to decryption, ensuring the consistency and reliability of the entire computation process.

[0050] The following section supplements the specific implementation steps of the multi-secret obfuscated modal component homomorphic encryption method in this embodiment, taking into account the application scenario of medical and health data security analysis. 1) Parameter and model base generation; In a medical data analysis scenario, a hospital needs to encrypt a certain physiological indicator of two groups of patients and upload it to a cloud server for joint statistical analysis. The system first sets the security parameter K=10 and the length of the encoded random number b=5, and calculates the number of random numbers. =2; Let m = 2 for each encrypted message, n = 4 for the encryption modulus, and t = 2 for the confusion modulus. Next, generate s = r + m = four 5-bit prime numbers as the encoding modulus, such as... and generate encryption template. This provides a mathematical foundation for subsequent message encoding and encryption.

[0051] 2) Definition of key generation and concealment rules; To ensure the security of the ciphertext, the system generates a key W={1,2,1,1} that matches the number of encryption moduli. Each element W[j] represents the column index in which the j-th real moduli should be placed in the subsequently generated random matrix. In this embodiment, the key indicates that the first real moduli is placed in column 1, the second in column 2, and the third and fourth in column 1. This key is kept only by the data holder and is used for subsequent encryption embedding and decryption extraction.

[0052] 3) The message is encoded in plaintext; The two sets of blood glucose values ​​to be encrypted at the hospital are as follows: (Units have been standardized) First, generate r=2 random numbers. To enhance security, the Chinese Remainder Theorem is used to encode all messages and random numbers into a single plaintext X, and then calculate... and obtain , , and its inverse , , , Finally obtained =4139; Furthermore, to demonstrate the subsequent homomorphic computation, this step also provides another set of message encryption, with two input messages respectively. (Units have been standardized), generate r random numbers based on the number of encoded random numbers. The encoding model used here is still based on... Since the encoding modulus remains unchanged, therefore here , , According to the Chinese Remainder Theorem, the message is encoded into plaintext. ; This process maps multiple secrets to a single integer while mixing in random noise to prevent the direct exposure of the original information.

[0053] 4) Encrypt and generate ciphertext; right and In the encryption module respectively The actual modulus components are calculated below. ; ; Generate two 4s respectively A list of random numbers of size 2 and ; Based on the key W={1, 2, 1, 1}, the ciphertext can be obtained. and ; ciphertext and encryption model base The encrypted structure, sent to the cloud server, obfuscates real data with random values, enhancing its resistance to attacks.

[0054] 5) Homomorphic computing in the cloud; The cloud server received the encrypted message. Then, without decryption, homomorphic addition is performed, with corresponding elements added modularly according to their respective modular bases to obtain the result calculated under the encrypted modular base. :

[0055] This step requires no decryption and effectively protects data privacy.

[0056] 6) Decryption and result extraction; The data holder uses key W to extract the ciphertext. The true modulo components are 14, 22, 15, and 8; through the true modulo components and the encrypted modulo base Calculate plaintext ,here , , ; plaintext Separate models The messages after homomorphic computation are respectively , The result of adding it to the original message , The results were completely consistent, verifying the correctness of the homomorphic operation and the reliability of the decryption process.

[0057] The multi-secret obfuscated modular homomorphic encryption method in this embodiment achieves secure aggregation calculation of data in the encrypted state by uniformly encoding and obfuscating multiple sets of medical indicators, and accurately restores the statistical results after decryption. The whole solution effectively supports cross-institutional collaborative analysis while protecting the data privacy of all participants, and can meet the secure calculation needs of data that is available but not visible in fields such as medical care and finance.

[0058] Example 2; like Figure 2 As shown, this embodiment provides a multi-secret, obfuscated modal component homomorphic encryption system, including: System parameter initialization module: Generates a set of encoding templates and a set of encryption templates based on security parameters and system configuration; Key generation module: Generates a key associated with the cryptographic modulus set and defines the hiding rules of the real modulus components in the ciphertext structure; Message encoding module: Encodes multiple secret messages to be encrypted and random numbers into plaintext based on the encoding module set; Ciphertext generation module: Calculates the real modulus component of the plaintext for each encryption modulus, generates a random list, and replaces the specified column element of the corresponding row in the random list with each real modulus component according to the key to obtain the ciphertext; Homomorphic operation module: Performs homomorphic operations on at least two ciphertexts under the encryption model base to obtain the result ciphertext; Result decryption module: Extracts the real modulus component from the ciphertext based on the key, reconstructs the plaintext, and then decodes it to obtain the secret message after homomorphic operation.

[0059] The system provided in this embodiment is built on the aforementioned multi-secret confusion modal component homomorphic encryption method. Through modular design, it realizes the complete process from parameter initialization, key generation, message encoding, ciphertext generation to homomorphic computation and decryption. While ensuring the correctness of multi-message parallel encryption and homomorphic operation, it enhances the ciphertext confusion and anti-analysis capabilities, and is suitable for high-security and high-efficiency ciphertext processing needs in scenarios such as cloud computing and privacy computing.

[0060] Example 3; like Figure 3 As shown, this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described multi-secret obfuscated modal component homomorphic encryption method.

[0061] Example 4; This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-secret obfuscated modal component homomorphic encryption method.

[0062] In the embodiments provided in this application, it should be understood that the disclosed methods, systems, devices, and media can be implemented in other ways. The embodiments of methods, systems, devices, and media described above are merely illustrative. For example, the division of modules or units is only a logical functional division, and there may be other division methods in actual implementation. Each functional unit can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0063] The units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0064] Computer programs include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. Computer-readable media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory, random access memory, electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0065] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-secret obfuscated modular component homomorphic encryption method, characterized by, The method comprises the following steps: S1, generating an encoding modulus set and an encryption modulus set according to security parameters and system configuration; S2, generating a key associated with the encryption modulus set, and defining a hiding rule of real modulus components in a ciphertext structure; S3, encoding a plurality of secret messages to be encrypted and random numbers into plaintexts based on the encoding modulus set; S4, calculating real modulus components of the plaintexts for each encryption modulus, generating a random list, and replacing each real modulus component with a specified column element of a corresponding row in the random list according to the key to obtain ciphertexts; S5, performing homomorphic operation on at least two ciphertexts under the encryption modulus to obtain a result ciphertext; S6, extracting real modulus components from the result ciphertext according to the key, reconstructing plaintexts, and decoding to obtain the secret messages after homomorphic operation.

2. A multi-secret obfuscated modular component homomorphic encryption method according to claim 1, wherein, The S1 comprises: Set the security parameter K and the encoding random number length b, calculate the number of encoding random numbers ; The number of secret messages to be encrypted is m, the number of encryption moduli is n, and the number of confusion modulus components is t. Generating s = r + m prime numbers of length b as encoding modulus and generating n encryption modulus .

3. A multi-secret obfuscated modular component homomorphic encryption method according to claim 2, wherein, The S2 comprises: A key W={W[1], W[2], …, W[n]} is generated, where 1≤W[j]≤t, n is the number of encryption moduli, t is the number of confusion modulus components, and W[j] is the column index where the jth real modulus component should be placed in the random matrix.

4. The multi-secret obfuscated modular component homomorphic encryption method of claim 1, wherein, The S3 comprises: Based on m messages to be encrypted , generating r random numbers ; Let , , and compute satisfy ; The plaintext X is calculated by the Chinese remainder theorem. wherein, , respectively represent the i-th message to be encrypted, a random number.

5. The multi-secret obfuscated modular component homomorphic encryption method of claim 1, wherein, The S4 comprises: For the jth encryption modulus base , calculate the real modulus component ; generating a random list R of size t, where ; Based on the key W, the real modulus component Replacing the random list In the middle of the The element of the W[j] column, get the ciphertext C.

6. A multi-secret obfuscated modular component homomorphic encryption method according to claim 1, wherein, The S5 comprises: Receiving at least two ciphertexts With Performing modulo addition or modulo multiplication on elements of their corresponding positions respectively, obtaining homomorphic computation result ciphertexts .

7. The multi-secret obfuscated modular component homomorphic encryption method of claim 1, wherein, The S6 comprises: real component sequence extracted from the resulting ciphertext ;​ Let , , and compute satisfies ; Computing a plaintext corresponding to a homomorphic result : The homomorphic operation message is decoded to obtain: Where k=1, 2, …, m.

8. A multi-secret obfuscated modular component homomorphic encryption system, comprising: It comprises: A system parameter initialization module: generating an encoding modulus set and an encryption modulus set according to security parameters and system configuration; A key generation module: generating a key associated with the encryption modulus set, and defining a hiding rule of real modulus components in a ciphertext structure; A message encoding module: encoding a plurality of secret messages to be encrypted and random numbers into plaintexts based on the encoding modulus set; A ciphertext generation module: calculating real modulus components of the plaintexts for each encryption modulus, generating a random list, and replacing each real modulus component with a specified column element of a corresponding row in the random list according to the key to obtain ciphertexts; A homomorphic operation module: performing homomorphic operation on at least two ciphertexts under the encryption modulus to obtain a result ciphertext; A result decryption module: extracting real modulus components from the result ciphertext according to the key, reconstructing plaintexts, and decoding to obtain the secret messages after homomorphic operation.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the multi-secret confusion modulus homomorphic encryption method of any one of claims 1 to 7.

10. A computer readable storage medium, the storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the multi-secret confusion modulus homomorphic encryption method of any one of claims 1 to 7.

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