Anti-quantum collaborative encryption method and device, electronic equipment and storage medium

Abstract

The invention relates to the technical field of data security, in particular to an anti-quantum collaborative encryption method and device, electronic equipment and a storage medium, and the method comprises the steps: judging whether an encryption demand exists or not; if the encryption demand exists, determining to-be-encrypted data based on the encryption demand, and obtaining public parameters determined by a plurality of users and corresponding to the to-be-encrypted data; and determining a random polynomial of each user, generating a private key of each user in the private key distribution based on the random polynomial, generating a public key fragment by using the private keys of all users, encrypting the to-be-encrypted data based on the public parameter and the public key fragment, and generating a target ciphertext. Therefore, the problem that privacy leakage is caused due to the fact that a collaborative technical scheme based on a traditional public key algorithm is easily and rapidly cracked by a quantum computer is solved, a collaborative encryption scheme capable of resisting attack of the quantum computer is constructed, collaboration is achieved, and meanwhile the risk of single-point leakage is reduced.

Description

Technical Field

[0001] The present application relates to the field of data security, and in particular to a quantum-resistant collaborative encryption method, device, electronic device, and storage medium. Background Art

[0002] With the rapid development of quantum computer technology, traditional encryption algorithms based on difficult problems such as large integer factorization and discrete logarithms face significant risk of being cracked by quantum computers. Furthermore, with the surge in demand for multi-party collaborative computing in the mobile internet and IoT environments, traditional single-point key management models are prone to privacy leaks.

[0003] The collaborative encryption schemes in related technologies are mainly designed based on the idea of Shamir's threshold secret sharing method and traditional public key algorithms such as RSA and SM2. Among them, the mainstream quantum-resistant public key cryptography algorithms are fully homomorphic encryption algorithms designed based on lattice difficulty problems, including BFV, BGV, CKKS, etc.

[0004] However, quantum computers, leveraging properties like quantum parallelism and quantum entanglement, can rapidly crack public-key cryptography schemes like RSA and elliptic curve cryptography. This also poses a severe challenge to the security of collaborative encryption schemes designed based on these cryptographic algorithms. Furthermore, despite the rapid development of quantum-resistant cryptographic algorithms and the emergence of a growing number of fully homomorphic encryption algorithms based on lattice-based hard problems, collaborative encryption schemes designed and constructed using these algorithms are rare. In summary, research on encryption schemes that are both quantum-resistant and collaborative is limited, and remains a significant technological gap. Summary of the Invention

[0005] The present application provides a quantum-resistant collaborative encryption method, device, electronic device and storage medium to solve the problem that collaborative technology solutions based on traditional public key algorithms can be easily quickly cracked by quantum computers, resulting in privacy leaks. It constructs a collaborative encryption solution that can resist quantum computer attacks, achieving collaboration while reducing the risk of single-point leakage.

[0006] The first embodiment of the present application provides a quantum-resistant collaborative encryption method, comprising the following steps:

[0007] Determine whether encryption is required;

[0008] If there is an encryption requirement, determining the data to be encrypted based on the encryption requirement, and obtaining multiple user-determined public parameters corresponding to the data to be encrypted;

[0009] A random polynomial for each user is determined, a private key for each user is generated in a private key distribution based on the random polynomial, public key fragments are generated using the private keys of all users, and the data to be encrypted is encrypting based on the public parameters and the public key fragments to generate a target ciphertext.

[0010] Optionally, in some embodiments, encrypting the data to be encrypted based on the public parameter and the public key fragment includes:

[0011] generating a public key according to the public parameters and the public key fragments;

[0012] The data to be encrypted is encoded, and the encoded data to be encrypted is encrypted using the public key to generate the target ciphertext.

[0013] Optionally, in some embodiments, after encrypting the data to be encrypted based on the public parameters and the public key fragments to generate the target ciphertext, the method further includes:

[0014] Determine whether a decryption request for the target ciphertext has been received;

[0015] If a decryption request for the target ciphertext is received, decrypting the target ciphertext using the private key of each user based on the decryption request to obtain a plurality of decryption result fragments;

[0016] The multiple decryption result fragments are aggregated to obtain aggregated fragments, and the data to be encrypted is obtained according to the aggregated fragments.

[0017] Optionally, in some embodiments, the common parameters include at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

[0018] A second embodiment of the present application provides a quantum-resistant collaborative encryption device, including:

[0019] A judgment module is used to judge whether there is an encryption requirement;

[0020] an acquisition module, configured to, when encryption is required, determine data to be encrypted based on the encryption requirement, and obtain multiple user-determined public parameters corresponding to the data to be encrypted;

[0021] The encryption module is configured to determine a random polynomial for each user, generate a private key for each user in a private key distribution based on the random polynomial, generate public key fragments using the private keys of all users, and encrypt the data to be encrypted based on the public parameters and the public key fragments to generate a target ciphertext.

[0022] Optionally, in some embodiments, the encryption module includes:

[0023] a generating unit, configured to generate a public key according to the public parameters and the public key fragments;

[0024] The encryption unit is used to encode the data to be encrypted and encrypt the encoded data to be encrypted using the public key to generate the target ciphertext.

[0025] Optionally, in some embodiments, after encrypting the data to be encrypted based on the public parameters and the public key fragments to generate the target ciphertext, the encryption module further includes:

[0026] a judgment unit, configured to judge whether a decryption request for a target ciphertext has been received;

[0027] a decryption unit configured to, upon receiving a decryption request for the target ciphertext, decrypt the target ciphertext using the private key of each user based on the decryption request to obtain a plurality of decryption result fragments;

[0028] The summarizing unit is configured to summarize the multiple decryption result fragments to obtain summarized fragments, and obtain the data to be encrypted according to the summarized fragments.

[0029] Optionally, in some embodiments, the common parameters include at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

[0030] The third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the quantum-resistant collaborative encryption method as described in the above embodiment.

[0031] The fourth aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the quantum-resistant collaborative encryption method as described in the above embodiments.

[0032] Therefore, this application has the following beneficial effects:

[0033] (1) This application implements a collaborative encryption algorithm based on quantum-resistant cryptography, based on the security of the Ring Learning With Errors (RLWE) problem, ensures the data security of multi-party collaboration, can resist the attack of quantum computers, and ensures the collaborative data security in the post-quantum era.

[0034] (2) The present application scheme selects two fully homomorphic encryption schemes that are similar in process but different in application scenarios for collaborative design. This facilitates the flexible selection of application scenarios while reflecting the generality and portability of the collaborative design of the present application.

[0035] (3) This application is safe and simple during the interaction process. Each user only interacts with a trusted third party. It is suitable for scenarios where the level of trust between nodes in the mobile Internet is low, effectively avoiding the risk of single point leakage and enhancing the robustness of the system.

[0036] (4) The collaborative design of this application does not change the security of the original quantum-resistant cryptographic system. By analyzing the situation of single-user decryption, it is theoretically proved that the collaborative process will not lead to the emergence of new security problems, and the security of data is still guaranteed by the grid difficulty problem.

[0037] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0039] Figure 1 This is a flowchart of a quantum-resistant collaborative encryption method provided according to an embodiment of the present application;

[0040] Figure 2 Schematic diagram of a block diagram of a quantum-resistant collaborative encryption device provided according to an embodiment of the present application;

[0041] Figure 3 A schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0042] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0043] The following describes the quantum-resistant collaborative encryption method, device, electronic device and storage medium according to the embodiment of the present application with reference to the accompanying drawings. In response to the problem mentioned in the background technology that the collaborative technical solution based on the traditional public key algorithm is easily cracked by quantum computers quickly, resulting in privacy leakage, the present application provides a quantum-resistant collaborative encryption method. In this method, by judging whether there is an encryption requirement, if there is an encryption requirement, the data to be encrypted is determined based on the encryption requirement, and the public parameters determined by multiple users corresponding to the data to be encrypted are obtained, and the random polynomial of each user is determined. The private key of each user is generated in the private key distribution based on the random polynomial, and the public key fragments are generated using the private keys of all users. The data to be encrypted is encrypted based on the public parameters and the public key fragments to generate the target ciphertext. In this way, the problem that the collaborative technical solution based on the traditional public key algorithm is easily cracked by quantum computers quickly, resulting in privacy leakage, is solved, and a collaborative encryption solution that can resist quantum computer attacks is constructed, achieving collaboration while reducing the risk of single-point leakage.

[0044] Specifically, Figure 1 A flowchart of a quantum-resistant collaborative encryption method provided in an embodiment of the present application.

[0045] like Figure 1 As shown, the quantum-resistant collaborative encryption method includes the following steps:

[0046] In step S101, it is determined whether there is an encryption requirement.

[0047] Specifically, the embodiment of the present application can determine whether there is an encryption requirement through user instructions. For example, when an encryption instruction issued by the user is received, it is determined that there is an encryption requirement.

[0048] In step S102 , if there is an encryption requirement, the data to be encrypted is determined based on the encryption requirement, and public parameters determined by multiple users corresponding to the data to be encrypted are obtained.

[0049] The common parameters include at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

[0050] It should be noted that the embodiment of the present application selects two fully homomorphic public key encryption schemes, BFV and CKKS, to encrypt and decrypt the encrypted data.

[0051] In the embodiments of this application, the BFV quantum-resistant collaborative encryption scheme is used as an example for illustration. The CKKS quantum-resistant collaborative encryption scheme is similar to the BFV quantum-resistant collaborative encryption scheme and is not described here to avoid redundancy. Specifically, when encryption is required, the data to be encrypted is determined based on the encryption requirement, and multiple users corresponding to the data to be encrypted are determined. The multiple users negotiate the public parameters of the quantum-resistant algorithm BFV, specify the cyclotomic polynomial and modulus, and initialize the noise distribution.

[0052] In step S103, a random polynomial for each user is determined, a private key for each user is generated in the private key distribution based on the random polynomial, public key fragments are generated using the private keys of all users, and the data to be encrypted is encrypted based on the public parameters and the public key fragments to generate the target ciphertext.

[0053] Furthermore, in some embodiments, encrypting the data to be encrypted based on the public parameters and the public key fragments includes: generating a public key according to the public parameters and the public key fragments; encoding the data to be encrypted, and encrypting the encoded data to be encrypted using the public key to generate a target ciphertext.

[0054] Specifically, after determining the public parameters, each user negotiates a random polynomial, samples the private key of the quantum-resistant public key algorithm from the BFV private key distribution, and uses the private key to generate public key fragments. After generating the public key fragments, the user transmits the public parameters and public key fragments to a third party. The third party uses the public key fragments to calculate the synthetic public key, that is, the public key of the quantum-resistant public key algorithm. Any data owner who wishes to encrypt data can use the public key to encrypt data.

[0055] The data owner encodes the plaintext, and after encoding, the public key of the quantum-resistant cryptographic algorithm BFV can be used to encrypt the plaintext to generate a target ciphertext containing randomness and noise. The target ciphertext is obtained through the quantum-resistant cryptographic algorithm and has the security of quantum computing resistance. It not only ensures data privacy, but also supports homomorphic operations, so that the encrypted data can be added and multiplied without decryption, ensuring data security while achieving flexible computing processing.

[0056] Optionally, in some embodiments, after encrypting the data to be encrypted based on public parameters and public key fragments to generate the target ciphertext, it also includes: determining whether a decryption request for the target ciphertext is received; if a decryption request for the target ciphertext is received, based on the decryption request, using each user's private key to decrypt the target ciphertext to obtain multiple decryption result fragments; aggregating the multiple decryption result fragments to obtain aggregated fragments, and obtaining the data to be encrypted based on the aggregated fragments.

[0057] Specifically, in the embodiment of the present application, after receiving a decryption request, each user uses the ciphertext and the private key fragments held by themselves to perform a decryption operation of the quantum-resistant cryptographic algorithm BFV to obtain the decryption result fragments and hand them over to a third party. After obtaining them, the third party aggregates the fragments and restores the plaintext. The key to this process is that only when all users work together can the correct plaintext be aggregated by decrypting the fragments. Even if a single user holds the decryption result fragments, he cannot restore the data, thereby ensuring data security.

[0058] Therefore, the embodiments of this application use quantum-resistant cryptographic algorithms based on lattice-based difficult problems. The security of lattice-based cryptographic systems is mainly based on various difficult mathematical problems on the lattice. The security of the two fully homomorphic public key encryption schemes, BFV and CKKS, selected in the embodiments of this application is based on the fault-tolerant learning problem on the ring. Both have the security of resisting quantum computing. At the same time, as fully homomorphic encryption schemes, BFV and CKKS meet the basic characteristics of homomorphic encryption, that is, after the operator performs addition or multiplication operations on the ciphertext, the result is a ciphertext of the original plaintext data after the operation is performed. In addition, there are features such as high-speed calculation of multiple ciphertexts and calculation of ciphertexts by the keyless party.

[0059] In addition, the embodiment of the present application fully utilizes the characteristics of the fully homomorphic encryption scheme and designs a distributed key generation method, which stores the private key in shards on multiple user nodes and allows each user to participate in the decryption operation, thereby achieving collaboration while reducing the risk of single-point leakage.

[0060] Finally, the embodiments of the present application select two quantum-resistant fully homomorphic encryption schemes that support different data types, precisions, and application scenarios as the basic schemes. Different encryption schemes are suitable for different application requirements, thereby meeting multi-party collaboration and privacy protection scenarios from high precision to flexible and efficient. Moreover, the embodiments of the present application have certain similarities in the collaborative design of the two fully homomorphic encryption schemes, which proves that the collaborative design of the embodiments of the present application is general and portable, and can adapt to more scenarios and quantum-resistant cryptographic algorithms.

[0061] In summary, the embodiments of the present application not only support operations in the encryption domain, including the BFV scheme supporting operations on encrypted integers and the CKKS scheme supporting operations on encrypted floating-point numbers, meeting diverse data processing requirements, but also realize privacy protection and multi-party collaboration, and are suitable for scenarios where multiple parties do not trust each other. In addition, the characteristics of post-quantum cryptography ensure that the scheme can resist potential attacks from quantum computing and ensure data security in future network environments; the distributed control and decentralization characteristics of the scheme distribute decryption authority to multiple nodes, reducing the risk of single-point private key leakage. Based on the above advantages, the embodiments of the present application can realize the secure storage of multiple types of data in different scenarios, with a wide range of application scenarios. It can be applied to mobile Internet, medical and health data, cloud computing and data analysis, Internet of Things data security and other fields, and has demonstrated significant superiority in protecting data privacy and improving security.

[0062] According to the quantum-resistant collaborative encryption method of the embodiment of the present application, by determining whether there is an encryption requirement, if there is an encryption requirement, the data to be encrypted is determined based on the encryption requirement, and the public parameters determined by multiple users corresponding to the data to be encrypted are obtained, and a random polynomial for each user is determined. The private key of each user is generated in the private key distribution based on the random polynomial, and the public key fragments are generated using the private keys of all users. The data to be encrypted is encrypted based on the public parameters and the public key fragments to generate the target ciphertext. In this way, the problem that collaborative technology solutions based on traditional public key algorithms are easily cracked by quantum computers, resulting in privacy leaks, is solved, and a collaborative encryption solution that can resist quantum computer attacks is constructed, achieving collaboration while reducing the risk of single-point leakage.

[0063] Next, the quantum-resistant collaborative encryption device proposed in accordance with an embodiment of the present application will be described with reference to the accompanying drawings.

[0064] Figure 2 4 is a block diagram of a quantum-resistant collaborative encryption device according to an embodiment of the present application.

[0065] like Figure 2 As shown, the quantum-resistant collaborative encryption device 10 includes: a judgment module 100, an acquisition module 200 and an encryption module 300.

[0066] The determination module 100 is used to determine whether there is an encryption requirement.

[0067] The acquisition module 200 is used to determine the data to be encrypted based on the encryption requirement when there is an encryption requirement, and obtain multiple public parameters determined by users corresponding to the data to be encrypted.

[0068] The encryption module 300 is used to determine a random polynomial for each user, generate a private key for each user in a private key distribution based on the random polynomial, generate public key fragments using the private keys of all users, and encrypt the data to be encrypted based on the public parameters and the public key fragments to generate a target ciphertext.

[0069] Optionally, in some embodiments, the encryption module 300 includes: a generation unit and an encryption unit.

[0070] The generating unit is used to generate a public key according to the public parameters and the public key fragments.

[0071] The encryption unit is used to encode the data to be encrypted and encrypt the encoded data to be encrypted using the public key to generate the target ciphertext.

[0072] Optionally, in some embodiments, after encrypting the data to be encrypted based on the public parameters and the public key fragments to generate the target ciphertext, the encryption module 300 further includes: a judgment unit, a decryption unit, and a summarization unit.

[0073] The judgment unit is used to judge whether a decryption request for the target ciphertext is received.

[0074] The decryption unit is configured to, upon receiving a decryption request for a target ciphertext, decrypt the target ciphertext using the private key of each user based on the decryption request to obtain a plurality of decryption result fragments.

[0075] The summarizing unit is used to summarize the multiple decryption result fragments to obtain summarized fragments, and obtain the data to be encrypted according to the summarized fragments.

[0076] Optionally, in some embodiments, the common parameters include at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

[0077] It should be noted that the explanation of the aforementioned embodiment of the quantum-resistant collaborative encryption method is also applicable to the quantum-resistant collaborative encryption device of this embodiment, and will not be repeated here.

[0078] According to the quantum-resistant collaborative encryption device of the embodiment of the present application, by determining whether there is an encryption requirement, if there is an encryption requirement, the data to be encrypted is determined based on the encryption requirement, and the public parameters determined by multiple users corresponding to the data to be encrypted are obtained, and a random polynomial for each user is determined. Based on the random polynomial, each user's private key is generated in the private key distribution, and public key fragments are generated using the private keys of all users. The data to be encrypted is encrypted based on the public parameters and public key fragments to generate the target ciphertext. In this way, the problem that collaborative technology solutions based on traditional public key algorithms are easily cracked by quantum computers, resulting in privacy leaks, is solved, and a collaborative encryption solution that can resist quantum computer attacks is constructed, achieving collaboration while reducing the risk of single-point leakage.

[0079] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0080] Memory 301 , processor 302 , and computer programs stored in the memory 301 and executable on the processor 302 .

[0081] When the processor 302 executes the program, the quantum-resistant collaborative encryption method provided in the above embodiment is implemented.

[0082] Furthermore, the electronic device further includes:

[0083] The communication interface 303 is used for communication between the memory 301 and the processor 302 .

[0084] The memory 301 is used to store computer programs that can be run on the processor 302 .

[0085] The memory 301 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0086] If the memory 301, processor 302, and communication interface 303 are implemented independently, the communication interface 303, memory 301, and processor 302 can be interconnected via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 3 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0087] Optionally, in a specific implementation, if the memory 301, the processor 302 and the communication interface 303 are integrated on a chip, the memory 301, the processor 302 and the communication interface 303 can communicate with each other through an internal interface.

[0088] The processor 302 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0089] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned quantum-resistant collaborative encryption method.

[0090] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0091] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0092] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A quantum-resistant collaborative encryption method, characterized in that: The following steps are involved: Determine whether encryption is required; If there is an encryption requirement, determining the data to be encrypted based on the encryption requirement, and obtaining multiple user-determined public parameters corresponding to the data to be encrypted; A random polynomial for each user is determined, a private key for each user is generated in a private key distribution based on the random polynomial, public key fragments are generated using the private keys of all users, and the data to be encrypted is encrypting based on the public parameters and the public key fragments to generate a target ciphertext.

2. The method according to claim 1, characterized in that The encrypting the data to be encrypted based on the public parameter and the public key fragment includes: generating a public key according to the public parameters and the public key fragments; The data to be encrypted is encoded, and the encoded data to be encrypted is encrypted using the public key to generate the target ciphertext.

3. The method according to claim 1 or 2, characterized in that After encrypting the data to be encrypted based on the public parameters and the public key fragments to generate the target ciphertext, the method further includes: Determine whether a decryption request for the target ciphertext has been received; If a decryption request for the target ciphertext is received, decrypting the target ciphertext using the private key of each user based on the decryption request to obtain a plurality of decryption result fragments; The multiple decryption result fragments are aggregated to obtain aggregated fragments, and the data to be encrypted is obtained according to the aggregated fragments.

4. The method according to any one of claim 1, characterized in that The common parameters include: at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

5. A quantum-resistant collaborative encryption device, characterized in that: include: A judgment module is used to judge whether there is an encryption requirement; an acquisition module, configured to, when encryption is required, determine data to be encrypted based on the encryption requirement, and obtain multiple user-determined public parameters corresponding to the data to be encrypted; The encryption module is configured to determine a random polynomial for each user, generate a private key for each user in a private key distribution based on the random polynomial, generate public key fragments using the private keys of all users, and encrypt the data to be encrypted based on the public parameters and the public key fragments to generate a target ciphertext.

6. The device according to claim 5, characterized in that The encryption module includes: a generating unit, configured to generate a public key according to the public parameters and the public key fragments; The encryption unit is used to encode the data to be encrypted and encrypt the encoded data to be encrypted using the public key to generate the target ciphertext.

7. The device according to claim 5 or 6, characterized in that After encrypting the data to be encrypted based on the public parameters and the public key fragments to generate the target ciphertext, the encryption module further includes: a judgment unit, configured to judge whether a decryption request for a target ciphertext has been received; a decryption unit configured to, upon receiving a decryption request for the target ciphertext, decrypt the target ciphertext using the private key of each user based on the decryption request to obtain a plurality of decryption result fragments; The summarizing unit is configured to summarize the multiple decryption result fragments to obtain summarized fragments, and obtain the data to be encrypted according to the summarized fragments.

8. The device according to any one of claim 5, characterized in that The common parameters include: at least one of a cyclotomic polynomial, a modulus, and an initialization noise distribution.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the quantum-resistant collaborative encryption method according to any one of claims 1 to 4.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the quantum-resistant collaborative encryption method as described in any one of claims 1 to 4.

Images