An anonymous public key encryption method and system suitable for edge computing

Abstract

This application discloses an anonymous public key encryption method and system suitable for edge computing. The method includes: a CA executing a key generation algorithm, generating public parameters based on the obtained security parameters, and executing the key generation algorithm twice based on the public parameters to obtain an encryption public key and a decryption public key; a DO executing an encryption algorithm, encrypting the message to be encrypted by the DO based on the encryption public key in combination with the encryption algorithm and the NIZKP proof algorithm to obtain a ciphertext, and uploading it to a cloud server CS for storage through an edge node EN; when the EN receives a data application request from the DC, it sends a ciphertext request to the CS and feeds the obtained ciphertext back to the DC, which executes a decryption algorithm and decrypts the ciphertext based on the decryption private key in combination with the decryption algorithm and the NIZKP proof algorithm. This application can provide the identity hiding function of the end user while resisting quantum computer attacks.

Description

Technical Field

[0001] The present invention relates to the field of electronic information technology network information security technology, and specifically to an anonymous public key encryption method and system suitable for edge computing. Background Art

[0002] The McEliece encryption scheme, a classic code-based cryptosystem proposed in 1978 and still in use today, differs from public-key encryption schemes commonly used in modern cryptography, such as RSA and ElGamal. Code-based cryptosystems are even resistant to attacks by quantum computers. However, the original McEliece scheme only achieves one-way security and cannot even achieve CPA security.

[0003] In 2008, Nojima et al. proposed the first large variant of the McEliece scheme that achieved CPA security. In 2009, Rosen et al. further expanded on Nojima et al.'s scheme and implemented the first McEliece variant that achieved CCA2 security. Subsequent work has continued to improve the security of the McEliece scheme. However, the vast majority of these schemes suffer from excessively large parameters, failing to maintain key privacy and lacking practicality.

[0004] Although IND-CCA2 security is one of the strongest security concepts for providing encrypted data privacy, in practice, PKE schemes must achieve not only data privacy but also key privacy. This requires that the confidentiality of the encrypted message and the privacy of the encryption key be simultaneously protected within the encryption system. The concept of key privacy was proposed by Bellare et al. in 2001. This property essentially means that the encryption key must be indistinguishable (IK), ensuring its anonymity. This can be considered under the context of CPA security or CCA security, resulting in two new security concepts: IK-CPA and IK-CCA. Many IK-CPA and IK-CCA schemes are based on RSA or ElGamal schemes. In 2007, Yamakawa et al. first studied IK-CPA-secure encryption schemes in the field of coding cryptography, attempting to develop a transformation mechanism for IK-CCA2-secure schemes in the random oracle model.

[0005] Currently, in the construction of smart grids in edge computing environments, the basic operation is to centralize user electricity usage data processing tasks on a data source platform, with computing performed at the "edge." This reduces computational latency while ensuring data protection. In edge computing, due to different power facility deployment options, edge computing service providers can be located in different locations, flexibly extending computing services to the network edge. However, this flexibility complicates the trustworthiness of edge computing, making it different from other network architectures. Edge computing network systems involve different functional entities, such as terminal intelligent devices, edge computing devices, and cloud centers. Edge computing devices serve as an intermediary between end users at the network edge and cloud servers. Currently, research on edge computing data privacy protection technologies has yielded limited exploratory results. Edge computing devices are closer to the data source and can collect more sensitive user identity information than cloud centers in the core network. However, due to the limited computing resources of end devices, it is difficult to execute expensive privacy protection algorithms. Therefore, ensuring the identity privacy of end users in edge computing services is a pressing issue.

[0006] Prior Art Document 1 (CN117254927A) discloses a public-key encryption method based on edge computing that is both leak-resistant and attribute-hiding. Prior Art Document 2 (CN116886340A) discloses an identity-based matching encryption system based on cloud-assisted edge computing. However, both Prior Art Documents 1 and 2 fail to conceal the end user's identity and are incapable of resisting quantum computer attacks. Summary of the Invention

[0007] To address the deficiencies in the prior art, the present invention provides an anonymous public-key encryption method and system suitable for edge computing, which can resist quantum computer attacks, protect the anonymity of smart grid users in an edge computing environment and the privacy of user data, and reduce the probability of leakage of sensitive information related to user identity.

[0008] The core concept of this invention is to first construct a non-interactive zero-knowledge proof system based on the LPN (Learning Parity with Noise) security assumption. Using a coding-based encryption algorithm capable of achieving Choice Plaintext Attack (CPA) security, the invention generates two sets of keys through a key generation algorithm, achieving an anonymous public-key encryption algorithm with CCA2 security. This scheme achieves higher confidentiality and security requirements (extending the CPA security of the original scheme to CCA2 security), enhancing data privacy protection mechanisms. It also ensures the anonymity of the encryption key, ensuring the confidentiality of the recipient's identity.

[0009] The present invention adopts the following technical solutions.

[0010] A first aspect of the present invention provides an anonymous public key encryption method suitable for edge computing, which is applied to an encryption system including a central authority CA, a cloud server CS, an edge node EN, a data owner DO, and a data recipient DC. The method includes:

[0011] CA performs key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters Twice, get two sets of system key pairs )and( ), and based on the system key pair and random string Generate the encrypted public key of the data owner DO and the decryption private key ,in, is the codeword length, 、 are the number of information bits in the codewords corresponding to the two sets of system keys, 、 are the number of erroneous decodings that can be corrected by the two sets of system keys, is a random string;

[0012] DO executes the encryption algorithm , Based on encryption public key Combine and NIZKP's proof algorithm for DO's encrypted message Encrypt and get ciphertext Upload to the cloud server CS storage through the edge node EN, The value range of the plain text;

[0013] When EN receives the data request from DC, it sends a ciphertext request to CS and sends the ciphertext to CS. Feedback to DC, DC executes the decryption algorithm , Based on the decryption private key Combine and NIZKP's proof algorithm for ciphertext Decryption;

[0014] in, 、 and They are the key generation algorithm, encryption algorithm and decryption algorithm that comply with IND-CPA security.

[0015] Optional, According to the obtained security parameters , generating public parameters ,include:

[0016] CA obtains security parameters , and generate the first binary Goppa linear code according to the security parameter, and the second binary Goppa linear code ;

[0017] A public parameter is obtained according to the first binary Goppa linear code and the second binary Goppa linear code .

[0018] Optional, based on public parameters implement The algorithm is executed twice to obtain two sets of system key pairs. )and( ),include:

[0019] Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the first binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) Get the first system key pair );

[0020] Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the second binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) to obtain the second system key pair ( );

[0021] in, All according to safety parameters Sure.

[0022] Optional, random string ,in, It's about parameters A uniform distribution of is the codeword length.

[0023] Optional, Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext ,include:

[0024] Get the encrypted public key and the message to be encrypted ;

[0025] DO random selection parameters and , and the random noise vector and ,in ;

[0026] DO is calculated as follows: and :

[0027] =[ | ] , =[ | ] , and order =( );

[0028] Combined with evidence ( , ) and string S in the ciphertext Run the NIZKP proof algorithm to get , and output the ciphertext .

[0029] Optional, Based on the decryption private key Combine and NIZKP proof algorithm for ciphertext Decryption, including:

[0030] Verification based on NIZKP proof algorithm and Is it consistent?

[0031] If the verification result is consistent, calculate or , to recover the plaintext, otherwise, the algorithm outputs the termination symbol.

[0032] Optional, calculate To recover the plaintext, including:

[0033] DC calculation ,in is a matrix The inverse matrix of

[0034] calculate ), get and return q bits of message =( ) ,in For a correctable An incorrect decoding algorithm.

[0035] A second aspect of the present invention provides an encryption system, including a central authority CA, a cloud server CS, an edge node EN, a data owner DO, and a data recipient DC, and further including: an anonymous public key encryption device suitable for edge computing, the device including:

[0036] Key generation module, used to execute the key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters Twice, get two sets of system key pairs )and( ), and generates the encryption public key of the data owner DO based on the system key pair and the random string and the decryption private key ;

[0037] Encryption module, used to execute encryption algorithms , Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext Upload to the cloud server CS storage through the edge node EN;

[0038] Decryption module, used to execute the decryption algorithm , Based on the decryption private key Combine and NIZKP proof algorithm for ciphertext Decrypt.

[0039] The third aspect of the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is loaded into the processor, the anonymous public key encryption method suitable for edge computing is implemented.

[0040] A fourth aspect of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned anonymous public key encryption method suitable for edge computing.

[0041] Compared with the prior art, the beneficial effects of the present invention include at least:

[0042] (1) This invention addresses the anonymity requirements of encryption keys, ensuring the identity of the receiving user is hidden. It provides an encoding-based public key encryption algorithm with adaptive selective ciphertext security (higher security). While protecting the privacy of encrypted data, this invention also provides anonymity protection for the encryptor's identity. In addition, this invention is not only applicable to the security of modern cryptographic theory, but also supports the privacy protection requirements of network data in future quantum computing network scenarios. The proposed method can resist quantum computer attacks.

[0043] (2) The present invention achieves the functional requirements of the present invention by introducing an encryption algorithm with chosen plaintext security (lower security than adaptive chosen ciphertext security), utilizing double encryption with the encryption algorithm, and combining it with a non-interactive zero-knowledge proof system. The system selected by the public key encryption algorithm of the present invention only needs to meet chosen plaintext security (lower security) to be used to construct the scheme of this invention and achieve the intended functionality. The performance requirements for the basic scheme are reduced, which improves the general applicability of the present invention.

[0044] (3) The present invention mainly consists of three algorithms: key generation algorithm , encryption algorithm , and decryption algorithms Through performance analysis, the solution of the present invention has great advantages in terms of security and anonymity protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort. Among them:

[0046] Figure 1 A schematic flow chart of an anonymous public key encryption method suitable for edge computing provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] The following are some mathematical symbols and basic definitions used in the scheme of the present invention.

[0049] (1) Explanation of symbols

[0050] for , [n] represents the set {1,2,...,n}. Let Defined as a binary finite field The set of all Hamming weights on r vectors is the set of all vectors that satisfy and The set of vectors x.

[0051] (2) Linear code

[0052] If C is a finite field A [n, k] (n>k) linear error correction code on the network, the elements of C can be expressed as an n-dimensional linear space A k-dimensional linear subspace on the , with codimension nk. If the matrix is a generator matrix of C, then C can be expressed as , that is, the row vectors of G form a basis of C.

[0053] (3) Syndrome decoding problem (SD problem)

[0054] If C is a [n, k] linear code, let H be the parity check matrix of C. Any vector The syndrome can be defined as . If a vector s randomly and uniformly selected from and an integer r < n are given, the syndrome decoding problem SD(n, k, r) is to find a vector such that . The vector x is a codeword of C if and only if .

[0055] In fact, the SD(n, k, r) problem has long been recognized as an NP problem and is widely used.

[0056] (4) Learning parity with noise (LPN)

[0057] When a pair is given, define as the Bernoulli distribution with as the parameter, then we define the following distribution as , then define

[0058] ,

[0059] where is a probabilistic polynomial algorithm, then the LPN(n, k, B(n, r)) problem is hard if the advantage is negligible for any dimension k.

[0060] The implementation system of this embodiment of the present invention comprises a central authority (CA), a cloud server (CS), an edge node (EN), a data owner (DO), and a data consumer (DC). The CA is responsible for generating system keys, user authentication and authorization, and generating encryption keys for the data owner (DO) and decryption private keys for the data consumer (DC). The cloud server (CS) provides persistent storage capabilities. The system model can be defined as a three-layer structure: cloud service layer, edge layer, and user layer. The cloud service layer, which includes the cloud server (CS) and the CA, serves as the core operational layer of the entire solution and is responsible for most data storage and persistence. The system access control solution is implemented by authenticating and distributing CA-generated parameters and CS data. The edge layer consists of numerous edge nodes (EN) from different domains. The solution uses these ENs to partially transmit and decrypt data, outsourcing the decryption process to the ENs to reduce end-user computing overhead. DO and DC at the user layer play the roles of data owner and data user respectively. Data generation, upload, application and download mainly occur at the user layer.

[0061] Combine Figure 1 As shown, Example 1 of the present invention provides a public key encryption method suitable for edge computing. Based on the IK-CPA secure encryption algorithm, a dual encryption system is constructed using the non-interactive zero-knowledge proof system (NIZKP System) technology to achieve stronger key privacy and data privacy security requirements. The method includes:

[0062] S1. CA executes the key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters twice, and obtain two sets of system key pairs ( )and( ), and generates the encryption public key of the data owner DO based on the system key pair and the random string and the decryption private key ; This is an IND-CPA-compliant key generation algorithm.

[0063] Key generation algorithm in S1 It is executed by the data service provider's central authority CA, and the process is as follows:

[0064] S1.1. When inputting safety parameters When , CA generates the first binary Goppa linear code according to the security parameter, and the second binary Goppa linear code , according to the first binary Goppa linear code and the second binary Goppa linear code, the public parameter is obtained .

[0065] S1.2. Based on public parameters Get parameter group and , and respectively with parameter groups and Execute for input The algorithm is repeated twice to obtain two sets of key pairs ( ) and( ) .

[0066] S1.2 specifically includes:

[0067] Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the first binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) Get the first system key pair );

[0068] Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the second binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) to obtain the second system key pair ( );

[0069] in, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, is a binary finite field OK A matrix of columns, All according to safety parameters Sure.

[0070] In some embodiments, All according to safety parameters The function is determined by the time complexity function.

[0071] S1.3. Randomly generate a string ,in It's about parameters A uniform distribution of , then the encryption public key of the data owner DO is , the decryption private key is .

[0072] S2, DO execute encryption algorithm , Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext Upload to the cloud server CS through the edge node EN for storage. This is an encryption algorithm that complies with IND-CPA security.

[0073] S2 encryption algorithm Executed by DO, specifically including:

[0074] S2.1. Obtaining the encryption public key and the message to be encrypted , for any .

[0075] S2.2. DO random selection parameters and , and a random noise vector and .

[0076] S2.3. DO calculation =[ | ] , =[ | ] , and order =( ).

[0077] S2.4, order is a NIZKP proof algorithm, Operation Algorithms and Evidence , ), and string S to get , output ciphertext .

[0078] S2.5, Ciphertext Upload to the cloud server CS storage through the edge node EN.

[0079] Specifically, The algorithm is the algorithm of the existing technical document (Group Encryption: Full Dynamicity, Message Filtering and Code-Based Instantiation, Public-Key Cryptography – PKC 2021, 24th IACR International Conference on Practice and Theory of Public Key Cryptography, May 13, 2021), and the embodiments of the present invention are not described here.

[0080] S3. When EN receives the data application request from DC, it sends a ciphertext request to CS and sends the obtained ciphertext to CS. The text is fed back to DC, which executes the decryption algorithm , Based on the decryption private key Combine and NIZKP's proof algorithm for ciphertext Decrypt.

[0081] Decryption algorithm in S3 Utilize the decryption private key and ciphertext , for any i q executes algorithms, including:

[0082] S3.1. Verification through NIZKP Proof Algorithm and( , , S) are consistent;

[0083] S3.2. If the verification result is consistent, calculate or , to recover the plaintext, otherwise, the algorithm outputs the termination symbol .

[0084] Specifically, through the NIZKP proof algorithm verify and( , , S) are consistent, The algorithm is the algorithm of the existing technical document (Group Encryption: Full Dynamicity, Message Filtering and Code-Based Instantiation, Public-Key Cryptography – PKC 2021, 24th IACR International Conference on Practice and Theory of Public Key Cryptography, May 13, 2021), and the embodiments of the present invention are not described here. It is understandable that , The proof algorithms for the prover and verifier respectively undergo multiple rounds of interactive verification.

[0085] Specifically, calculate The steps to recover the plaintext are: DC calculation ,in, is a matrix The inverse matrix of ), get and return q bits of message =( ) ,in For a correctable An incorrect decoding algorithm.

[0086] Specifically, calculate The steps to recover the plaintext are: DC calculation ,in, is a matrix The inverse matrix of ), get and return q bits of message =( ) ,in For a correctable An incorrect decoding algorithm.

[0087] Optional, 、 and They are the key generation algorithm, encryption algorithm, and decryption algorithm in the McEliece encryption system that complies with IND-CPA security.

[0088] The correctness analysis of the above encryption method and the security analysis of IK-CCA2 are given below.

[0089] First, perform a correctness analysis.

[0090] The above IK-CCA-secure scheme is correct with a high probability. This depends on two facts: a) the correctness of the underlying encryption scheme; and b) the random encryption system is indeed IK-CPA-secure and has pseudo-random ciphertext.

[0091] Next, IK-CCA2 safety analysis was performed.

[0092] If the above encryption algorithm is successfully broken by the adversary, then the following two assumptions must be true: a) Distinguish and is computationally infeasible (i.e., ciphertext indistinguishability); b): System ( , ) is zero-knowledge (i.e., the anonymity of the encryptor is protected). If the underlying random encryption scheme is IK-CPA secure in the standard model, and ( , ) is a NIZKP system, then the algorithm achieves IK-CCA2 security under the LPN security assumption in the standard model.

[0093] In summary, the embodiments of the present invention provide an anonymous and highly secure cryptographic algorithm suitable for edge computing environments. This algorithm protects the privacy of user data while also preserving the anonymity of the encryptor's identity. It also provides a solution that supports both modern and post-quantum cryptographic systems. Furthermore, this method is simple and straightforward, unlike traditional signature algorithms, making it more suitable for edge computing environments with limited computing power.

[0094] Embodiment 2 of the present invention provides an encryption system, which includes a central authority CA, a cloud server CS, an edge node EN, a data owner DO, and a data recipient DC, and also includes an anonymous public key encryption device suitable for edge computing. The anonymous public key encryption device runs the anonymous public key encryption method suitable for edge computing as described in embodiment 1, and the device includes:

[0095] Key generation module, used to execute the key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters Twice, get two sets of system key pairs )and( ), and generates the encryption public key of the data owner DO based on the system key pair and the random string and the decryption private key ;

[0096] Encryption module, used to execute encryption algorithms , Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext Upload to the cloud server CS storage through the edge node EN;

[0097] Decryption module, used to execute the decryption algorithm , Based on the decryption private key Combine and NIZKP proof algorithm for ciphertext Decrypt.

[0098] Embodiment 3 of 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. When the computer program is loaded into the processor, the anonymous public key encryption method for edge computing described in embodiment 1 is implemented.

[0099] Embodiment 4 of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements an anonymous public key encryption method suitable for edge computing according to embodiment 1.

[0100] Compared with the prior art, the beneficial effects of the present invention include at least:

[0101] (1) This invention addresses the anonymity requirements of encryption keys, ensuring the identity of the receiving user is hidden. It provides an encoding-based public key encryption algorithm with adaptive selective ciphertext security (higher security). While protecting the privacy of encrypted data, this invention also provides anonymity protection for the encryptor's identity. In addition, this invention is not only applicable to the security of modern cryptographic theory, but also supports the privacy protection requirements of network data in future quantum computing network scenarios. The proposed method can resist quantum computer attacks.

[0102] (2) The present invention achieves the functional requirements of the present invention by introducing an encryption algorithm with chosen plaintext security (lower security than adaptive chosen ciphertext security), utilizing double encryption with the encryption algorithm, and combining it with a non-interactive zero-knowledge proof system. The system selected by the public key encryption algorithm of the present invention only needs to meet chosen plaintext security (lower security) to be used to construct the scheme of this invention and achieve the intended functionality. The performance requirements for the basic scheme are reduced, which improves the general applicability of the present invention.

[0103] (3) The present invention mainly consists of three algorithms: key generation algorithm , encryption algorithm , and decryption algorithms Through performance analysis, the solution of the present invention has great advantages in terms of security and anonymity protection.

[0104] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0105] The present disclosure may be a system, method and / or computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0106] A computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punched card or raised structure in a groove on which instructions are stored, and any suitable combination thereof. As used herein, a computer-readable storage medium is not to be construed as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse passing through a fiber optic cable), or an electrical signal transmitted through an electrical wire.

[0107] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to be stored in the computer-readable storage medium in each computing / processing device.

[0108] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, the state information of the computer-readable program instructions is used to personalize an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), so that the electronic circuit can execute the computer-readable program instructions, thereby implementing various aspects of the present disclosure.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. An anonymous public key encryption method suitable for edge computing, applied to an encryption system, wherein the encryption system includes a central authority CA, a cloud server CS, an edge node EN, a data owner DO, and a data receiver DC, characterized in that: The method comprises: CA performs key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters Twice, get two sets of system key pairs )and( ), and based on the system key pair and random string Generate the encrypted public key of the data owner DO and the decryption private key ,in, is the codeword length, 、 are the number of information bits in the codewords corresponding to the two sets of system keys, 、 are the number of erroneous decodings that can be corrected by the two sets of system keys, is a random string; DO executes the encryption algorithm , Based on encryption public key Combine and NIZKP's proof algorithm for DO's encrypted message Encrypt and get ciphertext Upload to the cloud server CS storage through the edge node EN, The value range of the plain text; When EN receives the data request from DC, it sends a ciphertext request to CS and sends the ciphertext to CS. Feedback to DC, DC executes the decryption algorithm , Based on the decryption private key Combine and NIZKP's proof algorithm for ciphertext Decryption; in, 、 and They are the key generation algorithm, encryption algorithm, and decryption algorithm that comply with IND-CPA security. According to the obtained security parameters , generating public parameters ,include: CA obtains security parameters , and generate the first binary Goppa linear code according to the security parameter, and the second binary Goppa linear code ; A public parameter is obtained according to the first binary Goppa linear code and the second binary Goppa linear code ; According to public parameters implement The algorithm is executed twice to obtain two sets of system key pairs. )and( ),include: Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the first binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) Get the first system key pair ); Randomly select an integer and satisfy , Defined as plaintext space; randomly select a generator matrix of the second binary Goppa linear code =[ | ] , a non-singular matrix and a random permutation matrix , and complies with and =[ | ];return and ( , , ) to obtain the second system key pair ( ); in, All according to safety parameters Sure; Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext ,include: Get the encrypted public key and the message to be encrypted ; DO random selection parameters and , and the random noise vector and ,in, ; DO is calculated as follows: and : =[ | ] , =[ | ] , and order =( ); Combined with evidence ( , ) and string S in the ciphertext Run the NIZKP proof algorithm to get , and output the ciphertext ; Based on the decryption private key Combine and NIZKP proof algorithm for ciphertext Decryption, including: Verification based on NIZKP proof algorithm and Is it consistent? If the verification result is consistent, calculate or , to recover the plaintext, otherwise, the algorithm outputs the termination symbol.

2. The anonymous public key encryption method for edge computing according to claim 1, characterized in that: Random string ,in, It's about parameters A uniform distribution of is the codeword length.

3. The anonymous public key encryption method for edge computing according to claim 1, characterized in that: calculate To recover the plaintext, including: DC calculation ,in is a matrix The inverse matrix of calculate ), get and return q bits of message =( ) ,in For a correctable An incorrect decoding algorithm.

4. An encryption system, comprising a central authority CA, a cloud server CS, an edge node EN, a data owner DO and a data receiver DC, characterized in that: Also includes: An anonymous public key encryption device suitable for edge computing, the device executing the anonymous public key encryption method suitable for edge computing according to any one of claims 1 to 3, the device comprising: Key generation module, used to execute the key generation algorithm described According to the obtained security parameters , generating public parameters , and execute according to the public parameters Twice, get two sets of system key pairs )and( ), and generates the encryption public key of the data owner DO based on the system key pair and the random string and the decryption private key ; Encryption module, used to execute encryption algorithms , Based on encryption public key Combine And NIZKP proof algorithm for DO to be encrypted message Encrypt and get ciphertext Upload to the cloud server CS storage through the edge node EN; Decryption module, used to execute the decryption algorithm , Based on the decryption private key Combine and NIZKP proof algorithm for ciphertext Decrypt.

5. An electronic device comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the steps of the anonymous public key encryption method suitable for edge computing according to any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the anonymous public key encryption method suitable for edge computing described in any one of claims 1 to 3 are implemented.

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