Public key encryption method and system against leakage and attribute hiding based on edge computing

Abstract

The application discloses an anti-leakage and attribute hiding public key encryption method and system based on edge calculation and belongs to the technical field of electronic information technology and network information security technology.The technical problem to be solved by the application is the leakage of private data on an untrusted server in edge calculation.The technical scheme adopted by the application is as follows: S1, a trusted authority inputs security parameters;S2, system public parameters are generated as a main public key and a main private key of the system;S3, a data owner and a data user simultaneously register, are authenticated, are verified for legality and are encrypted;S4, whether the attribute of the data user satisfies an access strategy in a ciphertext is judged; if yes, decryption is successful; and if not, decryption fails.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology and network information security technology, specifically to a public key encryption method and system based on edge computing that is resistant to data leakage and has hidden attributes. Background Technology

[0002] With the development of emerging technologies such as the Internet of Things, big data, and cloud computing, traditional cloud computing is unable to handle the massive amounts of data generated by network edge devices. Therefore, edge computing has emerged. Due to the open characteristics of edge computing, such as content awareness, real-time computing, and parallel processing, data security and privacy issues that already exist in cloud computing environments become more prominent. In edge computing environments, large amounts of sensitive data are stored on untrusted remote servers, typically using public-key encryption to ensure data security. However, with the development of cryptanalysis techniques, attackers can extract information from physical devices with a very high probability through side-channel attacks, leaking the decryption key, in addition to authorized users. Currently, a few studies have explored leak-resistant inner product public-key encryption techniques; however, these only provide selective security, not adaptive security, and can only be constructed based on composite number groups. In fact, schemes based on prime number groups are often more efficient than those based on composite number groups.

[0003] Inner product encryption (IPE) is a special type of public-key encryption algorithm. Compared to traditional public-key cryptography (PKC), IPE provides users with more fine-grained and complex access control policies. In an IPE public-key encryption scheme, the ciphertext and key are associated with vectors x and y, respectively, and only x and y satisfy x = ... T The user can only decrypt correctly when y = 1. Inner product encryption can be seen as a generalization of identity-based encryption. It can be used as a tool to construct cryptographic schemes such as predicate encryption, attribute-based encryption, and public-key searchable encryption, and has wide applications in emerging fields such as edge computing.

[0004] In edge computing network services, storing large amounts of sensitive data on untrusted remote servers typically employs encryption techniques, particularly public-key encryption, to ensure data security. However, with the development of cryptanalysis techniques, attackers can extract information from physical devices and leak decryption keys with a very high probability through side-channel attacks, in addition to authorized users possessing the decryption keys. Therefore, constructing inner product public-key encryption algorithms resistant to leakage attacks has significant theoretical and practical implications.

[0005] In traditional security adversarial games between challengers and attackers, it is typically assumed that attackers cannot access the authorized decryption key applicable to the challenge ciphertext. However, this assumption no longer holds true if an attacker with the capability to leak encryption exists. Furthermore, traditional cloud-based anti-leakage encryption only considers static attributes such as occupation and age. In real-world applications, data access control also needs to consider factors such as time and location. For example, doctors can only access the hospital database and view patient records during working hours and within the hospital's location; students can only access the academic affairs system and library databases while enrolled at school. Due to the mobility and real-time nature of edge computing, the impact of time and location changes must be considered. Moreover, due to the diverse and heterogeneous nature of data, its perceptual nature, and the resource constraints of terminals, traditional cloud-based anti-leakage encryption access control methods are no longer suitable for edge computing environments.

[0006] The commonly used solutions generally suffer from the following problems:

[0007] (1) In previous security adversarial games between challengers and attackers, it was generally assumed that attackers could not access the authorized decryption key applicable to the challenge ciphertext. However, this assumption no longer holds if there is an attacker with the ability to leak information.

[0008] (2) Most schemes are based on composite order groups. In fact, the inner product public key encryption scheme in prime order groups is much more efficient than the scheme based on composite order groups. Therefore, the research on related schemes in prime order groups has important theoretical and practical significance.

[0009] (3) Although there are two leak-resistant anonymous inner product public-key encryption schemes based on prime order groups, unfortunately, they only achieve selective security and cannot achieve adaptive security. That is, there is no inner product public-key encryption scheme based on prime order groups that can simultaneously achieve adaptive security and attribute hiding. Summary of the Invention

[0010] The technical objective of this invention is to provide a public key encryption method and system based on edge computing that is resistant to data leakage and has hidden attributes, in order to solve the problem of privacy data leakage on untrusted servers in edge computing.

[0011] The technical objective of this invention is achieved as follows: a public-key encryption method based on edge computing that is resistant to data leakage and attribute hiding, the method being as follows:

[0012] S1. Enter security parameters from a trusted authority (TA);

[0013] S2. Generate system public parameters as the system's master public key and master private key;

[0014] S3. Both the Data Owner (DO) and the Data Consumer (DU) simultaneously register, authenticate, verify legitimacy, and encrypt.

[0015] S4. Determine whether the data user attributes satisfy the access policy in the ciphertext:

[0016] ① If the conditions are met, then decryption is successful;

[0017] ②If the conditions are not met, decryption will fail;

[0018] The specific steps for data owners to register, authenticate, verify legitimacy, and encrypt data are as follows:

[0019] S3-101. The Data Owner (DO) registers by submitting their identity information to a trusted authority.

[0020] S3-102, Data owner certified by a trusted authoritative institution;

[0021] S3-103. Determine if the data owner is legitimate:

[0022] ① If it is illegal, registration will be refused;

[0023] ②If valid, proceed to step S3-104;

[0024] S3-104. A trusted authority assigns a set of predicates y to the data owner and uses the Predicate Coding Function (PCF) framework to calculate and generate the data owner's public and private keys.

[0025] S3-105. The data owner uses their public key and the Predicate Encoding Function Framework (PCF framework) to formulate access control policies and encrypt messages;

[0026] The specific procedures for data users to register, authenticate, verify legitimacy, and encrypt data are as follows:

[0027] S3-201. Data users must register by submitting their identity information to a trusted authority.

[0028] S3-202, Data users certified by trusted authoritative institutions;

[0029] S3-203, Determine if the data user is legitimate:

[0030] ① If it is illegal, registration will be refused;

[0031] ②If valid, proceed to step S3-204;

[0032] S3-204. A trusted authority assigns a public-private key pair to a data user based on the user's identity information.

[0033] S3-205, the Edge Node (EN) returns the plaintext function obtained by the Cloud Storage Server (CSS) to the data user.

[0034] As a preferred option, the predicate encoding function framework includes two tools, as follows:

[0035] (i) Matrix distribution Requires output in polynomial time. The specific execution process for a full-rank k matrix over p (where p is a prime number) is as follows: Randomly select... The output matrix A is in the following form:

[0036]

[0037] Wherein, once the matrix distribution Given a matrix A, we can let vectors

[0038] Satisfy A T a ⊥ =0 and a ⊥ ≠0;

[0039] (i) Let This is a polynomial-time algorithm. When the input security parameter λ is given, the algorithm... Output a parameter set Where p is a prime number with respect to the parameter λ; G1, G2, G T Let G1 and G2 be cyclic groups of order p; g1 and g2 are generators of groups G1 and G2, respectively; e := G1 × G2 → G T It is a computationally efficient and non-degenerate bilinear mapping;

[0040] The predicate encoding framework satisfying the anti-leakage and attribute hiding properties in a prime group is as follows:

[0041] Modulo p integer group - Linear anti-leakage predicate coding in, It is an attribute set; It is a predicate set; the predicate encoding P contains the initialization phase Setup(1 λ The key generation algorithm is KeyGen(mk, y), the encryption algorithm is Enc(mpk, x, m), and the decryption algorithm is Dec(mpk, sk).y ct x Five deterministic algorithms And it satisfies the following properties:

[0042] (1) Linearity: For any All meet linearity on -;

[0043] (2) Attribute Hiddenness: For any property satisfying P(x,y)=0 And all of them The following two distributions are indistinguishable:

[0044] and {x,y,z,r};

[0045] Wherein, the random numbers w and r are respectively taken from and

[0046] (1) Leakage Resistance: To achieve the leakage resistance property of the user's private key, for any key satisfying P(x,y)=0... And all of them The following two distributions are indistinguishable:

[0047] and {x,y,r};

[0048] Wherein, the random numbers w and r are respectively taken from and

[0049] More preferably, the initialization phase Setup(1 λ The details are as follows:

[0050] make These are the parameters of the predicate encoding P; executed by a trusted authority, which calculates and returns the master public key and master private key, as follows:

[0051] Organization administrator execution And distributed from a (k+1)×k dimensional matrix Random sampling (A, a) ⊥ ) and (B, b ⊥ ), and randomly select vectors. sum matrix

[0052] Select a random vector and And calculate and output the master public key mpk and master private key mk of the inner product public key encryption algorithm as follows:

[0053] and mk := (B, k, W1, ..., W) N ).

[0054] More preferably, the key generation algorithm KeyGen(mk, y) is as follows:

[0055] The encryption key used to generate the DO is executed by a trusted authority.

[0056] For users requesting to join, a trusted authority administrator will assign a set of predicates to each user based on the user's identity information.

[0057] A trusted authority administrator randomly selects redundant vectors. To prevent attribute leakage, the redundant information set is blinded using PCF transformation, thus achieving the attribute hiding function.

[0058] Output about the predicate Decryption key: sk y :=(z, K0, K);

[0059] Where K0:=[Br]2,

[0060] The calculated user key has data management permissions and cannot be accessed without authorization.

[0061] More preferably, the encryption algorithm Enc(mpk, x, m) is as follows:

[0062] Data owners formulate corresponding access control policies based on their own security needs. The access control policy is represented by user attribute x, such as "(attribute 1 AND attribute 2) OR attribute 3".

[0063] Based on the access control policy, the ciphertext is calculated using the predicate coding function framework and then uploaded to the cloud server for storage via the edge node;

[0064] Random selection The output ciphertext is as follows:

[0065]

[0066] Better, the decryption algorithm Dec(mpk, sk) y ct x The details are as follows:

[0067] When a data user sends an access request, the request is first sent to an edge node. The edge node then sends an authentication request to a trusted authority, using the data user's identity information to verify whether the user is a legitimate registered user.

[0068] If the user is not a registered user, their data access request will be denied.

[0069] If the user is a registered user, the edge node takes the master public key, the user's private key, and the ciphertext as input, requests the cloud storage server to decrypt the ciphertext, and sends the calculated function m′ about the plaintext to the requesting user.

[0070]

[0071] More specifically, the performance analysis of this method is as follows:

[0072] ① Correctness analysis: For any equation P(x, y) = 1 The following derivation process holds true for all of them:

[0073]

[0074] In the above equation, the linearity property of bilinear mapping can be used to prove that the method is correct.

[0075] ② Security Analysis: If the k-Lin assumption holds, then this method simultaneously achieves anti-leakage and attribute hiding functions; specifically as follows:

[0076] For all polynomial-time attackers who satisfy the following two conditions

[0077] (1) A maximum of q leak queries can be executed;

[0078] (2) The master private key mk must not be leaked, and the decryption key sk must be leaked at most L. sk Bit.

[0079] A public-key encryption system based on edge computing that is leak-proof and attribute-hiding includes a data owner (DO), a data consumer (DU), a cloud storage server (CSS), a trusted authority (TA), and an edge node (EN).

[0080] Data owners formulate access control policies based on their own security needs, encrypt data according to the access control policies, and upload the encrypted data to the cloud storage server provider for storage.

[0081] Data users download the encrypted ciphertext from the cloud storage server provider and decrypt the data using their own private key;

[0082] Cloud storage servers are used to store encrypted data from data holders;

[0083] Trusted authorities are trusted by all entities to reliably execute and correctly respond to digital forensics requests from data holders, and to generate and distribute keys for all users.

[0084] Edge nodes are edge computing devices used for storing and securely computing large amounts of user data, and for securely and conveniently collaborating with cloud server applications.

[0085] An electronic device includes: a memory and at least one processor;

[0086] The memory contains computer programs;

[0087] The at least one processor executes the computer program stored in the memory, causing the at least one processor to perform the public-key encryption method based on edge computing that is resistant to leakage and attribute hiding, as described above.

[0088] A computer-readable storage medium storing a computer program that can be executed by a processor to implement the leakage-resistant and attribute-hiding public-key encryption method based on edge computing as described above.

[0089] The public-key encryption method and system based on edge computing with anti-leakage and attribute hiding of the present invention have the following advantages:

[0090] (i) This invention takes into account security, application and efficiency, and constructs a leak-proof inner product public key encryption method that achieves adaptive security and attribute hiding function on prime number order groups, which effectively reduces the parameter length and improves the computational efficiency.

[0091] (II) This invention is dedicated to solving the problem of privacy data on untrusted servers being leaked when attacked by adversaries in edge computing environments. It proposes the first general framework of an inner product public key encryption algorithm in prime order groups that has both attribute hiding and anti-leakage properties, achieving anti-leakage property while maintaining attribute hiding function. Furthermore, this invention achieves a higher level of adaptive security under the bounded leakage model.

[0092] (III) This invention first provides a predicate encoding function to implement the attribute hiding function, and then uses the function to construct a specific inner product public key encryption algorithm that combines attribute hiding and anti-leakage properties, effectively solving the problem of privacy data leakage on remote servers of edge computing;

[0093] (iv) This invention realizes the construction based on prime number groups: a general predicate encoding transformation with anti-leakage and attribute hiding functions is proposed, which can perfectly extend the parameters in composite number groups to prime number groups;

[0094] (v) The present invention achieves anti-leakage function: during the generation of user key, by adding "redundant" information to the user private key, the attribute encoding transformation is blinded, thereby preventing attribute leakage;

[0095] (vi) The present invention improves the security of traditional solutions: Compared with the selective security of traditional solutions, the present invention is applicable to edge computing scenarios and achieves adaptive security based on the k-Lin assumption under the bounded leakage model. Attached Figure Description

[0096] The invention will be further described below with reference to the accompanying drawings.

[0097] Appendix Figure 1 This is a flowchart of a public-key encryption method based on edge computing that is leak-resistant and attribute-hiding. Detailed Implementation

[0098] The following detailed description of the public key encryption method and system based on edge computing with anti-leakage and attribute hiding based on the present invention is provided with reference to the accompanying drawings and specific embodiments.

[0099] Example 1:

[0100] As attached Figure 1 As shown, this embodiment provides a public-key encryption method based on edge computing that is resistant to data leakage and attribute hiding. The method is as follows:

[0101] S1. Enter security parameters from a trusted authority (TA);

[0102] S2. Generate system public parameters as the system's master public key and master private key;

[0103] S3. Both the Data Owner (DO) and the Data Consumer (DU) simultaneously register, authenticate, verify legitimacy, and encrypt.

[0104] S4. Determine whether the data user attributes satisfy the access policy in the ciphertext:

[0105] ① If the conditions are met, then decryption is successful;

[0106] ②If the conditions are not met, decryption will fail;

[0107] The specific steps for data owners to register, authenticate, verify legitimacy, and encrypt data are as follows:

[0108] S3-101. The Data Owner (DO) registers by submitting their identity information to a trusted authority.

[0109] S3-102, Data owner certified by a trusted authoritative institution;

[0110] S3-103. Determine if the data owner is legitimate:

[0111] ① If it is illegal, registration will be refused;

[0112] ②If valid, proceed to step S3-104;

[0113] S3-104. A trusted authority assigns a set of predicates y to the data owner and uses the Predicate Coding Function (PCF) framework to calculate and generate the data owner's public and private keys.

[0114] S3-105. The data owner uses their public key and predicate coding function framework to formulate access control policies and encrypt messages;

[0115] The specific procedures for data users to register, authenticate, verify legitimacy, and encrypt data are as follows:

[0116] S3-201. Data users must register by submitting their identity information to a trusted authority.

[0117] S3-202, Data users certified by trusted authoritative institutions;

[0118] S3-203, Determine if the data user is legitimate:

[0119] ① If it is illegal, registration will be refused;

[0120] ②If valid, proceed to step S3-204;

[0121] S3-204. A trusted authority assigns a public-private key pair to a data user based on the user's identity information.

[0122] S3-205, the Edge Node (EN) returns the plaintext function obtained by the Cloud Storage Server (CSS) to the data user.

[0123] The predicate encoding function framework in this embodiment includes two tools, as follows:

[0124] (i) Matrix distribution Requires output in polynomial time. The specific execution process for a full-rank k matrix over p (where p is a prime number) is as follows: Randomly select... The output matrix A is in the following form:

[0125]

[0126] Wherein, once the matrix distribution Given a matrix A, we can let vectors

[0127] Satisfy A T a ⊥ =0 and a ⊥ ≠0;

[0128] (ii) Order This is a polynomial-time algorithm. When the input security parameter λ is given, the algorithm... Output a parameter set Where p is a prime number with respect to the parameter λ; G1, G2, G T Let G1 and G2 be cyclic groups of order p; g1 and g2 are generators of groups G1 and G2, respectively; e := G1 × G2 → G T It is a computationally efficient and non-degenerate bilinear mapping;

[0129] The predicate encoding framework satisfying the anti-leakage and attribute hiding properties in a prime group is as follows:

[0130] Modulo p integer group - Linear anti-leakage predicate coding in, It is an attribute set; It is a predicate set; the predicate encoding P contains the initialization phase Setup(1 λ The key generation algorithm is KeyGen(mk, y), the encryption algorithm is Enc(mpk, x, m), and the decryption algorithm is Dec(mpk, sk). y ct x Five deterministic algorithms And it satisfies the following properties:

[0131] (1) Linearity: For any All meet linearity on -;

[0132] (2) Attribute Hiddenness: For any property satisfying P(x,y)=0 And all of them The following two distributions are indistinguishable:

[0133] and {x, y, z, r};

[0134] Wherein, the random numbers w and r are respectively taken from and

[0135] (3) Leakage Resistance: To achieve the leakage resistance property of the user's private key, for any key satisfying P(x,y)=0... And all of them The following two distributions are indistinguishable:

[0136] and {x,y,r};

[0137] Wherein, the random numbers w and r are respectively taken from and

[0138] In this embodiment, the initialization phase Setup(1) λ The details are as follows:

[0139] make These are the parameters of the predicate encoding P; executed by a trusted authority, which calculates and returns the master public key and master private key, as follows:

[0140] ①Organization administrator execution And distributed from a (k+1)×k dimensional matrix Random sampling (A, a) ⊥ ) and (B, b ⊥ ), and randomly select vectors. sum matrix

[0141] ② Select a random vector and And calculate and output the master public key mpk and master private key mk of the inner product public key encryption algorithm as follows:

[0142] and mk := (B, k, W1, ..., W) N ).

[0143] The key generation algorithm KeyGen(mk, y) in this embodiment is as follows:

[0144] ① The encryption key used to generate the DO is executed by a trusted authority.

[0145] ② For users requesting to join, the administrator of the trusted authority will assign a set of predicates to the user based on the user's identity information.

[0146] ③ A trusted authority administrator randomly selects redundant vectors. To prevent attribute leakage, the redundant information set is blinded using PCF transformation, thus achieving the attribute hiding function.

[0147] ④ Output about the predicate Decryption key: sk y :=(z, K0, K);

[0148] Where K0:=[Br]2,

[0149] The calculated user key has data management permissions and cannot be accessed without authorization.

[0150] The encryption algorithm Enc(mpk, x, m) in this embodiment is as follows:

[0151] ① Data owners formulate corresponding access control policies according to their own security needs. The access control policy is represented by user attribute x, such as "(attribute 1 AND attribute 2) OR attribute 3";

[0152] ② Based on the access control policy, the ciphertext is calculated using the predicate coding function framework and then uploaded to the cloud server for storage via the edge node;

[0153] ③ Random selection The output ciphertext is as follows:

[0154]

[0155] The decryption algorithm in this embodiment is Dec(mpk, sk). y ct x The details are as follows:

[0156] When a data user sends an access request, the request is first sent to an edge node. The edge node then sends an authentication request to a trusted authority, using the data user's identity information to verify whether the user is a legitimate registered user.

[0157] If the user is not a registered user, their data access request will be denied.

[0158] If the user is a registered user, the edge node takes the master public key, the user's private key, and the ciphertext as input, requests the cloud storage server to decrypt the ciphertext, and sends the calculated function m′ about the plaintext to the requesting user.

[0159]

[0160] In this embodiment, the performance analysis of the method is as follows:

[0161] ① Correctness analysis: For any equation P(x, y) = 1 The following derivation process holds true for all of them:

[0162]

[0163]

[0164] In the above equation, the linearity property of bilinear mapping can be used to prove that the method is correct.

[0165] ② Security Analysis: If the k-Lin assumption holds, then this method simultaneously achieves anti-leakage and attribute hiding functions; specifically as follows:

[0166] For all polynomial-time attackers who satisfy the following two conditions

[0167] (1) A maximum of q leak queries can be executed;

[0168] (2) The master private key mk must not be leaked, and the decryption key sk must be leaked at most L. sk Bit.

[0169] Symbol Definitions: First, some symbol definitions used in this embodiment are given: For natural numbers Define [n] and <n>Let the sets {1, 2, ..., n} and {0, 1, ..., n} be given. Let (p, G1, G2, G...) T Let g1, g2, e) denote an asymmetric bilinear group on a prime-order p-group, containing the bilinear mapping e: = G1 × G2 → G T For s∈{1,2,T} and a group of integers modulo p... A matrix A on the y-axis is defined as follows: Given [A]1 and [B]2, then define e([A]1, [B]2) := [A]1, [B]2. T B] T .

[0170] In inner product public-key encryption algorithms, the ciphertext and private key are respectively associated with the attribute vector. predicate vector Related, a ciphertext ct x It can be correctly decrypted if and only if a private key sk exists. y Satisfy x T y = 0. In this invention, mpk and mk represent the master public key and master private key of the inner product public key encryption algorithm, respectively, and sk... y This indicates that the expression is composed of mk and user predicates. The generated user private key, ct x This indicates that the mpk file and user attributes are used. The generated ciphertext.

[0171] The design concept of this embodiment is based on the following description used in most inner product public-key encryption schemes (which all use composite order bilinear groups):

[0172]

[0173] msk: α, u, w1, ..., w n ,

[0174]

[0175]

[0176] First, we consider how to extend the traditional composite order group scheme to the prime order group. Specifically, this invention considers using [A]1 and [B]2 to replace g1 and g2 respectively, where the matrix... The variables in the above equation can be transformed into the following form:

[0177]

[0178] Therefore, the inner product public-key encryption scheme for prime number groups can be set as follows:

[0179]

[0180] Then, an inner product public-key encryption scheme with both anti-leakage and attribute hiding capabilities is constructed. Starting with the CGW15 scheme (JieChen, Romain Gay, and Hoeteck Wee. Improved dual system ABE in prime-ordergroups via predicate encodings, EUROCRYPT 2015, pages 595-624, Springer. An inner product public-key encryption scheme with attribute hiding capabilities), its attribute hiding techniques are reviewed as follows:

[0181]

[0182] Where w is a vector; Transform the attribute hiding encoding.

[0183] In the CGW15 scheme, attribute hiding is achieved by satisfying the following two conditions:

[0184] (1) Attribute hiding: For all The distribution of {x, y, z} is statistically indistinguishable from that of {x, y, z}, where random numbers w and r are randomly selected from... and

[0185] (2)W i B (i.e., the variable highlighted in red) This needs to be hidden. Note that if attribute hiding only considers local hiding, it will be exposed.

[0186] The CGW15 scheme's attribute hiding functionality relies on an attribute hiding encoding transformation function, which only holds true when P(x, y) = 0. However, this encoding is easily compromised by attackers with leakable capabilities. This is because an attacker can compromise the private key sk that satisfies the condition P(x, y) = 1. y Inquiry to leak encoding transformation

[0187] Improvement in this embodiment: Expression (2) in the CGW15 scheme is extended and transformed to provide both attribute hiding and anti-leakage functionality. This invention uses information about sk... y The bounded leakage model, through the private key sk y "Redundant" information is added to protect attribute hiding encoding transformation.

[0188]

[0189]

[0190]

[0191] in

[0192] In this situation, even if the attacker can obtain sk y The leak caused x T y = 0 holds true, while sk y Encoding transformation in (Right now, It remains hidden because we added random information. Make it blind. As long as sk can be strictly limited. y Even with minimal leakage, the attribute hiding encoding still holds true. Therefore, we obtain an inner product public-key encryption scheme on a prime group that simultaneously achieves both leakage resistance and attribute hiding properties.

[0193] Example 2:

[0194] This embodiment provides a public key encryption system based on edge computing that is resistant to data leakage and has hidden attributes. The system includes a data owner (DO), a data consumer (DU), a cloud storage server (CSS), a trusted authority (TA), and an edge node (EN).

[0195] Data owners formulate access control policies based on their own security needs, encrypt data according to the access control policies, and upload the encrypted data to the cloud storage server provider for storage.

[0196] Data users download the encrypted ciphertext from the cloud storage server provider and decrypt the data using their own private key;

[0197] Cloud storage servers are used to store encrypted data from data holders;

[0198] Trusted authorities are trusted by all entities to reliably execute and correctly respond to digital forensics requests from data holders, and to generate and distribute keys for all users.

[0199] Edge nodes are edge computing devices used for storing and securely computing large amounts of user data, and for securely and conveniently collaborating with cloud server applications.

[0200] The algorithm used in this system is as follows:

[0201] S2-1, Initialization Phase Setup(1) λ The details are as follows:

[0202] make These are the parameters of the predicate encoding P; executed by a trusted authority, which calculates and returns the master public key and master private key, as follows:

[0203] ①Organization administrator execution And distributed from a (k+1)×k dimensional matrix Random sampling (A, a) ⊥ ) and (B, b ⊥ ), and randomly select vectors. sum matrix

[0204] ② Select a random vector and And calculate and output the master public key mpk and master private key msk of the inner product public key encryption algorithm as follows:

[0205] and mk := (B, k, W1, ..., W) N ).

[0206] S2-2, The key generation algorithm KeyGen(msk, y) is as follows:

[0207] ① The encryption key used to generate the DO is executed by a trusted authority.

[0208] ② For users requesting to join, the administrator of the trusted authority will assign a set of predicates to the user based on the user's identity information.

[0209] ③ A trusted authority administrator randomly selects redundant vectors. To prevent attribute leakage, the redundant information set is blinded using PCF transformation, thus achieving the attribute hiding function.

[0210] ④ Output about the predicate Decryption key: sk y :=(z, K0, K);

[0211] Where K0:=[Br]2,

[0212] The calculated user key has data management permissions and cannot be accessed without authorization.

[0213] S2-3, The encryption algorithm Enc(mpk, x, m) is as follows:

[0214] ① Data owners formulate corresponding access control policies according to their own security needs. The access control policy is represented by user attribute x, for example, "(attribute 1 AND attribute 2) OR attribute 3";

[0215] ② Based on the access control policy, the ciphertext is calculated using the predicate coding function framework and then uploaded to the cloud server for storage via the edge node;

[0216] ③ Random selection The output ciphertext is as follows:

[0217]

[0218] S2-4, Decryption Algorithm Dec(mpk, sk y ct x The details are as follows:

[0219] When a data user sends an access request, the request is first sent to an edge node. The edge node then sends an authentication request to a trusted authority, using the data user's identity information to verify whether the user is a legitimate registered user.

[0220] If the user is not a registered user, their data access request will be denied.

[0221] If the user is a registered user, the edge node takes the master public key, the user's private key, and the ciphertext as input, requests the cloud storage server to decrypt the ciphertext, and sends the calculated function m′ about the plaintext to the requesting user.

[0222]

[0223] Example 3:

[0224] This invention also provides an electronic device, including: a memory and a processor;

[0225] The memory stores the instructions executed by the computer.

[0226] The processor executes computer execution instructions stored in the memory, causing the processor to execute the public key encryption method based on edge computing that is resistant to leakage and attribute hiding, according to any embodiment of the present invention.

[0227] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor can be a microprocessor or any conventional processor.

[0228] Memory is used to store computer programs and / or modules. The processor implements various functions of the electronic device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory. Memory can mainly include a program storage area and a data storage area. The program storage area can store the operating system, at least one application program required for a function, etc.; the data storage area can store data created based on the use of the terminal, etc. In addition, memory can also include high-speed random access memory, and can also include non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart memory cards (SMC), secure digital cards (SD cards), flash memory cards, at least one disk storage device, flash memory devices, or other volatile solid-state storage devices.

[0229] Example 4:

[0230] This invention also provides a computer-readable storage medium storing multiple instructions, which are loaded by a processor to cause the processor to execute the public-key encryption method based on edge computing with anti-leakage and attribute hiding according to any embodiment of this invention. Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the above embodiments is stored, and the computer (or CPU or MPU) of the system or apparatus may read and execute the program code stored in the storage medium.

[0231] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0232] Examples of storage media used to provide program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RYM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0233] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0234] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion unit connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion unit execute some and all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0235] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.< / n>

Claims

1. A public-key encryption method based on edge computing that is resistant to data leakage and attribute hiding, characterized in that, The method is as follows: S1. Input security parameters from a trusted authoritative organization; S2. Generate system public parameters as the system's master public key and master private key; S3. Data owners and data users simultaneously register, authenticate, verify legitimacy, and encrypt data. S4. Determine whether the data user attributes satisfy the access policy in the ciphertext: ① If the conditions are met, then decryption is successful; ②If the conditions are not met, decryption will fail; The specific steps for data owners to register, authenticate, verify legitimacy, and encrypt data are as follows: S3-101. Data owners must register by submitting their identity information to a trusted authority. S3-102, Data owner certified by a trusted authoritative institution; S3-103. Determine if the data owner is legitimate: ① If it is illegal, registration will be refused; ②If valid, proceed to step S3-104; S3-104. A trusted authority assigns a set of predicates y to the data owner and uses the predicate coding function framework to calculate and generate the data owner's public and private keys. S3-105. The data owner uses their public key and predicate coding function framework to formulate access control policies and encrypt messages; The specific procedures for data users to register, authenticate, verify legitimacy, and encrypt data are as follows: S3-201. Data users must register by submitting their identity information to a trusted authority. S3-202, Data users certified by trusted authoritative institutions; S3-203, Determine if the data user is legitimate: ① If it is illegal, registration will be refused; ②If valid, proceed to step S3-204; S3-204. A trusted authority assigns a public-private key pair to a data user based on the user's identity information. S3-205, The edge node returns the function about the plaintext obtained by the cloud storage server to the data user; The predicate encoding function framework for a prime group that satisfies the properties of leak resistance and attribute hiding is as follows: mold p Integer group - Linear anti-leakage predicate coding ;in, It is an attribute set; It is a set of predicates; the predicate encoding Includes the initialization phase Setup ( KeyGen (key generation algorithm) Encryption algorithm Enc () ) and the decryption algorithm Dec( Five deterministic algorithms ( And it satisfies the following properties: (1) Linearity: For any , All meet Linearity on -; (2) Attribute hiding: For any property that satisfies of And all of them The following two distributions are indistinguishable: and ; Among them, random numbers and Taken from and ; (3) Leakage resistance: In order to achieve the leakage resistance property of the user's private key, for any condition satisfying the following... of And all of them The following two distributions are indistinguishable: and ; Among them, random numbers and Taken from and ; Indicates the user predicate; and These represent the master public key and master private key of the inner product public key encryption algorithm, respectively. Indicates user attributes; Indicates by and user predicates The generated user private key; Indicates by and user attributes The generated ciphertext; Key generation algorithm KeyGen Specifically as follows: The encryption key used to generate the DO is executed by a trusted authority. For users requesting to join, a trusted authority administrator will assign a set of predicates to each user based on the user's identity information. ; A trusted authority administrator randomly selects redundant vectors. , To prevent attribute leakage, the redundant information set is blinded using PCF transformation, thus achieving the attribute hiding function. Output about the predicate Decryption key: ; in, , ; The calculated user key has data management privileges and cannot be accessed without authorization; Encryption algorithm Enc( The details are as follows: Data owners formulate corresponding access control policies based on their own security needs. These access control policies are determined by user attributes. express; Based on the access control policy, the ciphertext is calculated using the predicate coding function framework and then uploaded to the cloud server for storage via the edge node; Random selection The output ciphertext is as follows: 。 2. The public-key encryption method based on edge computing for leak resistance and attribute hiding according to claim 1, characterized in that, The predicate encoding function framework includes two tools, as follows: (i) Matrix distribution Requires output in polynomial time. Full rank The matrix is ​​executed as follows: randomly select... Output matrix The format is as follows: ; Wherein, once the matrix distribution Define matrix A Let the vector ,satisfy and ; (ii) Order For a polynomial-time algorithm, when the input security parameter is... At that time, the algorithm Output a parameter set ,in, p It's about parameters. prime numbers; The order is respectively p cyclic group; They are groups Generators; It is a computationally efficient and non-degenerate bilinear mapping.

3. The public-key encryption method based on edge computing for leak resistance and attribute hiding according to claim 2, characterized in that, Initialization phase Setup( The details are as follows: make It is a predicate encoding The parameters are executed by a trusted authority, which calculates and returns the master public key and master private key, as follows: Organization administrator execution and from ) 3D matrix distribution Random sampling and And randomly select vectors sum matrix ; Select a random vector and It also calculates and outputs the master public key for the inner product public key encryption algorithm. and the master private key They are respectively: and .

4. The public-key encryption method based on edge computing for leak resistance and attribute hiding according to claim 1, characterized in that, Decryption algorithm Dec( The details are as follows: When a data user sends an access request, the request is first sent to an edge node. The edge node then sends an authentication request to a trusted authority, using the data user's identity information to verify whether the user is a legitimate registered user. If the user is not a registered user, their data access request will be denied. If the user is a registered user, the edge node takes the master public key, the user's private key, and the ciphertext as input, requests the cloud storage server to decrypt the ciphertext, and calculates a function about the plaintext. Send to the applicant: 。 5. The public-key encryption method based on edge computing for leak resistance and attribute hiding according to claim 1, characterized in that, The performance analysis of this method is as follows: ① Correctness analysis: For any expression satisfying the equation of The following derivation process holds true for all of them: ； In the above equation, the linearity property of bilinear mapping can be used to prove that the method is correct. ② Security Analysis: If If the assumption holds true, then this method simultaneously achieves anti-leakage and attribute hiding capabilities; specifically as follows: For all polynomial-time attackers who satisfy the following two conditions : (1) A maximum of a limited number of times can be executed. The second leak was questioned; (2) The master private key must not be disclosed. And for the decryption key Leakage shall not exceed Bit.

6. A public-key encryption system based on edge computing that is resistant to data leakage and attribute hiding, characterized in that, The system employs the key generation algorithm and encryption algorithm as described in claim 1; the system includes data owners, data users, cloud storage servers, trusted authoritative institutions, and edge nodes; Data owners formulate access control policies based on their own security needs, encrypt data according to the access control policies, and upload the encrypted data to the cloud storage server provider for storage. Data users download the encrypted ciphertext from the cloud storage server provider and decrypt the data using their own private key; Cloud storage servers are used to store encrypted data from data holders; Trusted authorities are trusted by all entities to reliably execute and correctly respond to digital forensics requests from data holders, and to generate and distribute keys for all users. Edge nodes are edge computing devices used for storing and securely computing user data, and for securely and conveniently collaborating with cloud server applications.

7. An electronic device, characterized in that, include: Memory and at least one processor; The memory contains computer programs; The at least one processor executes the computer program stored in the memory, causing the at least one processor to perform the public-key encryption method based on edge computing that is resistant to leakage and attribute hiding as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that can be executed by a processor to implement the public-key encryption method based on edge computing that is resistant to leakage and attribute hiding as described in any one of claims 1 to 5.

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