Efficient fine-grained access control method for fog computing

Abstract

The invention discloses an efficient fine-grained access control method for fog computing, and relates to the technical field of access control. According to the method, in a cloud-fog cooperative computing architecture, a data owner entrusts ciphertext storage to a cloud storage platform, enjoys elastic storage service at low cost, and outsources partial decryption operation to a fog node, so that an authorized data acquirer can obtain data access service through lightweight operation. Therefore, a CP-ABE mechanism supporting double-stage decryption is innovatively designed, and a private key sk of an original CP-ABE is divided into two parts, namely a conversion key and a decryption key, based on a key splitting idea. The most resource-intensive strategy matching operation is executed by the fog node, and the data acquirer terminal only needs to carry out lightweight final decryption operation. The whole access control process comprises seven stages of system initialization, key generation, data outsourcing, request initiation, data retrieval, primary decryption and secondary decryption. According to the method, the problem of coarse-grained and high-cost data access privacy protection when cloud computing faces massive ciphertext sharing scenes and diversified retrieval requirements of users in the existing access control technology is effectively solved, the dependence on high computing and decryption overhead is avoided, and safe outsourcing part decryption and fine-grained access control are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of access control and provides an efficient fine-grained access control method for fog computing. Background Art

[0002] In the cloud-fog collaborative computing architecture, resource-constrained terminal devices hand over heavy computing and storage tasks to fog computing nodes and the cloud for collaborative processing, thereby obtaining efficient and convenient computing and storage services, effectively reducing the burden on terminal devices. However, in data sharing scenarios, data interactions between end users must be managed through reasonable access control policies to prevent unauthorized access and ensure the security and privacy protection of shared data.

[0003] Attribute-Based Encryption (ABE), as a one-to-many public key encryption technology, is widely used on public cloud storage servers. It is a cutting-edge technology for achieving flexible and fine-grained access control of encrypted data. ABE is mainly divided into two types: ciphertext policy ABE (CP-ABE) and key policy ABE (KP-ABE). CP-ABE allows the access policy formulated by the data owner to be bound to the ciphertext, and the attribute set of the data user to its decryption key. The ciphertext can be decrypted only if and only if the attribute set of the data user satisfies the access policy in the ciphertext, which is suitable for data sharing scenarios. KP-ABE operates in a way that the access policy and the attribute position are interchanged, that is, the access policy is bound to the key, and the attribute set is hidden in the ciphertext, which is more suitable for broadcast encryption scenarios.

[0004] How to achieve secure data sharing among end users in fog computing scenarios, avoiding reliance on high-cost decryption mechanisms while efficiently identifying and retrieving valuable data from massive ciphertexts, remains a critical and challenging issue. Summary of the invention

[0005] The present invention aims to solve the problem of high-cost data acquisition end-user decryption in traditional access control schemes, so as to design a scheme that allows data owners to control the scope of authorization by defining access policies and realize lightweight and secure data sharing. To this end, an efficient and fine-grained access control method for fog computing is provided, which supports outsourcing partial decryption.

[0006] Specifically, the method allows the data owner terminal to rely on the cloud storage platform for remote data storage and management, so as to share the data with multiple authorized data acquirer terminals. Under the premise of ensuring the security of sensitive data, the method supports outsourcing partial decryption to reduce the decryption overhead of the data acquirer terminal. Specifically, based on the one-to-many access control implemented by Ciphertext-Policy Attribute-Based Encryption (CP-ABE), the method innovatively proposes an optimized CP-ABE scheme that supports a two-stage decryption mechanism. The mechanism performs the first stage of outsourced decryption by the fog node, and the second stage of decryption (i.e., final decryption) is completed by the data acquirer terminal. Furthermore, the mechanism divides the original CP-ABE private key sk into two parts, namely the conversion key tk and the decryption key sk, where the two parts of the key are associated with each data acquirer terminal and its corresponding set of attributes. Most importantly, by using the conversion key tk, the high overhead caused by the bilinear mapping pairing at the access control layer is eliminated, while the decryption key sk ensures the security of complete data decryption.

[0007] Specifically, the access control system architecture involves five entities: key generation center, cloud storage platform, fog node, data owner terminal and data acquirer terminal. Their responsibilities are as follows:

[0008] (6) Key Generation Center: Mainly responsible for initializing system modules and user management (distributing encryption keys to new data owner terminals and generating data acquisition keys associated with their attribute sets for data acquirer terminals, including conversion keys and decryption keys).

[0009] (7) Cloud storage platform: It has huge storage resources and is responsible for storing and managing the ciphertext uploaded by the data owner’s terminal. When receiving a data retrieval request from a fog node, it is responsible for retrieving the corresponding ciphertext and forwarding it to the relevant fog node.

[0010] (8) Fog nodes: They have abundant computing resources and temporary file caching capabilities, and are responsible for the first stage of outsourced decryption.

[0011] (9) Data owner terminal: allows to encrypt its own data and outsource the ciphertext to the cloud storage platform. Each ciphertext is associated with a custom access policy.

[0012] (10) Data acquirer terminal: It is associated with a set of attribute sets and possesses the decryption key sk, and undertakes the second stage of decryption, that is, performing the final decryption operation.

[0013] Furthermore, the specific implementation steps of the CP-ABE scheme supporting dual-stage decryption include:

[0014] Step 1, System Initialization Phase (Setup): The key generation center takes the security parameter λ as input and first generates the group parameter par: = (p, e, G1, G2, G T , g1, g2), where G1, G2 and G T are all multiplicative cyclic groups of prime order p, e: G1×G2→G T is a bilinear map, and the generators g1∈G1, g2∈G2. Then, the key generation center randomly selects an integer And the collision-resistant hash function H is specified: {0, 1} * →G2, to map any length string to the multiplication cyclic group. Next, calculate and output the system's public key pk = (par, H, e(g1, g2) α ) and the master private key msk = α. The public key pk is broadcast and distributed to all other entities, including the data acquirer terminal, the data owner terminal, the fog node and the cloud storage platform, while the key generation center is responsible for maintaining the master private key msk to ensure that it is not leaked. This step can be formally expressed as: Setup(1 λ )→(pk,msk).

[0015] Step 2, key generation phase (KeyGen): The data acquisition terminal submits its own attribute set to the key generation center to complete identity registration. After the key generation center confirms the identity of the data acquisition terminal, it uses the public key pk, the master private key msk and the attribute set related to the data acquisition terminal to generate a key. As input, two integers r are randomly selected, Output conversion key And the decryption key sk = β. The components of the conversion key tk are obtained by calculating the following formula: Subsequently, in the pair of keys generated based on the attribute set of the data acquirer terminal, the conversion key tk is maintained by the fog node (transmitted by the key generation center through a secure channel) for primary decryption. The decryption key sk is kept by the data acquirer terminal (transmitted by the key generation center through a secure channel) for secondary decryption, i.e., final decryption. This step can be formally expressed as:

[0016] Step 3, data outsourcing phase (Enc): the data owner terminal uses the public key pk and linear secret sharing access strategy (Limit the authorized access of the data acquirer terminal to the resource), the sensitive file msg to be protected is taken as input, and the ciphertext is output Specifically, the data owner terminal first randomly selects a secret value Regenerate random vector calculate Then, randomly generate The components of the ciphertext C are obtained by calculating the following formula: ct3=msg·e(g1,g2) αs This step can be formally expressed as: Subsequently, the data owner terminal outsources the ciphertext C to the fog node for storage. For frequently used files, the fog node can perform short-term storage locally, create local copies and manage ciphertext data. At the same time, it can choose to upload the ciphertext to the cloud storage platform for long-term storage.

[0017] Step 4, request initiation phase: the data acquirer terminal selects the data to be acquired according to the demand and submits a data access application to the fog node. The application can be transmitted in the form of a file identifier ID so that the fog node can identify and process the request.

[0018] Step 5, data retrieval phase: The fog node receives a data access request from the data acquirer terminal and retrieves the corresponding ciphertext file C locally according to the file identifier ID. If the local retrieval fails, a retrieval request is submitted to the cloud storage platform, and the returned result is passed to the fog node for further processing.

[0019] Step 6, primary decryption phase (PDec): The fog node takes the ciphertext C and the transformation key tk as input and outputs the primary decrypted ciphertext PTC. In particular, if the attribute set associated with the data acquirer embedded in the transformation key tk is Satisfy the access control policy specified by the data owner terminal in the ciphertext Then there exists a constant set {ω i} i∈I , which can meet the conditions Thus recovering Finally, the following formula is calculated to obtain the components of the decrypted ciphertext PTC:

[0020]

[0021] Otherwise, the identity authorization fails and returns a failure message ⊥. This step can be formally expressed as: PDec(C, tk)→PTC / ⊥.

[0022] Step 7, secondary decryption phase (TDec): The fog node returns the first decrypted ciphertext PTC to the data acquirer terminal. The data acquirer terminal takes the first decrypted ciphertext PTC and the decryption key sk as input, and outputs the second decrypted ciphertext msg, i.e., the plaintext bidding document. By calculation: msg = ptc1 / (ptc0) βThis step can be formally expressed as: TDec(PTC, sk)→msg / ⊥.

[0023] Furthermore, the bilinear mapping is specifically defined as follows: Let G1, G2 and G T is the cyclic multiplicative group of prime order p, and let G T As the value range of the pairing mapping e. If the mapping e: G1×G2→G T A map is called a bilinear map if it satisfies the following properties:

[0024] (1) Bilinear: For any a, And any g1∈G1, g2∈G2, we have

[0025] (2) Non-degeneracy: e(g1, g2)≠1.

[0026] (3) Computability: For all g1∈G1, g2∈G2, computing e(g1, g2) is efficient.

[0027] Furthermore, the linear secret sharing scheme is specifically defined as follows: for the participant set If the following conditions are met, the LSSS is called linear (defined in superior):

[0028] (1) Each participant’s share comes from The vector space on .

[0029] (2) There exists a matrix It is called the share generation matrix, which contains rows and n columns. For each matrix The i-th row of Consider the column vector in is the secret to be shared, is a randomly selected value, then constitutes A vector of secret shares. will be assigned to participant x i ,in Representation Matrix The i-th row, v i Representation vector The i-th element in .

[0030] Moreover, set An LSSS access policy, for any set of authorization attributes Where Ω represents the attribute universe, ① there is a set of effective shares Where I = {i:π(i)∈A}; ② There is also an effective algorithm (such as Gaussian elimination) to calculate a set of constants By calculating The secret s can be recovered from the effective share.

[0031] Further, the correctness analysis of the CP-ABE scheme supporting two-stage decryption is as follows:

[0032] If the bidder attribute set Satisfy the access control policy defined by the bidder Then we can successfully calculate:

[0033]

[0034] Furthermore, because ptc1=ct3, to reconstruct msg, we can calculate:

[0035]

[0036] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0037] 1. The present invention provides an efficient and fine-grained access control method for fog computing. Specifically, the method allows data owners to entrust ciphertext storage to cloud storage platforms in a cloud-fog collaborative computing architecture, enjoy elastic storage services at a lower cost, and outsource some decryption operations to fog nodes, so that authorized data acquirers can obtain data access services through lightweight operations. An innovative CP-ABE mechanism that supports two-stage decryption is designed. Based on the idea of ​​key splitting, the original CP-ABE private key sk is divided into two parts: a conversion key and a decryption key. The most resource-intensive policy matching operations are handed over to fog nodes for execution, while the data acquirer terminal only needs to perform lightweight final decryption operations. It not only allows data owners to customize access policies and ensures that only data acquirers who meet specific conditions can decrypt ciphertexts and access data content, but also avoids data acquirers from relying on high computing and decryption overheads.

[0038] 2. The present invention significantly improves the flexibility of the system while optimizing the use of access control computing resources. The entire access control process includes seven stages: system initialization, key generation, data outsourcing, request initiation, data retrieval, primary decryption and secondary decryption. In addition to achieving secure outsourced partial decryption and fine-grained access control, the present invention introduces a linear secret sharing scheme LSSS in the designed CP-ABE model. By representing the access policy as a matrix structure and mapping the specified attribute set into a linear equation system, flexible and highly expressive access control can be achieved. In addition, the linear attribute mapping feature of LSSS also supports dynamic permission management, allowing the system to adapt to attribute updates and changes in user roles in real time to meet changing security requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the system model of the method of the present invention.

[0040] Figure 2 The figure is a schematic diagram of the system flow of the method of the present invention. Specific implementation methods

[0042] In order to make the purpose, technical solution and advantages of the present invention more clear, the technical solution in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] like Figure 1 , Figure 2 As shown, the present invention provides an efficient fine-grained access control method for fog computing, comprising the following steps:

[0044] Step 1, System Initialization Phase (Setup): The key generation center takes the security parameter λ as input and first generates the group parameter par: = (p, e, G1, G2, G T , g1, g2), where G1, G2 and G T are all multiplicative cyclic groups of prime order p, e: G1×G2→G T is a bilinear map, and the generators g1∈G1, g2∈G2. For the convenience of calculation, in the present application example, the multiplication cyclic group and the bilinear map on it are generated based on the A-type elliptic curve (r: 20 bits, q: 64 bits). The specific values ​​of the parameters of the elliptic curve are as follows:

[0045]

[0046] The selected generators are g1 = [279428722562766074, 283004173644393411], g2 = [1591688547331950915, 1136866245810624930]

[0047] Then, the key generation center randomly selects an integer α=254957 and specifies a collision-resistant hash function H: {0, 1} * →G2, to map any length string to the multiplication cyclic group. Next, calculate and output the system's public key pk = (par, H, e (g1, g2) α =[240739359614661777, 482917595898864424]) and the master private key msk=α=254957.

[0048] The public key pk is broadcast and distributed to all other entities, including the data acquirer terminal, the data owner terminal, the fog node and the cloud storage platform, while the key generation center is responsible for maintaining the master private key msk to ensure that it is not leaked.

[0049] Step 2, key generation phase (KeyGen): The data acquisition terminal submits its own attribute set to the key generation center to complete identity registration. After the key generation center confirms the identity of the data acquisition terminal, it uses the public key pk, the master private key msk and the attribute set related to the data acquisition terminal to generate a key. As input. Assume that in this application embodiment, It means that the data acquirer terminal has three attributes A1, A2 and A3, that is, m=3, i takes values ​​between 1 and 3. Then, two integers r=248301 and β=170870 are randomly selected and the conversion key is output. And the decryption key sk = β. The components of the conversion key tk are obtained by calculating the following formula: Based on this embodiment, the specific values ​​obtained are:

[0050]

[0051] Subsequently, in the pair of keys generated based on the attribute set of the data acquirer terminal, the conversion key tk is maintained by the fog node (transmitted by the key generation center through a secure channel) for primary decryption. The decryption key sk is kept by the data acquirer terminal (transmitted by the key generation center through a secure channel) for secondary decryption, i.e., final decryption.

[0052] Step 3, data outsourcing phase (Enc): the data owner terminal uses the public key pk and linear secret sharing access strategy (Limit the authorized access of the data acquirer terminal to resources), the sensitive file msg to be protected is taken as input, and the ciphertext is output Specifically, assuming that in the embodiment of this application, the threshold access strategy defined by the data owner terminal is (A1, A2, A3, 3), the secondary strategy means that only the data acquirer terminal including these three attributes has the right to access the data. Then, the threshold access strategy is transformed by the linear secret sharing scheme LSSS to form a new matrix access strategy The specific expressions are as follows:

[0053]

[0054] So, the matrix of rows Column n=3.

[0055] The message to be encrypted is selected as msg=[1012005667202653401, 35682848487295859].

[0056] Then, the data owner terminal first randomly selects a secret value Regenerate random vector calculate Based on this embodiment, the specific values ​​are:

[0057]

[0058] Next, randomly generate t1, t2, The components of the ciphertext C are obtained by calculating the following formula: ct3=msg·e(g1,g2) αs Based on this embodiment, the specific values ​​obtained are:

[0059]

[0060] Subsequently, the data owner terminal outsources the ciphertext C to the fog node for storage. For frequently used files, the fog node can perform short-term storage locally, create local copies and manage ciphertext data. At the same time, it can choose to upload the ciphertext to the cloud storage platform for long-term storage.

[0061] Step 4, request initiation phase: the data acquirer terminal selects the data to be acquired according to the demand and submits a data access application to the fog node. The application can be transmitted in the form of a file identifier ID so that the fog node can identify and process the request.

[0062] Step 5, data retrieval phase: The fog node receives a data access request from the data acquirer terminal and retrieves the corresponding ciphertext file C locally according to the file identifier ID. If the local retrieval fails, a retrieval request is submitted to the cloud storage platform, and the returned result is passed to the fog node for further processing.

[0063] Step 6, primary decryption phase (PDec): The fog node takes the ciphertext C and the transformation key tk as input and outputs the primary decrypted ciphertext PTC. In particular, if the attribute set associated with the data acquirer embedded in the transformation key tk is Satisfy the access control policy specified by the data owner terminal in the ciphertext Then there exists a constant set {ω i} i∈I , which can meet the conditions Thus recovering Finally, the following formula is calculated to obtain the components of the decrypted ciphertext PTC:

[0064]

[0065] Obviously, in this specific example, the threshold access policy defined by the data owner terminal is (A1, A2, A3, 3), and the attribute set of the data acquirer terminal is That is, it has the three attributes of A1, A2 and A3, which satisfies the access policy. Based on this embodiment, the specific values ​​obtained are: ptc0 = [1502289685870898500, 1497760706195125670], ptc1 = [517992441214706670, 1574228771057736489].

[0066] Step 7, secondary decryption phase (TDec): The fog node returns the first decrypted ciphertext PTC to the data acquirer terminal. The data acquirer terminal takes the first decrypted ciphertext PTC and the decryption key sk as input, and outputs the second decrypted ciphertext msg, i.e. the plaintext bidding document, by calculating: msg = ptc1 / (ptc0) β Based on this embodiment, the specific value obtained is: msg = [1012005667202653401, 35682848487295859], which is equal to the original encrypted value, and the access is successful, and the solution is correct.

[0067] The above implementation examples are only used to illustrate the technical solution of the present invention rather than to limit it. A person skilled in the art may modify or convert the technical solution of the present invention without departing from the spirit and scope of the present invention. The scope of protection of the present invention shall be based on the claims.

Claims

1. An efficient fine-grained access control method for fog computing, characterized in that: The method allows the data owner terminal to store and manage data remotely on the cloud storage platform so as to share the data with multiple authorized data acquirer terminals. Under the premise of ensuring the security of sensitive data, the method supports outsourcing partial decryption to reduce the decryption overhead of the data acquirer terminal. Specifically, based on the one-to-many access control implemented by Ciphertext-PolicyAttribute-Based Encryption (CP-ABE), the method innovatively proposes an optimized CP-ABE scheme that supports a two-stage decryption mechanism. The mechanism performs the first stage of outsourced decryption by the fog node, and the second stage of decryption (i.e., final decryption) is completed by the data acquirer terminal. Furthermore, the mechanism divides the original CP-ABE private key sk into two parts, namely the conversion key tk and the decryption key sk, where the two parts of the key are associated with each data acquirer terminal and its corresponding set of attributes. Most importantly, by using the conversion key tk, the high overhead caused by the bilinear mapping pairing at the access control layer is eliminated, while the decryption key sk ensures the security of complete data decryption. Specifically, the access control system architecture involves five entities: key generation center, cloud storage platform, fog node, data owner terminal and data acquirer terminal. Their responsibilities are as follows: (1) Key Generation Center: Mainly responsible for initializing system modules and user management (distributing encryption keys to new data owner terminals and generating data acquisition keys associated with their attribute sets for data acquirer terminals, including conversion keys and decryption keys). (2) Cloud storage platform: It has huge storage resources and is responsible for storing and managing the ciphertext uploaded by the data owner’s terminal. When receiving a data retrieval request from a fog node, it is responsible for retrieving the corresponding ciphertext and forwarding it to the relevant fog node. (3) Fog nodes: They have abundant computing resources and temporary file caching capabilities, and are responsible for the first stage of outsourced decryption. (4) Data owner terminal: allows to encrypt its own data and outsource the ciphertext to the cloud storage platform. Each ciphertext is associated with a custom access policy. (5) Data acquirer terminal: It is associated with a set of attribute sets and possesses the decryption key sk, and undertakes the second stage of decryption, that is, performing the final decryption operation.

2. According to claim 1, an efficient fine-grained access control method for fog computing is characterized in that: The specific implementation steps of the CP-ABE scheme supporting two-stage decryption include: Step 1, System Initialization Phase (Setup): The key generation center takes the security parameter λ as input and first generates the group parameter par: = (p, e, G1, G2, G T , g1, g2), where G1, G2 and G T are all multiplicative cyclic groups of prime order p, e: G1×G2→G T is a bilinear map, and the generators g1∈G1, g2∈G2. Then, the key generation center randomly selects an integer And the collision-resistant hash function H is specified: {0, 1} * →G2, to map any length string to the multiplication cyclic group. Next, calculate and output the system's public key pk = (par, H, e(g1, g2) ɑ ) and the master private key msk = ɑ. The public key pk is broadcast and distributed to all other entities, including the data acquirer terminal, the data owner terminal, the fog node and the cloud storage platform, while the key generation center is responsible for maintaining the master private key msk to ensure that it is not leaked. This step can be formally expressed as: Setup(1 λ )→(pk,msk). Step 2, key generation phase (KeyGen): The data acquisition terminal submits its own attribute set to the key generation center to complete identity registration. After the key generation center confirms the identity of the data acquisition terminal, it uses the public key pk, the master private key msk and the attribute set related to the data acquisition terminal to generate a key. As input, two integers r are randomly selected, Output conversion key And the decryption key sk = β. The components of the conversion key tk are obtained by calculating the following formula: Subsequently, in the pair of keys generated based on the attribute set of the data acquirer terminal, the conversion key tk is maintained by the fog node (transmitted by the key generation center through a secure channel) for primary decryption. The decryption key sk is kept by the data acquirer terminal (transmitted by the key generation center through a secure channel) for secondary decryption, i.e., final decryption. This step can be formally expressed as: Step 3, data outsourcing phase (Enc): the data owner terminal uses the public key pk and linear secret sharing access strategy (Limit the authorized access of the data acquirer terminal to the resource), the sensitive file msg to be protected is taken as input, and the ciphertext is output Specifically, the data owner terminal first randomly selects a secret value Regenerate random vector Calculating λ i =M i (s||v) T . Then, randomly generate The components of the ciphertext C are obtained by calculating the following formula: This step can be formally expressed as: Subsequently, the data owner terminal outsources the ciphertext C to the fog node for storage. For frequently used files, the fog node can perform short-term storage locally, create local copies and manage ciphertext data. At the same time, it can choose to upload the ciphertext to the cloud storage platform for long-term storage. Step 4, request initiation phase: the data acquirer terminal selects the data to be acquired according to the demand and submits a data access application to the fog node. The application can be transmitted in the form of a file identifier ID so that the fog node can identify and process the request. Step 5, data retrieval phase: The fog node receives a data access request from the data acquirer terminal and retrieves the corresponding ciphertext file C locally according to the file identifier ID. If the local retrieval fails, a retrieval request is submitted to the cloud storage platform, and the returned result is passed to the fog node for further processing. Step 6, primary decryption phase (PDec): The fog node takes the ciphertext C and the transformation key tk as input and outputs the primary decrypted ciphertext PTC. In particular, if the attribute set associated with the data acquirer embedded in the transformation key tk is Satisfy the access control policy specified by the data owner terminal in the ciphertext Then there exists a constant set {ω i } i∈I , which can meet the conditions Thus recovering Finally, the following formula is calculated to obtain the components of the decrypted ciphertext PTC: Otherwise, the identity authorization fails and returns a failure message ⊥. This step can be formally expressed as: PDec(C, tk)→PTC / ⊥. Step 7, secondary decryption phase (TDec): The fog node returns the first decrypted ciphertext PTC to the data acquirer terminal. The data acquirer terminal takes the first decrypted ciphertext PTC and the decryption key sk as input, and outputs the second decrypted ciphertext msg, i.e., the plaintext bidding document. By calculation: msg = ptc1 / (ptc0) β This step can be formally expressed as: TDec(PTC,sk)→msg / ⊥.

3. According to claim 2, an efficient fine-grained access control method for fog computing is characterized in that: The bilinear mapping is specifically defined as follows: Let G1, G2 and G T is the cyclic multiplicative group of prime order p, and let G T As the value range of the pairing mapping e. If the mapping e: G1×G2→G T A map is called a bilinear map if it satisfies the following properties: (1) Bilinear: For any a, And any g1∈G1, g2∈G2, we have (2) Non-degeneracy: e(g1, g2)≠1. (3) Computability: For all g1∈G1, g2∈G2, computing e(g1, g2) is efficient.

4. According to claim 2, an efficient fine-grained access control method for fog computing is characterized in that: The linear secret sharing scheme is specifically defined as follows: If the following conditions are met, the LSSS is called linear (defined in superior): (1) Each participant’s share comes from The vector space on . (2) There exists a matrix It is called the share generation matrix, which contains rows and n columns. For each matrix The i-th row of Consider the column vector in is the secret to be shared, is a randomly selected value, then constitutes A vector of secret shares. will be assigned to participant x i ,in Representation Matrix The i-th row, v i Representation vector The i-th element in . Further, set An LSSS access policy, for any set of authorization attributes Where Ω represents the attribute universe, ① there is a set of effective shares Where I = {i:π(i)∈A}; ② There is also an effective algorithm (such as Gaussian elimination) to calculate a set of constants By calculating The secret s can be recovered from the effective share.

5. According to claim 2, an efficient fine-grained access control method for fog computing is characterized in that: The correctness analysis of the CP-ABE scheme supporting two-stage decryption is as follows: If the bidder attribute set Satisfy the access control policy defined by the bidder Then we can successfully calculate: Furthermore, because ptc1=ct3, to reconstruct msg, we can calculate:

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