Anti-quantum searchable inner product function encryption method, storage medium and equipment

Abstract

The invention discloses an anti-quantum searchable inner product function encryption method, a storage medium and equipment. Comprising an initialization stage, a server key generation stage, a user key generation stage, a token generation stage, an update key generation stage, a conversion key generation stage, a function key generation stage, an encryption stage, a keyword trap door generation stage, a matching stage, a ciphertext conversion stage, a decryption stage and a revocation stage. According to the method, the user is supported to carry out keyword search on the ciphertext, the inner product value of the encrypted data is calculated, and the keyword search capability and the inner product calculation capability are entrusted to other users. When the function calculation permission of the user changes, the method can cancel the specific function calculation permission of the user, and the number of times of interaction between the user and the central mechanism is only 1. Meanwhile, the method can resist quantum attacks.

Description

Technical Field

[0001] This invention belongs to the technical field of computer security, and mainly relates to a quantum-resistant searchable inner product function encryption method, storage medium and device. Background Technology

[0002] Traditional encryption algorithms can protect data security, but they do not support selective computation of ciphertext; that is, users either receive the entire plaintext or no information from it. However, in practical applications, users may only allow access to the function values ​​of the encrypted data, such as the mean or variance, rather than all the information.

[0003] Inner product operations can be used to calculate the mean and weighted average of data, and have important applications in data analysis and artificial intelligence. In inner product function encryption, the function key and ciphertext are each associated with a vector, and the user can use the function key to calculate the inner product of the vector in the key and the vector in the ciphertext. With the rapid development of quantum computing, inner product function encryption based on traditional hardness assumptions faces significant threats, such as the discrete logarithm problem and the composite residues problem. Lattice-based inner product function encryption is considered one of the key solutions to resist quantum computing attacks and ensure information security.

[0004] However, in existing function encryption, users cannot search for keywords. Considering the dynamic changes in user permissions, their designated function computation permissions need to be updated and revoked. Furthermore, when an internet connection is unavailable, users need to temporarily delegate their keyword search and function computation capabilities to others. Summary of the Invention

[0005] This invention addresses the problems existing in the prior art by providing a quantum-resistant searchable inner product function encryption method, including an initialization phase, a server key generation phase, a user key generation phase, a token generation phase, an update key generation phase, a transformation key generation phase, a function key generation phase, an encryption phase, a trapdoor generation phase, a matching phase, a ciphertext transformation phase, a decryption phase, and a revocation phase. This method allows users to perform keyword searches on the ciphertext, calculate the inner product value of the encrypted data, and delegate keyword search and inner product calculation capabilities to other users. When a user's function calculation permissions change, this method can revoke the user's specific function calculation permissions, and the number of interactions between the user and the central institution is limited to one. Furthermore, this method is resistant to quantum attacks.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a quantum-resistant searchable inner product function encryption method, comprising the following steps:

[0007] S1. Initialization Phase: Central Organization Enter a security parameter Output master key and common parameters Cancel list and system status :

[0008] ;

[0009] S2, Server Key Generation Phase: Central Organization Enter master key Server identity and common parameters Output the server's private key :

[0010] ;

[0011] S3, User Key Generation Phase: Central Institution Enter master key ,User ID and common parameters Output user key

[0012] ;

[0013] S4, Token Generation Phase: Central Institution Enter the master private key ,User ID System status and common parameters Output token and the updated status :

[0014] ;

[0015] S5. Key Generation Update Phase: Central Institution Enter the master private key Regarding vectors Cancellation list ,vector ,time System status and common parameters Output update key ,Right now

[0016] ;

[0017] S6. Key Generation Stage: Cloud Server Enter token Update key ,vector and common parameters Output conversion key :

[0018] ;

[0019] S7. Function Key Generation Stage: Data Users Enter user key ,vector ,time and common parameters Output short-term function key :

[0020] ;

[0021] S8, Encryption Phase: Data Owner Enter server identity ,User ID Keywords ,time ,vector and common parameters Output ciphertext ,Right now

[0022] ;

[0023] S9. Trapdoor Generation Stage: Data Users Enter user key Server identity Keywords ,time and common parameters Output trapdoor :

[0024] ;

[0025] S10, Matching Phase: Cloud Server Input Trapdoor Server private key ciphertext and common parameters The output match result is 0 / 1:

[0026] ;

[0027] S11, Ciphertext Conversion Stage: Cloud Server Input conversion key ciphertext ,vector and common parameters Output converted ciphertext ,Right now

[0028] ;

[0029] S12, Decryption Stage: The entrusted party (DD) inputs the converted ciphertext. Function key ,vector and common parameters Output the inner product value :

[0030] .

[0031] As another improvement of the present invention, it also includes step S13, the revocation stage: central mechanism Input vector ,User ID Time t, about vector Cancellation list System status and common parameters Output the updated cancellation list ,Right now

[0032] .

[0033] To achieve the above objectives, the present invention also adopts the following technical solution: a non-transitory machine-readable storage medium storing executable code thereon, wherein when the executable code is executed by the processor of an electronic device, the steps of any of the methods described above are implemented.

[0034] To achieve the above objectives, the present invention also adopts the following technical solution: a computer device, including a memory, on which executable code is stored;

[0035] A processor for executing the executable code, causing the computer device to perform the steps of any of the methods described above.

[0036] Compared with existing technologies, this invention uses keywords, timestamps, and public keys to encrypt data, allowing users to generate keyword trapdoors and function keys to perform keyword searches and function calculations on the encrypted data. By outsourcing computation, the server bears most of the user's computational burden, thus reducing user overhead. Furthermore, by embedding timestamps in the keyword trapdoors and function keys, the ability to revoke and delegate the user's keyword search and function calculation capabilities can be achieved. This invention has the following beneficial effects:

[0037] (1) Through steps S9 and S10 of the present invention, the present invention supports users to perform keyword searches on encrypted text;

[0038] (2) Through steps S5, S6, S11 and S13 of the present invention, the method of the present invention supports the revocation of specific user permissions;

[0039] (3) Through steps S7 and S9 of the present invention, the present invention supports users to temporarily entrust keyword search and function calculation capabilities to others;

[0040] (4) Through step S1 of the present invention, in the method of the present invention, the user only needs to interact with the central institution once;

[0041] (5) Through steps S1-S13 of the present invention, the method of the present invention can resist quantum computer attacks and keyword guessing attacks. Attached Figure Description

[0042] Figure 1 This is a flowchart of the steps of the method of the present invention. Detailed Implementation

[0043] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0044] Example 1

[0045] Quantum-resistant searchable inner product function encryption methods, such as Figure 1 As shown, it includes the following steps:

[0046] S1. Initialization Phase: Central Organization Enter a security parameter Select a positive integer , N, a positive real number , prime number To ensure the correctness and safety of the solution, the parameters should meet the following conditions: ; .

[0047] Let set and Next, the central organization Selecting the FRD function and hash function .

[0048] Then, the central organization Running the trapdoor generation algorithm Randomly selected Initialize a tree with at least A binary tree with leaf nodes .make , , , .in ; The group of order q is a prime number; It is an n-dimensional vector space, where each vector component belongs to ; for An n-order square matrix composed of elements; It is a positive integer; For length is A 0 / 1 string; A set of n rows and m columns of elements.

[0049] Finally, the central organization Set Cancel List System status Master private key Common parameters .

[0050] For ease of illustration, in this invention we let .

[0051] The FRD function and trapdoor generation algorithm used in the above steps The definition is as follows:

[0052] FRD function: Let It is a prime number. It is a positive integer. It is a polynomial function. If for different... , If it is full rank, then It is an FRD function.

[0053] Trapdoor generation algorithm For any prime number q and integer q The algorithm outputs a matrix. Passive A short base ,in .

[0054] S2, Server Key Generation Phase: Central Organization First, run the left sampling algorithm. and Then, the central organization send Give cloud server .in, for One of the elements; For matrix The corresponding trapdoor; for One of the elements; It is a positive real number; For the set of integers 3D vector space; for One of the elements; for ; for One of the elements; Composed of integer elements OK, A set of matrices with columns; for One of the elements.

[0055] The left sampling algorithm used in the above steps The left sampling algorithm is defined as follows: Input matrix , ,grid A short base ,matrix real numbers Output and Follows a Gaussian distribution .

[0056] S3, User Key Generation Phase: For user identity... Central institutions Computation of Left Lattice Basis Extension Algorithm and user key Send to data users .in, For one Elements in; For matrix The trapdoor.

[0057] The left-side lattice basis expansion algorithm used in the above steps The following definition applies: Left-Lattice Basis Expansion Algorithm Input matrix , ,grid A short base real numbers Output base Follows a Gaussian distribution .

[0058] S4, Token Generation Phase: Given user identity Central institutions Select an undefined leaf node and... Stored in that node. For each node. ,if If not defined, then Random selection ,make And Stored on the node Then, CA runs the left sampling algorithm. Update system status And send Give it to the cloud server CS.

[0059] The path algorithm used in the above steps The path algorithm is defined as follows: From the root node to the node A set of nodes on the path.

[0060] S5. Key Generation Update Phase: Given a vector For each The central CA runs the left sampling algorithm. Next, the central CA sends... Give it to the cloud server CS.

[0061] The KUNodes algorithm used in the above steps is defined as follows:

[0062] KUNodes(BT, ,t):

[0063] .

[0064] if , Add to to the set .

[0065] :

[0066] if ,Add to to the set ;

[0067] if ,Add to to the set .

[0068] if Add the root node to the collection .

[0069] Return Y.

[0070] S6. Key Generation Phase: Cloud Server CS Reads , .if cloud server Output Otherwise, cloud server choose ,calculate , ,in Next, the cloud server CS received... .

[0071] S7. Function Key Generation Stage: Given a vector Data user DU runs the left sampling algorithm And send Data entrusted to the agent .

[0072] S8. Encryption Phase: Data Owner (DO) is randomly selected. Sampling according to Gaussian distribution ,calculate

[0073]

[0074] .

[0075] Next, DO will encrypt the text. Uploaded to cloud server CS.

[0076] S9. Trapdoor Generation Phase: Given keywords Data user DU runs the left sampling algorithm Random selection , Sampling according to Gaussian distribution , , Next, data user DU calculates... , , and the trap door Send to the entrusted party DD. Among them, for One of the elements; for One of the elements; for One of the elements; It is the set of m-order square matrices whose elements are only -1 or 1; for One of the elements; It is a discrete Gaussian distribution over an m-dimensional integer lattice; for Discrete Gaussian distribution over an integer lattice; To obey A short integer vector with a distribution; To obey A short integer vector with a distribution; for One of the elements; for One of the elements; for The transpose of the matrix; for The transpose of the matrix; For hash functions; for One of the elements; represent The binary form, Represents XOR.

[0077] S10, Matching Phase: The cloud server CS first calculates... , , , .if If the server returns 0, it will return 1; otherwise, it will return 1.

[0078] S11, Ciphertext Conversion Stage: Cloud Server CS Computation mod and send Give it to the entrusted party DD.

[0079] S12, Decryption Phase: The entrusted party calculates DD. mod and output ,in Make is the minimum value and .

[0080] S13, Revocation Phase: Given user identity Time t, about vector Cancellation list Central CA added arrive And return a new .

[0081] In summary, the quantum-resistant searchable inner product function encryption method proposed in this invention supports user keyword searches; supports users selectively calculating encrypted data; supports the revocation of some user function calculation capabilities; and supports users temporarily delegating function calculation and keyword search capabilities to other users. Furthermore, this method is resistant to quantum computer attacks, and in this invention, the number of interactions between the user and the central institution is only 1, independent of the number of functions. It represents a new generation of data encryption method with good performance and wide applicability.

[0082] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A quantum-resistant searchable inner product function encryption method, characterized in that, Includes the following steps: S1. Initialization Phase: Central Organization Enter a security parameter Output master key and common parameters Cancel list and system status : ； S2, Server Key Generation Phase: Central Organization Enter master key Server identity and common parameters Output the server's private key : ； S3, User Key Generation Phase: Central Institution Enter master key ,User ID and common parameters Output user key : ； S4, Token Generation Phase: Central Institution Enter the master private key ,User ID System status and common parameters Output token and the updated status : ； S5. Key Generation Update Phase: Central Institution Enter the master private key Regarding vectors Cancellation list ,vector ,time System status and common parameters Output update key : ； S6. Key Generation Stage: Cloud Server Enter token Update key ,vector and common parameters Output conversion key : ； S7. Function Key Generation Stage: Data Users Enter user key ,vector ,time and common parameters Output short-term function key : ； S8, Encryption Phase: Data Owner Enter server identity ,User ID Keywords ,time ,vector and common parameters Output ciphertext : ； S9. Trapdoor Generation Stage: Data Users Enter user key Server identity Keywords ,time and common parameters Output trapdoor : ； S10, Matching Phase: Cloud Server Input Trapdoor Server private key ciphertext and common parameters The output match result is 0 / 1: ； S11, Ciphertext Conversion Stage: Server Input conversion key ciphertext ,vector and common parameters Output converted ciphertext : ； S12, Decryption Stage: The entrusted party (DD) inputs the converted ciphertext. Function key ,vector and common parameters Output the inner product value : 。 2. The quantum-resistant searchable inner product function encryption method as described in claim 1, characterized in that: It also includes step S13, the revocation phase: central agency Input vector ,User ID Time t, about vector Cancellation list System status and common parameters Output the updated cancellation list ,Right now 。 3. The quantum-resistant searchable inner product function encryption method as described in claim 1, characterized in that: In step S1, the central mechanism Selecting the FRD function and hash function where n is a positive integer; The group of order q is a prime number; It is an n-dimensional vector space, where each vector component belongs to ; for An n-order square matrix composed of elements; It is a positive integer; For length is 0 / 1 strings; central organization Running the trapdoor generation algorithm Obtain the master key Where m is a positive integer; A set of n rows and m columns of elements; for One of the elements; For matrix The corresponding trapdoor.

4. The quantum-resistant searchable inner product function encryption method as described in claim 1, characterized in that: In step S2, the central mechanism Running the left sampling algorithm and Obtain the server's private key Central institutions send Give cloud server ;in, for One of the elements; For matrix The corresponding trapdoor; for One of the elements; It is a positive real number; For the set of integers 3D vector space; for One of the elements; for ; for One of the elements; Composed of integer elements OK, A set of matrices with columns; for One of the elements.

5. The quantum-resistant searchable inner product function encryption method as described in claim 1, characterized in that: In step S3, the central mechanism Computation of Left Lattice Basis Extension Algorithm Obtain the user key and user key Send to data users ;in, For one Elements in; For matrix The trapdoor.

6. The quantum-resistant searchable inner product function encryption method as described in claim 1, characterized in that: In step S9, a keyword is given. Data user DU runs the left sampling algorithm Random selection , Sampling according to Gaussian distribution , , Data user DU calculation , , and the trap door Send to the agent DD; where, for One of the elements; for One of the elements; for One of the elements; It is the set of m-order square matrices whose elements are only -1 or 1; for One of the elements; It is a discrete Gaussian distribution over an m-dimensional integer lattice; for Discrete Gaussian distribution over an integer lattice; To obey A short integer vector with a distribution; To obey A short integer vector with a distribution; for One of the elements; for One of the elements; for The transpose of the matrix; for The transpose of the matrix; For hash functions; for One of the elements; represent The binary form, .

7. A non-transitory machine-readable storage medium, characterized in that: It stores executable code that, when executed by the processor of an electronic device, causes the processor to perform the steps of the quantum-resistant searchable inner product function encryption method as described above.

8. A computer device, characterized in that: include: Memory, on which executable code is stored; A processor for executing the executable code, causing the computer device to perform the steps of the quantum-resistant searchable inner product function encryption method as described above.

Images