Inner product encryption method, device and system based on GR-LWE problem

Abstract

The invention discloses an inner product encryption method, device and system based on a GR-LWE problem, and belongs to the technical field of information encryption, and the method comprises the following steps: generating a main public key and a corresponding main private key based on a dihedral non-exchangeable group ring and preset security parameters; obtaining vector data used for decryption, and carrying out operation on the vector data and the main private key to generate a decryption key used for decryption operation; vector data to be encrypted and plaintext data to be encrypted are obtained and are operated with the public key part in the main public key to generate a ciphertext; and a decryption key is used for carrying out decryption operation on the ciphertext, and when and only when the inner product result of the vector data for decryption and the vector data to be encrypted is 0, correct plaintext data can be obtained. According to the invention, an inner product encryption scheme is expanded to the dihedral non-exchangeable group ring, so that the security of the encryption scheme is improved, and long-term security guarantee is provided for resisting quantum computer attacks.

Description

Technical Field

[0001] The present invention relates to an inner product encryption method, device and system based on the GR-LWE problem, and belongs to the technical field of information encryption. Background Art

[0002] With the emergence of complex networks and cloud computing, researchers have proposed cryptographic schemes with various characteristics to address security issues arising in these more complex environments. Inner product encryption is a generalization of identity-based encryption and attribute-based encryption. In an inner product encryption system, each ciphertext is compared with the vector and each secret key is associated with the vector If and only if Inner product encryption has many useful applications. For example, it can support subset, conjunction and range queries of encrypted data and polynomial evaluation.

[0003] It is well known that lattice cryptography is more resistant to quantum attacks than traditional cryptography. In 2011, Agrawal et al. proposed the first lattice-based inner product encryption scheme, which was based on the learning with errors (LWE) problem. Subsequently, lattice-based inner product encryption schemes have been widely proposed. However, most inner product encryption schemes based on the error-tolerant learning problem suffer from the problem of excessively large key sizes or small message spaces.

[0004] In order to achieve higher computational efficiency and higher security, Fang et al. proposed an improved solution based on the Ring Learning with Errors (RLWE) problem. However, the security of the solution based on the Ring Learning with Errors problem is based on the conjecture problem on the ideal lattice rather than on the general lattice. However, there may be more efficient algorithms for solving the ideal lattice problem of algebraic integer rings than for general lattice problems. For example, Cramer and Ducas et al. gave an approximate factor for solving the principal ideal lattice of the cyclotomic number field as The proposed method is to approximate the SVP problem. Related attacks exploit the commutative structure of algebraic integer rings and other properties. Therefore, the present invention proposes an inner product encryption method based on the GR-LWE problem. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes an inner product encryption method, device and system based on the GR-LWE problem.

[0006] The technical solution adopted by the present invention to solve the technical problem is: In a first aspect, an embodiment of the present invention provides an inner product encryption method based on the GR-LWE problem, comprising the following steps: Step 1: Generate a master public key and a corresponding master private key based on a dihedral non-commutative ring group and preset security parameters. The master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations. Step 2: Obtain vector data for decryption, and perform a calculation on the vector data with the master private key to generate a decryption key for decryption operation; Step 3: Obtain the vector data and plaintext data to be encrypted, and perform a calculation on them with the public key portion of the master public key to generate ciphertext; Step 4: Use the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

[0007] As a possible implementation of this embodiment, step 1 includes: Initialize the operating environment of the key generation center and enter a security parameter and a parameter , is a set of integers, is the dimension of the correlation vector; Run the trapdoor generation algorithm TrapGen to generate vectors and the trapdoor associated with it ,in and are the dimension parameters of the lattice space, is a group ring, q is the modulus; is the trapdoor matrix on the group ring; Pick uniformly random vectors ,in is the number of bits of binary decomposition of the attribute element; and selects a uniform random element ; Output master public key and the master private key .

[0008] As a possible implementation of this embodiment, step 2 includes: Enter the master public key , Master Private Key and vector ; set up The binary decomposition of is: in }; Defining a vector and vector ; calculate ,in , Gaussian distribution parameters; Output decryption key .

[0009] As a possible implementation of this embodiment, step 3 includes: Master public key ,information and vector ; Select a uniform random vector and a uniform random element ; sampling ,in express The upper deviation is Gaussian distribution, Gaussian distribution parameters; calculate ; Select a uniform random matrix ,calculate ; calculate ; Output ciphertext .

[0010] As a possible implementation of this embodiment, step 4 includes: Enter the master public key , decryption key and ciphertext ,calculate ; make , output message .

[0011] In a second aspect, an embodiment of the present invention provides an inner product encryption device based on the GR-LWE problem, comprising: an initialization module, which generates a master public key and a corresponding master private key based on the dihedral non-commutative group ring and preset security parameters, wherein the master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations; A key generation module, which obtains vector data for decryption and performs a calculation on the vector data with the master private key to generate a decryption key for the decryption operation; An encryption module, which obtains the vector data and plaintext data to be encrypted, and performs operations on the vector data and the public key portion of the master public key to generate ciphertext; The decryption module uses the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

[0012] In a third aspect, an embodiment of the present invention provides an inner product encryption system based on the GR-LWE problem, which implements the inner product encryption function by constructing the GR-LWE problem based on a dihedral non-commutative group ring. The system includes a key generation center, a sender, and a receiver. The key generation center performs the operation environment initialization and key generation algorithm to generate the master public key, the master private key and the decryption key; The sender performs an encryption operation on the message based on the master public key to generate a ciphertext; The receiver performs a decryption operation on the ciphertext based on the master public key and the decryption key to obtain a plaintext message.

[0013] As a possible implementation of this embodiment, the process of the key generation center generating the master public key, the master private key, and the decryption key is as follows: Enter a security parameter and a parameter , is a set of integers, through Algorithm generates vectors and trapdoor ,Pick uniform random vector and uniform random elements , output the master public key and the master private key ,in, , ; Enter the master public key , Master Private Key and vector ,Will The binary decomposition of , construct vector and the concatenated vector , calculated by the SampleLeft algorithm satisfy , output the decryption key .

[0014] As a possible implementation of this embodiment, the process of the sender generating the ciphertext is as follows: Enter the master public key ,information and vector , select a random vector and elements , sampled Gaussian noise ,calculate ; calculate

[0015] calculate , and output the ciphertext .

[0016] As a possible implementation of this embodiment, the process for the receiver to obtain the plaintext message is as follows: Enter the master public key , decryption key and ciphertext ,calculate ; structure , output plaintext message .

[0017] The technical solution of the embodiment of the present invention can have the following beneficial effects: The present invention extends the inner product encryption scheme to dihedral non-commutative group rings, and utilizes the structural characteristics of non-commutative group rings to effectively resist the current attack algorithms against the ideal lattice of algebraic integer rings, especially attacks utilizing the commutative structure of algebraic integer rings, thereby improving the security of the encryption scheme; the present invention's solution based on the GR-LWE problem inherits the quantum resistance of lattice cryptography, providing long-term security protection against quantum computer attacks; the present invention maintains the efficient computing characteristics of the ring structure, and compared with the inner product encryption scheme based on general lattices, has higher computing efficiency in the key generation, encryption and decryption processes, and is suitable for practical application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of an inner product encryption method based on the GR-LWE problem according to an exemplary embodiment; Figure 2 is a schematic diagram showing an inner product encryption device based on the GR-LWE problem according to an exemplary embodiment; Figure 3 The present invention is a flowchart showing an inner product encryption system based on the GR-LWE problem according to an exemplary embodiment for realizing an inner product encryption function. DETAILED DESCRIPTION

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments: In order to clearly illustrate the technical features of this solution, the present invention is described in detail below through specific implementation methods and in conjunction with the accompanying drawings. The disclosure below provides many different embodiments or examples for realizing different structures of the present invention. In order to simplify the disclosure of the present invention, the components and settings of specific examples are described below. In addition, the present invention may repeat reference numbers and / or letters in different examples. This repetition is for the purpose of simplicity and clarity and does not itself indicate the relationship between the various embodiments and / or settings discussed. It should be noted that the components illustrated in the accompanying drawings are not necessarily drawn to scale. The present invention omits descriptions of well-known components and processing technologies and processes to avoid unnecessary limitations on the present invention.

[0020] To maintain the efficiency of the ring structure while resisting attacks on the difficult problem of ideal lattices of algebraic integer rings, this paper considers using group rings to construct the Group Ring Learning with Errors (GR-LWE) problem, particularly when the underlying group is non-commutative. Based on the GR-LWE problem, this paper proposes an inner product encryption scheme that maintains the efficiency of previous lattice schemes while resisting currently proposed attack algorithms on ideal lattices of algebraic integer rings, offering enhanced security.

[0021] This invention provides an inner product encryption scheme based on GR-LWE, which is based on a dihedral non-commutative group ring. The scheme includes four algorithms: initialization, key generation, encryption, and decryption. The scheme includes a key generation center, a sender, and a receiver.

[0022] Definition of group ring and dihedral group. Group ring: given a finite group and commutative rings , group ring The elements in are the form and , n is the order of the group. Dihedral group: a order dihedral group, using Represents a set ,satisfy Then there is , Right now , which has the property of being non-commutative.

[0023] Non-commutative group ring LWE problem: given a dihedral group , construct group ring ,in, is the modulus, It's a model Finite field. Given a vector Real numbers , and vector ,in represents the dimension of the vector, For uniform distribution, express The upper deviation is The search problem instance is given as and , find out the secret . Determine the problem instance as given and ,Will and from In the uniform distribution Distinguish them.

[0024] Based on the proposed non-commutative group ring LWE problem, function-rich cryptographic applications can be constructed. The present invention provides an inner product encryption scheme based on the non-commutative group ring LWE problem.

[0025] Example 1 like Figure 1 As shown, an inner product encryption method based on the GR-LWE problem provided by an embodiment of the present invention includes the following steps: Step 1: Generate a master public key and a corresponding master private key based on a dihedral non-commutative ring group and preset security parameters. The master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations. Step 2: Obtain vector data for decryption, and perform a calculation on the vector data with the master private key to generate a decryption key for decryption operation; Step 3: Obtain the vector data and plaintext data to be encrypted, and perform a calculation on them with the public key portion of the master public key to generate ciphertext; Step 4: Use the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

[0026] As a possible implementation of this embodiment, step 1 includes: Initialize the operating environment of the key generation center and enter a security parameter and a parameter , is a set of integers, is the dimension of the correlation vector; Run the trapdoor generation algorithm TrapGen to generate vectors and the trapdoor associated with it ,in and are the dimension parameters of the lattice space, is a group ring, q is the modulus; is the trapdoor matrix on the group ring; Pick uniformly random vectors ,in is the number of bits of binary decomposition of the attribute element; and selects a uniform random element ; Output master public key and the master private key .

[0027] As a possible implementation of this embodiment, step 2 includes: Enter the master public key , Master Private Key and vector ; set up The binary decomposition of is: in }; Defining a vector and vector ; calculate ,in , Gaussian distribution parameters; Output decryption key .

[0028] As a possible implementation of this embodiment, step 3 includes: Master public key ,information and vector ; Select a uniform random vector and a uniform random element ; sampling ,in express The upper deviation is Gaussian distribution; calculate ; Select a uniform random matrix ,calculate ; calculate ; Output ciphertext .

[0029] As a possible implementation of this embodiment, step 4 includes: Enter the master public key , decryption key and ciphertext ,calculate ; make , output message .

[0030] This paper extends the inner product encryption scheme to dihedral noncommutative group rings, proposing an inner product encryption method based on GR-LWE. This method provides long-term security and is currently believed to be resistant to attacks by quantum computers. Furthermore, the use of noncommutative group rings makes this method resistant to currently proposed attack algorithms on ideal lattices of algebraic integer rings, making the inner product encryption method even more secure.

[0031] Example 2 like Figure 2 As shown, an inner product encryption device based on the GR-LWE problem provided by an embodiment of the present invention includes: an initialization module, which generates a master public key and a corresponding master private key based on the dihedral non-commutative group ring and preset security parameters, wherein the master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations; A key generation module, which obtains vector data for decryption and performs a calculation on the vector data with the master private key to generate a decryption key for the decryption operation; An encryption module, which obtains the vector data and plaintext data to be encrypted, and performs operations on the vector data and the public key portion of the master public key to generate ciphertext; The decryption module uses the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

[0032] It should be noted that the above modules in this embodiment correspond to the steps described in Example 1, and the examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the contents disclosed in the above Example 1.

[0033] Example 3 An embodiment of the present invention provides an inner product encryption system based on the GR-LWE problem, which implements the inner product encryption function by constructing the GR-LWE problem based on a dihedral non-commutative group ring. The system includes a key generation center, a sender, and a receiver. The key generation center performs the operation environment initialization and key generation algorithm to generate the master public key, the master private key and the decryption key; The sender performs an encryption operation on the message based on the master public key to generate a ciphertext; The receiver performs a decryption operation on the ciphertext based on the master public key and the decryption key to obtain a plaintext message.

[0034] As a possible implementation of this embodiment, the process of the key generation center generating the master public key, the master private key, and the decryption key is as follows: Enter a security parameter and a parameter ,pass Algorithm generates vectors and trapdoor ,Pick uniform random vector and uniform random elements , output the master public key and the master private key ,in, , ; Enter the master public key , Master Private Key and vector ,Will The binary decomposition of , construct vector and the concatenated vector , calculated by the SampleLeft algorithm satisfy , output the decryption key .

[0035] As a possible implementation of this embodiment, the process of the sender generating the ciphertext is as follows: Enter the master public key ,information and vector , select a random vector and elements , sampled Gaussian noise ,calculate ; calculate

[0036] calculate , and output the ciphertext .

[0037] As a possible implementation of this embodiment, the process for the receiver to obtain the plaintext message is as follows: Enter the master public key , decryption key and ciphertext ,calculate ; structure , output plaintext message .

[0038] like Figure 3 As shown, the inner product encryption system based on the GR-LWE problem of the present invention constructs the GR-LWE problem based on the dihedral non-commutative group ring to perform inner product encryption. The specific process includes the following steps: Step 1: The key generation center initializes the operating environment and generates the master public key and master private key.

[0039] Enter a security parameter and a parameter , do the following: Run Algorithm, generate vector and the trapdoor associated with it , superscript and All the parameters are known. uniformly random vectors ,in and . Select a uniform random element . Output the master public key and the master private key .

[0040] Step 2: The key generation center generates the receiver's decryption key.

[0041] Enter the master public key , Master Private Key and vector , do the following: for ,set up The binary decomposition of is: in }; Defining a vector and vector ; calculate ,in . Output decryption key .

[0042] Step 3: The sender performs the encryption operation. The sender enters the master public key ,information and vector , select a uniform random vector and a uniform random element .sampling ,in express The upper deviation is Gaussian distribution of . Calculate .for and Do the following: Select a uniform random matrix ,calculate .calculate Output ciphertext .

[0043] Step 4: The receiver decrypts the message.

[0044] Enter the master public key , decryption key and ciphertext ,calculate ;make , output message .

[0045] By designing specific key generation, data encryption, and decryption steps, this invention allows conditional decryption based on mathematical relationships while protecting data privacy, thus achieving conditional access control. Decryption succeeds only when the inner product of the encrypted data and the vector corresponding to the key is 0; otherwise, decryption fails, and no additional information is leaked.

[0046] 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 it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. An inner product encryption method based on the GR-LWE problem, characterized in that: The following steps are involved: Step 1: Generate a master public key and a corresponding master private key based on a dihedral non-commutative ring group and preset security parameters. The master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations. Step 2: Obtain vector data for decryption, and perform a calculation on the vector data with the master private key to generate a decryption key for decryption operation; Step 3: Obtain the vector data and plaintext data to be encrypted, and perform a calculation on them with the public key portion of the master public key to generate ciphertext; Step 4: Use the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

2. The inner product encryption method based on the GR-LWE problem according to claim 1 is characterized in that: The step 1 comprises: Initialize the operating environment of the key generation center and enter a security parameter and a parameter , is a set of integers, is the dimension of the correlation vector; Run the trapdoor generation algorithm TrapGen to generate vectors and the trapdoor associated with it ,in and are the dimension parameters of the lattice space, is a group ring, q is the modulus; is the trapdoor matrix on the group ring; Pick uniformly random vectors ,in , , is the number of bits of binary decomposition of the attribute element; and selects a uniform random element ; Output master public key and the master private key .

3. The inner product encryption method based on the GR-LWE problem according to claim 2, characterized in that: The step 2 comprises: Enter the master public key , Master Private Key and vector ; set up The binary decomposition of is: in }; Defining a vector and vector ; calculate ,in , Gaussian distribution parameters; Output decryption key .

4. The inner product encryption method based on the GR-LWE problem according to claim 3 is characterized in that: The step 3 comprises: Enter the master public key ,information and vector ; Select a uniform random vector and a uniform random element ; sampling ,in express The upper deviation is Gaussian distribution, Gaussian distribution parameters; calculate ; Select a uniform random matrix ,calculate ; calculate ; Output ciphertext .

5. The inner product encryption method based on the GR-LWE problem according to claim 4 is characterized in that: The step 4 comprises: Enter the master public key , decryption key and ciphertext ,calculate ; make , output message .

6. An inner product encryption device based on the GR-LWE problem, characterized in that: include: an initialization module, which generates a master public key and a corresponding master private key based on the dihedral non-commutative group ring and preset security parameters, wherein the master public key includes a public key portion used for subsequent encryption operations, and the master private key is used to generate a decryption key, wherein the decryption key includes a decryption key portion used for decryption operations; A key generation module, which obtains vector data for decryption and performs a calculation on the vector data with the master private key to generate a decryption key for the decryption operation; An encryption module, which obtains the vector data and plaintext data to be encrypted, and performs operations on the vector data and the public key portion of the master public key to generate ciphertext; The decryption module uses the decryption key to perform a decryption operation on the ciphertext. The correct plaintext data can be obtained only when the inner product result of the vector data used for decryption and the vector data to be encrypted is 0.

7. An inner product encryption system based on the GR-LWE problem, characterized in that: Based on the dihedral non-commutative group ring, the GR-LWE problem is constructed to realize the inner product encryption function. The system includes a key generation center, a sender and a receiver. The key generation center performs the operation environment initialization and key generation algorithm to generate the master public key, the master private key and the decryption key; The sender performs an encryption operation on the message based on the master public key to generate a ciphertext; The receiver performs a decryption operation on the ciphertext based on the master public key and the decryption key to obtain a plaintext message.

8. The inner product encryption system based on the GR-LWE problem according to claim 7, characterized in that: The process of generating the master public key, master private key and decryption key by the key generation center is as follows: Enter a security parameter and a parameter , is a set of integers, through Algorithm generates vectors and trapdoor ,Pick uniform random vector and uniform random elements , output the master public key and the master private key ,in, , ; Enter the master public key , Master Private Key and vector ,Will The binary decomposition of , construct vector and the concatenated vector , calculated by the SampleLeft algorithm satisfy , output the decryption key .

9. The inner product encryption system based on the GR-LWE problem according to claim 8, characterized in that: The process of the sender generating ciphertext is as follows: Enter the master public key ,information and vector , select a random vector and elements , sampled Gaussian noise ,calculate ; calculate ; calculate , and output the ciphertext .

10. The inner product encryption system based on the GR-LWE problem according to claim 9, characterized in that: The process for the receiver to obtain the plaintext message is as follows: Enter the master public key , decryption key and ciphertext ,calculate ; structure , output plaintext message .

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