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A technology of fully homomorphic encryption and matrix addition, applied in secure communication devices, digital transmission systems, electrical components, etc., can solve problems such as impracticality and slow speed
Inactive Publication Date: 2013-08-21
SUZHOU UNIV
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In 2011, payman used a partial homomorphic encryption algorithm to encrypt matrix elements in the document "Efficient and Secure Delegation of Linear Algebra" to achieve matrix homomorphism.
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Embodiment 1
[0048] 1. Initialization module: the user specifies the dimension of the key to be generated , Select the key space and matrix element value range, and generate the required key through the key generator.
[0049] The specific steps are as follows:
[0050] (1) User input dimension , select the keyspace and the range of element values in the matrix . see figure 2 As shown, the parameters input in Figure 21 are , where G indicates that the key space is .
[0051] (2) Key generator generate key : Includes random integer invertible matrix generator and matrix invertor . The key generation details are as follows:
[0052] a) Generate an invertible matrix : Dimensions of the given matrix , the keyspace and an invertible matrix range of element values in , using a random integer invertible matrix generator to generate an integer invertible matrix , . see figure 2 As shown, 22 in the figure is the generated invertible matrix.
[0053] ...
Embodiment 2
[0073] 1. Initialization module: the user specifies the dimension of the key to be generated , Select the key space and matrix element value range, and generate the required key through the key generator.
[0074] The specific steps are as follows:
[0075] (1) User input dimension , select the keyspace and the range of element values in the matrix . see image 3 As shown, the parameters input in 31 in the figure are ,in I represents the keyspace and .
[0076] (2) Key generator Generate key: Includes random integer invertible matrix generator and matrix invertor . The key generation details are as follows:
[0077] a) Generate an invertible matrix : Dimensions of the given matrix , the keyspace and an invertible matrix range of element values in , using a random integer invertible matrix generator to generate an integer invertible matrix , . see image 3 As shown, 32 in the figure is the generated invertible matrix.
[0078] b) find...
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Abstract
The invention discloses a matrix fully homomorphic encryption method. The matrix fully homomorphic encryption method comprises an initialization module, an encryption module, a decryption module and a matrix fully homomorphic module. The initialization module is used for generating secret keys needed by encryption and decryption according to dimensions of matrices to be encrypted, encryption types and ranges of matrix element values. The encryption module is used for utilizing encryption algorithms and the secret keys to conduct encryption on plaintext matrices and outputting ciphertext matrices according to the given plaintext matrices. The decryption module is used for utilizing the secret keys and decryption algorithms to conduct decryption on ciphertext matrices and outputting the plaintext matrices according to the given ciphertext matrices. According to the matrix fully homomorphic module, additive operation and multiplying operation of the matrices meet homomorphic properties of the matrices, output generated by the additive operation and the multiplying operation of the matrices still meets the homomorphic properties, namely, fully homomorphic properties of the matrices are met. The matrix fully homomorphic encryption method has the advantages of meeting safety requirements, meeting fully homomorphic requirements of the matrices and remarkably increasing the operating rate of the ciphertext matrices.
Description
technical field [0001] The invention relates to a homomorphic encryption algorithm, in particular to a matrix fully homomorphic encryption algorithm. Background technique [0002] The advantage of the openness of the Internet is that it facilitates our lives, but the biggest disadvantage is that the security of private information in the network is seriously threatened. Therefore, network security has attracted more and more attention in recent years. There are many security methods to protect private information, one of which is to encrypt information. At present, the commonly used methods are symmetric key encryption algorithm and public key encryption algorithm. For example, symmetric key encryption algorithms include DES, AES, etc. Key encryption algorithms include RSA, ECC, IBE, etc. The purpose of designing this type of algorithm is only to protect the security of information, that is, it only encrypts plaintext information, but ciphertext usually cannot be used for c...
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