Batch Homomorphic Encryption Scheme Based On RLWE

In the development of big data and distributed cloud environment,storage methods are also accompanied by technological innovation,from local storage to cloud storage,from local operation and maintenance to third-party hosting.Changes in storage methods affect the development of technology.Using the characteristics of ciphertext operations can solve the confidentiality and privacy protection of user data.After recent years of development,the homomorphic technology has developed from an ideal solution to real applications.Among them,the linear error learning solution based on the loop is the most widely used in the same type.Although the homomorphic scheme has advantages in storage properties,the scheme is limited by the complexity of calculations,the number of calculations,and noise interference;in the research and development,the calculation complexity has been reduced to the order of low exponents,and the noise has been carried out in the circuit layer through analog-to-digital conversion.Control,but the scheme is relatively shallow in the optimization of transmission efficiency.For this reason,establishing a new transmission system and optimizing the magnitude of the transmission efficiency of the scheme is the main research direction of this scheme.In order to increase the batch concurrency,we need to construct a new mapping method This paper proposes a batch processing fully homomorphic encryption scheme based on linear error learning on the ring.main tasks as follows.1.It is necessary to construct a several-for-one mapping relationship for the batch scheme to realize batch processing;based on this idea,it starts from the isomorphic mapping domain and uses integer coding to realize the plaintext from the integer domain to the polynomial.Since the plaintext and ciphertext are all in the ring structure,the plaintext polynomial domain is converted to the cyclic polynomial domain,and then the cyclotomic polynomial properties and the optimized recursive remainder theorem are used to construct a several-for-one mapping relationship to realize the batch processing.2.It constructs a ciphertext update algorithm suitable for batch processing based on the re-linearization algorithm and modular conversion algorithm in Fan and Vercauteren's scheme to expand the scheme from partial homomorphism to full homomorphism;The algorithm uses the re-linearization key to reduce the dimensionality of the product ciphertext in the batch process,uses the modular conversion algorithm to optimize the ciphertext noise at the same level,and then optimizes the homomorphic operation steps of the scheme.3.This paper conducts a proof analysis from the three aspects of scheme homomorphism,decryption correctness and scheme feasibility proof to verify the feasibility of the proposed batch processing scheme;The correctness is proved from homomorphic addition and multiplication respectively to ensure that the ciphertext operation is decrypted during the calculation process of the scheme.in order to ensure the correctness of the decryption,the ciphertext is decrypted and verified by the key,and the ciphertext noise after decryption is evaluated;finally,This article verifies that the program is CPA safe.4.Combined with the analysis of the difficulty of RLWE and the selected attack strategy,the parameter selection under the security level is determined.Furthermore,it determined the relationship between the minimum multiplication depth and the fully homomorphic depend on the maximum multiplication depth and model security analysis;Except for a comparative analysis of the efficiency of batch processing schemes is given.In this paper,the efficiency of the scheme is improved and the homomorphism is extended.It can not only be applied to the privacy and security issues of cloud servers:secure execution of confidential programs on third-party servers,ciphertext retrieval based on privacy protection,and secure update of outsourced data Wait;But can also be widely used in a variety of practical application scenarios such as protecting genomics genetic data,strengthening national security infrastructure data protection,and preventing the leakage of sensitive data and control commands in control systems.