Design And Research Of LWE-based Multi-bits Homomorphic Encryption

With the development of cloud computing technology and the increasing popularity, in manyapplication scenarios it needs to submit data to the "cloud", in order to make full use of its strongdata processing ability. However, in the traditional model, it requires users to submit data by theplaintext, which brought the serious security hidden danger to the safety of user data. Therefore thecryptographer put forward the so-called homomorphic encryption (HE) concept, which can berealized in a secure way to outsource data to the third party for processing, and will not pose a threatto the security of user data.Since the homomorphic encryption was proposed, it has always been full of internal andexternal scholars, especially in2009, Gentry proposed the first fully homomorphic encryptionscheme, which opened up a new era of fully homomorphic encryption.Since then, by Gentry’sstructural model, researchers design a lot of fully homomorphic encryption algorithms.According to the research results of fully homomorphic encryption as well as the problems, theencryption scheme is structured by the extensive research of the improved method。Specificpractices are as follows: The research on fully homomorphic encryption has been transferred towhat is based on LWE; In order to improve the efficiency of homomorphic operation, people beginto adopt the method of encrypting multiple bits, which improves the efficiency of homomorphicoperation to a certain extent; Gentry’s first fully homomorphic encryption scheme provides ageneral method for constructing FHE, and with the in-depth study, it appears that the structure ofFHE scheme can not adopt the construction pattern of Gentry, namely constructing a level fullyhomomorphic scheme without bootstrapping.The main target is in order to improve the fully homomorphic encryption algorithm’s runningefficiency in this paper. In view of the current status of fully homomorphic encryption algorithm forsingle bit encryption, by introducing multi bit encryption thought as well as the tensor productoptimization technique and truncating vector technique, we construct a multi bit optimization fullyhomomorphic encryption scheme based on LWE. Compared with the existing algorithms, theefficiency has been improved significantly. The specific work is as follows:By adopting the thought of multi bits encryption, we propose a new public fully homomorphicencryption scheme based on Regev scheme in this paper. Compared with the previous fullyhomomorphic scheme, the plaintext space of this scheme is, which can encrypt a plaintextbits vector, not a single bit as before. Meanwhile, by truncating the least significant bits from every element of the ciphertext vector and optimization in the tensor product, we can further improve theefficiency of the encryption scheme significantly: the efficiency can be improved about40%-60%compared with that in original one.