A Fully Homomorphic Encryption System That Supports Multi-bit And Multi-key Encryption

In recent years,with the development of cloud computing technology,users store more and more data on cloud servers,which also increases the risk of data leakage,which brings great challenges to cloud computing,how to safely calculate these data has become a hot research topic.The full homomorphic encryption provides a good solution to above the problems.The full homomorphic encryption is a special kind of encryption scheme.One of its remarkable features is that it allows anyone to calculate the ciphertext directly,and the decryption result is equal to that of the plaintext,avoiding the risk of data leakage.However,most traditional full holomorphic encryption scheme only support the single-bit and single-key case,that is,only one bit information can be encrypted at a time and the objects of homomorphic operation are limited to ciphertext encrypted under the same key.Compared with single-bit and single-key full homomorphic encryption,multi-key full homomorphic encryption is more practical.Multi-key full homomorphic encryption can encrypt multiple bits at a time and enable ciphertext encrypted under different public keys to carry out homomorphic operation.In this paper,we design a full homomorphic encryption scheme to support multi-key and multi-bit encryption.The main work is as follows:(1)The traditional full homomorphic encryption scheme is based on the CRS model,which to some extent weakens the ability of each user to generate public keys independently.In this paper,we first design a multi-bit homomorphic encryption scheme without CRS model.This scheme is based on a DLWE homomorphic encryption scheme which supports multi-bit encryption security proposed by Li Zengpeng et al.,by modifying its key generation algorithm,it becomes a multi-bit homomorphic encryption scheme without CRS model.The public key generation of the scheme does not need to use the common matrix,and only needs to be randomly selected by each user.(2)Then,the single key ciphertext in the above scheme is extended to multi-key ciphertext by using Link algorithm,so as to realize multi-key fully homomorphic encryption(MFHE)scheme.Multi-key full homomorphic encryption allows homomorphic operations between ciphertexts encrypted with different keys,and ultimately achieves multi-bit and multi-key full homomorphic encryption(MMFHE)scheme.