Design And Reseatch On Fully Homomorphic Encryption Scheme Over The Integers

The coming of cloud computing and the Internet of things times has taken a lot of convenience to people. However, the threaten of its security is growing increasingly. The importance of cloud computing and the Internet of things security shows a gradually rising trend, which becomes an important factor to restrict the development of cloud computing and the Internet of things. It is a key issues of cloud computing and the Internet of things security that how to solve the cipher text index and processing, privacy protection and the copyright protection of digital products. While the fully homomorphic encryption algorithm becomes a very good method to solve this problem. Fully homomorphic encryption allows the user do operation on any encrypted data, which means that the specific operation on the corresponding ciphertext data is equivalent to the operation on the plaintext, and the decryption of the results is the desired result. The homogeneity allows the users do trusted computing to encrypted data on the untrusted terminal after they encrypt the information.But the research progress of fully homomorphic encryption algorithm just is at a standstill, and didn’t reach the "fully homomorphic encryption". In2009, based on ideal lattices, a kind of mathematical object, the IBM researcher, Craig Gentry constructed the first fully homomorphic encryption scheme, and proved that a bootstrappable homomorphic encryption can be changed into a fully homomorphic encryption. The significance of his groundbreaking research is really fundamentally solving fully homomorphic encryption, which makes the theory become a practical possibility. And the implementation of the homomorphic encryption can solve the problem of information security when data and its operation are delegated to the cloud providers or information interaction in the Internet of things. Because of the superiority of fully homomorphic encryption compared with traditional encryption methods, it can ensure the information security of cloud computing and the Internet of things. Based on the idea of Craig Gentry, the scientists around the world did lots of further research, but in fact, however, due to the complexity of the homomorphic encryption operation is too complicated and the cipher and the key length is too big, its operation efficiency is in a low level and can’t be used in practical application.For the improvement of the homomorphic encryption’s efficiency, this paper mainly do the work as follow:First, we analyzed the significance and current situation of the development of fully homomorphic encryption, and introduce the theory knowledge and application prospect of fully homomorphic encryption. Then we expounded the ideas of Gentry’s classic fully homomorphic encryption scheme, discussed its design thought and realization process, and analyzed emphatically implementation procedure, efficiency and security of this scheme by using the DGHV scheme as example. Last, based on the above analysis, by constructing a somewhat homomorphic encryption scheme, squashing the decryption circuit and bootstrapping, we put forward a fully homomorphic encryption scheme over the integers, proved its homomorphism and security, and analyzed its efficiency. Compared with the original plans, it has certain advantages in public key size and calculation efficiency. The size of somewhat homomorphic encryption scheme’s public key is O(λ7), the degree of augmented decryption circuits’ polynomial is about64A log2λ, which is better than DGHV scheme. Instead of processing1bit information per time, it can process4bit information at a time, which speeds up the processing speed of the algorithm, and improves the efficiency of the scheme.