Research On The Key Technologies Of Fully Homomorphic Encryption In Cloud Computing

In recent years, with the rapid development of cloud computing technology, the security issues, especially the data security issue, becomes increasingly prominent, which has seriously hampered the development of cloud computing. With the character of ciphertext processing, the technology of fully homomorphic encryption can slove the data security issue in cloud computing, which can ensure the error-free data processing on ciphertext without the private key in the cloud, and the result of the processed ciphertext can be decrypted by the user correctly, and is just equal to the result of the plaintext processing. Because fully homomorphic encryption over the integers has the advantage of conceptual simplicity, and it is also easy to understand, DGHV scheme is chosen as the base of our research. It will be studied intensively and improved.In this thesis, two problems in DGHV scheme are presented:firstly, the re-encryption process is too complex, and secondly, the public key is oversized, then, two improved schemes are proposed, which are designed to reduce the complexity and improve the efficiency. In addition, a cloud computing prototype system based on the homomorphic encryption is designed to show that how to apply the homomorphic encryption technology in cloud computing. The main contents of this thesis are shown as follows:(1) EDO-FHE scheme over the integers is proposed. This scheme is based on the encryption depth optimization. Firstly, the depth of the permitted circuits of the somewhat scheme is computed to infer a decision threshold; then, the given function is decomposed to some sub-functions, whose highest degree is the decision threshold; at last, the homomorphic calculation is applied directly inside every sub-function, but among the sub-functions, the re-encryption process is added to refresh the ciphers and reduce the noise. In those existing fully homomorphic encryption schemes over the integers, the given function is decomposed into bool circuits, and the re-encryption process can be added before every step. Therefore, EDO-FHE scheme will reduce the time of re-encryption process compared to those existing schemes. And then, it can reduce the time complexity and improve the efficiency of the FHE scheme.(2) A public key compression scheme (CS-FHE scheme) over the integers is proposed. Before applying the technology of twice square, the technology of twice combination is introduced, and then the size of the public key space is decreased to O(λ3.75). The idea of the technology of combination-square public key compression is presented as follows. Firstly, a given sequence of integers is combined pairwisely to generate a new sequence; and then the sequence is divided into two parts, two integers are chosen from each of them and taken a multiplication; at last, a new sequence of integers is gotten, which is used to encrypt. Thus, the CS-FHE scheme will decrease the size of the public key space, and reduce the space complexity and improve the efficiency of the scheme.(3) Finally, a data processing verification system based on homomorphic encryption is designed. It is based on a somewhat homomorphic encryption algorithm. It is shown that the ciphers can be processed directly, and the result of the cipher processing is just equal to the result of the plaintext processing. The system consists of three modules:data acquisition module, data processing module and the user terminal module respectively. The data acquisition module is responsible for collecting the data and homomorphic encryption of them; and the data processing should process the data in the cloud and send the result to the user terminal, finally, the user terminal module decryts the result and gets the plaintext. We show the data process of homomorphic encryption by collecting temperature data and calculating the average value of them in this system. The correctness of this system is also verified too.