Full Homomorphic Encryption Scheme And Its Application Of Finite Prime Field

With the development of information technology, on the one hand, people grad-ually realize the importance of information security, and also pay more and moreattention to privacy information. On the other hand, along with the developmentof technology. In order to achieve more efcient, more convenient, the way of in-formation storage has been gradually changed into the way of centralized storage.A practical question is how to implement trusted storage on untrusted third party.Fully homomorphic encryption has the following property: The result of operatingcipertexts is the ciphertext of the result of operating plaintext. So the problem canbe solved by fully homomorphic encryption.Although fully homomorphic encryption was put forward early, it has beenlittle progress. Until2009, the frst one was presented by Gentry, which bring it intothe new era. This paper is mainly on the research of fully homomorphic encryptionover fnite prime feld and its application. Specifc work is as follows:1.This paper introduces the key technology of fully homomorphic encryption,and the technology of decryption circuit compression, recrypt technology and secu-rity were analyzed and studied systematically.2.The existing fully homomorphic encryption scheme based on integers is intro-duced. For the problem of plaintext space is too small, respectively put forward twofully homomorphic encryption schemes whose plaintext spaces are fnite prime feldFpand n dimensional vector space Fn2over F2. Base on the two schemes, a fullyhomomorphic encryption scheme whose plaintext space is Fnpis proposed. In addi-tion to our scheme and original schemes are analyzed and compared, the ciphertextof the proposed scheme is quite small in this paper, and the time of encryption anddecryption is short.3.This paper presents a fully homomorphic encryption scheme on matrix overfnite prime feld Fp. Apply to image encryption, and put forward a fully homomor-phic encryption scheme which is suitable for image encryption. With secret elementsdiscard processing method, a fast fully homomorphic encryption scheme on matrixis put forward. Finally the fully homomorphic encryption of the image is on thedisplay.