| The appearance of the fully homomorphic encryption (FHE) has significant senses on thedevelopment of computer science and technology, and some authoritative scholars even believe thatFHE will be the savior of cloud computing. FHE has the advantageous properties of performingcomplicated processing on ciphertext directly without being decrypted. In the other words, forarbitrarily computation on the ciphertext, the decryption result of it is the same as computation on theplaintext directly. Thus, there are a lot of applications of FHE technology, e.g. cloud computing,electronic voting, multi-party communication and etc. The fully homomorphic encryption schemeproposed recently are constructed in accordance with Gentry’s FHE technique. However, theefficiency of the present FHE scheme is extra low and far from practical application. How to improvethe efficiency and security of fully homomorphic encryption become the focus and pitfall of academicresearch.This thesis firstly introduce the background, related work, applications and main problems ofFHE scheme in detail, and give a briefly introduction to Gentry’s FHE technique. Then combinedwith Gentry’s homomorphic encryption technique, we introduce a FHE scheme over the integer whichwas proposed by Dijk and Gentry et al. And we analyze and prove the security of the scheme.This paper proposes an improved fully homomorphic encryption scheme aimed at increaseingthe efficiency of FHE scheme, which is based on Gentry’s FHE technique too. The improved schemecan encrypt2bit plaintext each time and at same time reduce the public key size by employingJean-Sebastien’s technique, accordingly the improved scheme is more efficient than Dijk’s schemeand has smaller public key size. The public key size of the proposed scheme is (7), while Dijk’sscheme’s is (10).Finally, we analyze the security of the proposed scheme is based on two hardproblem, i.e the error-free approximate greatest common divisor problem and sparse subset sumproblem. |
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