Research On Fully Homomorphic Encryption Over The Integers

Fully homomorphic encryption system allows arbitrary operation to be carried out on encryped data, and the decryption of the result equals the result of the same operation on plaintext. Since the first concept of fully homomorphic encryption has been put forward more than 30 years ago, there has been a mass of attempts to develop the system. Finally in2009 Gentry achieved the fully homomorphic encryption system using ideal lattice, which greatly stimulates the research enthusiasm of cryptology. Especially with the rapid development of cloud computing, the speciality of operation on encrypted data makes homomorphic encryption scheme stand out and have unparalleled advantage comparing with traditional encryption scheme. This speciality makes homomorphic encryption have broad application prospects on multi-party computation, encryption spam filtering,commissioned storage of encrypted data, indexing and query of encrypted data besides cloud computing.This paper mainly studies the fully homomorphic encryption over the integers, whose specific work are as follows:(1)Based on Error-Free approximate GCD problem, a leveled fully homomorphic scheme using approximate eigenvector method and ciphertext flattening operation is proposed, which can achieve leveled fully homomorphic scheme without squashing decryption circuit and makes the public key size reduce from ( )13O%l to ( )10O%l. Then we compare two schemes in theory.(2)Using the method of increasing dimension in order to reduce the number, we improve the BDGHV scheme and present a shorter public key size BDGHV scheme, called SPB scheme. Compared to BDGHV scheme, the public size of SPB scheme reduces from( )8O%l to ( )6.5O%l. Then we analyze the correctness and security of SPB scheme. At last we compare two schemes.(3)We give the detailed realization of fully homomorphic encryption scheme over the integers including DGHV scheme, BDGHV scheme and SPB scheme. Then we compare those schemes. Finally we put forward an electronic voting application of SPB scheme, and this application verifies the availability of fully homomorphic encryption. All of those simulation use the Crypto++ library, GMP library and GNU g++ compiler on the ubuntu...