Research Of Homomorphic Cryptographic Algorithm With Provable Security

With the rapid development of Internet technology,the importance to protect personal privacy has been increasingly highlighted.A very important means to protect the privacy of personal information is encrypting sensitive personal information.Traditional encryption technology can't evaluate ciphertext.If ciphertexts are calculated,we get data with no significance.Homomorphic encryption can evaluate ciphertexts.We can get corresponding plaintext result,after the evaluated ciphertext decrypted.In this way,users'personal information can be protected through encryption.At the same time,the evaluation process could be left to the third party,which doesn't need to be trusted.Provable security is a very important means to estimate the security of public-key encryption scheme.At present,cryptographers proposed many fully homomorphic encryption schemes,however,most of which without strict security proof.Therefore,the main work of this paper is research of homomorphic cryptographic algorithm with provable security.The main work is as follows:Firstly,a highly efficient fully homomorphic encryption scheme with shorter public keys is presented.According to Gentry's thought,the DGHV scheme is improved by changing integer selection mode and modulus.The scheme in this paper can encrypt k bits once,which is based on the same difficult problem with original scheme,keeping the same security.The public key size is reduced fromO?4?(?¹⁰)to O?4???⁷?.Secondly,an additive homomorphic encryption scheme based on LWE is presented.The homomorphic encryption schemes based on lattice are studied,and the existing schemes with Learning with Errors are introduced,such as BV11b,BGV12,13GSW.The methods of building those schemes are analyzed deeply.Based on this,the reduction between AGCD and LWE is studied,and an additive homomorphic public key encryption scheme with IND-CPA security is proposed.The security of the scheme does not depend on the assumption difficulty of SSSP,but relies on the difficulty of LWE problem.Finally,a fully homomorphic encryption scheme based on NTRU is proposed in this paper.NTRU and Flattening technology of 13GSW are studied deeply and combined together.The scheme proposed is fully homomorphic.Its IND-CPA security is proved under the standard model using the theory of provable security.In addition,the multi-key homomorphism of the scheme is analyzed,and a multiparty computation protocol is proposed.At the end of the paper,the work is summarized and the next step is prospected.